University of Windsor Scholarship at UWindsor
Electronic Theses and Dissertations Theses, Dissertations, and Major Papers
1-1-1972
Hydrofluoric acid production studies: An investigation into the kinetics of reaction between fluorspar and sulfuric acid.
Danilo Candido University of Windsor
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Recommended Citation Candido, Danilo, "Hydrofluoric acid production studies: An investigation into the kinetics of reaction between fluorspar and sulfuric acid." (1972). Electronic Theses and Dissertations. 6111. https://scholar.uwindsor.ca/etd/6111
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. HYDROFLUORIC ACID PRODUCTION STUDIES:
AN INVESTIGATION INTO THE KINETICS OF REACTION BETWEEN FLUORSPAR AND SULFURIC ACID
A Dissertation Submitted to the Faculty of Graduate Studies through the Department of Chemical Engineering in Partial Fulfilment of the Requirements for the Degree of Doctor of Philosophy at the University of Windsor
by
Danilo Candido
Windsor, Ontario
1972
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Sally, Paul and Cathy.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABSTRACT
The reaction between flotated fluorspar and concentrated
sulfuric acid was investigated in a batch and a continuous
reactor system.
Conversion-time data were obtained with the batch
reactor in the range of 25 0 - 350°F »
Two series of runs were conducted in the continuous
reactor. The first,varying temperature (300 - 450°F) and 4-1 the acid:spar ratio (0.95 ~ 1 *0 5 ) and the second, a 2
fractional factorial design of experiments, varying
temperature (370 and 450°F), mixing speed (15-8 and 25
r.p.m.), calcium carbonate content of the fluorspar (3-5 and
7.14 % by wt.).and the fineness of the fluorspar (2 levels).
By means of statistical analysis of the data, it was
shown that three rate models provide a satisfactory fit.
The results indicated that the reaction is diffusion
controlled (activation energy 16,000 Btu/lb.mole), and
that the reactivity of the spar is appreciably enhanced by
an increase in the calcium carbonate content. No appreciable
change in the reactivity was detected with a change in
the fluorspar fineness. The mixing speed seems to enhance
the reaction at 25 r.p.m. levels .only when the calcium
carbonate of the fluorspar is 3*5 % by wt.
ii.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGEMENTS
The author primarily wishes to express his
gratitude to Dr. G. P. Mathur for his able quidance and
encouragement. His sense of perspective was of great
help during the course of this work.
My thanks also go to Dr. M. Adelman whose knowledge
of chemical analysis techniques was of great help.
The co-operation of the many people at Alcan is
also acknowledged; Mr. Gerard Auger of the Alcan Works
Laboratory, who was responsible for the chemical analysis
of the many samples, and Messrs; Edgar Dernedde and
Steve Monahan who were most helpful with their suggestions.
I also wish to take this opportunity to thank
Mr. Otto Brudy, Superintendent of the Central Research
Shop who helped me in the construction of the equipment.
Thanks are due also to Mr. George Ryan, the Chemical
Engineering Technician, for his capable help.
The financial support of the Aluminum Company of
Canada (ALCAN) who funded the project is gratefully
acknowledged. Also, the aid of the National Research
Council of Canada by way of Graduate Fellowships is
truly appreciated.
i'ii
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Page i * ABSTRACT ii
ACKNOWLEDGEMENTS iii
TABLE OF CONTENTS iv
LIST OF FIGURES I ' ix LIST OF TABLES xi
I. INTRODUCTION 1
II. LITERATURE SURVEY 5
III. THEORY . 10
A. General 10
B. Classification of Solid Fluid Reactions 11
1. Classification Based on the Phases in Which Various Species Appear. . 11
2. Classification According to the Manner by which the Reaction Progresses. 12
a. Heterogeneous reactions. 12
b. Homogeneous reactions. 13
c. Reactions accompanying phase changes of solid components or evolution of volatiles. 13
3. Order of Solid-Fluid Reactions. 13
C. Unreacted-Core Shrinking Model. 16
D. Temperature Effects. 23
E. The Abyss. 25
iv
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IV. APPARATUS AND EXPERIMENTAL PROCEDURE 27
A. The Continuous Reactor. 28
1. The Reactor. 28
2. Solids Feeding. 31
3. Acid Feeding. 32
4. Solids Removal. 33
5. The Scrubber. 33
B. Experimental Procedure for the Continuous Reactor Runs. 34
C. The Batch Reactor. 36
D. Experimental Procedure for the Batch Reactor. 37
E. Operational and Equipment Difficulties. 37
1. The Reactor. 38
2. The Solids Feed System. 38
3. Acid Feed System. 40
4. Solids Removal System. 42
5. The Scrubber. 42
V. REACTOR AND KINETIC MODELS 52
A. The Continuous Reactor, 52
B. The Rate Equation. 54
VI. EXPERIMENTAL RESULTS AND ANALYSIS 6l
A. Experimental Results. 6l
v
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1. Qualitative Observations. 6l
a. Batch reactor. 61
b. The continuous reactor. 62
2. Continuous Reactor Data. 63
3. Batch Reactor Data. 64
B. Analysis of Batch Data. 65
C. Analysis of Continuous Reactor A-Runs. 73
D. Fitting the Arrhenius Equation to the. Batch and Continuous Reactor Data . Simultaneously. 77
E. Predicted Conversion Errors. 79
F. The Factorial Experimental Design. 84
1. Planning the Design. 85
2. Analysis of Factorial Runs Data. 89
VII. DISCUSSION OF RESULTS 151
A. The Results. 151
1. The Batch Reactor. 151
2. The Continuous Reactor. 152
B. Interpretation of Results. 155
1. Mixing in the Continuous Reactor. 155
a. The effect of calcium carbonate content. 155
b. The effect of mixing rate. 158
vi
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2. Effect of Fluorspar' Size Reduction. 159.
C. Interpretation of Rate Equations. l6l
D. Comparison of Results to Previous Works. 167
1. The Work of Ostrovskii and Amirova. 167
2. The Works of Gnyra and Menard and Whicher. 168
E. Thermal Effects. 169
F. The Silica Reaction. 170
VIII. CONCLUSIONS 172
BIBLIOGRAPHY 175
NOMENCLATURE 179
APPENDICES 185
I. MODEL DISCRIMINATION AND DETERMINATION OF RATE CONSTANTS 185
A . Using Batch Data . 185
B. The Continuous Reactor Data. 187
1. Initialization. 190
2. Linear Approximation and Steepest Descent. 192
II. THERMODYNAMIC CONSIDERATIONS. 204
III. ANALYSIS OF THE DATA OF PUXLEY AND WOODS.. 208
IV. SAMPLE TREATMENT AND MASS BALANCES 210
A. Sample Treatment. 212
B. Mass Balances . 222
vii
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D. Nomenclature for Mass Balance Program. 231
VITA AUCTORIS 281
viii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF FIGURES Page III.l Schematic Diagram of Concentration Profile for the Unreacted-Core Shrinking Model 17
iv. i Schematic of Reactor Assembly ^5
IV. 2 Reactor Details 46
IV .3 Reactor Mixers 47
IV. 4 Reactor Interior Showing Position of Central and Rear Flange Thermocouples 48
i v .5 Solids Metering Hopper Assembly ^9
i v .6 Metering Auger 50
iv. 7 Solids Out Auger and Solids Out Port 51
v.i A Typical Tracer Response 58
vi. l Batch Reactor Conversion-Time Data and Conversion Curves Predicted by the Least Squares Fit of Model 6 97
VI. 2 Batch Reactor Conversion-Time Data and Conversion Curves Predicted by the Least Squares Fit of Model 7 98 v i .3 Batch Reactor Conversion-Time Data and Predicted Conversion Curves from the Least Squares Fit of Model 9 99
vi. 4 Batch Reactor Conversion-Time Data and Conversion Curves Predicted by the Least Squares fit of Model 10 100
v i .5 Batch Reactor Conversion-Time Data and Conversion Curves Predicted by the Least Squares Fit of Model 11 101
vi. 6 Arrhenius Plot of Apparent Rate Constants of Model 9 with Non-Linear Equation Lines of Best Fit 102
ix
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VI 7 Arrhenius Plot of Apparent Rate Constants of Model 9 with Linear ized - Equation Lines of Best Fit 103
VI 8 Arrhenius Plot of Apparent Rate Constants of Model 10 with Non-Linear Equation Lines of Best Fit 104
VI 9 Arrhenius Plot of Apparent Rate Constants of Model 10 with Linearized Equation Lines of Best Fit 1Q5
VI 10 Arrhenius Plot of Apparent Rate Constants of Model 11 with Non-Linear Equation y Lines of Best Fit 106
VI 11 Arrhenius Plot of Apparent Rate Constants of Model 11 with Linearized Equation Lines of Best Fit 107
VII 1 Reacting Scheme of Lumps 160
AIV 1 Initial Solids Out Samples Handling Scheme 245
AIV 2 Modified Solids Out Samples Scheme 246
x Il
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V.l List of Reaction Models 59
VI.1 Fluorspar Compositions 108
VI.2 Run Parameters for the Continuous Reactor Runs with Mixers at 10 r.p.m., Using Fluorspar Newfluor-A 109
VI.3 Run Parameters for the Continuous Reactor Factorial Runs 110
VI.4 Fractional Age Distribution of Solids Leaving Reactor (E(t)At)^ 112
VI.5 Batch Conversion-Time Data 116
VI.6 Least Squares Analysis of Models Using Batch Data 117
VI.7A Least Squares Fit of the Batch Data Apparent Rate Constants, to the Non-Linear Arrhenius Equation 118
VI.7B Least Squares Fit of the Batch Data Apparent Rate Constants to the Linearized Arrhenius Equation 119
VI.8 Average Conversion of Spar and Apparent Rate Constants for A-Runs 120
VI.9 Least Squares Fit of the Continuous Reactor Data Apparent Rate Constants to the Linearized Arrhenius Equation 121
VI.10 Least Squares Fit of the Continuous Reactor Data Apparent Rate Constants to the Linearized Arrhenius Equation 122
VI.11 Least Squares Fit of the Continuous Reactor and Batch Reactor Data Apparent Rate Constants to the Non-Linear Arrhenius Equation 123
XI
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VI.12 Least Squares Fit of the Continuous Reactor and Batch Reactor Apparent Rate Constants to the Linearized Arrhenius Equation 124
VI.13 Table of Residuals for the Least Squares Fit of the Apparent Rate Constants of the A-Runs of the Continuous Reactor to the Non-Linear Arrhenius Equation 125
VI.14 Table of Residuals for the Least Squares Fit of the Apparent Rate Constants of the A-Runs of the Continuous Reactor to the Linearized Arrhenius Equation 128
VI .15 Table of Residuals for the Least Squares Fit of the Apparent Rate Constants of the A-Runs of the Continuous Reactor and the Batch Reactor to the Non-Linear Arrhenius Equation 131
VI.16 .Table of Residuals for the Least Squares Fit of the Apparent Rate Constants of the A-Runs of the Continuous Reactor and the Batch Reactor to the linearized' Arrhenius Equation 134
VI. 17 Predicted Conversions' 137
VI. 18 Observed Conversion of CaF-^ and Apparent Rate Constants of Runs IF to 10 F 140
VI.19 Natural Logarithm of the Apparent Rate Constants with the Coded Factors 141
VI.20 Mean rifferences of In k 142
VI.21 Analysis of Variance 143
VI.22 Regrouping the F-Runs 144
VI.23 Least Squares Estimate of the Parameters 'of Equation (vi-42) from the Factorial Experiments Apparent Rate Constants 145
Xll
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V I . 24 Least Squares Estimate of .the Parameters of Equation (VI.42) Using the Apparent Rate Constants of the A and F runs as well as the Batch Reactor 146
vi. 25 Analysis of Residuals for Least Squares Fit of Equation (VI-42) to all the Apparent Rate Constants 147
vi. 26 Predicted Conversions 150
AII.l Thermodynamic Data of Reactants and Products 206
All. 2 Thermodynamic Quantities for the Principle Reactions Occuring in the Reactor 207
AIII.l Reaction Constants for Puxleyrs Data Assuming -Zero Order Kinetics 209
AIV. 1 Utility of Sample Analysis 247
AIV. 2 Analysis of Synthetic Samples 249
AIV. 3 Results of Solids Out Sample Analysis 250
AIV. 4 Scrubber Liquor Samples Analysis 252
AIV.5 Gas Transfer Line Sludge 256
AIV. 6 SiO Content of Solids, Of Solids out Sample Where Only The Scrubber Effluent Analysis was Done 257
AIV. 7 Mass Balances and Conversions Using the Reported Solids Out Analysis Assuming CaCO^ Formation During Filtration; No Solids Out Flow Correction 259
AIV. 8 Mass Balances and Conversions Using Reported Solids Out Analysis Assuming CaCO Formation During Filtration; Solids Out Flow Corrected to Force a Sulfate Balance 262
xiii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I INTRODUCTION
Hydrofluoric acid was produced for the first time
about 200 years ago by the treatment of fluorspar (calcium
fluoride) with concentrated sulfuric acid according to
the endothermic reaction
CaFg + HgSO^ ------► CaSO^ + 2HF (l"1)
Industrial manufacture of HF began in 1931 and HF
has since become an important chemical product. Some of
its uses are in the manufacture of fluorinated hydrocarbons
(freons), in the manufacture of flurocarbons and their
polymers (Teflon or Kel-F), as a catalyst and reaction
medium for the alkylation of olefins, etc. However, the
main use for HF is in the manufacture of cryolite (Na^AlFg),
which is used as electrolyte in the manufacture of
aluminum.
Hydrofluoric acid is largely produced by contacting
fluorspar with concentrated sulfuric acid (93-98$ by weight)
in heated, stationary or rotary, steel reactors ^0-60
feet long in which the HF and CaSO^ are produced and
removed continuously. In stationary reactors mixing is
accomplished with internal paddles.
1
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Crude fluorspar varies in its calcium fluoride content
from 5 0 to 90$ ,and after grinding to the desired fineness,,
must be passed through a flotation process to remove
undesirable impurities. The chief impurities remaining in the
flotated spar are silica (SiO^) and calcite (CaCO^) in
concentrations of 1 - 3 % and 1 t 5$ respectively and
lead to the side reactions.
Si02(s)+ 4HF(g) *SiF4(g) + 2^0(1,g) (1-2)
CaC03 (s) + H2S04(1)— * CaS04(s) + HgO(l,g) (1-3)
+ C02 (g)
The two reactions, of course, reduce the yield of HF as
well as cause contamination of the gaseous stream.
The chief difficulties with this method of HF
manufacture are:
(1) poor mixing of the reactants upon initial contact
(2) high corrosion of the reactor walls and mixing paddles
(3) inefficient heat transfer through the reactor walls due to deposition of scale.
Many attempts have been made to enhance the mixing
and heat transfer and to reduce the corrosion of the
reactor. While they are rot disajs sed here one may refer
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. to the patents in the Bibliography for details.
The present state of the art of hydrogen fluoride
production from fluorspar and sulfuric acid is largely
based upon qualitative and often conflicting evidence.
No data are available on the effects of temperature, mixing
rate, and fluorspar impurities on the reaction.
Lump formation within the reactor has been observed
to affect the HP production to a significant degree
(refer to patents in Bibliography). Studies of the
reaction under batch conditions undertaken thus far [2b v 26)J
do not account for this lump formation due to the small
quantities of reactants used in those studies.
The scope of this study was to estimate the effect of
(a) temperature
(b) mixing speed
(c) moles of acid per mole of CaF^ added
(d) fineness of the fluorspar
(e) CaCO^ content of the spar
on the reaction, by carrying out experimentation using ! a stirred, continuously fed reactor, under isothermal
conditions. The data of the continuous reactor were
augmented by carrying out additional experimentation in
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. a batch reactor also maintained at isothermal conditions,
Sufficient quantities of reactants were added to the
batch reactor so as to make lump formation possible.
The approach was to obtain batch conversion-time
data and analyse this data with the aim of obtaining a
suitable rate model. The rate model found to suitably
correlate the batch data was then to be used to analyse
the continuous reactor data in order to determine the
apparent rate constants for each run,to determine the
effects of temperature, mixing rate, spar fineness and
the CaCO^ content of the fluorspar.
I
i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. II. LITERATURE SURVEY
As indicated in the previous chapter, the major
reaction that occurs upon contacting fluorspar with
sulfuric acid is
CaFg + HgSO^ » CaSO^ + 2HF (H-l)
Several side reactions that Occur simultaneously are
CaCOg + HgSO^ * CaSO^ + CC>2 + HgO (H-2)
Si02 + 4HP --- > SiF^ + 2H20 ( H “3)
These reactions are due to impurities present in the
flotated fluorspar.
Traube and Reubke (32) £qUncj that an additional
reaction can occur in the mix according to the equation
HF + HgSO^ c > FSO^H + HgO
Data on the reaction kinetics of reaction (il-l),
(II-2) and (II-3) are scarce.
Puxley and Woods obtained batch data in the
temperature range 125-250°C, using a platinum crucible
while stirring the mix with a platinum bar. However,
their data suffer because of a .lack of temperature
control. They also encountered difficulties in mixing
•5
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the reaction mass.
Rowe in 1955, analysed the data of Puxley and
Woods and hypothesized a possible kinetic model of the
form 2 CS R_ = 1 - exp - - s ds ■IT H - s ]
(n-5) s = J ~ t (a + btn )
where R represents the rate of disappearance of the /\ • acid or spar on A molar basis, and a, b and n are
parameters. Rowe was inclined to believe that the
diffusion of H^SO^ to the reacting interface controls the
reaction rate. However, he stressed that the equation
was identical for the case where diffusion of HF away
from the reacting interface is the controlling step. (24) More recently Ostrovskii and Amirova x ' conducted
batch experiments on the fluorspar-sulfuric acid reaction
by suspending a platinum dish in a steel tube furnace. 4* O The furnace temperature was maintained at - 2 C of the
desired temperature. Dry air was passed through the
tube at a rate of 5 litres per hour. The extent of
reaction was determined by following weight loss with
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. time. They used 99.2$ sulfuric acid and fluorspar of
98$ purity. The temperature range in their investigation
was 85 - 145°C. Ostrovskii and Amirova concluded that
in this temperature range, the rate of disappearance of
CaFg is controlled by the chemical reaction at the
unreacted core surface. They fitted their data to the
model
(1 - x ) "2/3-l = ^ (II-7 ) R P
Where x is the fractional degree of conversion: t is B the reaction time (min.); k is the rate constant
(cm/min.); R is the original diameter of the reacting P particle (cm.). If the particle size of the fluorspar
is maintained constant equation (II-7) reduces to the
form
(1 - xb)"2/3- 1 = kXt (II- 8 )
where k 1 is the apparent rate constant (min. 1).
Equation (II-7) was derived from the pseudo steady-
state unreacted shrinking core model to be discussed in
Chapter II .. Ostrovskii and Amirova found that
k 1 = 7.75 X 1010 exp F- 2 — -?1 (min. 1) in the range L r t J
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 8
of 85 - 103°C and k1 = I .38 X 10^ exp - (min. 1)
o R T in the range of 105-145 C. ; Differences in-the values
of the activation energy were attributed to the lack of
formation of FSO^H above 100°C
Blumberg and Blumberg and Starvinou as well
as Palmer in carrying out various experimental
studies of the reaction of silica particles with aqueous
solutions of hydrofluoric acid, concluded that the reaction
may be restricted by any diffusion process and can be
described by the irate model
Ra = kQ exp [ S[HF] . (II-9)
where S is the exposed area of the solids, kQ the
frequency factor and [HF] the concentration of HF in the
reacting solution.
Unfortunately, information on the silica reaction for
the fluorspar-acid system is limited to qualitative
speculation. Gnyra and Whicher in a qualitative
experimental study observed that the state of primary
mix was an important criterion for the silica reaction.
The longer the initial mix remains wet the greater was
the extent of conversion of the silica .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Gnyra carried out a qualitative study on the
effects of the CaCO^ content in the fluorspar. He
observed an enhancement of acid penetration into the (2 1 ) spar with increased CaCO^ content. Menard and Whicherv '
in a semiqualitative study found that CaCO^ enhances the
setting rate of the reaction mass thus impedes further
mixing of the reactants.
Traube and Lange (Rl) v ' report a study on the effects of
temperature on the evolution of hydrogen fluoride from
the equimolar mixtures of 98$ H^SO^ and 99-7$ fluorspar.
They found that after one hour of contact time at 60r O C
approximately 12$ of the HF generated reacted with HgSOi|.
to produce FSO^H. For identical contact times the
amount of FSO^H formation decreased to 7$ at 80°C and to
nil at 100°C.
Traube and Lange further point out that FSO^H
formation is detrimental to the reaction of the spar
with the acid since the monobasic fluosulfonic acid takes
the place of the dibasic more reactive sulfuric acid^
thus retards the progress of the reaction.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. III. THEORY
A. General
In spite of the unquestionable importance of solid-fluid
reactions relatively few studies have been made on the
chemical kinetics and transfer rates of mass and energy in
heterogeneous non-catalytic systems. This is partially due
to the intricate relationships among the rates of chemical
reaction and the rates of mass and energy transfer. Even in
an isothermal reaction system the overall reaction rates
are influenced not only by the rate of chemical reaction
occuring in or at the surface of the solid, by
the mass transfer rates of fluids through the solid and
across the fluid-film surrounding the solid, but also by
factors such as solid reactivity, crystallite orientation,
crystallite size, surface characteristics, impurities, etc.
A typical solid-fluid reaction may be considered to
occur through the following steps: (1) diffusion of the
fluid reactants across the fluid film surrounding the solid,
(2) diffusion of the fluid reactants through a porous * i layer, (3) adsorption of the fluid reactants at the solid i reactant surface, (4) chemical reaction with the solid
surface, (5) desorption of the fluid products from the
10 I
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solid reaction surface, and (6) diffusion of the product
away from the reaction surface through the solid porous
media and through the fluid film surrounding the solid.
In some particular systems the steps may be somewhat altered.
Since these steps occur consecutively, if any one of them
is much slower than the others that step becomes the
controlling or rate-determining step. However, the majority
of solid-fluid reactions are apparently influenced simul
taneously by more than one step.
A rigorous treatment of the phenomenon seems unattain
able even for the solid of simplest geometry. Besides, a
great number of difficulties exist in practical systems,
such as the changing size and shape of the solids during
the reaction and formation of product around the solid
reactant which may crack or ablate.
B Classification of Solid-Fluid Reactions
1. Classification Based on the Phases in Which Various Species Appear
Noncatalytic fluid-solid reactions may be characterized
by one of the following schemes:
solid reactants >- fluid products (A)
solid reactants > fluid and solid products (?)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. fluid and solid ------► fluid products (C) reactants
fluid and solid ---- ■--- ► solid products (d ) reactants
fluid and solid ------► fluid and solid reactants products (E)
Examples of each type of reaction may readily be found (•alt) in industry.' ’ The reaction of sulfuric acid with
fluorspar is of type E.
2. Classification According to the Manner by Which the Reaction Progresses.
Heterogeneous noncatalytic fluid solid reactions may
also be classified by the manner by which the chemical
reaction occurrs,the internal structure of the solid, the
geometry, and the relative velocities of chemical reactions
and diffusion of the reactants and products are four of the
many possible parameters that may be considered in following
the manner of occurrence.
a. Heterogeneous reactions. When the porosity
of the unreacted solid is so small as to make it
impervious to the fluid reactants, the reaction will occur
at the surface of the* solid or at the interface between the
unreacted solid and the porous product layer. Also, when
the chemical reaction is very rapid and the diffusion
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 13
sufficiently slow, the zone of reaction is narrowly confined
to the interface between the unreacted solid reactant and
the product.
b. Homogeneous reactions. In many cases the
solid contains enough voidage to allow free passage of the
fluid reactants and products, and the solid reactants are
distributed homogeneously throughout the solid phase. In
this case one can reasonably consider that the reaction
between fluid and solid phases occurs homogeneously throughout
the solid phase. This case has been treated thoroughly by
Wen ( W .
*•' c- Reactions accompanying phase changes of solid
components or evolution of volatiles. In some cases, prior
to the chemical reaction the solid changes phase because
of poor heat conduction in an exothermic reaction. The
solid may melt or sublime prior to or during contact with
the fluid. In such cases a homogeneous vapor phase reaction
tabes place either on the outside of the solid or in the
solid product layer formed around the unreacted solid.
3. Order of Solid-Fluid Reactions
Consider the following isothermal equimolal non-
catalytic reaction:
A(fluid) + B(solid)— > Fluid and/or solid product (III-1)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. If diffusion rates through the fluid-film and porous solid
layer are very fast the overall rate of solid-fluid reaction
is solely determined by the inherent chemical reactivity
of the solid and fluid reactants. In the case of a gaseous
fluid one can also quantitatively describe the mechanism (31} on the basis of the Langmuir adsorption isotherm '
However the resulting equations involve more then two
arbitrary constants and often as many as seven v 1. . The
resulting equations, although desirable from a theoretical
viewpoint, are in practice difficult to handle.
Provided no extrapolation beyond the range investigated
is allowed, and the surface phenonenon controls the rate of th the solid-fluid reaction one may often use an n order rate
model to fit the data. Based on adsorption isotherms the
order may vary from zero to two depending on whether the gas
reactant is strongly or weakly adsorbed (34}v Experimental
studies indicate many gas solid reactions to have this
range of order of reactions, depending on conditions such
as reactant activity, pressure, temperature activity, etc.w(3J
Thus the rate of* reaction of fluid component A, r^ and
for solid reactant S, r can be represented as
r ar (III-2) A S
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 15
where a is the • stoichiometric coefficient (the number of
moles of fluid component A that will react with 1 mole of
solid reactant S, and m and n are the order of reaction
with respect to solid reactant S and fluid reactant A
respectively. Depending upon particular conditions the
rate may be expressed in terms of surface area or volume.
The units of r^ or rg depend on the rate expression, namely,
if kg is used the rate is in moles per unit area per unit
time, whereas if k is used the rate is in moles per unit v volume per unit time.
In many instances the concentration of solid reactant
may be considered constant so that the reaction rate expression
reduces to . .
/ m where k = k c S S S
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 16
C. Unreacted-Core Shrinking Model
Consider the case Where a fluid reacts with the solid
producing a fluid and a porous solid product or an ash layer
according to equation (III-1). The porous product shall
hitherto be referred to as the ash layer. The unreacted
solid is impervious to fluid A because it is densely packed
but the porous product allows fluid A to diffuse in, and
the fluid product to diffuse out.
Consider a spherical particle having an initial radius
being reacted by A. Initially the reaction occurs on the
outside surface of the particle but as the reaction proceeds
the reaction surface will withdraw into the interior of the
solid phase. The external radius is considered to remain
the same. This assumes that no deformation of the ash
layer occurs and that the bulk density of the ash is the
same as that of the solid reactant. The fluid reactant A
must first move through various layers of resistance prior
to reaching the unreacted core. Figure III.l illustrates
the resistances as well as the concentration profile within
the particle. Refering to Figure III.l C , C , and
C are designated as the fluid reactant concentrations in Ac
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 17
Fluid Film /
Ash
Solid Reactant
Ca o So CAS
'Ac
Figure III.l, Schematic Diagram of Concentration
Profile for the Unreacted-Core Shrinking
Model.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. . 18
the bulk stream, at the particle surface, and at the surface
of the core, respectively R , r and r are radii of the p c particle, of the unreacted core and at any point in the ash
layer respectively.
A fundamental equation relating the material balance of
component A may be written as
S2c Sc A * ^ ' D eA \ 2 ( m - 4 ) St \ Sr Sr
R > r > r P c
The boundary conditions for the spherical particles
are:
at the solid particle surface R
SC D A eA = k ^ (C mA v Ao - CAS> Sr R
at the moving interface, r
a k C eA s Ac Sr ) r_
SC, and / Sr - D eA = a cSo ( — 5 Sr / r St J where k is the mass transfer coefficient of component A mA
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. from the hulk of the fluid phase to the solid surface across
the film, and c is the solid reactant concentration in the * So unreacted core which is assumed constant, e is the voidage
of the porous layer of the particle and D is the effective
diffusivity coefficient of the fluid reactant in the ash
layer at t = o, r = R c p The reaction at the solid surface is assumed to he
first order with respect to the fluid reactant A and zero
order with respect to the solid reactant.
Analytical solutions to equation (III-4) using the
boundary conditions of equation (lll-5)are difficult except
in a few special cases v('34') '. It rs customary to let
= o and obtain an approximate solution. This
technique is known as the pseudo steady state solution and
is reasonably accurate in most solid-gas reaction systems
except for systems at extremely high pressures and very
low solid reactant concentrations. However, for solid-
liquid systems the error involved becomes excessive unless
the liquid reactant concentration is very low (3 v ’ 34}1.
If we let equation (III-4) it becomes
P * /d C_ 2 dC \ °=DeA^^F + 7 —) R>r^rc (IIX-6)
and using the boundary conditions the solution is readily
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 20
obtained to yield a concentration profile:
1 1 1 + DeA ak r r r s c ( H I - 7 ) Ao 1 + D D eA eA ale r k R s c mA p
The time required for the particle to reduce the unreacted
core from R to r is given by p c
a V s o t = CAo R“
r \ . R 1 - rc 1 - _S A + R. ( H I - 8 ) ak R 2D eA
If one wishes to reduce these equations to the usual
reaction rate form,one considers the number of moles of A
disappearing per unit time, M , which can be expressed as
2 2 2 M, = % R N = %r n = l|-7rr N. A p As A,ash c Ac
and
■(HI-9) M A = % C AO 2 r a k r R2lCp mA c s e A c
In order for the fluid to react at-the surface of the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. core it must diffuse through the film and ash layer to the
reacting surface. The three terms in the denominator of
equation (III - 9) represent the three resistances in series
for the reaction considered.
If the fluid-film resistance is much greater than that
of the ash diffusion and surface reaction it is said to he
a film resistance controlled phenonenon and equation (ill - 9)
reduces to
(III - 10)
When ash diffusion controls then
(111-11)
P
When chemical reaction controls
dr c (111-12) dt C So
In terms of the fractional conversion of B.
r 3 ( h i - 1 3 ) 1 x. B P
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I 22
equations (HI-10) (III-11) and (111-12) may be expressed as
follows:
= 33 CAo (111-14)
^ V ^
for film diffusion controlling
' 1 /3 = 33 DeAgCRQ (1 ' V (III-15) at cso 1 - (1-XB )1/3
for ash diffusion controlling, and
d* 3a k 'c 2/3 — B = s - A-9. (1 - x B ) (HI-16) dt c R So p
when chemical reaction controls.
The above derivations are based on a system where the
concentration of the fluid reactant is constant. In some
instances this reactant concentration decreases in proportion
to the degree of conversion of the solid reactant. Or
CA " CSo
and A = c '0 / C Bq _ (III-18)
where ci is now the initial solid concentration on a So fluid concentration basis (moles of solid reactant initially
present per volume of fluid), and is the initial fluid
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 23 reactant concentration.
Applying equation (111-17) to equations (111-1*1-),
(ill-15) and (HI-16) one obtains
_ 3a kma c'S o (A - axg) (III-19)
dt CSoRp
when film diffusion is controlling,
1/3 ? 0 b = 3aDeACSo (A - axB) (1 - xB) (111-20) at c r 2 - - x n )1/^ So p 1 v(1 B '
for the case where ash diffusion is controlling, and
„ 33 V s o (A " (1 ‘ X B>V 3 at c r2 ’ (1 1 1- 2 1 ) So p
for a chemical reaction controlled reaction.
D. Temperature Effects
The Boltzmann law describing the energy distribution of
molecules in a substance establishes the character of the
relationship between the rate of a physical or a chemical
process and temperature.
- E •/kT Ni = - e 1 (111-22) Z v '
where N is the total number of molecules, is thenumber
of molecules with energy E^, k is the Boltzmann constant and
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Z is the distribution function.
The form of the equation for the distribution of the
molecules in terms of energy will depend on the form of the
problem, butt the distribution will always take the form
containing the Boltzmann factor e Accordingly,
the constant for the reaction rate involving solids is
\ expressed by
K = Ae" Q/RT (I II-23')
in which the value of A and Q will depend on the limiting
process of the reaction.
If the process is limited by the chemical reaction
itself, the pre-exponential multiplier A is equal to PZQ,
p being the probability or steric factor and Zq the number of
binary encounters between reacting particles; Q is the energy
of activation of the chemical action and it depends on the
bond forces between the particles of each of the original
species and the repulsive forces between the approaching
particles (for heterogeneous processes which include
reactions in the crystalline mixtures Q is the apparent
energy of activation).*
In a process limited by the diffusion of a species, the
velocity of reaction is determined by the value of the
diffusion coefficient which may often be expressed in the
form
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 25 D = Ae"Q/RT (III-24) €i\
where A now depends on the frequency of oscillations of the
diffusing species and Q is the energy of motion of the
diffusing species.
In any case, the greater the value of Q, the activation
energy, the greater the change in the process rate with
changes in temperature. In diffusion controlled processes,
the activation energy will be relatively low yielding
velocity changes of 10-4C$ with temperature changes of 10°C.
When the process is limited by the chemical step the activation
energies will be relatively high and a 1 0 ° C rise in temperature
will increase the velocity by 2-4 times or more^^.
E. The Abyss
To reiterate, the shrinking core model is a reasonable
description of the phenomenon when a fluid reactant reacts
with an impervious spherical solid producing a fluid reactant
and a solid ash. The particle radius remains constant and
does not deform during the reaction. In order for the pseudo
steady state equations to remain valid, the fluid reactant
should be in relatively low concentrations.v ’ '
As is true of many fairy tales, the real situation is
far from the ideal that one would wish it to be.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. No attempts have been made here to account for heat
transfer effects. For a highly exothermic reaction the
interior of the particle would increase in temperature
while for an endothermic reaction cooling would occur. This (o 2 8 ) problem has been treated elsewherev ' but the resulting
equations are much too bulky to consider here.
Another problem which has received little or no attention
is the treatment of non-spherical particles. As well, very
little treatment has been accorded to changes in the
surface area of the unreacted cere as pointed out by Cannon
and Denbighin the latter phenomenon, if the reaction
rate per unit area of core decreases with greater conversion,
the surface non-uniformity will tend to be smoothed out,
because the rate of reaction will be less at a point of
deeper penetration. If the rate of reaction per unit area
remains constant, the non-uniformity will be constant or
increase.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IV APPARATUS AND EXPERIMENTAL PROCEDURE
Because the reaction of fluorspar with sulfuric acid
may be strongly affected by imposed dynamic forces, it was
necessary that the reaction be studied under dynamic
conditions similar to those imposed by the industrial process.
More specifically, mixing cannot be properly accounted for
in a batch reacting system, because of the nature of the
reacting material.
Furthermore, because the reaction is highly endothermic,
the temperature of the reacting mass is difficult to control
in a batch process unless very small quantities are used.
But with very small quantities of reactants, one cannot but
help avoiding the lump formation which may play a significant
role in the reaction.
At the same time, the usefulness of the continuous
reactor data have limitations if they are not isothermal
and the feed rates are not constant.
In the construction of the continuous reactor assembly
attention was focussed towards achieving the following:
(a) Temperature was to be maintained constant at all
reactor points.
(b) The acid and feed rates had to be accurate.
* 27
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (c) Solids entrainment in the product gases was to he
kept to a minimum.
(d) An accurate measure of the amount of hydrogen
fluoride produced had to be obtained.
(e) The mixing rate was to be constant during any run.
Figure IV.1 is a schematic diagram of the continuous I reactor assembly.
As discussed in sectionVI the data of the continuous
reactor are limited in their usefulness for testing kinetic
models. To supplement the continuous reactor data it was
necessary to carry out batch experiments.
In the construction of the batch reactor, all the
attention was focussed towards temperature control.
A, The Continuous Reactor
1. The Reactor
The reactor was a 5 inch diameter, flanged, cold
rolled steel pipe 14 inches long. A semicylindrical heater
along the reactor bottom was used to heat the main reactor
body. Flange heaters, on the flange perimeters, were used
to eliminate axial temperature variations. Figure IV.2 shows
the details of the reactor.
The semicylindrical heater was 5 3/4 inch I.D. and was
12 inches long, fitting snugly between the reactor flanges.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. It was rated at 2300 watts at 230 volts.
The flange heaters were of 9 inch I.D. and 1 1/2 inches
wide. Both heaters were rated at 1225 watts at 115 volts.
A proportional controller using the central thermocouple
as sensor served to control the semicylindrical heater. The
flange heaters were manually controlled by way of variable
transformers.
The reactor contents were mixed by 1/8 inch thick, 1
inch wide, paddles constructed from old lawnmower blades.
A photograph of the mixers is provided in Figure.IV.3 . Some
space between the two sets of paddles was necessary to provide
clearance for the central thermocouple.
The forward paddles were coated with a hard stellite
alloy to prevent excessive corrosion by the environment.
To prevent undue fouling of the reactor walls, which
would hinder heat transfer, the clearance between the
paddle edges and the reactor wall was kept to as low a
value as possible.
A 1/4 h.p. electronically controlled D.C.' motor provided
the drive for the mixers. The range of mixing could be
varied from 1 to 44 r.p.m. with an accuracy of roughly 2fo.
To achieve the low r.p.m. values a 60 to 1 gear reducer was
necessary. The high reduction provided for a very powerful
mixing.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Three chrome 1-alumel thermocouples were used to measure
temperatures at various points in the reactor. These were
ceramic insulated thermocouples protected by a stainless
steel sheath of 1/8 inch diameter. To prevent error in
temperature measurement due to stray currents or stray
magnetic fluxes, the thermocouple junctions were ungrounded.
One eighth inch NPT adjustable compression fittings were
used to fasten the thermocouples to the reactor walls.
The first thermocouple was inserted through the forward
flange 13/^ inches above the reactor bottom. It extended
approximately 3/^ inches into the reactor. It was installed
so as not to interfere with the stirrers.
The second thermocouple was inserted through the top of
the reactor and extended to about 1/8 in above the reactor
bottom. This thermocouple was held in place by a 3/8 inch
diameter slotted stainless steel rod. This rod does not
interfere with the thermocouple reading as illustrated in
the photograph in Figure IV.ty. The restraining rod prevented
the thermocouple from becoming fouled in the mixer paddles.
The third thermocouple was inserted;through the rear i flange and its position is also illustrated in Figure IV.4.
i A Honeywell multipoint strip chart recorder measured
. and recorded the temperatures. (
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 31 All the thermocouples used were checked for accuracy
by immersion into boiling distilled .water and noting the-
tempe rature re spon se.
. 2. Solids Feeding
Fluorspar was fed to the reactor through a double
hopper arrangement. The first hopper, as illustrated in
Figure 3V. 5, was equipped with a 3/8 inch diameter helical
auger. The auger was driven by an electronically controlled
variable speed, 1/6 h.p. D.C. motor. The auger rotation
rate determined the rate of spar flow.
As shown in Figure IV.6, a 5 inch long mixing auger
pushed the solids toward the feeding tube where it was carried
off by the smaller auger. However, unless further mechanical
aid was provided, tunneling occured,producing erratic or no
flow. To overcome this, two 3 inch diameter variable speed
stirrers were installed in the hopper to maintain the powder
in a semifluid state.
The powder out of the metering auger fell into a second
hopper equipped with a constant speed 5/8 inch diameter
constant speed auger. This auger, similar to the solids out
auger shown in Figure IV.7, bad a substantially higher
capacity than the metering auger, and easily pushed all of
the powder falling into this second hopper into the reactor.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 32
The accuracy of the spar feeding system was usually
better than 1%. '
3- Acid Feeding
Sulfuric acid was pumped by means of an electronically /gv controlled variable speed Masterflex ^ tubing pump. The
pump tubing was of Viton but the rest of the line was 1/4 inch
teflon tubing. A rotameter was used to measure the flow which
was controlled by the r.p.m. of the pump.
The viscosity of concentrated sulfuric acid is highly
dependent on temperature. This meant that day to day
temperature variations caused deviation of the rotameter
calibration, which is highly dependent on the fluid viscosity.
To overcome this problem, it was necessary to insure that the
temperature of the acid as it entered the rotameter be
constant.
To achieve constant temperature, the acid was passed
through a glass coil immersed in a constant temperature bath.
The bath temperature was controlled so as to maintain the / o desrred temperature (about 39 C) at the rotameter entrance.
A thermometer with 0 . 1 ° C graduations was installed at the
rotameter entrance to indicate the acid temperature..
The teflon tubing between the rotameter and the reactor
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. was wrapped with heating tape to heat the acid to approximately
2 0 0 ° F prior to its entry into the reactor.
The accuracy of the acid feeding was better than 1 per cent.
ty. Solids Removal
The solid products from the reaction were removed
by means of a 1 inch diameter wood auger bit. This auger,
as shown in Figure IV.7, extended 1 inch into the reactor
and was encased in a teflon sheath. To facilitate flow, a
solids out port, also shown in Figure 3V.2, was installed
inside the reactor wall.
The auger was driven at speeds.of 1-60 r.p.m. by an.
•electronically controlled variable speed 1/6 h.p. D.C. motor.
5* The Scrubber
The fumes produced in the reactor were drawn out of
the reactor through a 1 inch teflon tube. This line was wrapped
with heating tape to prevent undue condensation of the
vapours.
The schematic of Figure IV.1 gives an adequate view of
* the scrubber assembly.
The vent scrubber provided the vacuum necessary to
withdraw the reactor fumes. This vacuum was controlled by
adjusting the exhaust valve.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The caustic makeup (Na^CO^ solution) was filtered to
prevent fouling of the control valve.
The circulating pump provided outlet pressures of
about 40 p.s.i. to create more than an adequate vacuum.
The efficiency of the vent scrubber was 100 $ v as substantiated by analysis of the exhaust by means of a
Drager gas detector. The analysis indicated that no hydrogen
fluoride was present in the exhaust.
> B. Experimental Proceedure for Continuous Reactor Runs
prior to reactor startup, the solids and
acid feeding systems were both calibrated at the desired
levels. Recalibration of the solids feeder was necessary
because temperature and humidity conditions altered the
calibration from day to day. The recalibration of the acid
rotameter was necessary because of slight variations in the
concentration of the acid used.
The reactor was then heated to the desired temperature
level and feeding of spar and acid was begun. The reactor
was operated for about,four hours to allow steady-*state
conditions to be achieved. At about that time, 5 grams of
nickel sulfate were added to the reactor by way of the
second hopper. The nickel sulfate served as a tracer for
the determination of the residence time distribution.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Samples of the solids out for tracer analysis were
taken in the following intervals of time, 0-3# 3~6, 6-9# 9- 1 2 ,
12- 1 5 , 15- 2 0 , 20-25 , 25-3 0 , 30-40, 40-50, 5 0 - 6 0 , 60-70, 70-80,
8 0 -1 0 0 , 100-120, 120-140, 140-160, 160-180, 180-200, 200-220,
and 220-240 minutes. Sufficient time was allowed to insure
that all the tracer had left the reactor. These samples also
served for the determination of the solids out flow rate.
Solids out samples for chemical analysis, were taken in
the time intervals of 120-140, 140-160, 160-180, 180-200,
200-220 and 220-240 minutes. These samples were taken
simultaneously with the tracer samples, and were collected
with a spoon and immediately quenched in 500 of 1 N NaOH
solution. Scrubber liquor effluent samples were taken in the
same time intervals.
While the reactor was running, the variable transformers
for the flange heaters needed adjusting to maintain
temperatures constant.
Periodic checking of the solids feeder accuracy was
also done during each reactor run. This was easily 1i accomplished by collecting the solids from the metering auger i for a 1 minute interval. If a slight deviation of flow was 1I noted,the r.p.m. of the drive motor was adjusted to
•compensate. This constant checking of feed rate was mandatory
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. because variation in flow could occur during a run due to
ambient temperature and humidity variations. In this way
slight deviations could properly be remedied before they
became serious.
The spar sample collected from - the metering auger, was
not discarded,but slowly added to the reactor when the next
sample to check the feed rate was being taken.
After shutdown, the reactor was completely dissassembled
and washed, then reassembled for the next run.
The treatment .of the samples is discussed in
Appendix IV.
C. The Batch Reactor
To supplement the data of the continuous reactor,the
batch reactor was constructed and operated.
It is a fairly simple piece of equipment consisting of
a 3" diameter steel pipe with a blind flange. The pipe walls
were machined down to 1/8 inch thickness to facilitate good
heat transfer. The flange was also 1/8 inch thick to
facilitate good heat transfer. Heaters were used on the bottom
plate and on the wall. A thermocouple was centrally located
on the flange. The temperature was recorded on a strip
chart recorder and controlled by an on-off temperature
controller which regulated the bottom heater.
• Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 37 D. Experimental Procedure for the Batch Reactor
The reactor, with a pre weighed amount of fluorspar was
preheated to the desired temperature level. A preweighed
amount of acid was simultaneously heated to about 1 0 ° C higher
than the desired running temperature.
The acid was then added to thei preheated fluorspar while manually stirring with a stainless steel spatula.
Stirring was continued until the mixture hardened and the
spatula was employed to break up the larger granules.
In each of these runs roughly 40 grams of spar and
48 grams-of acid were used. Great care was taken to ensure
that equimolar quantities of reactants were used.
Four samples were taken at predetermined times for each
of the runs and quickly quenched in 100 mis of IN NaOH
solution.
Although the temperature dropped about 2 0 ° F upon initial
contact of the reactants the period of this drop was only
about 45 seconds to one minute, after which the temperature
was maintained to +- 8 n° F.
E. Operational and Equipment Problems
Some of the difficulties which were encountered, and
could recur, with the equipment, have already been briefly
dealt • with in the previous discussion. Here an attempt
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 38
is made to make the reader aware of other problems which had
to be overcome. The chief of these 'problems was the solids
feed system.
1. The Reactor
In a move to save costs, a variable transformer
rather than a temperature controller was employed to control
the heating of the semicylindrical heater. Although this * manual control was satisfactory below 3 5 0 °F it proved to be
rather poor at the higher temperatures.
2. The Solids Feed System
The original solids feed system consisted of a
hopper with a machined screw for feeding and stirrers to
maintain the spar in a fluid state. The stirrers were
necessary to prevent ratholing (a stable arch forming).
Moreover the spar tended to adhere to the screw, often
causing all flow to cease. At best, the spar flow rate was
erratic and dependent more on the position of the hopper
stirrers than on the screw rotation rate.
The same hopper was equipped with a different screw
(a wood bit auger) which provided better stability of the
spar flow rate so long as the position of the hopper stirrers
was not disturbed. However, when the calcium balance
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. problems, as discussed elsewhere arose, it was suspected that
during the actual running of the reactor the outlet port of
the feeder was clogging. Since no adequate method of
measuring the spar feed rate during reactor operation was
available no adjustment to the screw r. p.m.could be made to
compensate for the fouling action.
\ At that time, the solids feed port was on the forward
reactor flange rather than in the portal above the reactor
as shown in Figure IV.2. The putty-like reactor contents
could easily have been the cause of the fouling. In addition ,
the corrosive action of the reactor fumes caused substantial
corrosion of the screw feeder and enhanced the adherence of
the spar to the screw.
In desperation a solids feeder was rented from the
Vibra Screw Corporation. This feeder was found to be
unsatisfactory due to its inconsistent performance. Further
more, it was bulky and extremely noisy.
However, the design of their auger was considered to
be satisfactory and a new feeder was designed employing
this auger. The new feeder was described previously and
it proved to be quite satisfactory.
Initially, it was thought advisable to vibrate the
hopper by use of pneumatic vibrators. However, vibration
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. was found to be.unnecessary so long as the hopper stirrers were
powerful enough to rotate at a constant r. p. m..
To eliminate blockage of the solids feed a solids feed
port was constructed atop the reactor. However this did not
prevent corrosion of the feeding auger by the fumes.
To allow for periodic checking of the solids flow rate,
a second hopper was employed to transfer the solids into the
reactor. This last change was very important on two counts.
Firstly, it eliminated all interference of the solids metering
by the fumes and solids in the reactor. Secondly, the solids
flow rate could be monitored continuously even during reactor
operation allowing one to compensate for minor deviations in
flow rates.
3. Acid Feed System
Originally the sulfuric acid was gravity fed through
insulated 1/4 inch sch. 40 mild steel pipe from a heated
5 litre glass tank. Due to the extremely low flow rates
required (7 - 15cc/min), it was necessary to use needle
valves to regulate flow. A rotameter was used for metering
purposes. Corrosion of steel pipe is reportedly iow enough
to make its use practical for this purpose. However,
sufficient corrosion occurred to cause fouling of the needle
valves. The steel pipe was subsequently replaced with teflon
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 41 tubing. The performance of this line was satisfactory until
such time when commercial grade 'acid was fed to the system in
place of the analytical grade used for testing. Severe
fouling with the commercial grade acid led to the belief
that a metering pump would need to be used to improve flow
control.
A metering pump was subsequently purchased and proved
satisfactory for a while. After a period of time, the pump
chech valves began to foul badly resulting in undesirable
flow rate inaccuracies.
The final solution proved to be the use of a variable
speed tubing pump to control the flow rate,, and the rotameter
for metering. Although this arrangement gave steady acid
flows, the rotameter calibration still fluctuated from day
to day. This fluctuation was eventually attributed to day
to day room temperature fluctuations. To overcome this
inaccuracy the use of the temperature bath was initiated.
Simultaneously, because of the extremely low flow rates
involved, it was found that heating the acid in the reservoir
was undesirable because by the time it entered the reactor
it would be cooled down considerably. Wrapping the teflon
tubing with heating tape to heat the acid prior to its entry
into the reactor proved to be a practical solution.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. f
It must be pointed out that these changes were not
necessarily made in chronological order.
4. Solids Removal System
Initially this system used a 3 A inch diameter machined
screw to remove the solids. This screw proved unsatisfactory
even when the solids out port was added. When a 3 A inch
diameter wood bit auger replaced that screw, satisfactory
results were obtained.
The size of the auger was later changed to 1 inch
diameter to facilitate a more efficient solids removal.
Although this large auger will handle partially wet solids
it will not work if the solids are too wet.
5. T h e .Scrubber
The first scrubber consisted of a flanged 36 inch
long 5 inch diameter steel pipe. The pipe was packed with
P.V.C. rings. A vacuum was applied to the scrubber by means
of two laboratory size jet ejectors. The fumes were drawn
out of the reactor through a 3/A inch aluminum and steel
pipe. Steel pipe was used to construct a U-tube trap to
catch any liquid that might flow from the scrubber into the I transfer line. Other parts of the transfer line were of
•aluminum. i
«
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The major problem encountered with this equipment was
the rapid corrosion of the transfer line pipe and the fouling
of both the transfer line and the scrubber with solids
entrained in the gases.
Fouling of the transfer line caused vacuum build up in
the scrubber followed by flooding of the scrubber because
the vacuum prevented the liquid from flowing out.
All this, of course, led to a very unstable operation
and sometimes led to the profuse spewing of dangerous fumes
into the immediate area.
By fortunate circumstance, the author was made aware of
a new piece of equipment available that could eliminate these
problems. A pilot plant size jet scrubber that would serve
to scrub the gases, as well as provide the necessary vacuum
for withdrawing the fumes out of the reactor, was being
marketed.
Deployment of this jet scrubber proved very satisfactory.
Although some fouling of the teflon transfer line did occur
when the equipment was initially put into operation,
adequate adjustment of. the exhaust valve ■ prevented undue
solids carryover. The use of heating tapes on the transfer
line also helped to maintain it fairly dry and eliminated
fouling.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Another problem which also needed to be dealt with was
the fouling of the caustic makeup needle valve. Solids
precipitated out by caustic addition to tap water were the
direct cause of this problem. The addition of a filter
to, the feed line was a simple solution to the problem.
«
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4=- ui r > EFFLUENT EXHAUST CAUSTIC MAKEUP TANK SCRUBBER VENT HOLDING PUMP CIRCULATING FILTER T. W, T. Y TEFLON FLANGE HEATERS HEATERS THERMOWELL
ACID FIG. FIG. IV.1, Schematic of Reactor Assembly METERING METERING . FEEDER SCREW VARIABLE SPEED TUBING PUMP TE F L O N TUBING l/4 FLUORSPAR BATH L „ J CONSTANT ! TEMPERATURE•§ !
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. \
46
Ui u O Ui o z
Ql
O UJ 2 a: UJ o o U. a <0 o o. oUJ m i—i Si _ l CO Ui ’H z Ul u 2 o o h* +> UJ nv ui uj CO v> o a. z — hU) U. a CO © U1 O J O I K n u-)_ V o +> o tc o < (0 CO CL o 1“ Pi Ui CC z UJ (0 X < H C5 O CM > _I hi < o H P4 REMOVED FLANGE WITH VIEW FRONT
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 47 FIG. VI.3 FIG. VI.3 Reactor Mixers
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 48 Thermocouples. FIG. FIG. IV.4 Reactor Interior Showing Positions of Central and Rear Flange
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
7'4- PILLOW BLOCKS; ALUMINUM BLOCKS; PILLOW HOPPER FLANGES AND FLANGES HOPPER HOPPER; STAINLESS SHEET STAINLESS HOPPER; MATERIALS OF CONSTRUCTION I W I
PILLOW BLOCKS PILLOW SHEATH 3“ DIAMETER 3“ RUBBER GASKETS RUBBER FEEDER SCREW TO THREADS ■RESTRAINS SCREWS ■RESTRAINS •HOPPER FLANGES •HOPPER THREADS FOR TABLE BOLTS TABLE FOR THREADS Solids Metering Hopper Assembly .5 FIG. FIG. IV HOPPER MIXING SECTION MIXING v j :
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. < o h ~ ~ H r o
« to
<0 III
0.
OCO H CO lu UICO
lco cc FIG. FIG. IV.7 Solids Out Auger and Solids Out Port
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V. REACTOR AND KINETIC MODELS
The Continuous Reactor
Tracer data ( a typical output curve is shown in
Figure V. I), indicated that the reactor was not an ideal plug
flow reactor, nor was it an ideal continuous stirred tank
reactor.
The initial approach was to consider mass and energy
balances of both the macroscopic flow and of the microscopic (27) reacting particles. This apporach was taken by Sood\ ‘ but
led to an impractical set of equations solvable, if at all,
by use of advanced numerical techniques. The second approach
was to eliminate energy balances, and treat the reactor as a
tanks in series model ^9 *2 0 )^ T^e approach was
dramatically different, and was based on the premise that
mixing in the reactor does not occur in the manner assumed
by the first two approaches. The approach outlined below,
attempts to account realistically for the observed phenomena
occuring in the reactor.
At the entrance, the reactor is partially filled with
a pasty mixture of reactants and products. The rest of the
reactor is partially filled with hard, grey, substantially
dry granules. This is not a step change, but the trans
formation from a vet to a dry mixture occurs in the early
52
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 53
sections of the reactor. In any case, once the granules have
formed interaction among them is negligible. This results
in many non-interacting batch reactors which remain in the
reactor for varying lengths of time due to non-ideal flow.
From the tracer data, one can obtain E(t), the residence
time distribution of the particles leaving the reactor. These
data, combined with the average conversion of the output
stream may be used to obtain a rate constant for an assumed
kinetic model.
The starting point for this analysis is the expression
| Mean value of ^fraction of /^fraction of < the fraction of CaF exiting CaFg unconverted I unconverted granules that for granules V remained in S- remaining in the / < all \ the reactoror I reactor for a elements J for time t ,to \ time___ t. to ( t.+At. t+At. V^i 1 J V i i J (V-l) n or (1 - xB) = (E(t)(At))i. (V~2) i = 1
xB(t^) = average conversion of B obtained for a stream of
age between t .and t+At„ N 1 X 1 (t.) + (t. + At.) — = v i' v l_____ l ’ i
[E(t)(At)]^ = fraction of stream with ages between t^ and
t. + At. i l
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5^
In most instances, E(t) is not easily expressed in an
analytic form. Also, unless the kinetic rate expression is
of a simple form, x ft*. ) is not easily expressed in
analytic form. Therefore, although it as possible to
\ express equation ( V-l) in the integral form
XB = J XB (t) E(t)dt (V-3) o
it is impractical to work with it.
B. The Rate Equation
We begin by adopting the moles of calcium as a basis
for expressing concentration. Thus X = gm. moles of A per
gram mole of calcium present in the reacting mass. If, for
example, the feed were pure CaP^ the initial concentration
of CaEg, xBo> :*-s unity since there is one gram mole of CaFg
per mole of calcium in the reacting mass. This basis of
concentration is chosen because the total number of moles
of calcium does not change as the reaction proceeds.
Using this basis, one can write the reaction rate term as
I
BCa dt
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 55
dX. or 1 = /(*,xa,xb) ( v " 5 ) dt
where k is an arbitrary rate constant.
The function^ (k,x ,X ), may take many forms, one of n D which is
i(k,xA ) = k XA (v-6)
In terms of fractional conversion one can let
= X„ (1 - x ) B Bo B y
and X A = X_ - x x = X_ (A - x) A AO B BO Bo' '
since one mole of A reacts with one mole of B. And, A is
the molar ratio of acid to spar expressed as gm. moles of
acid per gram mole of spar in the initial reacting mixture.
Equation (v -6) then became
dx — = k (a - x ) . (v-7) dt B
and k has dimensions of 1/time.
The above model is one of many considered for correlating I the rate of evolution of hydrogen fluoride.
Prior to discussing these equations one should list the
peculiar phenomenological aspects of the reaction of sulfuric
acid with fluorspar.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (1 ) CaFg crystals are not porous and fairly pure.
(2) The reaction yields a solid and a fluid product.
(3) The solid product is quite porous and adheres to
the unreacted material.
(if) The liquid reactant decreases in amount in
proportion to the degree of conversion.
(5) The initial solid particles are not spherical
and surface irregularities tend to be smoothed
out as the reaction proceeds.
(.6 ) The solid particles are not of a uniform size, but
are quite fine. (mean particle diameter of 20
to 30 ijl)
Items (1) through (4) would seem to point to the
validity of using the shrinking core model. At the same
time, because the acid was of high concentration, the validity
of the pseudo steady state assumption was in question.
However, as discussed in Appendix I, treatment of the
reacting system must be kept as simple as possible because
only one rate constant value may be determined from the
data on the continuous reactor. In reality, equation (III-9),
which is a relatively simple equation, cannot be used because
three rate constants would need to be determined.
With the restriction of having only one rate constant in
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 57
a model, one is limited in the amount of sophistication
possible.
One can begin by simply attempting to fit the data to
an empirical equation of the form
For simplicity m and n were chosen to be integer values or
zero. Models ,1, 2, 3, ^, and 5 are of this type.
Recalling that in the reaction the surface concentration
of the solid may be considered constant while the con
centration of the fluid reactant is decreasing in proportion
to the amount.of conversion one can use equations (111- 1 9 )*
(III-20)* and (111-21) referred to in the THEORY (section III).
These equations are included in Table V.l as Models 1, 7 and
6 respectively. Model 6 is valid for the case where one
assumes a first order reaction with respect to A on the
surface. If a second order reaction with respect to A is
assumed the equation of Model 15 is obtained.
Models 9* 10* 11* 12, and 13 are empirical variations
of the diffusion controlling equation of Model 7-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 58
o FIG. FIG. V.1 A Typical Tracer Response.
CO
3i.nN.rn U3d m o 33>join 30 swvao
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 59 TABLE V.1 List of Reaction Models
Model Units of Rate Model No. Constant (a)
1 m i n . 1 X 1 = k iX B o ^ A - x B^
i i d x R 2 min. X ■ — - = k2XBo^A"xB^1_XB^ dt
minT1 X"2 — = k3XB0^A“xB) d t ■/
. d X r > , O min.-1 — = k4 (1-XB>
1 d x R - mi nT = k 5 ( l - x B ) d t
m i n T 1 V1 — - = k6XBo^A“xB ^ 1"xB^2/3 dt
m1„-l .-1 dxB . k XB0(A-1;b ) < 1 - x b ) 1 / 3
7 T 7 1-(1-XB)1/3
dxB _ XBo(A-xB)(l-xB)2X3 • n -1 v -1 B _ I min. X - k d t ° l - ( l - x B )
. _i _2 d x B X B o ^ A " x B^ ^ 1- X B^ min. X = kq -- - y r o — dt 9 l-d-Xg)1^
(a) X = concentration ’in moles per mole of calcium
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 60
TABLE V 1 Coritd
Model Units of Rate Model No. Constants
v-2 _ k XBo(A~xB)2 (1~xB)1/3 10 dt ' 10 l - d - x , ) 1/ 3
11 min*m in "1 Xx "2 dXB— - — kk o / o dt 11 l-( l- x B)z/3
_.._-l v-2 dxB _ XBo^A_XB^ ( l - XB> 12 min. x l 2 dt l-(l-xB)
m in "1 X "1 XBo (A“ XB ^ 1' XB) 13 im n. x dXB - k i q * dt • xB
2/3 dxB _ , XBo:^A“XB^ 1”XB^ 14 min.. - 1 Xv - l = k1/t------dt 14 1-(1-Xg) '
15 mi nT 1 X’ 2 ^ ^
. -1 v-l dxB _ XBo^A“XB ^1_XB^1/3xB 16 min. x " Kir i/o d t 16 l-xB-(l-x B)1/3
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. VI EXPERIMENTAL RESULTS AND ANALYSIS
A Experimental Results
1. Qualitative Observations
Several points need to be documented on the basis
of visual observations made during the operation of the
batch and continuous reactor.
a. Batch reactor
When the hot acid was added to the preheated
fluorspar a rapid frothing ensued, the intensity of which
increased with increasing temperature. In the runs at 350°F
the acid had to be added less rapidly to prevent boilover of
the contents. Runs at temperatures above 350°F were
impossible in the batch reactor because addition of the acid
would necessarily have been so slow so as to affect the results.
After the frothing stage, the reactants took on a
putty-like appearance,which, if left unmixed, would have set
as one mass. However, with mixing by use of a spatula the
setting action produced granules of various sizes (5 / 8 inch
to 1/8 inch diameter with some powder). The larger granules I seemed to be wetter than the others i.e. they contained a Ii greater proportion of acid. ! i The putty-like stage lasted about 5 minutes in the 250 F
•runs but only about 2 minutes in the 350°F runs.
61
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In one experiment,1/8 inch diameter crystals of
relatively pure CaF^ were immersed in a beaker containing
sulfuric acid at about 250°F. Small bubbles of gas were i evolved which dissolved in the acid (HF is soluble in H^SO^
at 250°F to 1.8$ by weight HF content). The solids product
layer did not appear until the crystals had reacted for
some time. This product layer formed initially on the
crevices of the crystals but soon covered the entire unreacted
surface and adhered very firmly to it. Examination under a
microscope revealed that the product layer was not sponge-like
but rather more like Plaster of Paris. The microscopic
examination also revealed that the surface irregularities
had been somewhat smoothed out.
b. The continuous reactor.
Some of the points mentioned here have already
been covered in the other sections of this thesis. They
are reconsidered here only by way of a summary.
In the feed end of the reactor, the reacting mass, which
only partially filled the reactor, consisted of a putty-like
material. The entire forward reactor interior was-thickly
coated by this putty. About 6 inches beyond the reactor entrance
the paddles were only slightly coated and the reactor
contents consisted of slightly wet granules which became
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. fairly dry as they travelled to the reactor exit. While some
of the exiting granules were of 1/4 inch to 3 / 1 6 inch
diameter, they were in the main ahout 1/16 of an inch or
less in diameter.
In a run which is not documented in this thesis, pure
synthetic CaF^ was fed into the reactor. Operation of the
reactor using this spar was impossible because fairly large
lumps formed which could not be handled by the solids out
auger. The lumps were also fairly wet indicating low
conversions. With the same reactor conditions, but using the
synthetic spar to which a 5$ by weight CaCO^ content had been
added, the large lumps did not form nor were the solids out
as wet as in the above run.
Even after 8 hours of operation the solids out flow rate
pulsated to a large extent. When large pulsations occured,
the temperatures were also observed to fluctuate slightly.
Runs in which high flow fluctuations occured were normally
discarded because the tracer response for these runs could
not be relied upon as being representative. Only two runs j , * | were discarded for this reason. j
2. ------Continuous Reactor Data i Table VI.1 contains the compositions, and the mean
particle diameters, of the spars used in runs 10A to 19A and I
i
4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 64
IP to 10P of the continuous reactor. Sulfuric acid, of 98 . 8 f o
by weight purity was used in all these runs. Table VI.2-
shows the experimental parameters of the A runs carried out.
Table VI.3 contains the run parameters of the factorial
runs IF to 1OF.
The results of the mass balances as well as the
conversions obtained for all the samples taken are included
in APPENDIX IV.
Table VI.4 shows the fractional age distribution of
the solids leaving the reactor calculated from the percent
nickel out data and the solids out flow rates using the
equation
| Fraction of solids out W.C.
J stream which consists = (E(t>At) (VI-1) a of elements of age n W ,C . I between t . and t . + At. L 3 3 L 1 j = 1 where W^ = weight of solids out duringthe interval i
= average $ Ni content of solids out during the interval
and n = total number of intervals
3• Batch Reactor Data
The conversions-time data of the batch reactor runs
using fluorspar Newfluor-A is contained in Table VI.5*
conversion values were calculated from the % Ca-F2
filtered solids samples reported by the lab.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. B. Analysis of Batch Data.
The conversion-time data of Table VI.5 were subjected
to the analysis outlined in APPENDIX I. Only three models
were seen to yield a fairly linear plot of integral (I)
versus time (t). These models were: model 9* 10* an(3 H
of Table V.l.
**» _ *9 (A-XB>2 i> KB >2/3 Model 9 — ” — ------7/5------at l - (i-xB )1/3
^ . = k10 XBo (A-Xb) ^1_XB^ Model 10 — T/T------at l - (i-xB)1/3
_ k lX XBo (A XB^ Model 11 at i - (1-XB)S/3
All other models contained in Table V.l yielded non-linear
integral versus time plots.
The apparent rate constants of the three models were
estimated by least squares regression as
discussed in Appendix I and are shown in Table VI.6. For
comparison purposes this analysis was also done for models
6 and 7*
dx_ X_ (A—x ) (1-xV>2/3 B _ 6 Bo ' B m B' Model 6 dt _ *7 xEo (a-xB )(i-sB )1/3 Model 7 1 - ( l - x ^ / 3
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 6 The correlation coefficients for I vs. t for all models
are included in Table VI .6 and indicate a high association
between I and t. However the correlation coefficient is
only a measure of association and in no way should be
interpreted as the final criterion of the goodness of fit
of these models.
A more accurate measure of the goodness of fit of a 2 model is the ratio MS,„/S„ where MS,„ is the mean square AR E * AR ^ of the residuals about the regression. i.e.
Y V ^ \2 MS = Bi ~ XBi' (VI-2) (n - 1 )
/\ xB^ = the conversion predicted by the rate model at a time t^ using the determined k value.
x . = the conversion obtained by experiment. Bi n = number of data points. 2 S_ is the mean square due to pure error and was evaluated E from the replicate values of x^ at a time t^ using the
following equation m n. a . 2 ■ I 3 , - ,2 SE =j=l i = 1 (XBij ^ i ) (VI-3) ------nr £.(*. " *) j = 1 3
n. = no. of replicates available at a time t. 3 x
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 67
x„. = mean value of replicates at a time t. Bi * i m = total no. of time levels at which replicates were available 2 -4 The S value calculated is 8-97 X 10 with 23 degrees of E freedom and is a measure of the experimental error.
If a model is to fit the data and MS„„ value for the AR regression should not be significantly greater than the
experimental error. If it is significant it indicates
that there is a bias in the model (i.e. the residuals are
unduly high).
The MS,_ values were calculated after having obtained AR ^ the least squares estimates of the apparent rate constants. 2 The F ratio (MSAR/SE ) alon9 with the 95$ confidence
interval of the apparent rate constants were included in
Table VI.6 .
The F ratios are significant at the 5$ or lower level
of significance for all three temperature levels for
model 6 , and for the 300 and 350°F temperature levels for
model 7- None of the F ratios are significant for models
9 , 10 and 11 indicating that these three models fit the data.
As well, the MSAR values in Table 6 are of equal size, i indicating that none of the models may be considered a better fit. t It must be stressed that the above, analysis does not
prove that the three models are the correct models, but proves
only that the null hypothesis that these models fit the
data cannot be rejected.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 8
Figures VI.1, VI.2, VI.3, VI. and VI.5, show the
experimental data and the conversion curves predicted by-
models 6 , 7 , 9 , 1 0 and 11 using the least squares estimates
of the apparent rate constants. Figure VI.1 and VI.2
illustrate the lack of fit of models 6 and 7 to the data.
Having obtained the apparent rate constants for each
of the models at three temperature-levels, the next task was
to fit these constants to the Arrhenius equation of the form
k = kT exp
where E is the apparent activation energy (Btu/lb.mole), T
is the temperature (°R), (1/T) is the mean (1/T) value, and
R is the gas constant (Btu/lb.mole °R). The aim was to
obtain the best estimate of the two parameters k^ and E.
There were two approaches used for the least squares
estimate of the parameters. The first approach was to
estimate the parameters of the non-linear equation (VI-4)
while the other was to linearize it by taking the natural
logarithm of both sides of the equation for easier
approximation of the parameters. However, linearization
simply for easier approximation of the parameters is an
invalid procedure unless the true regression model itself is
intrinsically linear
If the model is intrinsically non-linear, the regression
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. equation is r r ‘ 1 + e1± (vi-5) = *T exP T. \ T x . I
i = 1 , 2 ...... n
where is the random error with the expected value of 0 2 and normally distributed about 0 with a variance 0^ , where 2 0^ is the variance of the apparent rate constants. Put
more simply is the increment by which an individual k^
may fall off the regression curve, the expected value of
which is zero and whose variance is expected to equal the
variance of k at all levels of k. If the variance of k .is
independent of the level of the temperature, the variance of
e„. must also be assumed to be constant, lx (2 1 ) Using the program GAUSHAUS v ' the least squares
estimates of the non-linear parameters k^ and E were obtained.
The values of the parameters obtained are shown in Table VI-7A 2 along with the variance of resxduals S , Rj X
2 £ ( k . - k .)2 8 *R,k = r L t — i : ( v i - 6 ) tf - p
p = no. of parameters in the regression equation = 2 ;
n = no. of data points. Because there were only 3 temperature
points n - p = l(i.e. the variance about regression had only
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 70
one degree of freedom) the resulting estimates of the standard
error of E and k^ (by linear approximation) also had only
one degree of freedom and the 95% confidence intervals of
E and k^ were very large and ignored. The (1/^P) value for a . 3 all three models was I.3196 X 10 °R ^ so that the
equation were
- 2 2 1 9 0 k = 0.102 exp (VI-7) 9 R - T 757.8 J
for model 9
- 2 0 5 2 0 k 1() = 0.0775 exp (vi-8) R 757.8
for model 10
-.21480 1 and k^^ = 0.176 exp (Vi-9 ) R T 757.8 J
for model 11. The k values had units of (min. -1 X -2 )
where X represents concentration in terms of moles per mole
of calcium. The superscript ^ denotes predicted value.
Suppose now one assumes that the regression equation
is intrinsically linear, of the form.
r 1 k . = k exp 1 T • A (VI-10) T. l
i = 1,2 n
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 71
which can be linearized to the form
1 = In - f ri (In k)± kT + e2i (VI-11) R I T: T
1,2 . n
so that = In
Rewriting equation (VI-10) in the form
k. = k. f6. (VI-12) i i x
where '-E 1 - k. = km exp x . T Hi 1 (VI-13) _ T. \ T /- . T X
i = 1,2 . m • n
k^ is the estimate of k^ from the regression equation using
the best estimates of k^ and E. However, in equation
(VI-10)^ is a random factor by which the rate constant k^
differs from the regression equation and is valid only if A the error (k^ - k^) is proportional to the size of k^.
For equation (VI - 11), is assumed to be normally
distributed about the mean zero with a constant variance 2 In Ik) The best estimates of the linear parameters kT and E of
equation (VI-11) were determined by least
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 72 squares (13 ' ') and are reported in Table VI.7B along with the
variance of residuals
JfexTkjL - (Ink’ (VI-14) R In k n - p
Again it is fruitless to consider confidence intervals because
there is only one degree of freedom for the variance of
residuals. The (1/T) value for the models was _qo -1 1.3196 X 10 R so that the Arrhenius equations estimated
were -19530 ri - 1 k^ = 0.104 exp (vi-15) R -T 757.8 _
for model 9
xx f - 1 8 1 5 0 1 - 1 k1Q = 0.0812 exp-< ----- (VI-16) R -T 757.8
for model 10, and
C- 18940 1 - 1 = 0.185 exp (VI-17) 11 V LT 757-8 for model 11.
Because there were only three data points it is
impossible to determine which of the regression equations
(intrinsically linear or intrinsically non-linear) fits best.
However by either approach the activation energy was in the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. order of 20,000-Btu/lb. mole.
C. Analysis of Continuous Reactor A-Runs.
Using the method outlined in APPENDIX I the apparent
rate constants were determined for runs 11A to 19A. The
apparent rate constant values are shown in Table VI.8. The
apparent rate constants from the batch data were included
in this table by way of a summary.
The acid:spar ratio (a ) used in the calculation of the
apparent rate constants of the continuous reactor runs were
those labelled "corrected acid:spar ratio " This corrected
acid:spar ratio accounted for acid boiloff and reaction with
CaCO^.
As will be discussed in section VII of this thesis, once
the reaction between spar and acid has proceeded to some degree
the acid in the'reaction mass is in the form of CaSO^’H^SO^ (24'I crystals'1 ' or liquid H2S°4 caP i H aries of the ash
layer. In either case the vapour pressure of H^SO^ would be
reduced and boiloff inhibited. The boiloff, therefore, was
more likely to occur in the early stages of the reaction when
the mix was still wet.
When the mix is still wet and conversion was low, the 2 term (A-x b ) in the rate equations was not so sensitive to
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the value of A. The acid boiloff was thusly best considered
as an acid bypass.
Furthermore, because CaCO^ would immediately react on
contact with sulfuric acid;the acid so consumed was considered
as unavailable for reaction with calcium fluoride.
Corrected acid:spar ratio
r moles of HgSO^in moles of HgSO^ required for-i\ reaction with CaCO^
I moles of H^SO,. boiled °ffj 1 J [moles of CaFg into reactor]
The continuous reactor data were subsequently fitted to
the non-linear and linearized Arrhenius equation
Because now there were 9 data points an approximation of the
95$ confidence interval was more meaningful
The least squares analysis of the data is contained in Tables
VI.9 and VI.10.
The estimates of the variance of k due to pure error, 2 S .. values of Table VI.9 were calculated using the values E, k of the rate constants obtained at each temperature level
(i.e. at each temperature three runs were carried out varying
only the acid:spar ratio).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 75
m n - i , x S 2 y y’ (k... ir) E,k ih i4 1 ^ 3 (VI-18) m
I (“ i - 1} j = 1
Where m = number of temperature levels at which replication
was done = 3, an<2 n^ = number of replicates at any one
I temperature = 3* 2 2 The use of S , or S 1 , *(for the intrinsically
linear model) as measures of variance due to pure error
presupposes that the acid:spar ratio was properly accounted
for by the rate equation. If the rate equation had not
properly accounted for the acid:spar ratio, the errors about
regression would not be randomly distributed but correlated
to the level of the corrected acid:spar ratio. A plot of
the errors in Tables VI.13 and VI.14 vs. the acid:spar ratio,
as well as tests to ascertain the randomness of the errors,
revealed that the errors were indeed randomly distributed and
not correlated to the corrected acid:spar ratio. Nor was
there any apparent correlation detected between the level of
the rate constant (or In k) and the errors about regression.
The above statements hold for both the residuals of the
non-linear and linearized Arrhenius equations. The data,
therefore, do not reveal whether it is more appropriate to
use the non-linear or linear models. Both approaches satisfy
the data rather well.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 76
The following equation was used to calculate the
estimate of the variance due to pure error of In k, S E,ln(k)’ n . 2 (In k)±j - (In k ) j)
SE, ln(k) m £ (nj " 1) (vi-1 9 ) j = 1
2 2 Because the SE k or SE 2.n(k) va:l-ues -*-n Takles VI.9 and 2 VI.10 were larger than the S values in all cases there was R no reason to assume that the regression equations did not
adequately fit the data.
By least squares fit of the non-linear Arrhenius equation
to the continuous reactor data the following equations
were obtained;
16200 1 (VI-20) kg = 0.317 exp R T 828.8
for model 9
- 15270 ’ 1 1 ' k^ = 0.206 exp (VI.21) R _ t . 828.8 ,
for model 10, and i - 15800 " 1 1 1 “k,^ = 0.524 exp (VI-22) R _ t 828.8 . 1
for model 11, where T = R.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 77
By least squares fit of the linearized Arrhenius
equation to the continuous reactor data, the following
equations were obtained;
- 17000 r 1 ✓a . *9 = 0*307 exp (vi-23) 1 R T 828.8.
for model 9
- 15700 k1Q = 0.202 exp (VI-24) T 828.8
for model 10
- 16500 1 ki:L = 0.510 exp (VI-25) R T 828.8 J
for model 11.
The parameters estimated by either non-linear or linear
least squares revealed that for the continuous reactor data
the activation energy was in the order of 16,000 Btu/lb. mole
and did not vary significantly from model to model. Furthermore,
on the basis of the 95$ confidence intervals, the hypothesis
that the activation energy values for the non-linear models • | are not significantly different from the linear models, could I not be rejected. 1 D. Fitting the Arrhenius Equation to the Batch and Continuous Reactor Data Simultaneously
In the above analysis, the batch reactor apparent rate
constants and the continuous reactor apparent rate constants
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7 8 were regressed to the Arrhenius equation separately. It
was of interest to see if the A runs and batch data could
be fitted to an overall Arrhenius equation.
The least squares estimates of E and ^obtained for the
non-linear and linearized Arrhenius equation contained in
Tables VI.11, and VI.12 respectively were obtained. As in 2 . „2 , ' 2
were compared and, as in previous results, because the S E 2 2 or S , values were larger than the S values there was no E,k ^ R lack of fit of either the non-linear or linear model nor
was one model discernably superior to the other.
Examination of the residuals in Tables VI.15 and VI.16
did not indicate any correlation between the residuals and
the size of k. or In k. or between the residuals and the r l corrected acid:spar ratio.
More significantly, examination of the residuals of
the batch reactor data points indicates that the overall
Arrhenius equation does adequately fit these points.
By least squares fit of the nonrlinear Arrhenius
equation to the batch "reactor and continuous reactor data
simultaneously, the following equations were obtained: 16400 / 1 (VI.26)
for model 9-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 15200 /' 1 = 0.166 exp (VI-27) R \ T 809.9
for model 10, and
- 15900 / 1 k 11 = 0.414 exp (VI-28) 809.9
for model 11. Using least squares for the linearized
Arrhenius equation the equations were
/S '- 17900 / 1 k = 0.234 exp (VI-29) y R \ T 809.9
for model 9,
y\ - 16100 / 1 k 1Q = 0.161 exp (VI-30) R ' T 809.9
for model 10, and
- 17200 /1 k,, = 0.396 exp } (— "11 (VI-31) R \ T 809.9
for model 1 1 .
The log of the apparent rate constants vs. 1/T plots,
with the various regression equations obtained by the
least squares fit of the linear and non-linear models are i shown in Figures VI.6 , VI.7, VI.8 , VI.9, ivi.10 and VI.11.
E. Predicted Conversion Errors. j
Having estimated the parameters for the non-linear
and linearized Arrhenius equation by least squares, it was
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. appropriate to determine how well the rate equations, using
the rate constants calculated from the Arrhenius equation
(with the appropriate estimated parameters), predicted the
conversion of spar in the continuous reactor runs 11A-19A.
Again it was necessary to use the exit age distribution.
Calculation of the conversions was accomplished as outlined
in Appendix 1 .
The conversions obtained using models 9* 10 and 11 are
shown in Table VI.1 7 . For this table the conversions under
columns 1, 2, 3 and 4 were obtained using the rate constants
from the Arrhenius equation whose parameters were estimated
as follows
Column (1) least squares fit of the non-linear Arrhenius equation to the continuous reactor data.
(2) least squares fit of the linearized Arrhenius equation to the continuous reactor data least squares fit of the non-linear
(3) least squares fit of the non-linear Arrhenius equation to the continuous reactor and batch reactor data
(4) least squares fit of the linearized Arrhenius equation to the continuous reactor and batch reactor data.
The variance of errors in Table VI.17 was obtained
from the following equation
Variance = (VI-32)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 81
V = degrees of freedom = 7
x_. = observed conversions Bi = predicted conversions
The standard deviation of the errors was the square
root of the variance. The largest standard deviation
obtained was 0.0124 (fractional conversion).
In order to determine if the variance calculated as
above was larger than expected, it was necessary to determine
the inherent errors due to sampling, analysis of the samples,
and deviation of the flow rates.
Calculation of the extent of conversion of fluorspar
was based on the determination of the fluorine content of the
scrubber liquor samples.
% CaF,p conversion
= r ( g/1. of fluorine in scrubber liquor)
1 X (caustic liquor flow rate) X
I 2 MW L ______F__ _
CaFg into reactor (VI-33)
From replication of analysis of samples it was possible
to calculate the variance due to analysis as 2 2 S = 0.00620 (g./l. of fluorine) A*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 82 with 176 degrees of freedom.
In addition to the analysis error there was a sampling
error due to the inherent fluctuations of the reactor.
Because six samples were taken for each of the runs, the 2 variance due to sampling, S , could be estimated. Its value s was determined to be
S 2 = 0.01068 (g./l.of fluorine)^ * with 9^ degrees of freedom.
For each sample at least 2 replicate analysis were done
so that the variance due to analysis and sampling for each
sample, S 2, was (^5) JP
sp2 = ss2 + SA 2/n (VI-3 4 )
where n = no. of replicate analyses = 2
S 2 = 0.0137 (g./l. of fluorine)2 F
The standard deviations of the spar and the scrubber
liquor feed rates were both estimated at 1%.
The fluorspar feed rate for most of the runs was about
500 g/hr. and the caustic liquor feed rate was usually 70.5
litres per hour.
For a variable, y, which is calculated from a function
of x^, x , x„ . . . the variance of y may be estimated as ^ J
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 83
follows ^ 3 )
».2 y v ^ y x i \ * x 2 J x2 \ b x 3 J 3
(VI-35)
so that for equation (VI-33) the relationship was
2 2 f 70.5 X 78/3 8 ”) 2 2 J2.57 X 78/38*^ 2
X B F L 500 SL C 500
2 C 2.57 X 70.5 X 78/38
SsF I (500)2
2 2 where S = (70.5 X 0.01) was the variance of the . SL 2 2 scrubber liquor feed rate and S = (500 X 0.01) SF was the variance of the spar feed rate and
2 —R 2 S = 1.21 X 10 (fraction conversion) XB 2 S was the estimate of the variance of the conversions XB calculated from one sample. However, the conversion for
each run was based on the average of six samples and 2 S_ , the variance of the average conversion calculated using XB six samples, was
S2 = S2 /6 = 2.02 X 10“^ *B B
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 84 I and S = 0.0142 (fractional conversion) B
The variance of the observed converions having been
- 4 ' estimated to be 2.02 X 10 , it can now be compared with
the variance of errors of Table VI.1J. In this table the -4 largest variance of errors obtained is 1.545 X 10 which 2 is smaller than the S— value. XB A An examination of the errors (x . - x . ) does not E l E l indicate a correlation between these errors and the corrected
acid:spar ratio.
From this analysis it may be concluded that there was
no lack of fit of models 9> 10 and 11 to the data and a
comparison of the variances (F ratio test) of table VI-17
indicated that none of the models could be assumed superior
to the others.
F. The Factorial Experimental Design.
The objective in the factorial experiments was to
establish the effects of mixing speed, CaCO^ content, and
the fineness of the spar on the reaction. Factorial design
was preferred over the classical one. at a time experimental
design, as the former ‘is generally more efficient. The
classical design is not readily applicable to situations where
large interactions between factors are possible. An
orthogonal experimental design is more practical because it
not only allows the experimenter to obtain an estimate of
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 8 5
the effect of each factor but also to estimate the' effect
of the interactions between the factors.
1. Planning the design
The form of the orthogonal experimental design chosen
is dependent on the degree of the equation which one chooses
to estimate the response surface.To start with, one
may assume that the response surface, in this case, can i be adequately described by the equation
k = ko C°MmSS exp £ - (^- (VI-36a)
where C = wt. % CaCO^ content of the spar, M = mixing rate
(r. p.m.), T = temperature (°R), S = mean partial diameter
of the spar, R = gas constant (Btu/lb. mole °R), E =
activation energy Btu/lb.mole and k^, c, m, and s are
constants.' Equation (VI-36a) may be linearized by taking the
\ natural logarithm of both sides
Ink = In k + cln mln M+ sin o c+ s
+ (INTERACTION) (VI~36b)
and one could obtain estimates of kQ,m, c, s and E by 2|—1 use of a 2 fractional factorial design requiring only
8 experiments. The resulting equation will be, of course,
highly empirical but at the same time provide for a linear
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 86 approximation of the response surface.
Due to the fact that each experiment was expensive,
requiring a significant amount of time and effort on the
part of the experimenter, and costly analysis of the samples
by the lab at Arvida, it was decided to carry out the least
number of experiments possible. The 2 4— 1 fractional
factorial design seemed to be a good choice.
Originally, the factorial design was constructed about
the base point
T = 830°R, M = 10 r. p. m. and C = 5 % and coded
factors X , X , X , and X, were chosen such that 1 <2 3 T*
X^ = - 1 M = 5 r. p. m.
X = + 1 M = 20 r.p.m.
x2 = - 1 C = 3.5#
x 2 = + l c = 7.14- %
X = - 1 spar of normal fineness
X^ = + 1 spar ground to a greater fineness
X. = - 1 T = 760 °R
X. = + 1 T = 910 °R
However3at 760°R (360°F) the reactor could not be
operated much higher than 10 r.p.m. because the slightly
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 8 7
shorter residence times at the higher mixing rate caused
the exiting solids to he too wet to he properly handled hy
the solids out auger. Furthermore, reactor operation at
5 r.p.m.was thought undesirable because, as was observed
in run 2F, the solids out flow rate fluctuated very badly.
In this run, little or no flow of solids for significant I time periods was observed.
Subsequent analysis of the scrubber liquor samples
from run 2F indicated no unduly high fluctuations of the
fluorine content. Furthermore, there were no undue
irregularities in the tracer curve. However, by the time
the lab data was made available.,'the decision to change
the levels of the factorial runs had been made and the
experimentation had already been completed.
The new base point chosen for the 2 4-1 factorial
experimental design was T = 868 R, M = 19-8r.p. m.and C = $%•
The base point for temperature was chosen so that the low
temperature level was 830°r (370°f) and the upper level was 910°r
(450°f), and the base point for mixing rate was chosen so
that 25 r.p.m.was the highest mixing speed and the lower
mixing rate was the log mean of 10 and 25 r„p.m..
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 8 8
= -1 M = I5.8 r.p.m. X1 = + 1 M = 25 r p.m. X1 = - 1 c = 3-5 % X2 = 4* 1 c = 7 .1*1- X2 = - 1 regular spar (Newfluor A. and B) X3 = + 1 reground spar (Newfluor Af and BF) X3 - 1 T = 830 °R X4 = = + 1 T = 910 °R X4
1 n( M/19 • 8) with X, = ------(vi-3 7 ) X 1 (l.n (25/19-8))
m c/5.0 (VI-38) X2 ln(5- 0/3 -5)
- - (1/t - 1/868) X„ (vi-39)
830 868
The factorial design was as follows.
ITATION X! X2 *3 X4 X1X2X3
1 -1 -1 -1 -1 a d 4-1 -1 -1 4*1 b d -1 . +1 -l +1 a b +1 + 1 -1 -1 c d -1 -1 +1 +1 a c +1 -1 +1 -1 b c -1 + 1 + 1 -1 abed +1 +1 +1 .+1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 8 9
The approach used for the design of the experimental
scheme was discussed thoroughly "by Box and Hunter (7) v ' and
the method of analysis of the factorial design experiments (2 7 11 14 IT 3*5^ may be found in most applied statistics tests. ' ’ * ’ * ’ '
In the above experimental design the effects of factors
X^,. X^, and X^ may clearly be determined but the
interaction effects i.e. X,X X^ etc. are confounded 1 2 ’ 2 3 ’ with one another. This point will become more apparent as
the analysis of the experimental scheme is discussed.
The equation which was to be fitted to the data was
(lnk)^= In k^ + mln M + cln C+ sin S
E r 1 /T + (ERROR) (VI-40) R [ T. VP- ^ 1
2. Analysis of Factorial Runs Data
The apparent rate constants for runs IF - 10F were
determined by the method outlined in Appendix I. Table VI.18
contains the variables and the coded variables, the average
conversions, and the apparent rate constants for the runs
IF - 10 F.
In Table VI.19 are shown the coded variables with the
natural logarithm of the apparent rate constants.
Before considering the analysis of the factorial
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. experiments it may be recalled that in the A runs there "was
a measure of the variance of the natural logarithm of the 2 apparent rate constants due to pure error. These SE
values were reported in Tables VI.10 and VI.11.
Details of the analysis of the factorial design
experiments are not included in this thesis to conserve
space.
In Table (VI.20) are shown the results of the factorial
experimental design analysis. (Recall that runs IF and 2F
were not part of the factorial experimental design). The
mean difference values or mean effect of the factor is the
average change of tie to k value with a change in the factor
level from -1 to +1
eg. for the factor + X^> X^ X^ the mean effect is
(ad + ab + ac + abed) -(1+bd+c+bc) — ------(vi-4l) 4
The change in the .1c value is, at least in theory, due to
the effect of change in X^ plus the interaction effect | Xg Xg X^. In practice however, it is very unlikely that a
three factor interaction would have an effect on the system
(2,7,8,11,14,17)_ BUt? for the case where the mean effect
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9 1
is due to a two factor interaction such as X X + X X
the statistical analysis of the data must often be fused with
the judgement of the experimenter.
In any case, it must first be determined whether the
mean effect of the factors is greater than that expected
by pure chance i.e. significant. Although this can most
directly be accomplished by conducting t tests on each
mean effect to determine if it is significantly larger than
zero (14) ' it. is . more expedient to use the Analysis of
Variance method.
The Analysis of Variance Table is shown as Table VI.21.
The mean square values are easily calculated as
MS = (MEM EFFECT)2 (VI-41)
2
and are the contributions to the total variance by the effect.
The P test or variance ratio test is a test to determine
if the variance of In k due to a factor is significantly
larger than that expected by chance alone.
f (1,6,0.95) = 5-99* F(l,6, 0.975) = 8.81 and f (1,6,0.99)
13-75.
The results in Table VI.21 indicate that, as expected,
temperature has a very strong influence on the apparent
rate constant. It also turns out that the calcite content
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 92 $ of the fluorspar also has a very significant favourable
influence. Although the effect of increasing the mixing
rate is slightly favourable the analysis of variance
indicates that it is not statistically significant at the
5% level of significance. At the same time, the spar
fineness, within the range studies, does not have any
significant effect on the apparent rate constant. The
interaction effect X^ + X^ X^ may be classified as
statistically marginally significant and will be explored
further by grouping the data as shown in Table VI.22.
In this table the data are grouped according to the
calcite content of the spar and temperature, bearing in
mind that the spar fineness does not significantly influence
the apparent rate constants observed. By grouping the data in
this fashion one notes that the apparent rate constants do
/ not vary to any large degree with increased mixing when the
CaCO^ content of the spar is 7-1^ With the CaCO^ content
at 3.5%, however, the apparent rate constants increase very
sharply when the mixing rate is 25 r.p.m.
One may hypothesize the reasons for this result on the
basis of the physical phenomenon. ! 1 When the CaCO^ content of the fluorspar is relatively
low (3.5 fo) the blending action produced by the foaming
may be insufficient to produce homogenous mixing of the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. reactants. At the same time, the stirrers may not have served
to enhance the blending unless they rotated at relatively
high speeds i.e. 25 r. p. m.. At rotation speeds lower than
25 r. p. m. the stirrers may well have served only to agitate
the macroscopic mass rather than blend the reactants. If
the CaCO^ content of the spar is augumented, the resulting
blending action is more extensive and the higher rotation of
the stirrers is unnecessary.
The above hypothesis would explain why the interaction
term X^ X^ + X^ X^ is statistically marginally significant.
It can be ascribed as due to the contribution of X^ X^
(mixing X CaCO^ content). There is no reason to expect an
interaction effect due to spar fineness and temperature,
since the effect due to spar fineness is negligible.
At this point it would seem logical to attempt to fit
the data to an equation of the form
1
+ I*m + €. 1 (VI-42)
where 1 = 0 if C = 7 .14 $ or M <25 r. p. inland 1 = 1 if
account for the increase in the In (k) values when the mixing
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9 4
rate is at 25 r.p.m. and the calcite content of the spar
is 3.5 fo. Equation (VI-12) is not continuous with respect to
the mixing parameters because as was noted in Table VI.22
an increase in mixing did not alter the apparent rate constant
until the mixing rate was raised to 25 r.p.m.
Use of least squares to estimate the non-linear model
parameters is inappropriate because the factorial experimental
design is useful only for approximation of parameters of
inherently linear equations.
Table VI.23 shows the least squares estimate of the
linear model parameters with the data of the factorial
experiments only. The parameter estimates in Table VI.24
were obtained by least squares fit of all the apparent rate
constant values (continuous and batch reactor).
The results show that the apparent activation energy
estimates in Table VI.23 were not significantly different
from those in Table VI,12 and Table VI.24. This indicates
that the estimation of the parameters is quite accurage by
use of only eight experiments in which four factors are varied.
The final equations correlating the apparent rate i constants to the temperature, CaCO^ content of the spar,
1 * 0.122 and mixing, are model 9; ^ • M
17410 ri
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 95
S\ /-> ooo -15810 f 1 - 1 1 * 0.116 model 10; k 1Q = 0.05l4cu'oo° • M exp R L T 809.9 { 1) (VI-114) 0.964 ..I* 0.120 -16770 ri - 1 model 11; = 0.115C • M exp r Lt 809.9.
(vi-45)
where I = 0 if C = 7.14 % or M <25 r p m and I = 1 if C = 3.5 ^ and M = 25 r. p. m.,
2 The variance of residuals S values in Table VI.23 R 2 and VI. 24 are smaller than the SE ^.^values indicating that
the errors are not significant , and examination of the
residuals of Table VI.25 indicated that they were randomly
distributed and not correlated to corrected acid: spar ratio
or the size of the apparent rate constants.
As was done for the A runs, the predicted conversions
were calculated using the reaction rate models combined with
equations (VI-43), (VI-44) and (vi-45). The predicted
conversions obtained are shown in Table VI.26. The standard
deviations of the errors are 0.00875, 0.00934 and 0.00892
(fractional conversion) for models 9, !0 and 11 respectively.
These standard deviations are lower than the S=r■**D (the standard deviation of the observed fractional conversion
based on an average from six samples) value of 0.0142
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. previously evaluated. This indicates that no lack of fit
of the models is detected. :Furthermore, because the
standard deviation of the errors in Table VI.26 are not
significantly different from one another (F ratio test),
there is no basis for assuming that any one of the models
is better than the others. 1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced
CONVERSION % IOQ 70 0 5 80 60-A 90 20 FIG. VI.1 Batch Reactor Conversion - Time Data and and Data Time - Conversion Reactor Batch VI.1 FIG. / A Conversion Curves Predicted by the the by Predicted Curves Conversion es qae i fMdl 6- Model of Fit Squares Least 0 5 0 2 15 10 IE (MINUTES) TIME 3 5 0 °F 0 5 3 XE ME AL TA EN IM EXPER 5 2 CT D TE IC D E R P t 0 3 7 9 5 3 1 0 0
9 0
8 0 A A
7 0
6 0 —A / □ /
4 0
O 3 0 EXPERIMENTAL PREDICTED
20
0 5 10 1520 2 5 3 0 35 TIME (MINUTES) FIG. VI.2 Batch Reactor Conversion - Time Data and Conversion Curves Predicted by Least Squares fit of Model 7
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. - 9 9 100
9 0
8 0 X
7 0
6 0
5 0
CC 4 0
3 0 EXPERIMENTAL PREDICTED
3 0 0 ° F 20
0 5 10 15 20 2 53 0 35 TIME (MINUTES)
FIG. VI.3 Batch Reactor Conversion-Time Data and Predicted Conversion Curves from the Least Squares Fit of Model 9 .
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1
100
9 0
6 0
7 0
6 0
50
4 0
3 0 EXPERIMENTAL PREDICTED _ O 2 5 0 ° F 0
3 0 0 °F □ 20 3 5 0 ° F A
10
0 _ I______!______I______I__ :____ 1______I______) 5 10 15 2 0 : 25 3 0 TIME (MINUTES) . V] .4 Batch Reactor Conversion-Time Data and Conversion Curves Predicted by the Least Sguares fit of Model 10.
of the copyright owner. Further reproduction prohibited without permission. 1 0 1
100
9 0
8 0
7 0
6 0
5 0
O 3 0 EXPERIMENTAL PREDICTED
25 0°E O
20
0 5 10 15 20 2 5 30 35 TIME (MINUTES) FIG. VI.5 Batch Reactor Conversion-Time Data and Conversion Curves Predicted by the Least Squares fit of Model 11.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced
1.00 CO N1NO 1H ±N3dVddV 31VH 1NV1SNOO JLL 9 ro o CVJ to CVJ co ro CO ro CO oo ro ro o o o o CC 102 ‘ •rl ■H VD m •a 5 G\ s 53 +) +> H " H r • u-r +1 # -p u + n fa fa < c c a) rt > a) H H 0 o o c faa n fa «
1.43 1.38 1.28 1.33
1.231.18 V I-2 3 V I-15 V I - 29 1000/T (l/°R) E Q U A T IO N E Q U A T IO N E Q U A TIO N BATCH REACTOR DATA CONTINUOUS REACTOR DATA 1.13 Equation Lines of Best Fit.
1.08 < 0.01 1.00 0 .4 0 0 .0 8 - 0 .8 0 0 .6 0 O .IO f- 0 .0 6 - FIG. VI.7 Arrhenius Plot of Apparent Rate Constants of Model 9 with Linearized‘ < o: z
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1701 1.38 1.33 L28 1.23 1000/T (l/°R) 1.18 EQUATION Vi-27 EQUATION VI-8’ EQUATION VI-2 CONTINUOUS REACTORBATCH DATA REACTOR DATA 1.131.08 Equation Lines of Best Pit.
! 0 . 0 0.02 1.00 0 .6 0 0 .8 0 0 .4 0 PIG. VI.8 Arrhenius Plot of Apparent Rate Constants of Model 10with Non-Linear Ct 0 .0Q_ 4 , , o.osj- m 0 .0 6 - a: a: o.iof- r - - O 0.20
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 i— 1.33 1.33 1.38 1.43
1000/T (l/°R) 1.18 1.18 ' 1.23 1.28 EQUATION EQUATION V I-24 VI-.16 EQUATION VI-30 BATCH REACTOR DATA CONTINUOUS REACTOR DATA 1.13 1.13 Linearized Equation Lines of Best Fit. 1.08 I.OO! 0.01 0.80! 0.02 0 .6 0 0.20 FIG. VI.9 Arrhenius Plot of Apparent Rate Constants of Model 10 with ^ . . 0 .0 8 0= 0.10 0.10 0= t= 0 .4 0
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 106 1.38 1.43 1.33 1.28
DATA
1.23 V I - 9 V I-22 V I-28 REACTOR 100 0/T 100 {l/°R) 1.18 EQ UATIO N E Q U A TIO N E Q U A T IO N BATCH CONTINUOUS REACTOR DATA ,13 Equation Lines of Best Fit. 1.08
0.02 1.00 0 .0 4 0.20 0 .8 0 2.00 FIG. VI.10 Arrhenius Plot of Apparent Rate Constants of Model 11 with Non-Linear ce CL < 0 .0 6 UJ 0.10 UJ < 0 .0 8 < O 0 .4 0 Ui <* 0.60 <*
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission 107 1.43 1.33 1.28 1.23 100 0/T (1/°R) 1.18 CONTINUOUS REACTOR DATA BATCH REACTOR DATA EQUATION VI 31 EQUATION VI 25 EQUATION VI 17 1.13 Equation Lines of Best Fit. 1.08 1.00 0.02 0 .0 4 0.06 0 .4 0 0.80 2 . 0 0 o.os 9 r § 0.10 PIG. VI.11 Arrhenius Plot of Apparent Rate Constants of Model 11 with Linearized
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TABLE VI.1 Fluorspar Compositions
$ by wht.
NEWFLUOR NEWFLUOR A B
CaFg 93-9* 90.36
CaCO^ 3-5 7.14
SiOg l.H 1.38
R O 0.1 0.096 £ O
Mean Particle 27|i 27p. Size
NEWFLUOR AF - Newfluor A Reground to A Mean Particle
size of 8jjl
NEWFLUOR BF - Newfluor B Reground to a Mean Particle
size of 8(i
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. H 0 0 0 0 Line (g-/i.) 14.45 62.5 31.82 32.1 Rate Sludge Flow Transfer 821 852 816 832 916890 0 822 816 Rate Flow Out Solids (g/hr.) .5 O 7 70.5 70.5 70.5 879 70.5 70.5 70.5 ' 70.5 57-0 Feed Rate ll/hr.) Caustic Liquor 8.22 2.33 8.24 4.28 1.15 2.00 0.90„. Acid 12.79- Per Cent Boiloff .0079 0.95^7 0.9995 1.0533 1.0555 1.0632 1 1.0096 Ratio As Fed Acid:Spar 1 ' ) 450 370 370 f Outlet (° 450 450 450 450 370 375 375 0.9519 370 Using Fluorspar Newfluor - A Centre 0
450 450 45 370 290 300 300 370 300 300 300 0.9502 1.01 300 300 3 00 360 Temperatures Inlet 495 496 494 495 504 450 496 470 463 5-07 (g/hr.) * Spar Feed Rate 642 642 619 648 580 579 582 592 575 fgAr . ) Feed Rate Acid a a A a TABLE VI.2 Run Parameters for the Continuous Reactor Runs with Mixers at 10 r.p.m. 19 18 16 15A 17A 13A 12A 14 llA Run No.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 110 0 0 6.56 2.4 2.36 14.68 25.04 48.66 33.78 33.1 Line (g/hr.) Sludge Transfer Flow Rate /hr.) 872 853 810 773 863 825 844 882 9 Out ( 832.9 Rate Solids ‘ ‘ 821 70.5 70.5 70.5 70.5 70.5 70.5 70.5 70.5 ' 70.5 Caustic Feed Rate Liquor (Litres/hr.) • 1.632.80 70.5 2.56 2.20 7-14 2.71 7-04 8.80 11.42 Acid Per Cent Boiloff 0.994 4.36 0.9957 1.D06 1.008 1.005 0.998 1.004, 1.004 1.007 Ratio Spar As Fed Acid 450 365 450 450 450 450 370 370 370 450 450 450 370 365 370 370 370 1.002 Centre Outlet 450 450 450 450 450 450 450 370 365 370 370 370 370 Inlet Temperatures (°F) • 499 499 497 498 501 500 500 502 502 500 Rate Spar Feed (g/hr.) 614 610 612 615 617 611 614 610 620 615 Rate Feed Acid (g/hr.) TABLE VI.3 Run Parameters for the Continuous Reactor Factorial Runs f f IF 6 2F 7F Run 8 9F 4F 5F No. 3F 10F
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 111 A Type Newfluor B Newfluor B Newfluor AF Newfluor AF Newfluor BF Fluorspar Newfluor A Newfluor B Newfluor BF NewFluor 450 NewFluor A 450 450 450 450 (°F) 370 370 370 370 365 Temperature . 8 8 27 27 27 27 27 ... 1 Particle Spar Diameter of Mean (in Microns)(in . wt. 7-14 8 7.14 7.14 7.14 7.14 8 • 3.5 3-5 3.5 27 3-5 3.5 b y Spar Calcite Content $ 15.8 25 25 15.8 15.8 20 25 25 5.05 Rate 15.8 Mixing (r. p. in.) p. (r. f f f IF 6 Run 2F 7F 8 9F No. 4 3F 5F 10F TABLE VI.3 Con't VI.3 TABLE
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE IV.4, Fractional Age Distribution of Solids
Leaving Reactor (E(t)At)^
(E(t)(At))i Values Time Interval Run 11A Run 12A (min)
0-5 0.1221 0.08268
5 - 1 0 0.2798 0.22774
10-15 0.1918 0.23075
15-20 0.1042 0.17607
20-25 0.0633 0.09187
25-30 0.0599 0.03 003
3 0 - 4 0 0.0386 0.07713
4 0 - 5 0 0.0232 0.02688
5 0 - 6 0 0.0244 0.03126
60-70 0.0169 0.01561
7 0 -80 0.0129 0.00747
8 0-100 0.0201 0.00250
100-120 0.0059 0
120-140 0.0059 0 \ 140-160 0.0108 0
160-180 0.0097 0 180-200 0.0083 0 200-220 0.0063 0 220-240 0 0 •>
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 113 TABLE IV.4 Con't
Time (E(t)At)± Values Interval (min) Run 13A Run 14A Run 15 A Run 16a Run 17A Run 18a
0-3 0.0068 O.O638 0.0008 0.0035 0.0008 0.0219 3-6 0.2211 0.2778 0.0668 0.0264 0.0791 0.1745 6-9 0.1214 0.1152 0.0648 0.1003 0.1322 0.1441 9-12 0.0709 0.1029 0.0805. 0.2699 0.1512 0.1313 12-15 0.0944 0.0760 0.0910 0.1670 O.O698 0.0710 15-20 0.1434 0.0991 0.1449 0.1365 0.1611 0.1216 20-25 O.O695 0.0712 0.1274 0.0923 0.0790 0.0601 25-30 0.0811 0.0597 O.IO967 0.0516 0 .0485 0. 0546 30-40 0.0763 0.0427 0.1116 0.0796 0.1058 0.0989 40-50 0.0344 0.0281 0.0677 0.0363 0.0564 0.0424 50-60 0.0265 0.0511 0.0251 0.0181 0.0361 0.0338 60-70 0.0127 0.0123 0.0241 0.0121 0.0187 0.0169 70-80 0.0072 0 0.0373 0.0068 0.0154 0.0177 80-100 0.0217 0 0.0457 0 0.0222 0.0059 100120 0.0080 0 0.0026 0 0.0193 0.0053 120140 0.0046 0 0 0 0.0069 0 1 4 0 1 6 0 0 0 0 0 0.0126 0 160-180 0 0 0 0 0.0054 0 1 8 0 2 0 0 0 0 0 0 0.0084 0 2 0 0 220 0 0 0 0 0.0018 0 2 2 0 2 4 0 0 0 0 0 0.0052 0
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE IV.4 Con't
Time (E(t)(At)). Values Interval (min) Run 19A Run IF Run 2F Run 3F Run 4F Run 5P
0-3 0.0142 0.0179 0.0 0.0197 0.0097 0.0237 3-6 0.0594 0.1041 0.0179 0.0949 0.0836 0.0532 6-9 0.1338 0.1414 0.1265 0.0715 0.1401 0.1442 9-12 0.1381 0.1157 0.1220 0.0803 0.1877 0.1475 12-15 0.1045 0.1022 0.0838 0.0826 0.1099 0.0934 15-20 0.1237 0.1899 0.1222 0.1893 0.1152 0.1447 20-25 0.0953 0.1056 0.1090 0.0975 0.08501 0.0763 25-30 0.0854 0.0595 0.0849 0.0864 0.1061 0.0796 30-40 0.1265 0.0623 0.1240 0.1051 0.0766 0.0697 40-50 0.0663 0.0350 O.O9 6 O 0.0423 0.0370 0.0356 5 0 - 6 0 0.0247 O.OI65 0.0276 0.0391 0.0161 0.0262 60-70 0.0649 0.0247 0.0243 0.0224 0.0096 0.0209 70-80 0.0171 0.0136 0 .0134 0.0143 0.0067 0.01802 80-100 0.0046 0.0116 0.0222 0.0146 0.0094 0.0113 100-120 0 0.0097 O.OI96 0.0035 0.0142 120-140 0 O.OO65 0.0088 0.0038 0.0139 140-160 0 0.0048 0.0055 0 0.0114 160-180 0 0.0051 0.0059 0 0.0089
180-200 0 0 1 0 0.0073 200-220 0 * 0 0 0 220-240 0 0 0 0
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE VI.4 Con1t
Time (E(t)At)3 Values Interval (min) Run 6F Run 7F Run 8F Run 9F Run 10F
0-3 0.0363 0.0779 0.0044 0.0237 0.0288 3-6 0.1267 0.1703 0.0564 0.0589 0.1506 6-9 0.1784 0.1874 0.1219 0.0925 0.1751 9-12 0.1074 0.1471 0.1107 0.0878 O.O996 12-15 0.0948 0.1089 0.1412 0.1486 0.1022 15-20 . 0.1149 0.1062 0.1303 0.1222 0.1119 20-25 0.0868 0.0768 0.1131 0.1015 0.0756 25-30 0.0599 0.0646 O.O676 0.0614 0.0591 30-40 0.0834 0.0223 0.1228 0.1131 0.0806 40-50 0.0459 0.0258 0.0398 0.0482 0.055 2 50- 60 0.0254 0.0126 0-.0307 0.0256 0.0291 60-70 0.0184 0 0.0198 0.0480 0.0226 70-80 0.0094 0 0.0223 0.0215 0.0057 80-100 0.0071 0 0.0141 O.OO85 0.0038 100-120 0.0049 0 0.0047 0.0076 0.00 120-140 0 0 0 0.0129 0.0 140-160 0 0 0 0.0082 0 160-180 0 0 0 0.0050 0 180-200 0 0 0 0.0045 0 200-220 0 0 0 0 0. 220-240 0 0 0 0 0
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TABLE VI.5 Batch Conversion - Time Data
o 250 F 300°F 35 0(3F Time of Fractional Time of Fractional Time of Fractional Sampling Conversion Sampling Conversion Sampling Conversion (minutes) of CaF^ (minutes) of CaFg (minutes) of CaFg
1 0.2871 1 0.3747 1 0.5426 2 0.3826 1 0.4358 1 0.5989 3 0.5148 2 0.4274 2 0.5621 3 0.4903 2 0.5627 2 0.6604 4 0.4703 3 O .6256 3 0.6548 4 0.4736 4 0.5724 3 0.7132 4 0.4681 4 0.6001 3 2/3 0.6877 4 0.4847 4 0.6178 4 0.7221 4 0.5119 4 0.6193 5 0.7418 6 0.5351 6 O.6 69O 7 0.7686 6 0.5609 6 0.6339 9 0.7913 6 0.5634 8 0.6694 11 0.7919 8 0.6046 8 0.6614 16 0.8219 8 0.6205 10 0.6982 16 2/3 0.7947 8 0.6433 10 0.7202 21 2/3 0.8607 10 0.6437 10 0.7238 25 0.8741 10 0.6234 10 1/3 0.7019 31 2/3 0.8891 14 0.6796 14 0.7372 14 0.6822 14 0.7196 18 0.7709 18 0.7394
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 117 TABLE VI.6 Least Squares Analysis of Models Using Batch Data
Model Temp. 95$ Confidence Correlation Mean Square P (b ) V Interval of Coefficient About Ratio 0 Apparent Rate of Regression F Constant I vs. t MsiiO AR
9 250 0.0459 - 11$ 0-9748 0.000904 18 1.01 3 0 0 0.0955 - 12$ 0.9602 0.001030 20 1.14 350 0.2558 - 14$ 0.9603 0.000804 16 < 1
10 250 0.0381 - 9.6$ 0.9748 0.000739 18 < 1 3 0 0 0.0748 - 12$ 0.9597 0.001081 20 1.21 350 0.188 - 8 .9$ 0.9762 0.001006 16 1.12
11 250 0.084 - 11$ 0;9749 0 .000824 18 < 1 3 0 0 0.171 - 12$ 0.9602 0.001032 20 1.14 350 0.444 - 14$ O .9721 0.000857 16 < 1
250 0.0880 - 13$ 0.9573 0.00518 18 5 - 78 (d) 6 3 0 0 0.130 - 22$ 0.9276 0.01203 20 13.4l(d ' 350 0.273 - 24$ 0.9722 0.01171 16 1 3 . 0 5 ^
7 250 0.0211 - 7-4$ 0.9693 0.000699 18 < 1 3 0 0 0.03 4 8 - 14$ 0.9452 0.002705 20 3.02 ^ 350 0.0747 - 22$ 0.9772 0.004275 16 4 .76 ^
(a) MSar= s(jBi - £Bi)2/y ; (b) P : S = 0.000897 with 23 degrees of freedom E (c) significant at the 5$ level of significance (d) significant at the 1$ level of significance
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 118 I TABLE V I .JA Least Squares fit of the batch data apparent
rate constants to the non-linear Arrhenius equation
t s 2 Model E kT R _o , o Variance of Residuals (Btu/lb mole) X 10 (min X i (k_^ - k^)^/(n-p) i -4 9 22.19 0.102 1.431 X 10
10 20.52 0.!o775 8.61 X 10" 5 - 4 11 21.48 0.176 4.544 X 10
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 119
TABLE VI.7B Least squares fit of the batch data
apparent rate constants to the Linearized
Arrhenius equation
Correlation Coefficient R Model E T Variance of (Btu/lb mole) X 10 ^ (min 1 X Residuals Z (ln ki - 1 m - e . ) 2/ (n - p)
9 19-53 0.104 -0.9924 0.02235 I 10 18.15 0.0812 -0.9920 0.02044
11 18.94 0.185 - 0.9922 0.02158
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 120 .698 0.444 0.171 0.0840 1.195 1.185 0.464 1.306 0.222 O 0.471 0.211 0.178 Model 11 ' 0.188 0.0748 0.0381 0.469 0.432 0.508 0.1812 0.266 0.188 0.0874 0.0948 0.0731 Model 10 Rate Constant Values .0955 O 0.256 0.0459 0.726 0.798 0.749 0.428 0.283 0.281 0.123 0.105 Model 9 Apparent 1 1 1 .9654 Ratio O 0.8749 0.8728 1.0080 0.9873 0.9308 0.9403 0.127 0.9982 1.0551 Corrected Acid:Spar - - - .8766 0.8019 0.8026 0.8431 0.7886 0.7463 0.7683 Conversion of CaFg Observed Average 250 350 300 450 450 O 430 ' 370 . 0.8249 370 370 300 300 0.6919 3 0 0 O p Temperature a a a 6 BATCH BATCH BATCH 19A i 17A 12A 15A 18 13A 14 11A No. Run TABLE VI.8 Average Conversion of Spar and Apparent Rate Constants for A runs for VI.8 Constants TABLE Rate Apparent Spar and of Conversion Average
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 121 ~3 _3 “ 3 7.60 X 10 1.26 X 10 Pure Error 2.868 X 10 E,k Variance Due to r3 -3 10 X x io"3'
.2 a n - p 1 .0 9 2 .5 5 9 R Residuals Variance of 0.0344 t +
0.524 - 0.0860 6.66 x 10 0 .2 0 6 0.317 - 0.0537 (min"1 X "2 X ) (min"1 r3 rate constants to the non-linear Arrhenius equation Least squares fit of the continuous reactor data apparent 3 .3 7 of Parameters Confidence Interval ■to - E 1 6 .2 15-27 - 3-35 15-8 ± 3.28 ' (Btu/lb' mole) X 10 9 11 10 Model TABLE VI.9
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. H ro to Due to 0.02310 0.02358 E,ln k Variance n - p R 0.02048 0.01990 0.0215 0.02121 v» v» 2 2 (In k^-ln k^) Pure Error Residuals Variance of Correlation Coefficient 0.0554 -0.9856 - 0.5104 0.307 -.0.0339 -0.9860 (min ^ X 3 r Least square fit of the continuous reactor data apparent rate constants ta the Linearized.Arrhenius equation 2.58 - E of Parameters $ Confidence Interval 15.68 - 2.5016.50 - 2.53 0.202 - 0.0216 -0.9845 17.02 (Btu/lb mole) X 10 95 9 li 10 Model TABLE VI.10
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ro 00 1 0 "3 lo"4 x x
E,k 7 .6 0 2.87 X 10"3 12.6 to Pure Error Variance Due 10"4 10~3 X X 1 1 l' R n - p 2. (k.-k.)2 2. Residuals Variance of 8.314 -5.004 x 10~3 0 .0 23 9 0.0595
- -
0.247 - 0.0371 1.920 .1 6 6 0.414 (min 1 X-2) -3 2 .3 2 2.35 2.41 95$ Confidence Interval - - of Parameters
Arrhenius equation reactor data apparent rate constants to the non-linear 1 5 .2 15-9 - 16.4 (Btu/lb mole) X 10 9 11 10 Model TABLE VI.11 Least squares fit of the continuous reactor and batch
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -2 -2 -2 10 10 to ■(=■ X 10 X X
2 .3 6 2 .1 5 2 .3 1 E, In k E, Pure Error Variance Due to -2 -2 -2 l l l R n - p H. (In k.-lnk. ) H. 2.121 X 10 1.990 X 10 2.048 X 10 Residuals Variance of .9892 -0.9891 -0.9883 -O Coefficient Correlation 0.0133 - 0.234 - 0.0206 0.161 0.396^ 0.0335 .75 1 .8 7 1 .7 9 I
data apparent rate constants to the linearized Arrhenius equation. - - -
of Parameters $ Confidence Interval 95 1 6 .1 1 7 .2 1 7 .9 (Btu/lb.mole) X 10 ^ (min 1 X 9 TABLE VI.12 Least squares fit of the continuous reactor batchand reactor 11 10 Model
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ERROR IN 3.8154E—02 -6.9357E-03 —3.3765E—02 -2.5145E-02 -3.1457E-03 —3.9872E—02 LINEAR TERM;
RATE 1.3C37E-01 1.3037E— 01 7.5983E-010595E—02 . -1 7.S983E-01 7•5903E—01 3.2127E-01Q707E—01 • 1 3.2127E-01 -3.8212E-02 CONSTANT PREDICTED • 1.3037E—01• 1.0523E—01 1•2723E—01 7.9799E-01 7.2607E-01 2.8306E-01 RATE OBSERVED CONSTANT
REACTOR TO THE NON-LINEARARRHENIUS EQUATION APPARENT RATE CONSTANTS OF THE A-RUNS OF THE CONTINUOUS RAT IO RAT 1 .0551E+00 1 9•9820E—01.2344E-01 1 9.4030E-01 8.7280E-01- 9.8730E—01 4.2835E-01 S • 7490E—01 S • AC ID—SPAR AC 9.3080E-01 MODEL 9 910.0 760.0 760.0 830.0.0080E+00 1 910.0 2.8140E-01 9.6540E—01 3.2127E-01 7.4924E-01 9 10.0 9 830.0 760.0 TEMP. 830.0 DEG.R TABLE VI.13, TABLE OF RESIDUALS FOR THE LEAST SQUARES FIT OF THE
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U> ERROR IN 1 . 1 1 . 1 51 6 E -0 1 B..1069E-04 3.66Q8E-02 •2.9793E-03•2. 189E-02 1 •3.3726E—02 ■3.5386E-02 .2061E-02-1 8231 • E■3 —02 LINEAR TERMS RATE 1 • 2 6 4 1 E —01 1 .2 6 4 1 E —01 1 • 2 6 4 1 E —01 7 .6 1 3 0 E - 0 1 3 .1678E-013 .1678E-013 . 1 6 7 8 E - 0 1 7 . 6 1 3 0 E - 0 1 7 . 6 1 3 0 E - 0 1 CONSTANT PREDICTED 1 .2 7 2 3 E - 0 1 1 . 0S 23E■ —01 1.2344E-01 7 . 2 6 0 7 E - 0 I 7 .4 9 2 4 E - 0 1 2 . 814 0 E —01 7 .9 7 9 9 E - 0 1 4.2835E-012.8306E-01 RATE CONSTANT OBSERVED RATIO 1080E+00 .O 1.0551E+00 9.6540E-018 . 7 4 9 0 E —O1 9.8730E-019 . 3 0 8 0 E - 0 1 8 .7280E-0I 9.9320E-01 9 .40.30E-0 1 AC IDAC —SPAR MODEL 9 BATCH REACTOR TO THE NON-LINEARARRHENIUS EQUATION RATE CONSTANTS OF THE A-RUNS OF THE CONTINUOUS REACTOR AND THE 9 1 C .0 710.0 810.0 1.0000E+00 1.OOOOE+OO 4.8940E-02 2.5580L-01 5.8706E-02 2.4763E-01 -1.2766E-02 8.1629E-03 7 6 0 . 0 •0 OOOE+OO 1 9 .S 5 0 0 E - 0 2 1 .2 6 4 1 E - 0 1 - 3 . 0 9 1 9 E - 0 2 9 1 0 . 0 91 0 .0 8 3 0 . 0 7 6 0 . 0 7 6 0 . 0 8 3 0 . 0 8 3 0 . 0 7 6 0 . 0 TEMP. DEG.R TABLE VI.15, TABLE OF RESIDUALS FOR THE LEAST SQUARES FIT OF THE APPARENT Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 132 m 2 n CM co CM CM ro CM CM n ro cm CM a 0 0 0 0 0 0 0 0 0 0 o 0 IN iu 1 1 1 1 1 1 1 1 1 1 1 1 H iu UJ UJ LU UJ IU UJ !U UJ UJ IU UJ VC Is n CM CM r~ Is- m sf o ro Is- o a n o •O O' *—< CM A CM p H ^H rH CM CM r-H CD 0 0 0 0 0 0 0 0 0 0 0 0 LU j- 1 1 1 1 1 1 1 1 1 1 1 1 L- LU 7 IU UJ UJ LU tu LU UJ !U LU UJ !:J UJ O t- < ro n 10 n-J rH CO CO CO Is- 10 Is- < I- vO O \0 •M- vf CM CM PJ r ^ H r H — r H r H < \ J r \ j — < O 0 O O O O 0 O O 0 0 I 1 1 1 1 I i 1 f 1 1 1 1 1 I 1 1 1i LU l - J LU LU LU UJ LU LU UJ u uj Ul Q h- /T. : u 2 O o O c - H O o O Is- m c CD > •0 o o O O' O CM in C0 CM \0 CO CO r H a LU h - < • — CO i n co — I s - O' C Is-- Is- • LU H CO Is - CO b CO CO o CO vO CD < r C0 D CO < 2 • • • •• • t ••• • • L- .0 a O CO Is O' OJ r H «H Ul n Is — i 2 o CJ ou m — 1 o »-* o *H fH o o o «H a o o o o o 3 O o O o o o • < 1 + 1 1 1 -L- 1 1 1 + + + O a o IU UJ LU LU UJ LJ IU tu LU UJ UJ IU > p-H (0 - . o F-l o o o O o o O o o o i i- CM If) ro m CO CO CO vf O' o o o UJ J Q < CO 10 o Is- o O CM in o o o J UJ - a O' o <3- CO ro O Is v-0 Is o o o B Q CJ • • •• • • • «> • •• • < O < O' — 1 O' O' O' r—4 CO O' CO •—< rH rH H s • a o o CD o o o o o o o o o a • •• • « • • • • • • • • e> o o O o o o o o o o o c UJ Ltl VO o CO ro n —• r-H *■— — O T-H H Q Is Is- Is- cc CO CO a a a Is Is CO Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. co CM n «—< CM CVJ CM CM CM CM CM CM z oc o O o o O O O o o OO O !jJ i I 1 i 1 1 1 i i 1 1 1 t— !J IU IU iu IU IU IU tu IU IU IU !U ac r> CM •o i "4 tH CM 3 CO CM O' o or cm r- h- CO to O r- CM CM O' sf O a < vD o co o CM o o •0 r- r- CO iH a iu •o CO •o r- O co CM O CO CO cn O' iu z •• • •• • •• • •• • *—« in CO in .—t in \0 r- f "1 _ « 1 _ o o o tH r*H t H Q o o O o o O o o o OO o IU 1- 1 1 1 1 1 1 + + + 1 1 1 H !U Z IU IU IU UJ IU IU litIU UJ IU IU !U O H < ■cr ^ H _ tH _■ O o O CM ^H r-H 0 O 0 0 0 a O o O 0 O O 1 1 1 1 1 I + + + 1 1 1 Q r- IU LU IU IU IU IU IU n IU IU LlJ UJ iU z CO r- CO r~ o O' r- o O' o Q D > < O CM o in C' rH in in in t t o tH tH tH O r-H H o O o rH cr o o O '0 O o o O a o O o • < 1 + 1 1 1 + 1 1 i + + + t-H tH a o llJ in UJ n llJ in llJ IU m LlJ IU in > t i to o rH o o o o o o o o o i H CM in CO CO CD CO CO r o: O o o O o o o o o o o O a r • r • r r r r r • r r • s o o o o o o o o o c OO o UJ UJ vO M3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4=- U) 5 . 6 7 5 8 E - 0 2 3 .1747E-01 5 . 4 0 9 8 E - 0 2 3 . 2 3 4 2 E - 0 2 2.3856E-02 ERROR IN -1 .7083E-01-1 - 2 . 3 2 7 7 E —01 •1 .3575E-01•1 -9.6804E-02 .0268E-01-1 -3.0694E-02-6.2107E-02 LOG TERMS LN CK ) ) LN CK PREDICTED ■ 1 . 1■ 6 500 2 + E . 1652E+00■1 . 1652E•1 00 + ■2 * 90 * 9■2 5 E + 0 0 •2.1158E+00+00 4E • 2-1 01 ■2.1158E+00■2.1158E+00 •2. 158E+00 1 -2 • 5Q00E —0 1 5Q00E 1 • -2 —0 -2.5800E-01-2.5800E—01 LN( l<) -3.0804E+00-2•3486E+00 -1.3633E+00 -2.0920E+00•2.2516E+00 -2.0617E+00 -8.4781E-0126 • -1 200 0+ E 26 • •1 700 9+ E -2.2565E-01-2.8869E-01 - 3 . 2 0 1 0 E —01 RATE 1 . 0 5 2 3 E —01 1 • 2 7 2 3 E —01 1 .2344E-011 4 . 5 9 4 0 E9 - . 0 5 2 5 0 02 E .5 - 0 5 2 3 0 E - 0 1 7 .4 9 2 4 E - 0 1 7 .2 6 0 7 E - 0 1 4 .2 8 3 5 E - 0 1 2 .8 1 4 0 E - 0 1 7 .9 7 9 9 E - 0 1 2 .0 3 0 6 E - 0 1 CONSTANT REACTORAND THE BATCH REACTOR TO THE LINEARIZED ARRHENIUS EQUATION APPARENT RATE CONSTANTS OF THE A-RUNS OF THE CONTINUOUS TABLE OF RESIDUALS FOR THE LEAST SQUARES FIT OF THE RATIO 6, • 9820E • **01 1OOOE+OO • O 1 •0 OOOE + OO OO + 1 •0OOOE 1 .0 OOOE+OO ) 1.0551E+00 9 •8730E—01 9 .6 5 4 0 E -8 0 . 7 1 4 9 0 E - 0 1 9 . 4 0 3 0 E - 0 1 9 •3080E—01 S .7 2 8 0 E - 0 1 -1 .0080E+00-1 MODEL 9 * * ACIO-SPAP VI.1 10.0 TABLE 7 1 0 . 0 7 6 0 . 0 8 9 1 0 . 0 9 1 0 . 0 7 6 0 . 0 7 6 0 . 0 7 6 0 . 0 8 3 0 . 0 3008 . - 91 0 . 0 8 3 0 . 0 DEG.R TEMP. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 135 1 .5 2 7 4 E - 0 1 1 .2 7 1 8 E - 0 1 2.5949E-01 ' 4.5913E-02 4 .7690E-02 ERROR IN -3.4678E-02 -8.7217E-02-1 .2405E-01- -1 . 1 3 6 8 E -0—3 1 .0670E-02 -1 .1 003E-01 -1 .3275E-01 LOG TERMS LN ( ) K PREOICTEO -3 .2339E+00 - 1 .t:8-1 400 0 E+ — 2.4 8— 3 100 E+ - 1 •- 51 8 400 0+ E .-1 5840E+00 -7 .2594E-01-7.2594E-01 -7 .L594E-01 -1.82518+00 —2•4831E+00—2.4831E+0—2•4831E+00 0 L N ( < ) —3•2535E+00 -1•6713E+00-1•7081E+00 -8.3963E-01 —2•5932E+00-1 •6723E+00 —2•3559E+00 -1 .3245E+00 -6 •7825E-01 -7.5661E-01 —2•4372E+00—2.6 1 59E+00 RATE 1 • 3 8 0 0 E —01 1 . 8 1 2 0 E —01 1.87Q0E-01 7 • 4 7• 7 3 0 E —02 2.6591E—01 5 . 0 7 5 0 E4.3187E-01 - 0 1 4 . 6 9 2 5 E - 0 1 3.3060E-02 8 . 7 40Q E —02 7.3 100E-029 . 4 S 0 0 E - 0 2 CONSTANT CONTO. RATIO 1 OOOOE+OO . 1 .OOOOE+OO1 1 0551E+00. 1 .0080E+001 OOOE+OO 0 . 1 9.3 080E-01 9.6540E-01 9 . 8 7 3 0 E - 0 1 8.7280E-01 3 . 7 4 9 0 E - 0 1 AC IQ AC -S P AR 9.9820E-01 9 . 4 0 3 0 E - 0 1 TABLE V I.16. MODEL 1U 8 3 0 . 0 8 3 0 . 0 8 3 0 . 0 10.0 9 9 1 0 . 0 9 1 0 . 0 7 1 0 . 0 7 6 0 . 0 8 1 0 . 0 7 6 0 . 0 7 6 0 . 0 7 6 0 . 0 TEMP. DEG.R Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced TA3LE V I . 16* CONTD _J O O Ld — a cr cr O M _J y j z u y a < 1 !U < < 0 a: IU 2 a u 7 1- •-< 0 c/J id r j — 1 » : rv * a j u cr 1— IU 0 1 UJ 0 0 0 1— T O1 CO U 10 —O I— _i O CM O < 2 —< -CM J- 2 a < D to cr — JM) UJ . . 0 0 !U O O' ■+ O O CM id 0 0 PM CM f cl* TA3LE V I •17 » PREOICTEO CONVERSIONS o _i O' a UJ © «-« u tou a < o u a J z U z o o o to u u < a h Z o II z z — — z I UJ z o o o 03 to UJ IU LU U I H J u o l l M o Z Z > z > to O D z • z z o z (0 o to o OJ n o vO r~ O' O' co CVJ vO n o —« o sT vT CO O h- in CO o co O' CVJ o si *—H CVJ O' ro ST in O OJ C3 3) CO Is- N O' ro o CO o O' in 7 ST O 6 o UJ —< n n O' •-* v0 O' x> vO O' > n V) CO —■ n 0) sj- CVJ o —< Ul CL z v0 oo sr 01 nj o N o o IJ EJ 1" 1^ v0 co Is- G3 CO 03 CO • t/3 > ...... r—H •3 z O o o o o o o o o o o X • o in o z z o o O z z u iU < z H a O CVJ ■-H n n CO o 33 •3 O' El •> U in CO m o Is- o CO ai m St Is- El i 1- - O' in si ro o Is- v0 Is- lL rH Z a < O' o o O' O' "J co O' co o • z ►—«z .•. .. • • . . ►—« o u "\ •H o o Cv —C o o o u > u < L> z El _l < J El to O z • < < < < < < < < < z < O D o —>01 sr ai m CO vO Is-O' < Z z z -< rH -< •- *—HrH — -1—• > STANDARD DEVIATION OF ERRORS 0.0123 0.0113 0.0124 0.0118 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced TA3LE V I • 1 7 » CONTU a U Ja 3J o> co a a a llJ ►—« CJ u o a 1 i 111 H Q o UIU LU > o IU Q o U o a 1—4 1- CM o > CO !U to o < o z 30 z z d U vO d a a u 1—4 01 X o (0 z (0 o z 0 _£ • a 1 — < o CM H n d < — CO o o o o o Is- O' 'in O' OJ t- r~ vO O' CO co o o o Is- Is- co r~ r-H in d o Is- Is- d r~ co O' < O' o o • • • • • • • • • • o 'Is- O' r— 4 O o o 3) co ■O' CO CO OJ in CO o :0 CM CO r- O1 d 10 vO CO <£ s o Is- •-« i — -v 0I-30 Is- 30 vO r- d X) ■ o • • • • O' o OCO CO '0 CO o O' o d o CO CM d 30 o o o •X) O' < d cm o o « » • • * • - , , - O' Is- •ro (O O O CO MO' CM d o >—4 OJ CO •O' CM OJ ro n d r-H CM r-H < o 3r~ 33 nv O' vO in O O • • • • • .O' CO o CO f- CJ3 '0 r~ Is- Md CM o r o o O o o o — o o ■n Is- od ■o m < 33 O' ro o O' d • » • • • • Q 0J O o O' o 3C 33 CO 33 0J d CO uo OJ 33 30 ro H r co — ’— CO O < 03 O 30 o co OJ • • * • \ < C0 CO 1- o o o o 33 o CO o >0 Is- o M3 OJ CO 33 o Is- o < CO O' O CO o ro d o *-> CO O rH Is- 0 • r • • • • • O' vO vO '0 I — Is- < o '0 d m CO Is- O d 3■ro 33 o CO O' On CO O' d o O o o OCO CO OJ o o o • • • « • • • • • • «H co o Is- 'o o O' Oo CO (3s vO CO o CO H r o m o < o OJ CO Oco CO o o d • • • O a «H LU o a o o r-H OJ lu iu CO rH <1* UJ > H < a r—4 •-H 01 d OJ < < z U c ■ — d OJ .— X c • • • • • i a o i — < h- • — o UJ a a o OJ o O OJ a O > LU o u. CO O to r—4 fH ■ — o o «-* vO < Q __ z Z o -H o r—4 • • J • 11 .792 H o - ? = ■ 1.648' O 0.413 0.971 0.4603 0.975 2.453 Model 63 10 .303 Constants 0.857 2.285 O.I 0.637 O 0.426 1.140 0.356 0.364 0.938 2.581 0.876 0.1820 Model Apparent Rate 9 .714 1.005 1.417 O 0.616 0.251 0.611 1.637 1.579 Model 2 of .8582 .8669 0.8182 O 0.8399 0.4870.8787 0.8155 0.8507 0.8594 0.8827 O CaF 0.8117 0.279 Conversion Observed .9682 Ratio O 0.9366 0.8925 0.9510 0.9736 . 0.9904 0.9766 0.9190 0.9329 Corrected 0.9762 Acid:Spar Coded value) BF (+1) BF BF(+1) B (-1) B (-1) B (-1) A (-1) A (-1) AF(+1) AF (+1) AF A (-1)“ (Fineness (Ne"wf luor) luor) (Ne"wf Used Fluorspar value) 7.14(+1) 7.14(+1) 7-14(+1) 7.14 3-5 (-1) 3-5 (-1)' 3.5 (-1) 3-5 (-1) 3.5 (coded Per Cent CaCO. of Spar Content ) ) 7-l4(+l) 1 1 value) 5.05 (coded r .p.m. r 15-8(-l) 25( (+ Rate 15.8(-1) 15-8(-l) 25 (+1) 25 (+1) 15*8(-1) 25 (+ 20 Mixing ObservedConversion of CaF^ Apparentand Rate Constants for Runs 1F-10F. 18 450(+l) 450(+l) 450(+l) 450 370(-l) 450(+l) 370(-l) 370(-l) 370(-l) 370 value) (coded Temperature F F F 6 7 F Run No. 8 2 F 9 F 4 4 F 1 1 F TABLE VI. 3 10 F ' 5 F ' Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. m 0.8973 0.8264 0.0294 0.94818 0.4996 -0.7765 +0.13103 -0.0253 -0.2332 -0.884 0.1324 1.0106 -1.0328 - -1.704 -1.194 - -0.8533 -0.0640 -0.451 -1.814 Rate Constant 00499 i 1.2765 0.49286. 0 +0.4568 - +0.3485 -0.1543 . - -0.4845 -0.3369 -0.7195 -0.4927 -1.3823 Natural Logarithm of Apparent Model 9 Model 10 Model 11 +1 -1 -1 -1 X4 -- +1 +11 + -1 +1 + 1 + - +1 +1 -1 +1 X 2 X3 Factors +1 - +1 -1-1 +1 +1 +1 -1 -1 -1 -1 -1 -1 -1 X 1 '+1 -1 -1 +1 Ratio 0.9329 0.9904 0.9366 0.9762 0-9737 0.9766 0.9510 0.9190 0.8925 0.9682 Corrected Acid:Spar 0.8827 0.8177 0.8507 0.8787 0.8399 0.8594 0.8182 0.8155 Conversion of CaF^ Observed abed ac ab c 0.8582 ad 1 be Design No. Code , Code, bd 0.8669 f f f f IF 2F 7 6 8 4 5F 9F Run No. 3F TABLE VI.19 Natural Logarithm of the Apparent Rate Constants with the Coded Factors 10F Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table VI.20 Mean Differences of In k Factors Mean Effect of Factor Model 9 Model 10 Model 11 mean In k -0.3389 -0.82176 0.15411 X x + x 2x 3x 4 0.21054 0.2377 0.2107 x 2 + x x x 3x 4 0.574467 0.5119 0.5516 0.046187 0.0257 0.03909 X3 + W 4 x4 + X 1X 2X3 0.8971 0.8819 0.8943 X1X2 + X3X4 -0.28931 -0.2718 -0.2842 x lx 4 + X 2X3 -0.11427 -0.0824 -0.10203 +0.01216 0.0304 0.02036 XlX3 + X2X4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. $ 5 > 1 > 1 > 1 6.996a 3.84 69.24° 26.34° Model 11 > 1 > 1 > 1 6.87a 5.26 72.37° Model 10 level of Significance level of significance Level of Significance ° 20 . a . Significant a . at the c Significant at the 1$ b Significant at the 2.5$ P Ratio MS/S^lnk > 1 > 1 9-336b 3.76 1.106 6 8 27.97° 24.37° Model 9 1 1 06 0.0231 2.483 0.0008 0.02081 0.1616 0.6086 0.003 1.5995 0.0888 MS 0.0215 2.3572 0.0137 0.14775 0.00132 1.556 0.524 0.1130 Model 10 Model Mean Square 0.0003 0.001852.7447 0.02611 0.1674 0.004-27 1.6096 0.6600 0.08865 Model 9 6 0.0236 1 7 1 1 1 1 1 1 of Degrees Freedom __ ) 9 * _____ 3 4 f i n e n e s s x 2 3 x s p a r CONTENT) (INTERACTIONS) (INTERACTIONS) (INTERACTIONS) ( (MIXING) 1 1 4 (ESTIMATED FROMA RUNS) TOTAL SUM OF SQUARES VARIANCE OF PURE ERROR ABOUT MEAN XlX3 + X2X3 X , X . + X ^ X „ x ^ X^ (TEMPERATURE) + xxx2 Source of Variance X (SPAR CaCO X ± Table VI.21 VI.21 Table Variance of Analysis Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE VI.22 Regrouping the F Runs CaCC>3 = 3 - 5 $ T = 37 0 ° F Run M i x i n g Apparent Rate Constant No. Rate RPM Model 9 Model 10 M o d e l 11 A runs 1 0 0 . 3 1 2 0 . 2 0 5 0.513 9 F 1 5 . 8 0.251 0.1630 0.413 1 F 2 0 0.279 0 . 1 8 2 0 0.460 6 F 25 0.487 0.3027 O .792 C a C 0 3 = 3 *5 $ T = 4 5 0 A runs . 1 0 0.772 0.484 1 . 2 8 0 5 P 15.8 0.714 0.426 1.14 0 10 F 25 1.005 0.637 1.648 CaCO = 7.14$ T = 370°F 3 8 F 15.8 0 . 6 1 6 0.355 0.971 4 F 25 0 . 6 1 1 0.364 0.975 II ►3 0 -£=• C a C0 3 = 7.14$ VJ1 2 F 5.05 1 . 5 7 9 0.876 2.453 3 P 15-8 1 . 6 3 7 0.938 2.581 7 F 25 1 . 4 1 7 0.857 2.285 THE APPARENT RATE CONSTANT FOR THE A RUNS WAS TAKEN FROM THE VALUE OF K PREDICTED BY THE LINEAR LEAST SQUARES FIT OF THE ARRHENIUS EQUATION TO THE CONTINUOUS REACTOR AND BATCH REACTOR DATA. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4=- Ul 6 0.0231 0.0236 0.0215 Y= 2 2 0.00705 0.00450 SR SR ^ V = 4 0.9962 0.265 0.9928 0.00912 0.186 m ^ ^ 502 511 . . 0.510^0.233 0.99^3 0 0 3.09 ^ 78 . 1 6 16.83-3.52 l6.55-2.47 of Parameters Coefficient * 0.226 c E-10 3 . - $ Confidence Interval Correlation from the Factorial Experiments Apparent Rate Constants. Rate Apparent Experiments Factorial the from 077 95 . 1.131-0.283 1 1.158-0.322 0 k 0.0826 0.0492 0.0343 Table VI.23 VI.23 Table Equation of (VI-42) Parameters of the Estimate Squares Least 9 11 10 Model > Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 = = E, In k In E, Y 0.0231 0.0215 s2 17 0.0148 0.0143 0.0158 0.0236 < Y= runs as runs 0.9929 • 0.9922 the A and P A and the Correlation Coefficients m 0.386^0.198 0.393-0.204 0.9930 0.37^0.195 Constants of Constants 16.77^1-30 15.81^1.29 IT.41-1.35 Batch Reactor Data. Reactor Batch 1 0.196 c c 3 E>1(T • ^ of of Parameters Confidence Interval Confidence 888 . Using the Apparent Rate Apparent the Using Least Squares Estimate of the Parameters of Equation Equation of (VI-42) the of Parameters Estimate Squares Least well as well the as 0 0.964^0.199 1.012-0.206 95$ o k 0.115 0.0514 Table VI.24 Table 9 0.0644, 11 10 Model Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 147 c CVJ OJ rH rH- cvj o cviinvop-rHCvioocococ^invocvjcovooocr\invo fd O CO CVl 1T\C0 in O 1A4- (Ti CVIHCVJHSOOHVD^OOH p i cjvvocvjvd^- invo HcncovoHVDcviiAOinoooovoo *0 O O .rH m OOOOOOrHrHOOOOOrHOOrHrH 0) V oooooooooooooooooooooo • ••••••••••••••••••••• 0 G I I I I I I I I I I I I I Pi «H fd in „ ^ c P < r M Ht-inH4-VOVO(r)VO^-VDNOOOIOHOOt^04-^OOV o *0 HOrlCYlHH^-OaiOH(MH{nOVO(n4-(nO^-0 -H -H 1 OOOHOOOOOOOOOOOOOOiHOOrH 11 co rt o om ^ « 1 J ""j ■ "-J" —-J- o a m LninLr\inLr\Lr\LnLfMr\LnLntnLnHHH.tAinHHLnin « 'ER id -h H o w mmmmmonmmmmmmmt-t>-[>-mmo-t>-onm > CT\ 0 rH • I-1 0 CM rQ 13 g „ oooooooooooooooooooooo fd O 0 Pi vovovommcorHH h h vo h m >h .h m rH m >h m m *h EH S E-fO t--C'-t--cooococncr\aM>-C'-cococr\cr\ooavco av co co cr\ Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced Table VI. 25 Con't _ g • V I 1— F*0 S 0 05 0 O Or 0 w u q £ q u w 3 JJ T3 m VCJVCOCO OCACVl r COCn C O -C ^ O O O C -rH ^ O C O C D O D lV V C A C O CVICVJCVICOOOCOOO ) + J + H - 'CM 'CM H OOOOOOOOOOOOOOOOOOOOOO O O O O O O O O O rtf O rH O O O O O O O O O O O I -H ( w >(j ■o O O ! oooooooooooooooooooooo o o o o o o o o o o o o o o o o o o o o o o &! O I i— V O O ' rrt J ft JJ J O i—1 O OO i—! OO O < u rg 1— 1 « « I—I & Jj COft B.*H o 0 0 ^t^-corHi^ints-oocTvvocn c o v v T c o o - s t n i ^ i H r o c - ^ t .^ - c o v s o n c v o t r jj d ' p U t 4 0 H O O CO H 00 H 4- 0 0 rtfu (U > wp$£ 0) ow-h Q J .. .. QJ „ d 0 ro O o o 0 0 0 0 0 V£),H.=J- J = . H , ) £ V I H cu U £ “ £ & (U +> 0 h m 0 ( U S I II II I S U ( ^ to t cc rooorob-rn ci j> ^ ~ i no c o no o ovovovo c n nc enco cn cn cn cn o v o v o v o o o o cnoo co o cn o cn o \ o Pi C Ul/M a 4 w s-ro.H-vocorHCOOJCnco.=f-o30jvoco-H-vooos-voon[s- X +i' Ci C i I C V V Cl 7V r1C o 0 CVI r—1 CVl 00 VO C7VVO O CO vo CO CVl O IS o in CO J ; o o o o o o o o o o o o o o o o o o o o o o - ^ n i H H I V C O O O cu CO D O O Cn OV OO AnOO VO CO S-CnVO VO lACnCOVO COCO VO VO O W nO OD nC CO CO C oot-cnvococooon^onis-cocois-onvocvJOLnLnvocn lt o o o o o o o o o o o o o o o o o o o o o o v o v o v o c o o n 0 0 r j - ^ l r H l r . O O O o o o o o o o o o o o o o cn o o o o o ts-t^s-cocococncncni^is-coco o o o o CYoaocncnmoocnmmononooonts-is-is-ooooc^t^-onon I— I LriLnLricnLrMfMrvLnLTitnLnLnLnrH rH 0 0 0 0 0 0 0 0 0 O O O O O O O O O O O O O O O O O O O O O O \ 1 co 1 — t cn cn —t 1 1 i— 1 — 1 cvi co o s - s - co cn cn co - s - s o cvi co • i * • « 1 0 00 r r r H H rl rl I rl — V i ' O \ O - t = . \ ' c o . o co 1 i CI i O t-rl 00 —I 00 0 0 0 H H It— 0 0 l r tS- O Ii— 0 0 O l r O CVI I i— I — po OA 1 c O o co o OJ co CO 1 OJ 1 4 3 h 0 1 1 n n u i v c - g . o v - s i o o v o n c i v c cn - - I I I I I I I II I I I I 1 • 4 4 h -d- 1 I — J V C H f HVO V iH r ( O C n c ^ n c V O O C H H O O - n ( O C O C H H O O - h 0 hvo E u td u o id W a s s 1 —1 r—1 1 Cl CTn O V O C I V C V O O C O V - - C n C l P L O O CVl \ h — v v 0 o o Lninn c m cvi m co n n i n L o o cvi t— 00 vo 1 E-r t 0 0 \ ' 0 1 h 1 E —I o o o oo o o o o o h 1 oph 0 0 V LV T LV P L\ P L\ Pl A I l IP LP\ LP\ LP\ LP\ LTV LT\ LTVCVJ 1 1 • ______O un t— - f n O C - J ^ . I - r - ^ j - ' C J O - ' C O 1 1 jrj. I j ■ j 0 0 no no nc c cn co cn co cnco cnoo h — Cl — l V C H r H r J V C l V C i—I CVl<—I 1 CO O • • coh ih LTi 4 lo CVl 1 -CVIOO(nHVD in rH coh rH 1 LT\ 1 1 m on rH » • » t 0 O o CO 00 h 1 mm m __ 1 1 148 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced TABLE VI.25 Con't s ■o 0 cu EhO p 03 tp O P •O -H4J-P _Q Q id u < u t f -p *a O OOOOOOrHHrHOOOOCvlCVJOrHOCMOOrH O o >d iu co Cu ft P c -P cu ^ E ft *rl O p O CO P p E 0 p -.H P cu .. CQ U u d O P rd +J cu n > ) rd 0) ) a i P 0) (UtdCQ £ +0 ,-i X rH r*J a I 1 OQ O VC 0 i O V V C O m c C c OO O LTV VO VO 0J OWO CM cn cn VO m CO OJ CVI OJ iH OV CO 00 VO fOVQ V r CIVO -- p 00 H —I —I p p p L\OV —I — V OV p O V -p- V O CVl C— Ir— V O LT\ -p- .p- I -p- t— O I i— rH 0 0 -p- -p- O CVIV rH CVI C T T H C " O t"- C O LCO C rH LTV O LT\ C LCO O V \ r L o o o o o o o o o o o o o o o o o o o o o o D—LT\ D— 00 VO CVI CDCO X rHr-irH^i-^f-^i-oJcviojOHoo-=i-.^.=f-cr\OJi>-j=t-cr\j;i-[>- rHt~- CVlOVC— vovovocncnmHHHPVOHmHHcnHcnHcnmH vovovocncnmHHHPVOHmHHcnHcnHcnmH O C ) r ( H n i M ( O n i H O c O - p H - p - 4 A M f L - 4 H O C M < O C l r O — V lT\-=f- CVI O C O C— o LOi O C C ~ - C — C — C O C D 0 0O V 0 0 0 0 t '- t > - 0 0 0 0C O O V C OC O C O H C H l O r l r l C r H O l r C H l r OO V D t— iHVD VO COH OVO O ^}- CO 0 0 0 0 0 0 0 0 0 O O O O O O O O O O O O O O O O O O O O O O cncncncncncncncncncncncncnto-to-r^cnmto-C'—cncn OV LT\ p - OD m o t— VD S - - S t— VD o avo ovovovoco m ODavoo LT\OV - p o o CT\o ovovo ovovovo p- O avovooCM cn00 H 00 HOOOr Hrl— O O O O O O r—li—I O rH O O O O rp O O O O O rH O LcoLroLroLcoLcoLcoLcoLiOLcoicouoLcoicorH cti H , o o o o o o o o o o o o o o o o o o o o o o -COOOOOOOrHrHOOOOOOOOrHO. O H r O O O O O O O O H r H r O O O O O O O r-IC O O f-H CVCl " 0 V O J OQ >- CV10. VO. |-0 .= O -V p .= 0 1 V lC V -C t> O OOVQ V OJ VO CO CSV H - CVl L"- 00 if T C H O O H O O O H i O O O O O O O O O O J V C O O O * * * * I « I « ( I t » • « ( t I I I I « • « I » t I » ( ( « I « « I • •*••••••*••••••••••*** O rH I I I I I I I I I I II I I I I I II I I I I ' I I I I I II I I I II I 'I I vct CVI \0\ O m o J O 1 VO O 00 C\CO f—•P'VO LO00 C ^i ON - r .=)- rH t-— O C N ^=i- O C— 0 LCO 0 O V ' P • f-— O CF\ C 0 0 O O V 0 0 ^ 1 p h h V O 1 * CVl 1 I.L\ O O — VO CO CO C— H —I . LT\ CVJ 1 • 00 ovco 8 LTV _ CVI 1 » * *« • • LCO i v c o c o o v n c p r o w o i v c o v CrH V C V J I r H C V J C V l r H r H C V J n L i v c - t ^ o v - > i o o v o v o i v c OL T V L P \ L T \ L T \ L C O L C O L O L C O IT \ c — t^-mc^-cnovvo co o v v o n c - ^ c 1—i m cn - ^ t t l o 0 0 — -- r - p j - - t O rH \ T L D C O V O C C-~- \ ~ uu~ I] Ui l U u iv U II] ~ u u i~ n I ' l "J r^j",""J" C 00 CO O hhcohcohco LP\ 0 0 Q V ch rH 1 H r I O O T r CO CO—I LT\ rH CO VO T'j* D— lco Q V lco 1 r rHrH ■~T*J* "j* | C ( ,1 ■ * • H CO CO o O C o in \ O co lco 1^-9 150 VO COOO CU in m in C— CO cucut'-cucuooinvooo CO oo e -c o cncuo cn cu c-cu^-OrH^t-cocncooj in CU to Q) on c— c— rH ov oo cn o- o rHOOVOVDVD 00 LTV C— CM OJ cn cn £ »o ts-ts-vo oo co n-coco COCQCOCOOOCOCOOOOOCO t-co O O « • -rl ooo ooo ooo o o o o o o o o o o o o (0 a £ (0 £ £ 0 O •rl •£ to a) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. VII DISCUSSION OF RESULTS A. The Results 1. The Batch Reactor In section VI of this thesis, a thorough statistical treatment of the batch data established the \ following three rate models as satisfactory correlations for the entire range of the conversion-time data. CVl X dx (A - pp B = - b ) ^ 1 - Model 9 (VII-1) 1 dt - (1 - *B )1/3 dx k X 2 (A - Model B - b ) ^ 1 - *B>V 3 10 = 10 Bo (VII-2) dt 1 - (1 - * b )1/3 (A - Model 11 = * n xi0 - b ) ^ 1 - V S/3 ( v n - 3 ) dt 1 - (1 - * b )2/3 where XB = moles of CaF_ per mole of calcium in the feed, o ^ A = acid:spar ratio, xg = fractional conversion of CaF^, t = time (minutes), and k^, and are rate constants — 1 — 2 (min X ) where X is the molar concentration in moles per mole of calcium. 151 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ' 152 The statistical treatment of the data, also indicated that none of the three models can he considered as better than the others. It should be noted that the pseudo steady state solution for a heterogeneous reaction the rate of which is controlled by the diffusion of the liquid reactant through the ash layer to the unreacted core, did not adequately fit the data. For that model, the concentration of the liquid reactant on the ash perimeter is assumed to decrease in proportion to the amount of conversion of CaFg. The model equation is. Model 7 = k7 Xbo (A ~ XB ^ 1 ~ XB^ ^ (viI-4) dt 1 - (1 - xB )1/3 2. The Continuous Reactor The statistical treatment in section VI also established that-the following equations satisfactorily correlated all the apparent rate constants obtained from the batch and continuous reactor data. v ^ o1-©12 „ 1*0.122 f-17410/1 1 = 0.0644 C M . exp J f - ____ - (VH-6) L R 'T 809.9 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ?(- 1 5 8 1 0 / l 1 O (vn-7) L R 'T 8 0 9 . 9 'J r - 1 6 7 7 0 ,1 _ _ 1_ J (VI1_8) R \T 809.9^ where 1 = 0 when C = 'J,V\% or M <25 r.p.m. and 1 = 1 when C = 3-5$ an^ M = 25 r.p.m. C = CaCO^ content of the fluorspar (wht$), M = mixing speed (r.p.m.), R = gas constant (1.987 Btu/lh mole °R) and T = temperature (°R). The three rate models, 9* 1'0, and 11, along with the appropriate correlations of their apparent rate constants (equations (VII-5 )(VII-6 ) and (VII-7) respectively), were used to predict the conversions in the continuous reactor runs. All three models yielded very good results, and none of them could be considered as providing a better fit than the others. Analysis of the experimental data has demonstrated the following; « j j (1) The factorial experimental design was very i efficient in yielding a great deal of information with a minimum of effort. In particular, with only 8 runs, in Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 154 4 Which 4 parameters were varied, an estimate of the activation energy was obtained which was as accurate as that obtained with 9 runs, in which only 2 parameters were varied. (2) The activation energy values were in the order of 16,000 Btu/lb mole, and were indicative of a diffusion controlled mechanism. (3) The rate of CaF^ disappearance is proportional to the square of the fraction of acid unconverted. (4) Calcium carbonate plays a very important role in enhancing the reactivity of the spar. The reaction velocity is approximately linearly proportional to the CaCO^ content of the fluorspar. (3) In the range of 5 to 20 r.p.m., the variation in the mixing speed did not alter the reaction velocity. However, when the CaCO^ content was 3-5$ by wt., at 25 r.p.m. an enhancement of approximately was observed in the apparent rate constant. This enhancement did not occur when the CaCO^ content of the fluorspar was 7-14%, by w t . * | j (6) Fluorspar which was ground to approximately thrice the fineness of the normally ground spar did not Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 155 react with a greater velocity than the normally ground j spar. : ' In the discussions that follow an attempt is made to explain the ahove results on the hasis of the observed phenomena, B. Interpretation of Results 1. Mixing in the Continuous Reactor. a. The effect of calcium carbonate content. One needs only to refer to any one of the many patents on the manufacture of HF from acid grade fluorspar, to appreciate the difficulties encountered with the formation of large lumps within the reactors. But, aside from the run in which pure synthetic CaF^ was used as the fluorspar feed, the formation of large lumps did not occur in the continuous reactor used in this study. However, the solids leaving the reactor were quite coarse (1/4 inch to 1/16 inch with some powder), so that lumping or conglomeration, per se, was not completely eliminated. To understand how these lumps or granules formed one must first consider what the situation could be if Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 156 no CaCOg is present. When no CaCO^ is present, the acid, on contact with the cold spar, does not easily penetrate, but rather surrounds, a large conglomerate of unreacted fluorspar particles. As the particles on the conglomerate perimeter begin to react, CaSO^ crystals precipitate and bond the particles together to form a lump. Further reaction causes further binding of the mass. If the resistance to diffusion is also significantly high, the mass interior is largely void of acid, and the reaction proceeds only with the particles on the perimeter of the conglomerate. As the reaction continues, the diffusional resistance increases. When CaCO^ is present in the fluorspar, it reacts vigorously with the sulfuric acid to evolve COg gas bubbles, which, as they rise, cause agitation of the mass and penetration paths in their wake. The gas evolution occurs quite rapidly and creates good mixing before a significant amount of CaSO^ crystalizes out to bind the solids together into a large inpenetrable lump. Thus, the blending action enhances the formation of smaller conglomerates, in which the diffusion path is shorter. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 157 One may argue that HF evolution should also produce the same effect described above. The reason why this is not the case is that CaF^ does not react with sulfuric acid with the same vigor as CaCO^. Consider, that the spar coming into contact with the hot acid is very close to room temperature. At this temperature CaF^unlike CaCO^,reacts slowly with the acid. Two experiments to prove this hypothesis were carried out. In the first experiment, 2h g. of sulfuric acid at 200°F were added to 20 g- of pure synthetic CaF^ powder. Although some bubbles of HF were evolved, no appreciable frothing ensued. The acid, rather than penetrating into the spar, lay on the surface for some time. In the second experiment the conditions were the same as above but the fluorspar was a composite of 95$ ky wht. pure CaFg and 5 frothing followed the acid addition and penetration of the acid into the powder began almost immediately. The amount of CO^ evolution at initial contact of the reactants would likely be proportional only to the CaCO^ content, and the mixing effect may be expected to be directly proportional to the CO^ evolution. An Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 158 approximately first order dependence on the apparent rate constant on the per cent CaCO^ content, as observed, was perhaps not an anticipated result, but it can be easily explained as above, b. Effect of mixing rate. One might have expected that the mixing rate would play a prominent role in the reaction. However, while mixing does always play an important role in aiding the contact between the reactants as they enter, and in enhancing heat transfer by maintaining the wall deposits to a minimum, there is some question as to the effect the mix ing rate has at reducing the lump formation. In the run in which pure CaFg was fed to the reactor, lump formation was so prominent so as to render the reactor inoperable. This indicated that mixing at 10 r.p.m.was of little consequence in reducing lump formation. However, when the CaCO^ content was 3-5$ and the mixing speed was increased to 25 r. p.m. there was an abrupt * i increase in the reaction velocity (or the apparent rate j constant). This enhancement did not occur in the 25 r. p. m. runs, in which the CaCO^ content was 7.14$ by weight. I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 159 The conclusion one may draw from these observations is that a 3*5$ CaCO^ content results in a significant degree of micromixing, and further micromixing can only be effected by application of a high shearing action at 25 r. p. m.. With the CaCO^ content raised to 7.14$, micromixing is more extensive and only a much greater shearing action than that produced at 25 r. p. m. would further enhance the bleeding. The reaction scheme which arises out of the above discussions is illustrated in the Figure VII.1 . 2. Effect of Fluorspar Sizie Reduction. In the discussion entered into in the above, one concluded that the size of the conglomerates can be reduced by the presence of CaCO^ in the fluorspar. It is unlikely that the micromixing is sufficiently efficient to eliminate all conglomerate formation. If con glomerate formation had been eliminated the finer spar should have reacted with a greater velocity than the regular spar, since the mean path through which -the 1 acid would have been required to diffuse to reach the unreacted core, would have been shorter. However, with Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. liquid HgSO^ layer CaSO,, and acid unreacted particles behaving as unreacted core CaSO^ binding lump together time high acid concentrarion on perimeter —' CaSO., impregnated with ELSO,, unreacted particles time FIG. VII.1 Reacting Scheme of Lumps Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. , ’ * 161 the formation of conglomerates, whose sizes were determined not by spar fineness but by the CaCO^ mixing effect, the spar fineness, in the range studied, was not adete^nining factor on the reactivity of the fluorspar. C. Interpretation of Rate Equations (q) Budnikov and Gmstling in their studies of crystalline reactions, found that when diffusion controls the rate of reaction, the reaction velocity changes by 10 - 40% with a 10°C temperature change, but, if the reaction is controlled by the chemical step, the reaction velocity increases 2 - 4 times with a 10°C rise in temperature. The rate constants for the three models found acceptable in this investigation, did not vary by more than Kofo per 10°C rise, ii the temperature region studied. In light of the discussion in section B, one might expect diffusion control to refer to the diffusion of sulfuric acid to the unreacted core, or, in this case, the unreacted core of the conglomerate. The pseudo steady.state solution of a diffusion controlled unreacted core mechanism was considered in the THEORY section. The equation arrived at, in that section was Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 162 axB= 3aDeACSO (^--B)(l---B)1/3 2 (VII-o) dt C R 1 - (1 - x_) SO P v B ' The (A - xB) term was brought about by assuming that the bulb phase concentration of the fluid reactant, was proportional to the amount unconverted. By grouping the constants of equation (VII-8) and using molar rather than volumetric concentrations, the equation _ K X B- (*• - x )(1 - XB )1/3 ^ ------2------1/3 - B- (VII-4) 1 - (1 - xB )1/3 is obtained. However, the three models which were found acceptable in section VII are not 1inearily dependent on the fraction of acid unconverted. In particular, equation (VII-2) below dXB = *10 (A " ' XB>V3 dt 1 - (1 - x B ) is dependent on the square of the molar concentration of unreacted acid. Derivation of equation (VII-2) from equation (III-5) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 163 of the theory, may be easily accomplished by assuming that, in this case, the molar concentration of the acid on the ash perimeter is dependent on the square of the amount of acid unconverted, i.e. XAR~ P XBo (A ' , (VII-9) where ]3 is a proportionality constant. Because we are dealing with a rather complex reaction mass in which no liquid bulk phase exists, per se, the above assumption may not be totally unwarranted. However, this approach makes no attempt to consider the physical phenomena which may be occuring. It has already been mentioned that the reactor contents are, for the most part, incompletely reacted dry granules which, are found to contain a significant amount of acid. The acid may be present within the solid phase in the form of precipitated CaSO^-HgSO^as suggested by Ostrovskii and Amirova v(2b) ') or as entrained liquid. Diffusion of the acid toward the unreacted solid may occur by capillary action, but as the liquid content decreases the capillaries would also tend to retain the fluid rather than transport it. Yet overall conversions Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. of 91% or better are quite common in industrial reactors with acid:spar ratio addition close to unity. A possible explanation for these observations is a migration of sulfuric acid through the solid phase by way of the following scheme. Hg(SoJ) + Ca(SC)*1 ) f = ± Ca(HSO^) ^ j r cv i i - i o > Ca(SO^) + HgtSO^1) The ion exchange (H+ and Ca++ ion migration) would be from an area of high concentration to one of low concentration, and using the analogy to diffusion of electrolytes in concentrated solutions, the diffusivity could be proportional to the acid concentration at that point (£3). With the above assumption, the Fick's law equation would take on the following modified form. NA,ash = " /^Ca .kD XA — - (VII-11) dr XA = molar concentration of acid as a diffusing species in the ash (moles of acid per mole of calcium) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 165 SXA molar concentration gradient in the radial Sr direction (moles of acid per mole of calcium/cm) 3 /° = moles of calcium per cm. of the ash layer [ Ca = coefficient (cm./min.2 moles of acid per mole of calcium) 2 N = molar flux of acid (moles of acid/cm. min.) Aj ash A pseudo steady state mass balance on the ash layer gives ~ . d ( r^ X_ dX-A Pc a* *D — V A — )=■ 0 (VI1-12) dr d r with the boundary conditions' r = R X = X„n A AR (VII-13) r = r X_ = 0 c Ac Equation (VII-12) may be solved, using the boundary conditions, to obtain the concentration profile and the rate of change in the radius of the unreacted core (or the conglomerate), as A - dr [ r J ! _ _ c (Vll-14) dt C„ r \ R So Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 166 where R is the radius of the conglomerate, and C is b O the molar density of CaF^ in the unreacted conglomerate core (moles/cm.). If, one now makes the further assumption that the acid is largely trapped within the ash perimeter, and that its concentration (on a mole per mole of calcium basis) at the ash perimeter is linearily proportional to the fraction of acid unconverted, then XAR * ° XB0' (A - XB> (VII-15) where a is a proportionality constant. Equation (Vll-lty) may now be expressed in terms of the fractional conversion as ^ B = 3 f c * *D * X!o (A - xb )2(1 ~ XB >V 3 (V11' 16) dt cSo R2 1 - (1 - x b ) V 3 -■> , k , a, CgQ and R may all be assumed to be If / J Ca constants, equation (VII-16) may be altered to the form a*B _ k x|o (* - " xb>1/3 at i - (i - x )1/3 'VII-1T) B Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 167 where * 10 - 3 f>Ca \ (VII-18) I Equation (VII-17) is model 10, and is typical of the three models found to acceptably fit the data. It must be stressed at this point, that the above discussion "was only an attempt to explain the phenomena, and does not alter the fact that the three acceptable models are basically empirical in nature. D. Comparison of Results to Previous Works. 1. The Work of Ostrovskii and Amirova (24} Ostrovskii and Amirova v ' found that their data could be correlated by a chemical reaction controlled mechanism with the activation energy values of 37j4'00 (Btu/lb mole) in the 85 - 100°C range, and 16,560 (Btu/lb mole) in the 105-145°C range. They attributed the change in activation energy as being due to the lack of formation of FSO^H above 100°C. Formation of FSO^H would impede HF boiloff, and since they determined the extent of conversion by weight loss,with time, the rate would appear to be lower at the lower temperatures, and increase rapidly as the temperature increased, due to the dual effect of a higher surface reaction rate and a decreased Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 168 formation of FSO^H. While one cannot discount the rationality of such an argument, one can question whether it sufficiently explains a 50^ decrease in the activation energy. The decrease in activation energy is more characteristic of a change in the reaction mechanism from surface reaction control to ash diffusion control. Indeed, their activation energy in the 105-145°C range is very close to the values found in this work. There is also‘some question as to the validity of the experimental approach used by Ostrovskii and Amirova. By using very small reacting mixtures (0.1185 grams), which were well mixed prior to being introduced into the furnace, they eliminated the possible nonhomogeneity of the initial mix, and the lumping which seems to be a characteristic of the reaction mass. Extrapolation of their results to industrial conditions is, therefore, in question. 2. The Works of Gnyra and Menard and Whicher. The results obtained in this work on the effect of calcite content of the fluorspar, are in substantial agreement with the qualitative observations made by Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 6 9 (1*5 ^ (22 ^ Gnyra ' . Menard and VJhicher, ' ' on the other hand,, had suggested that due to the enhanced setting rates in the presence of calcite, calcite should have the effect of reducing mixing. This is not observed to be the case, so it might be concluded that the "needed" mixing is already accomplished, and that this mixing is helped by the presence of calcite, Prior to the setting. E. Thermal Effects Aside from efforts to maintain the batch reactor and continuous reactor at constant temperatures, no attempts were made in this study to consider thermal effects within the reacting solid. Qualitatively, however, because the reaction of CaF^ with is endothermic, cooling of the reacting core can be expected. The magnitude of the temperature drop can be influenced by (1) The diameter of the reacting conglomerate (2) The amount of H^SO^ entrained within the product ash layer (3) The thickness of the product ash layer (degree of conversion) Although one could estimate a thermal conductivity coefficient,it would be highly dependent on the degree of conversion. Furthermore, the diameters of the lumps Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 170 are difficult to establish. However, at this point one can foresee that CaCO^ played another positive role in the reaction. If the hypothesis previously considered can be deemed acceptable, the CaCO^ enhances good heat transfer by inhibiting large lump formation. It further enhances reactant heating by generating heat in its reaction with acid at the time when heat is most required. F. The Silica Reaction Silica reacts with HF to produce SiF^ and water. This important side reaction is detrimental to the economics of the process as it results in loss of HF and contamination of the HF stream. During the investigation, it was hoped that the necessary data to establish the kinetics of the silica reaction would be obtained from the . analysis of the product streams. However, the silica content of the fluorspar was very low (1 .31$ by weight) and small errors in the analysis in either the fluorspar or the product streams resulted in very poor mass i balances on silica. Often the mass balance indicated Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 171 more silica leaving in the solids out than entering with the fluorspar. Although not shown in the mass balances of Appendix IV, the extent of silica conversion, calculated on the basis of SiOg in the scrubber effluent, was usually 20$, and varied by only 1$ from one run to the next. If one accepts this result as representative one must conclude that silica must react very slowly. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. VIII CONCLUSIONS I A . On the basis of the experimental runs varying the temperature in the range of 250 - 4-5 0°F, and the per cent theoretical acid added in the range of 95 “ 1 0 5 , the following equations were seen to fit the experimental i data with acceptable accuracies dx 17900 1 xlo (A-KB)2(l - X r )2/3 B = 0.234 exp J - B' 173 dt R T 8 0 9 .9 J \ 1 - (1 - XB) (VIII-1) dx 16100 1 B = 0.161 exp B' 1/3 dt R .T 8 0 9 . 9 . 1 - (1 ' XE ) (VIII-2) 2,, __ ,2/3 dx - 17200 1 B = 0.396 exp 2/3 dt .T 8 0 9 .9 . 1 - (1 - * B ) (v i i i -3) B. On the basis of experimental runs varying the mixing in the range of 5 - 25 r. p. m., the CaCO^ content of the fluorspar in the range of 3-5 - 7«14^ by weight, the temperature in the range of 370 - 450°F, and varying the spar fineness by a factor of 3, the following conclusions were arrived at: 172 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 173 (1) The dependence of the reaction velocity on the temperature was quite pronounced and the activation energy values were in agreement with the results of Section A. (2) The CaCO^ in the fluorspar appreciably enhances the reaction velocity. (3) The degree of the fluorspar fineness does not seem to alter its reactivity. (4) Mixing rate affects the reactivity in a discontinuous fashion. On the basis of A and B above the following equations are recommended for scale—up and design. B = 0.0644c„1.012 MMI* 0.122 exp (-174101 dt R -T 809-9. 2 , ,2/n .2/3 Xb o (a -x b ) U- k b ) 1/3 1 - (1 - xB ) ( v m - 4 ) dx ^,.0.888 1-1.116 1 5 8 IO "1 1 B = 0.05l4c M exp dt . R _T 809.9. x!0 (A-xB )2 (l-x„)1/3B' 1/3 1 - (1 - xB ) (v i i i -5) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 174 1 - 1 = 0 .115C ° * 96V * 0 -1 2 0 e x p r- 1 6 7 7 0 dt R T 809-9 4 a (a-xb )2 (1-xb )2/3 2/3 ( v i i i - 6 ) where I = 0 if C = 7.141 or M < 25 r. p. m. and I = 1 if C = 3-5$ and M = 25 r. p. m. and x„ = fractional conversion of CaF^., B 2 ’ M = mixing speed (r. p. m.), C = vht % CaCO^ in spar, T = temperature (°R), A = acid:spar ratio corrected for boiloff and reaction with CaCO^, X = moles of CaFc per mole'of calcium in the fluorspar B 2 O and t = time in minutes. In section VI statistical analysis of the data indicated that all three of the models above equally fit the data. However, on the basis of the analysis considered in section VII, and also because it most resembles the theoretically derived equation VII-20 of the Theory section, one is apt to prefer model 10 (equation VII-2 and VII-6 above). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. BIBLIOGRAPHY 1 . Arsdel, W. B., Trans A.I. Ch. E., 42,, No. 1 13 (1947). 2. Bennett, C. A., Franklin, N. L., Statistical Analysis in Chemistry and the Chemical Industry, John Wiley and Sons Inc., New York, 1954. 3. Bischoff, K. B., Chem. Eng. Sci., _18, 711 (1963). 4. Blumberg, A. A., J. Fhys. Chem., 62, 1129 (1959)* 5. Blumberg, A. A., Starvinou, S.C., J. Phys. Chem., 64, 1438 (I9 6 0 ). 6. Boden, H., Report No. A-RR-69-O9 , Aluminum Laboratories Ltd., Arvida P.Q. March, 1 9 6 9 . 7. Box, G.E.P., Hunter, J.S. Technometrics 2, No. 3, 311 (1961). 8. Box, G.E.P., Wilson, K.B., J.R. Statist. Soc. B, 1 2 , No. 1 , 1 (1 9 5 1 ). 9. Budnikov, P.P., Ginstling, A.M., Principles of Solid State Chemistry, Translated by K. Shaw, Maclaren and Sons, London, 1 9 6 8 . 10. Cannon, K. J.,Denbigh, K. G.,Chem. Eng. Sci, _6, No. 4-5, 145 (1957). 11. Davies, 0. L., The Design and Analysis of Industrial Experiments, 2nd ed., Oliver and Boyd, London, 1956. 12. Dernedde, E., Private Communications, Aluminum Co. of Canada, ig67~1971. ■ !i 13. Draper, N. R., Smith, H., Applied Regression Analysis, John Wiley and Sons Inc., New York, 1 9 6 6 . 175 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 176 14. Duckworth, W. E., Statiscal Techniques in Technological Research, Methuen and Co. Ltd., London, 1 9 6 8 . 15- Gnyra, B., Report No. AW-108-5, Aluminum Co. of Canada. Ltd., Arvida, P.Q., Aug., I9 6 I. 16. Gnyra, B., Whicher, C.H., Report No. AW-248-TM-23, Aluminum Co. of CanachLtd., Arvida P.Q., Dec., 1 9 6 5 . 1 7 . Himmelblau, D. M., Process Analysis by Statistical Analysis, John Wiley and Sons, New York, 1970* 18. Levenspiel, O. L., Chemical Reaction Engineering, John Wiley and Sons, New York^ 1 9 6 2 . 1 9 . Levenspiel, O. L., Bischoff, K. B., Ind. Eng. Chem., .5 1 , 1431 (1959). 20. Levenspiel, O. L., Smith, W. K., Chem. Eng. Sci., 6 , 227 (1957). 21. Meeter, D. A., Program GAUSCHAUS, Numerical Analysis Laboratory, University of Wisconsin, Madison, Wisconsin, 1964 (Revised 1 9 6 6 ). T 22. Menard, W., Whicher, C. H., Report No. AW-248-TM-3, AluminumCo. of Canada Ltd., Arvida P. Q., Dec. 1955- 23. Moore, W. J., Physical Chemistry, 3^d ed., PP-340, Prentice-Hall inc., Englewood Cliffs, N. J., 1 9 6 2 . 24. Ostrovskii, S. V., Amirova, S. M., Zhurnal Prikladnoi Khimii, 4j2, No. 11, 2405 (Nov. 1 9 6 9 ). 25. Palmer, W. G., J. Chem. Soc. , 1.630 (1930). 26. Puxley, P. A., Woods, E. A., Report No. A-RR-74-48-20, Aluminum Laboratories Ltd., Arvida, P.Q., March, 1948. 27. Rowe, E. L., Report No. AW-248-TM-2, Aluminum Co. of Canada Ltd., Arvida, P.Q., Sept. 1955* Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 177 28. Shen, J., Smith, J. M., Ind. Eng. Chem., Fundamentals, .4, 293 (1965)* 29. Standard Methods for Chemical Analysis, Aluminum Laboratories Ltd.,(1947)- 30. Sood, R., Ph. D. Thesis, Part IV, University of Windsor, Windsor, Ont., 1 9 6 8 . 31. Traube, W., Lange, E., Ber. IO3 8 (1924). 32. Traube, W . , Reubke, E., Ber. ^4, 1618 (1921). 33. Volk, W., Applied Statistics for Engineers, McGraw Hill Co. Inc., New York, 1 9 5 8 . 34. Wen, C. Y., Ind. Eng. Chem., 60, No. 9,34 (1 9 6 8 ). 35* Youden, W. J., Statistical Methods for Chemists. John Wiley and Sons Inc., New York, 1 9 6 1 . Some Patents Dealing with HF Production U.S. 2,846,290 Aug. 5 , 1958 U.S. 3,071,437 Aug.19, 1959 U.S. 1,748,735 Feb.25, 1930 U.S. 2,932,557 Apr.12, i9 6 0 U.S. 2,967,759 Jan.10, 1961 U.S. 3,063,815 Nov.1 3 , 1962 U.S. 3,218,125 Nov.16, 1965 Br. 995,843 Aug. 6 , 1965 Br. 940, 289 Nov.28, 1963 Br. 554,127 Nov.18, 1941 Fr. 9 23,102 ' Jan. 30, 1963 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 178 Fr. 958,456 Dec. 26, 1963 Swiss 319,931 ' April 3, 1957 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. NOMENCLATURE L = length "0 = time A = acid:spar ratio corrected for acid hoiloff and reaction with CaCO , ((moles of H so. in - correction)/ (moles of CaPg in)). a = stoichiometric coefficient C = CaCO^ content in the fluorspar, ($ by wht.) C .C , = concentration of ‘the fluid reactant A AC « C C as shown in Figure III.l, (moles/L ) Ao AS C = initial concentration of the fluid An reactant in the bulk phase in equation (III-18), (Moles/L ) C = concentration of the solid reactant in the So unreacted core (moles/L-^). c/ = initial concentration of solid reactant referred to the volume of fluid (moles/L ) c = a parameter in equation (VI-36a) D = effective diffusivity of the fluid reactant eA in the ash layer, (L / 9 ) E = activation energy in the Arrhenius equation, (Btu/lb.mole). E (t) = residence time distribution of the solid stream leaving the reactor (E(t)'At). = fraction of solids out stream consisting of elements of ages between t. and At.. 3 l i F = ratio of variances 179 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 180 I = the integral of a rate model defined in equation (AI-4) k k = apparent rate constants for models 1-16 k, , in Table V.l, units as shown in table 16 k = mass transfer coefficient in equation D (VII-11), (cm /min.(moles of H^SO^/mole of calcium)). k = mass transfer coefficient across the ^ fluid film in equation (III-5), (L/0 ) k G = reaction rate constant based on the surface of^the unreacted -core,in equation (III-2). (L3tm+n-g}/moles j - 1-2 k of k = coefficients, (min X ). T o * v ' M = mixing speed, (r.p.m.) M = total flux of liquid reactant toward the unreacted core, (moles/0 ) MS = mean square as defined in equation (VI-41) MS = mean square about regression as defined in AR equation (VI-2) m = a coefficient in equations (ill-2) and (Vl-36a) or the number of levels at which replicate runs or samples were taken N = moles of CaF in the reacting mass in equation B (v-4) 2 N . .N, = molar flux of fluid reactant A through the A ash* Ac 3 ’ ash layer, through the unreacted core, and Ns through the outer particlg surface respectively, (moles/ 0 L ) N = moles of calcium in the reacting mass in equation (V-4) n = order of reaction in equation (III-2) or the total number of data points Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 181 n, = number of parameters in a regression ^ equation R = gas constant, I.9 S7 (Btu./lb.mole ° R ) or 1-987 (cal/gm. mole °K) R = radius of reacting particle or conglomerate in equation (VII-13), (l ) r ^ = radius of reacting particle, (L) r = distance from centre of spherical particle or conglomerate, ‘ (L) r = radius of unreacted core of conglomerate c or unreacted particle (l ) S = mean size of fluorspar particles (l ) 2 S = estimate of the variance of the fluorine A content * in the scrubber samples d^e to chemical analysis (g/1. fluorine) 2 S = estimate of the variance of the fractional conversions of the batch data due to pure error as defined in equation (VI-3) 2 SR ^ = estimate of the variance of k due to pure * error, defined in equation (VI-18) 2 SE ln.(k') = estimate variance of In k due to * ' ' pure error, defined in equation (VI-19) 2 S = estimate of the variance about regression, R it may refer to SR ^ or SR depending on whether the regression is non-linear or linear, respectively. 2 SR ^ ss estimate of the variance of k about * regression defined in equation (VI-6), (min X ) 2 S , . = estimate of the variance of In k about ' n'> ' regression, defined in equation (VI-14) (In(min X )) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 182 2 Sg = estimate of the variance of fluorine content of the scrubber liquor samples due to sampling or fluctuations in the reactor, (g./l. fluorine) 2 S = estimate of the variance of the spar feed rate (gm/hr.) 2 S O T = estimate of the variance of the 2 scrubber liquor feed rate, (litres/hr.) 2 S = estimate of the variance of the estimate X B of conversion of CaF^ from one scrubber liquor samples 2 S_ = estimate of the variance of the estimate of XB the conversion of CaF^ from the average of 6 scrubber liquor samples. s = s coefficient in equation (VI-36a) T = temperature (°R) or (°K) time = time usually in minutes X = molar concentration in the reaction mass (moles per mole of calcium) X = molar concentration of H^SO^ in the reaction mass, (moles of H^SO^ per mole of calcium) X = initial molar concentration of EhSO^ in Ao the reacting mass accounting for ooiloff and reaction with CaCO (moles of H2SOij. in - correction)/(molee of calcium in) X = molar concentration of H oS0,, on the AR perimeter . of the ash of thed 4 reacting conglomerate in equation (VII-13),(moles of H2S02j. Per mo-Le of calcium) X = molar concentration of CaF. in the reaction mass, (moles of CaF per mole of calcium) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 183 X.. = coded mixing speed defined in equation (VI-3 7 ) Xg = coded CaCO^ content of the fluorspar defined in equation (VI-3 8 ) X = coded fineness of fluorspar = -1 for regularly ground = +1 for reground fluorspar X, = coded temperature defined in equation 4 (VI-39) Xg = fractional conversion of fluorspar x = average fractional conversion in solids out stream in equation (V-2) xB (t*- ) = average fractional conversion of CaP^ for 1 stream elements of ages between t. and t. + At. 1 1 1 Greek Symbols a = a proportionality constant in equation (VII-1 5 ) £ = a proportionality constant in equation (VII-9) e = void fraction in ash layer in equation (lll-ty) -1 -2 e . = random error in equation (VI-5),(min X ) 'li -1 -2 = randon error in equation (VI-11) In (min X ) '2i = number of degrees of freedom — molar density of calcium in the ash layer in equation (VII-11),(moles of calcium cm ) (j^ = standard deviation of k alpout £he true regression equation (min X ) (Tlnfkl = standard deviation of In k jbout^the true ' ' regression equation In(min X ) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 8 4 = a random factor, by which the rate constant k. differs from the predicted rate constant k .} for the inherently linear equation of equation (VI-10) Superscripts = denotes predicted value Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX I. MODEL DISCRIMINATION AND DETERMINATION OF RATE CONSTANTS A. Using Batch Fata. The batch data consisted of conversion of fluorspar at various points in time. The data was analysed by the Integral Method of Analysis The procedure may be summarized as follows. 1. The reaction rate models listed in Table V.1 ‘ of section V were written in the form (AI-1) dt However, since A was always unity in the batch data, it was not a factor to be considered here. Also, the rate constant of each of the models could be separated from the conversion - dependent terms so that dx B (AI-2) dt 2. Equation(AI-2) was rearranged to the form (AI-3) /(*) 185 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 186 Now the left hand side of equation(AI-3) may he integrated to the form I (Ai-4) x = o The integral for all the models listed in Table V-l was easily obtained for the case when A=l. 3- The value of I was determined for each conversion versus time point and plotted versus time(t). 4. If the plot of I versus t was not linear the model was discarded. 5. If the plot of I versus t was fairly linear the line of best fit passing through the origin was determined by linear least squares and the slope was equated to the apparent rate constant value k. 6. The initial estimate of the rate constant . was refined by least squares regression of x onto B t. The criterion being to minimize Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 187 Because x ^ could not be expressed as an analytical function of k and t, the xl. values were determined by * Bi J the Newton-Raphson root seeking technique. The program (2 1 ) GAUSHAUS v ' employing the method of steepest descent was used to determine the best estimate of the rate constant. B. The Continuous Reactor Data The method employed was best illustrated by way of an example. Consider Run 9F Data. Average fractional conversion of CaF^ = 0.8.154 = 0.9408 g moles of H^SO^/g. mole of Ca+ ' in feed X = 0.9717 9 moles of CaF0/gm. mole of Ca"*+ in feed 60 c. The X, value above accounted for acid fuming Ao ^ AA = 0.9682 = acid:spar ratio corrected for fuming and reaction with CaCO^ The residence time distribution for the run was tabulated in section VI of the thesis. The rate constant of the rate model = kXBp(R - XB)a(1 - *B>V 3 (AI-6) at 1 - (1 - xB )1/3 2 was to be evaluated. For simplification let AK = k*Xr> . Do Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 188 As an initial estimate of AK let AK(1) = 0.10 Because the rate model was not easily integrated by direct analytical mathematical techniques the value of xB (t^) required in the summation below had to be obtained indirectly h - “ I (E(t)(At))±. (1 - (AI-7) i=l where (E(t)At)^ = fraction of solids out stream which consisted of elements of. ages between t. and t. + At. ' x i x ’ x ft.) = conversion of a stream with an average age of t. B l i and xB = observed average conversion in the exit stream. Knowing that rX B B = k xB t = AK-t (a i -8) / and that for this model 1 - (i - xE )1/3 (A - xB )^(1 - *b ) V 3 ( - 9) The discussion that follows will be in terms of the computer program used for the purpose of calculating the rate constant. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The program begins by evaluating the integral YI(j) for x = 0.001, 0.002 to x = 0.999 or x = AA - 0.001, d B < B if AA <1.0. XB YI(I) Fractional Conversion Integral 0.001 0.002 0 .5 0 0 0.5 01 0.999 But equation(AI~7) may be rewritten in the form aXB AK* t± (Al i(xB) so that the value of maY ke obtained by searching the Yl(l) matrix for the integral value equal to AK*t^ Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 190 and equating the corresponding X value to x (t.). These x (F. ) values were stored as the VXB(l) vector. B i The (E(t)*At)^ values were stored as the E(l) vector in the program. The sum SUM = E (I )•(1-VXB(I )) (AI-11) I =1 was calculated and compared to (1 - xB )(written in the program as (1 - XAVG)). (AI-12) AC(1) = SUM - (1 - XAVG) AC(I ) was a vector containing all the differences obtained for each estimate of.the rate constant AK(l). -5 If A C (I ) was less than 1.0 X 10 it was assumed that the rate constant value was accurate so as to satisfy the equation (1 - XAVG) = £]e(I)* i1 ~ VXB(I)) (AI-13) 1. Initialization For the initial estimate of the rate constant AK( 1) = 0.1 AC (1) = 0.03469. Because.AC(1) was positive it indicated that the rate constant estimate was too small since the calculated Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 9 1 amount of CaF^ .leaving the reactor was higher than that measured. A rough second estimate of the rate constant was obtained by letting AK(2) = AK(1) • 2 (AI-14) The figure below shows the expected response of AC(I) to the rate constant AK(l). t AC(I) 0 > AI< (I ) The exact nature of the response was not known but it was expected to have only one root. If AC(1) had been negative, the second estimate AK(2) would have been calculated by letting AK(2) = AK(l)/2 (AI-15) Using the AI<(2) value, a value for VXB(2) was calculated and the new SUM value calculated as per equation (AI-10) and AC(2) was calculated as per equation (AI-11) to be -0.0190*1-. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 192 Note that AC(2) was negative indicating that the true AK value lies between A K(l) and AK(2). Had the AC(2) value been positive the estimate for AK(3) would again have been obtained by letting AK(3) = AK(2) * 2. The successive AK(M) values would have been obtained by letting AK(M) = AK(M-l) • 2 (AI-16) ♦ until AC(M) became negative. The above was by way of initialization. Had the initial estimate AK(1) yielded a negative AC(1) value successive estimates of AK(l) would have been obtained by letting AK(M) = AK(M-l)/2i until a positive AC(I) value was obtained. 2. Linear Approximation and Steepest Descent The method of linear approximation was used to determine the next approximation of the rate constant AK(M+1). The method begins by searching the AC(l) vector from AC(1) to AC(M-l) for the smallest absolute value of AC(I) to be designated as AC(KK). Suppose now that AC(m ) was positive while AC(KK) was negative as shown Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 193 AC (M) AC(l) AK(M + I) AK(KK) o N~------AK(M) \ ! a k (i ) AC(KK) As shown the best approximation for the rate constant was one which would yield an AC value of 0. From the geometry of the figure |AC(KK) | • (AK(M+1) - AI<(M))= |a c (M)|- (AK(KK) - AK(M+1)) which yields AK(M+1) = |AC(KK)| • AK(M) + |a C (M)| • AK(KK) (AI-17) a c (k k )| + |a c (m )| The result would be the same if AC(M) were negative and AC(KK) was positive If on the other hand both AC(m ) and AC(KK) were positive as shown Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 194 a c (m ) AC (I) AC(KK) o a k (m ) AK(KK) a k (m +i ) AK(I)- Again from the geometry of the figure |a c (m .)|- (a k (m +l ) - a k (k k )) = |a c (k k )| • (a k (m +l ) - a k (m )) and AK(M+1) = | AC(KK)| «• AK(M) - |a c (M)| *AK(KK) (a i -18) Ia c (k k )| - |a c (m )| The reader can verify for himself that equation (AI -13) was valid for the cases where AC(m ) <[ AC(KK) and AC(m ) < 0, AC(KK)<0 where AC(M) ^ AC(KK). The procedure was simply to test if AC(M) and AC(KK) were both of the same sign. If they were equation(AI-13) was used and if not equation(AI-12) was used. In the program the equation was written as AK(M) = |a c (KK)|- AK(M-l) - SIGN 1 ’ (AC(M-l )| • AK(KK) |a c (k k )| - SIGN l* |a c (m - i )| (AI-18) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 9 5 where SIGN 1 = +1.0000 when AC(KK) . AC(M-1)> 0 and SIGN 1 = -1.0000 when AC(KK) • AC(M-1)<0 Successive estimates of the rate constant are shown below TRIAL AKAC 1 0.100 0.0347 2 0.200 -0.019038 3 0.1793 - 0.00522 4. 0.18572 +0.001223 5 0.1537 0.0000786 This rapid a convergence was rather unusual but convergence was usually accomplished in about 7 iterations. 2 However, the AK value was equal to k XB and o k = AK/ 2 = ‘ 0.163. / B Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 196 OJ u 1 z t.0 to o D X UJ cvj i— V z > < X z u. D o o j- in O f— j J- u tO ID •-« < z X u h—1 IU rtj o f- —« L5 a. r H X iu J- J < Ul < X u < X LU U H < > UJ X O x X > j- j— m 2 O rv a Id < Z - (lI o o .H z < — CL u. H z Hi t- o t—« ■o :0 < to u j f- z — < Z I- >- •> z UJ 1 o < < ■n X in < 0 o t— *—« J- o o CO H X -• a o ~7 ~7 C3. (0 D iu :n o o 5 o 2 a o in m o —« M X sT < -< x J- O H* < UJ a - a r - X a♦ UJ < U UUUvJUUUUUUUUUUOUU Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 9 7 UJ >- > X oZ «H 'J 72 J in z < •M z (VJ < o v 1 H IU a H o U © < o 2 ii H L H IU • z J O < a > H —t < (0 to © z (0 m o o Is- X u a • o ? IL) M r—* *■ H UJ o < in «- X x •— © r i o \IU >- n (J> X ( j < H < O •> a XU *-» 3 H o (VI a \ CJ < o » \ OZ * © iu a> co < 0 » 3 • a 1 o _ l u - CvJ o < < z < rH u Ql < \ > L a in z \ 3 ; r -H 3 0) _J *• X in o IU z • X CO UH ■o II o © 0J —■ ir j • O • • —1 H r-* :n a X X L —< * • :u —« X ~y •» .Z . . S; _ T _ o _ (0 — o in •1 —• S/© —t • Hi— •H•—•I—H < < a x H • ♦ •9®li.® © li. © © Ri I O IU CO — 0 D IIll *• » #■ » •• • *■ ,- •- * Ul • O • _ ~ ~ I X XXXXX X ~ X X O O' to cm ~ iL x r~ f~4 - 2 ce jJ xsO a o a0 ®© a0 a o\ :n m • • \\ -i■X ——< —n — n inin ~rH o O' O I L •'^CVlsT\Q.»**'»CL*'\ a * •> »■ » a V o X • NN. — — ■—<-Hl/lOOin o o ••OOUJnCJ' o O UJ O O' O O HO _ ... I . X XIIHX . _ 1. o O O O J • ~ uj < — u j — *mcvj——• U- —1 n •t/iin —ujo UJ o o • • o uj uj -1 COD' — o w w w w o O oO O —■ O * O O I :-SHHHHHHHH HHHHOHh* H H H n H • • —• O II II O + • V H H UJ < Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 198 D tO Z - o m M • *—4 O O o OJ _ o OJ o o O' o o c o o 4-4 o OJ OJOJ r*-4 — < •H C\l —1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 9 9 y y O' o O' < I-o LOa o o \ if) to i IU y ! l J D y O < y > < * I- o o J < a 1- o LO h < IU rx o u H L!) < < LX •> o 0 to pH CD 1- Id 1 < CO J IU * LU -J O < 7 h- > Li) Z o < o t O cO XI )- j - 1 cO a .0 D • Z 0 < 0 —J ■> rH O •-h CM • H O it 1 U O Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 200 o OJ X 1 y < :n i o • • — oj y o ~ H Z O \0 O S- '- I r - < r v0 n i n o o —» o y T) y OJ o o O J o OJD o v 0 < • t ■z o •• • •• o 9 9 o o !\J OJ o r > o OJ C v J n — * ■ > t - o * >1= J- • t- O\ N 9 V n y o o o * - > m y o z y o o o i H O J o o —« •-H D w o • J ) o o o 1 1 d > • o o 1 I r , y D “« —. o 2 o * > J * < O i n o f -< o O J w r H n o OJ W — ■ a i • r - »— 4 .-H •• o V o y o • 1 o •• o V o y O y r - H •V a o o •M m < o < C O a 2 n a —« n < o < O' V z i n O ' X 1 n w II II II U l w UJ II II n t-4 i i i i < II i H • ■ i r - « T — '■» • 1 o o o • U 1 o i o O o u p o n o g 7 1 V Z j - + h - + 2 r - 2 < i— - > > i - + f - + 1- < < z ■i- j — < z t - JT w T o II ZX OJ i7 V-- 1 3 n 2 w — it o — II 1 3 u _ •— V o ll V o U V o U . a II V o I L V o ll V o II V o IL V ►—« ii '/ o y •— • o I-M j r i j m y o 2 < o s < o — 1 ” 5 y o •— m V o < e > ; > o —• CO i n 2 < o i n m 1 3 n 0 . 1 r—1 I T ) v O < ) ■ < n r ~ 1 0 o o o o O O o O o o c (VI OJ (VI OJ OJ O l ( \ j n n n n Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 201 •ul J •0 J) M a lO UJ lO i— o m a X ,■» o 5 ■—« o X o ■X > T—« Ul 3 < z o X a z 3 X uj J 1- 3 3 3 3 0 3 3 3 3 3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 202 X 3 »-h < w •-* rH + vfl T—4 r-1 ♦ •> «— « — o r - + X «— < 3 w *-« ►-« < Q j - w 1 u i j K4 X >- * — - IU “ > 3 in IU Q *• < if) • 1 1 • ( it ra r~ CM CM 3 II < — 1- H 3 X o 3 3 H-* n in _J _1 + 3 z z 1 o o »-< CM i UJ UJ 3 CM < a. o o r-C >- cr Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced FUNCTION FUNC(X *AA) u o u o s o a liJ > < X D * — —• ll n OunD n CO u < *— — —< V ¥ o \ o IL o D Q o o <—i X II i • • • O < Q II • a 1 1 < < < X \ U X II li 1 < U Q z Q a o CD li u o: cr H- D Z LJ o 2 203 APPENDIX II THERMODYNAMIC CONSIDERATIONS The aims here were to establish whether the reactions were predetermined by possible equilibrium. The heats of reaction were also established. CaPg + h 2S04 > CaSO^ + 2 HP (AII-1) if HF + SiOg » SiF^ + 2 HgO (AII-2) CaCO^ + HgSO^--- > CaSO^ + HgO + COg (AII-3) Table AII.l contains all the thermodynamic data necessary for the determination of AF^ and AH^ for these three reactions. To determine AF^ from the tabled data the following equation was used AF|r ~ ZL12 = - dT (AII-4) T Table All. 2 contains the calculated values of AFT, AH,^ and K the equilibrium constant. The valueof K was obtained by use of the equation • RT lri k = - AFt (AII-5) 204- Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Since all the equilibrium constant values are relatively large one may assume that the reactions were essentially irreversible. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 206 T T T T ,298.15 T 2+ 472000 - 8246.0 t AH* T - AH Kcal/gm mole Kcal/gm 6.55T+0.00036T2- 17000 - 1928.0 4.28T+0.01053T2- 2212.0 ■ 7.30T+0.00123T - 2286 16.78T+0.0118T214-3T+0.00364T2- - 6052.0 47000 - 4429-0 33-2T - 9898.58 21.95T+0.00133 10.57T+0.00105T + 206000 - 39360 24.98T+0.00262T + 620000 - 9760.0 k 163.9 -316.475 -277.796 - - 64.7 - -204.64 - - 54.64 -375.855 - - 94.26 Kcal/gm mole Kcal/gm -269.57 AEV,298.15° . Thermodynamic Data of Reactants Products and Reactants of Data Thermodynamic 290.3 -343.335 - - - 64.2 -217.65 -193.91 -385.98 - - 57.80 Kcal/gm mole Kcal/gm - 94.05 -288.14 AHy,298.15°K s) s) s) i) g) s) g) g) g) CaSOj, CaF^ HF sio2 H2S01 SiF, V CO, 1 - - liquid 1 s - - solid s CaCO, g - - gas g Material Table AII.l Table Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 207 Table All.2 Thermodynamic Quantities for the Principle Reactions Occuring in the Reactor Temp 298.15°k 4oo°k 450°r 5 0 0 °k 550°k Reaction AFt (Kcal/gm mole) 1 - 4.179 -'9 -6 8 8 ‘ -1 2 .3 0 0 - 1 5 .6 0 6 -17-303 2 - 2 1 .6 9 -1 9 .6 9 -18.761 -17.770 - 1 6 .7*1-2 3 -31.905 -3 8 .1 2 2 -40.961 -43-932 -46.749 AH^ (Kcal/gm mole) 1 12.475' 11.3 10.777 10.331 9-931 2 -27.13 -27.555 -27.745 -27.964 - 2 8 .1 7 8 3 -13.141 -14.100 -14.944 - 1 5 -4 8 4 - 1 5 .9 8 4 K (Equilibrium constant) 1 1 .157X 103 1.964X105 8 .5 8 3 X 105 6 .627X 1 0 6 7 .508 XIO6 2 7 .927 x 1 0 15 6.288x1010 1.293 x 1 09 5 . 8 5 1X107 4.9^X106 3 2.447X1023 6.742x 1 o2 0 7 .8 2 IXI019 1 .5 9 5 XI019 3-769-1018 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX III ANALYSIS OF THE DATA OF PUXLEY AND WOODS The data of Puxley and Woods were fitted to a zero order reaction of the form - dN — k dt where k = gm. moles/min. The equation was valid for conversions up to 50$. Average k values.were determined at the 20$ and 5Q$ conversion levels and can be found in Table AIII.l. An Arrhenius plot was drawn to determine the activation energy. Figure (AIII-1) illustrates the In k vs. 1/T plot for 20$ and 50$ conversion and an average line was drawn through the points. Approximate values of the activation energy values were determined to be as follows. 20$ conversion E = ^570 cal/gm mole CaF^ 5C$ conversion E = 5^-50 cal/gm mole CaF^ Overall E = 5000 cal/gm mole CaFg Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 60S In In k 7.90 -8.355 “9.1 -4 10"4 10 x X 2.36 1.12 X 10“^ 3.653 k (gm.moles/min.) In k In -7-955 -8.34 -8.94 " 4 " 4 2.40X 10 1.32 X 10 3-47 x lo"^ k (gm.moles/min.) T°C At 20$ CaF^ Reacted At 50$ CaF^ Reacted 225 175 125 Table AIII.l Reaction Constants for Puxley's Data Assuming Zero Order Kinetics Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX IV SAMPLE TREATMENT AND MASS BALANCES In analysing the experimental data, the objective was to determine the extent of conversion of CaFg or H^SOj^ in the solids out stream. To establish the accuracy of the conversion determined, it was first necessary to ensure adequate mass balances. The figure below should aid the reader in under standing the ensuing discussion. CAUSTIC LIQUOR MAKEUP AC I H F , SO1^, HgQ SCRUBBER COg s SiF^ SOLIDS OUT CaSO^, C'aFg, SiO^ SCRUBBER EFFLUENT Aside from temperatures, the following parameters were measured. (1) Feed rates of acid and spar (2) Solids out flow rate (3) Caustic liquor makeup flow 210 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 1 1 (4) Solids Samples analysis (5) Scrubber effluent analysis. Knowing the caustic liquor flow rate, and the fluorine content of that liquor, one is able to calculate the amount of CaF^ converted to HF. If, at the same time, the amount of CaF^ exiting the reactor with the solids is known, one can again calculate the extent of CaF^ conversion. There were, therefore, two methods available for the determination of the extent of conversion. In the initial scrubber setup discussed in the Apparatus and Experimental Procedure section, it was impossible to obtain reliable liquor stream data due to the excessive fluctuations in ‘caustic makeup flow rate, and frequent flooding of the column. It was, therefore, necessary to rely solely upon the solids out analysis for the determination of the fractional conversion of the fluorspar. Also, no reliance could be placed upon the fluorine mass balances. The mass balances were, of course, based upon the premise that if the reactor was operating at steady state so that the following should be true. Ca in = Ca in solids out Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 212 F in = F out into scrubber-+ F out in solids out SO^ in = SO^ out into scrubber + SO^ out in solids out SiOg in = SiOg out into scrubber as SiF^ + SiO^ out in solids out The silica, entered the scrubber as SiF^ but it was easier to consider it in terms of SiO^, since it was anlaysed as SiO^. A. Sample Treatment Figures AIV.l and AIV.2 illustrate the methods used in handling the solids out samples. The quenching step was done in situ 3 as the sample was being collected, to ensure reaction termination. In the initial sample handling technique, only about 20 grams of sample were collected, but as the amount of quenching solution was increased from 100c.c. to 5 0 0 c.c. the amount of solids sample was also increased to about 80 grams. When the initial samples handling technique was being used, several discrepancies came to light that caused one to doubt the accuracy of both the handling, and subsequent chemical analysis of the samples. The first discrepancy, was that the volume of the sample Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 213 9 liquor was much lower than the expected 100 or I5 0 cc. originally added to the sample bottles. In addition, thie weight of the filtered solids was greater than that expected after accounting for dissolution of H^SO^. The discrepancy in weight was attributed to the formation of the hydrates of CaSO^ (CaSO^•1/2H^0 and CaSO^-SHgO). The volume discrepancy was attributed partly to the hydrate formation, but more largely to the physical entrainment of liquid within the filtered solids. It was safe to assume that very little if any of the hydrates of CaSO^ could form within the reactor because there was little or no water present in the reactor. Only 0.6 grams of w^ter per 100 grams of fluor spar could possibly have been present within the reactor. If one could account for H^O boiloff this figure would be much lower. Also, above 220°F, only the CaSO^'l/^H^O hydrate of gypsum could form. Nevertheless, subsequent analysis indicated that unless the sample solids were dried at 200°C or higher, as much as 5$ of the solids could consist of water of hydration. The major error caused by this water content, was its presence as an unaccounted for impurity in the solids. The major portion of this water of hydration Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 H must have formed after the quenching step. To eliminate the water of hydration, as well as to obtain an accurate measure of the amount of this water, two drying steps were necessary as shown in Figure AIV.2. Crushing of the solids prior to the filtration step was necessary because the solids set as one large mass upon standing in the quenching liquor. It took a con siderable amount of force to crush the solids into fine granules. The crushing step was carried out in the plastic sample bottles prior to decanting the liquid, using a 1 inch diameter 12 inches long glass rod. The crushed solids were easier to wash and did not entrain as much liquor. • ■ To obtain an estimate of the amount of entrained liquid,the solids were weighed while still wet after filtering and drying over night at 90°C. The drying step at 90° c was critical in that if the I solids were not dried for a sufficient period of time incomplete drying was a possibility. On the other hand, prolonged drying could also drive off some of the 'water of hydration. CaSO^ * 2H20 ----=► CaSO^» 1/2 HgO + 1 1/2 HgO / Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 215 Determination of Water of Hydration: An Example Consider Sample 8F-16 (1) Wet filtered solids Vht. = 80.87 9- (2) Weight of filtered solids dried at 90°C = 6 6 .19 (3) Weight of filtered solids dried at 200°C = 60.54 (4) Volume of liquor measured at filtering = 478c.c. (5) Volume of liquor entrained = (l)-(2) = 14.68 c.c. (6) Volume of liquor hydrated = (2)-(3) = 5*65 c.c. (7) Total liquor volume at filtration = (4)+(5) = ^93 c.c. (8) Total accountable liquor = (7)+(6) = 498.33 In the above example, it has been illustrated that all but 1.7 c.c. of the original liquid has been accounted for. However, no correction was attempted for the water formation by the reaction NaOH 4 - HgSO^ > Hg0 + NagSO^. Nor was any correction-attempted to account for density changes due to non-ideal solution behaviour. To obtain a measure of the accuracy of the analytical work being done at the Alcan labs, synthetic samples were compounded from pure reagents and sent for analysis. Table AIV.2 contains the results of the analyses and the compositions as prepared. These samples were handled by Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the modified sample handling technique of Figure AIV.2. Although the overall results were encouraging the analysis for samples 2 and 3 indicated a 6fo error in the CaF^ analysis. However, some of the problems encountered with the solids out samples did not occur with the synthetically compounded samples. The solids did not set upon standing, nor did they appear to take up any water of hydration. The author was often reminded by the lab people that although synthetic samples could be analysed within a high degree of accuracy, the results often could not be extrapolated to product stream samples. The product stream, may often contain impurities which interfere with the analysis. The determination of the SO^ content was especially sensitive to impurities that could promote reduction of BaSO^ during the fusion step in the SO^- (29) determination.x ' Another descrepancy encountered in some of the solids out samples analyses reported, was that the addition of the compositions of the dried filtered solids failed to add to 10C$. Quite often, the summation was lower than 9C$.. Furthermore, substantial amounts of CaCO^ were detected in these samples. Often, the CaCO^ content was Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 217 so high that if taken at face value, indicated more CaCO^ leaving the reactor than entering it.' While modifications in analytical techniques made at the Alcan Works Laboratory eventually corrected the lack of summation to 10C$, the results still indicated a high CaCO^ content in the solids. A likely explanation of the high CaCO^ content is that it was being precipitated out of solution or being formed in the solid phase by the following reactions CaSO^ (solid) <= > Ca++ + SO^ (AIV-1) HgCO^ + NaOH —> 2 Na+’ + CO^~ + 2 (AIV-2) 2 Na+ + CC>3= + Ca++ +S O ^ ^ z > CaCO^ +. 2Na+ + S0^_ (AIV-3) 2 Na+ + CO^~ + CaSO;+ (solid)^2 Na+ + SO^- + CaC0o ' (AIV-4) 5 The equilibrium in equations (AIV-3) and (AIV-4) shifted to the right due to the lower solubility of CaCO^. NaoC0 may have been present in the quenching ^ 3 solution or formed by contact of the caustic solution with air during the quenching or filtering steps. Carbon Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 218 dioxide dissolved in the distilled water, used for washing the solids after filtering, would also cause CaCO^ precipitation, but would not alter the SO^- content of the mother liquor. On the other hand, the reaction scheme indicated that if the CaCO^ was formed while the mother liquor was present, it would alter the S0^~ conteht of t the mother liquor, by the formation of Na^SO^. In any case, the precipitation of CaCO from what was originally D CaSO^, must be accounted for. Although CaCO^ formation would occur prior to, and after removal of the mother liquor, only the two extremes were subject to analysis. All the CaCOg detected in the samples was assumed to have been formed by way of equations (AIV-1) to (AIV-4). Because the reactor contents were much too reactive to CaCOg, it was safe to assume that none of it leaves unreacted. In addition to reacting with H^SO^ it will react with HF as follows 2 HF + CaCO^ — > CaFg + Hg0 + COg If the CaCO^ was assumed to have been formed after . the mother liquor was separated from the solids (CaCO^ formation after filtration), the SO^- content of the mother Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 219 liquor needed no correction but.the CaSO^ content of the solids was corrected as follows. Corrected °/o CaSO^ = $ CaSO^ detected in dry solids % CaCO^ detected ♦ /^caSO^ CaCO^ - (AIV - 5 ) When the CaCO^ was assumed to have been formed prior to the washing step, while the mother liquor was present, the CaCO present in the solids was considered to be an 3 impurity which must be corrected for. Corrected % CaSO^ % CaSO^ detected (AIV-6} in dry solids ~ 100 ^ - % CaCO^ ™ detected j j. j. J The $ CaF , % Si0o and % Ro0 were also corrected in this d d d 3 manner. The S04“ present in solution as CaSO^ was determined ++ from the Ca content of the solution, but further correction was necessary due to the fact that CaCO^ formation enhances dissolution of the sulfate ion. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 220 SO^- present in soluble CaSO^ or _ JCa detected volume put into solution ~ / • /1 * by CaCO formation (_ in ‘ ' liquor M W _ = f MW — 1 so4 grams of CaCO^ S0jj~ + (AIV-7) detected in sample MW_ ++ MW ^ Ca t CaCO. 3' Thus far, no mention has been made of the scrubber effluent samples. Treatment of these samples was much simpler, requiring only a filtration to remove any suspended solids present. The liquid was analysed for F , S0jj~ and SiO^ content. Because the scrubber liquor samples required no elaborate preparation for analysis, they were deemed more accurate. Furthermore, because the analysis was done by an automated technique, replicate analysis was accomplished easily, thus reducing the errors involved. A summary of the determinations carried out on the samples and their utility is given in Table AIV.l. In the Table is included the analysis of the sludge collected from the teflon transfer line, conveying the reactor gases to the scrubber. When the reactor was run at 450 °F, considerable amount of condensation occured in Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 221 the line to produce a sludge-like material consisting chiefly of condensed H^SO^. At 370°F the amount of this material was much less, while at 300°F almost none was formed. The sludge was removed from the line continuously, and its flow rate noted. At the Alcan lab it was filtered, and analysed as outlined in Table AIV.l. Tables AIV.3, AlV.ty and AIV.5 show the chemical analysis results for runs 11A through 10F. In some of the solids out samples, the % CaSO^ of the solids was not determined. However, for these cases the fo CaSO^ was calculated by difference. In the cases where it was reported, the summation of the percentages were reasonably close to 100^. In runs 16a to 10F only the scrubber effluent samples were analysed. Analysis of the solids out samples was time consuming and unnecessary once the mass balances had been established. Recalling that the primary aim of the analysis was to establish the extent of conversion, the scrubber effluent samples sufficed for that purpose. The analysis of the sludge samples was done only for the runs where a significant amount of this sludge was collected. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 222 For the runs where only the scrubber effluent analyses were done, it was also necessary that the Sio content of the solids out samples be determined. 2 The results of these analyses are shown in Table AIV.6 B. Mass Balances Basically, the solids out sample analyses were used only to establish a mass balance. The scrubber effluent analysis was used to establish a mass balance, and to determine the extent of conversion. In the discussion of sample treatment, the point was raised that in some of the solids out samples the summation of the components failed to add to 1 0 C $ . Compensation for this error was made by assuming that either the per cent CaF^ or per cent CaSO^ of these solids was erroneous. If the % CaF^ determination is assumed erroneous, it can be corrected by the following equation: % CaFg = 1 0 0 - ( f o CaSO^ + % SiO£ + fo RgO^ + % CaC03 ) If the % CaSO^ reported is assumed in error, then the corrected % CaSO^ can be determined as follows: % CaSO^ = 10($ - (% C aF g + < fo S iO g + % Rg0 + < fo CaCO Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 223 The mass balances using data with the above two alternate correction procedures are not reported here. All that needs to be said about those results is that they were not encouraging. Those mass balances indicated that usually less than 90$, and often less than 8C$, of ++ — the Ca and F being fed into the reactor could be accounted for in the outlet streams. Accounting for the presence of CaCO^ improved the results somewhat, but not to the point where the balances could be considered acceptable. Runs 1A - 6a and IE - 5E were all discarded due to difficulties in obtaining good mass balances. After modifications were made to the analytical techniques employed at the Alcan Laboratories, the addition of the compositions of the dry solids of the solids out samples was much closer to 100$. If one examines the data of table AIV.3 one notes that although the summations of the solid compositions were not exactly 100$, they were reasonably close to that value. Tables AIV.7, AIV.8, AIV.9 and AIV.10 show the results of the mass balances for runs 11A to 15A. Because the solids out flow was rather unstable, due to pulsations of the reactor, there was reason to believe Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 224 that an accurate measure of the solids out flow rate was unavailable. To compensate for this, a solids out flow correction was attempted on the basis of an accurate sulfate balance. The solids out flow rate was modified by forcing a sulfate mass balance. Corrected solids Measured solids out flow rate out flow rate .100+SO,. balance erroi And the SO^ balance error was SO^ balance error If the sulfate balance error was positive or negative, the solids out flow rate was decreased or increased respectively, to compensate for this error. Similarily ++ , _ Ca balance error F balance F in - F out error X 100 and SiOg balance X 100 error Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 225 The following relations were also used. S04“ out = (SO^~ out in solids out as HgSO^ or CaSO^) + (S0^~ out in Scrubber Effluent) + (S0^~ in sludge) Ca++ out = (Ca++ out in solids out as CaFg or CaSO^) ++ + (Ca out as sludge) F out = (F out as CaFg in solids out) + (F out in scrubber effluent) + (F out in sludge) SiOg out = (Si)^ out in solids out) + (Si) out in scrubber effluent) + (SiOg out in sludge) % CaFg reacted = CaFg in - CaFg out in solids X 100 CaF2 in '(H SO^ out in solids + H-SO. out in scrubber'' H 2S°4 ±n 4 f effluent in H 2S°^ X 100 fo SiOg reacted = SiOg in - SiOg outin solids X 100 SiOg in Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 226 A computer program was written to do the mass balances on the reactor. A nomenclature is provided for easier understanding of the program. Mass balances of sorts, using only the scrubber effluent analysis, were also calculated. For these calculations, the following identities were used. — 7Q (CaF0 reacted) = (F in scrubber)X(flow of scrubber)x __ effluent effluent 38 Every 38 grams of F in the scrubber effluent required that 78 grams of CaFg react — Q8 (HgSO^ reacted) = (F in scrubber) X (flow of scrubber)X effluent effluent 38 CaCO^ fed X 98 in fluorspar Too Every 38 grams of F in the scrubber effluent required that 98 grams of H^so^ react, and every 100 grams of CaCO^ in the fluorspar feed reacted with 98 grams of HgSO^. Solids flow out = (Total feed) - (C02 + HF + SiOg + HgS04 ) out into scrubber - (sludge flow) CO was formed from CaC0o d 3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 227 Insoluble solids out = (solids out) - (HgSO^ left in reactor) (HgSO^ left in reactor) = (HgSO^ fed) - (HgSO^ out into . scrubber + HgSO^ reacted + HgSO^ out in sludge) (SiOg in solids out) = Insoluble 70 SiO_ .in solids of X solids out solids out sample 100 This was the only point where a solids sample analysis was required. CaSO^ out in Insoluble CaFg unreacted + SiO, solids out solids out (Total CaSO^ out) = CaSO^ out in + CaSO^ out solids out in sludge % CaFg reacted = (CaFg reacted/CaFg in) X 100 The amount of CaFg reacted, was calculated on the basis of how much fluorine was detected in the scrubber effluent. The above calculations, were based on the premise that all the fluorine be accounted for. Whatever part of the fluorine that did not appear in the scrubber effluent must have appeared in the solids out as CaFg. The results obtained by this method of calculation are shown in Table AIV.ll. The average conversions shown in this table were the accepted conversion values used in calculating the rate constants for the reaction rate models. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 228 C. Discussion While fluctuations in the solids out flow rate occurred in most of the runs carried out in the continuous reactor, the mass balances in tables AIV.7 through AIV.ll may be considered to be reasonably good. There was, however, a persisting nagging suspicion that the solids out samples analysis was not entirely satisfactory. This « suspicion was based upon the fact that too many things can go wrong in the analyses. The analyses for fluorine content in the scrubber effluent were considered to be more reliable because replicate analyses were carried out. Without replication of analyses, however, the results could be sometimes misleading, because the error in one analysis could be very high due to instrument error. At the Alcan Works Laboratory the fluoride analysis was carried out by means of an automatic sample handling apparatus (Technicon). This equipment first carried out a sulfuric acid distillation, to drive all the fluorine from the original sample, and thus separate it from possible interfering ions. The amount of fluorine collected was subsequently determined by photometric analysis, using a Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 229 complexing reagent. This automatic analyser was subject to malfunctions when initially put into operation, which unfortunately was also the time the first analyses of the scrubber liquor samples were being carried out. However, once the Technicon analyser was functioning properly, the results were quite accurate, as was substantiated by having some of the samples check analysed by the Alcan Research Laboratories. In the research labs, the fluoride determination again required the distillation step-but using perchloric acid, and the amount of fluorine distilled out of the sample was determined by a recently developed potentiometric titration with La^O^)^ or (6} Th(NO^)^ solution, using an Orion Fluride electrode. ' The results indicated that there was no bias in the method used by the Alcan Works Laboratory. The standard error of single analysis was determined to be 0.079 9* Per litre in a 2.5 and an overall standard error in the estimate of the average fractional conversion of 0.0142. The average fractional conversion was calculated on the basis six samples for each run. The standard error in the estimate of the fractional conversion accounted for errors in the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. scrubber liquor flow rate, the spar feed rate as well as deviations observed from sample to sample within each run. The overall degree of accuracy can be considered as acceptable. Unfortunately, the analysis of the batch runs solids samples could not be analysed in replicate because of the time and costs involved. However, replicate samples were taken (samples taken at the same reaction time at the same temperature), and analysis of these samples allowed one to determine the pure error due to analysis and chance errors that could occur in any run. The pure error was determined to be 0.03 (fractional conversion). This error was significantly larger than the error in the continuous reactor determination of the fractional con version. It had been hoped that rather than relying on chemical analysis of the samples one could determine the degree of chemical conversion in the batch reactor by gravimetric techniques ie. following the weight of the reacting mass with time. However, this proved to. be very difficult unless very sophisticated equipment was used. Thermal conversion effects,.in particular, could not be adequately controlled. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. D. Nomenclature for Mass Balance Program By o r d e r appearance; All flows in grams per hour I = r u n no. ISAMP = sample no. RPM = rotation rate of reactor stirrers SPARF = soar feed rate CAUSTF = caustic liquor feed rate to scrubber (1i tres/hr.) ACIDF = acid feed rate SOLF solids out flow rate SSW = solids sample weight in grams DSOLW = weight of dried solids from solids out sample (grams) VSS = volume of 1iquor from sol ids out sample in l i t r e s FCL = fluorine in caustic liquor sample (g./l.) S 0 4 C L = sulfate in caustic liquor sample (g./l.) CACL = calcium in caustic liquor samDle (g./l.) SILCL = silica in caustic liauor sample (g./l.) S 0 4 S S = sulfate in solids out sample liquor (g./i.) CASS = calcium in solids out sample liquor (g./l.) P C A F 2 ' = per cent CaF2 in dried solids of solids out samp!e . Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 232 PCAS04 per cent CaSO^ in dried solids of solids o u t s a m p l e PSIL per cent silica in dried solids of solids o u t s a m p l e P C A C 0 3 per cent CaCO^ in dried solids of solids o u t s a m p l e P R 2 0 3 per cent R2^3 ^n dried solids of solids o u t s a m p l e S sludge flow rate out SL fraction of.sludge as liquid S L S 0 4 fraction of sludge liquor as SO^ SLF fraction of sludge liquid as fluorine SLSIL fraction of sludge liquid as silica SS fraction of sludge as solids S S C A S 0 4 per cent CaSO^ in sludge solids SSSIL per cent silica in sludge solids SCA calcium out as part of sludge SF fluorine out as part of sludge SS IL silica out as part of sludge S S 0 4 sulfate out as part of sludge S H 2 S 0 4 H2S04 out as part of sludge i SHF HF out as part of sludge CAIN calcium into reactor C A F 2 I N CaF2 i nto reactor FIN fluorine into reactor SILIN silica into reactor C 0 2 0 U T C02 out of reactor Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. S04IN = sulfate into reactor FS04CL = sulfate out in'caustic liquor ACIDCL = H2S04 out in caustlc' "liquor S0LS04 = soluble sulfate out of reactor in the s o l i d s o u t SCAS04 = soluble CaSo^ out of reactor in the s o l i d s o u t AC I DO = acid out of reactor in solids out TCAS04 = total CaSO^ out of reactor SILISO = silica out insolids out S040UT .= total sulfate out of reactor S04ERR = error in sulfate balance CAOUT = calcium out of reactor CAERR = error in calcium balance FOUT = fluorine out of reactor FERR = error in Fluorine balance CAF2R = CaF2 reacted PCAF2R = per cent CaFg reacted AC I DR = acid reacted PACIDR = per cent acid reacted TSILO = total Silica out SILERR = error in silica balance PSILR = per cent silica reacted A = solids out flow rate corrected to force a calcium balance CPCAF2 = corrected per cent CaF£ content of solids out sample solids. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 234 ’ —-4 l\l n ■If J cr Q !U » < »■ o X — XX z UJ UJ X a > O O X in o a i- o ►—« or ft—4 3 X X »-« M o XXXXUXXXXXXXXXXXXXX xxxxxxxxxxxx Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced in'Or~coo' — PR INT 3< ! < I S A M P PRINT 4 « SPARF PRINT 5 iAC IOF IL ►— a rr J \0 a o H* ocr co 2 9 9 * — a H (2 jr h- 2 1— a a —• —•>• — •—> •— ►— •— •— 10 a 1- u < a O . u OO' CO Z Z 2 o o 9 r u J ■T u u rcr cr H IL co o J < U _1 —« _ CO j cm * - r- 9 j O .0. 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O ) + ( TCAS04* (4 0 .0 /1 3 6 ♦0 ) ) + t C ACL.4C AUSTF 3 < l/l < U ll o X 6) u < u U < 2 1- U < • — O + 2 rH o N. 1 3 \ 2 'A o j on rjs o O O 0 O 3 O ro CO 03 CO 10 CO CO D 0 - 3 3 O' 03 33 0- O -0 :D ll 1 • O L O o L '— CO OJ O ■4 — 6- 03 -H 1- u < •— IL n o D o U U3 L _J D J- II l l l • • IL cO L D L H D O -f ii l l "0 3 rv 1- O L i — rv IL L •— LU a * — o o D 3 \ ■— * 2 O 4'' 2 — l II l • Ul O * < 03 ►—4 CO o u W >—4 u w 10 J 2 _J D —L— L— J D in -s l~ L J + II l f i O i- if) i — if) o n > _J D + ll 1 • 1 rv “H L'3 o in *-» 2 w < — • — 1- i/) k-* *-1 * _l —1 .— o o ill \ CO -J _j n — LiJ 2 2 o O 2 II 1 • ry U llJ - K-* •-* CJ a oU co 2 u 7lL •7 5 o < O -u < 1- U Ul UIL IU h- D u > J O 2 _l 2 < U u O' o u « — < < V~4 < 6 o o — •L ' 'O O ' ' ' Q 0 O O ' O' O' O' O 3 O 3 £0 Q Q Q O' O' O' O' O' O' O' H M n I ' O >O O O O O 0 ' .-0O' 0 .O' O' O' O' 'O'7> O' I) O' n M H O 3 ll 1 •M *—• ■7 ■I Q 7 If) *y \ < I/) o II < O i in 4 .o cnn m n n ti II 1 a « • — • — 'y u O IL < 2 b •— o u o 1 — o: w o 3 II • (M ('J a IL PRINT 17i3 100 r“< r-H O o 10 z II • CVJ '— « o o o O o to CM o -t on ro < to a i t-t a n z OJ o a -i- i- f z — r r * r o •0 C 0 cr ft co z —4 . o H«—* pH :n X II Q L < X L* lL < 3 _ o. o co t z l — n o O o o X CO ro 3 J o \ 3 ft-» m K* X * (JL o u. 3 < 3 (- X X II • • rH l o O 1 X CO (L O lL. < L J 0 < 3 3 3 i- r O + - ii u u u u u 3 uuuuuuu hi a c cr II L _J o c L 1 u z * — IL > h- X L-J 3 LlJ 7 l LsJ 1- LlJ CO 1 CO 3 o < 7 l- z X u _J 3 < o — J < _J 0 0 0 0 l l ) I u < l z TII D a O a Ll JX —. ■o o 0 0 0 0 0 0 o •o rv) OJ rvl :vj OJ OJ OJ ■\J ■\J 0 3 t~ \ o ~ n r~ o • O' sf • -« o !J * F U- in tV 3' *^C • II a o o •/) ♦ >!< o o LiJ o o »—1 Ll \ o • r- • *!< a 00 o Ul o o c r o Z • < • o ^-N rv U l i 4 o o ro fH 2 ; :~J z M Ul + o “h sj: 3 c f f z L— FI \ ►—t >-« o z o >-< o 1- tO U1 n ‘ • — «• cr •— O • < CO z U) - c r • o .J 3 j- 7 a 7a w O' iu o o *-* < o r~ • ■fl N x > o r“H CO Ul — i 3 \ z O u _ j o ■j j z n* \ a 3 C/ 4 w 3 z Ll o F-» w 3 3 • Z \ —« — 1 * 3 z o r 3 3 ro ro *-• _I J c r IL Ul CVI < 3 O' 0\ T'' z *—> —« a 1— •3 CVJ Ll . 3 11 * Q O *— •— U l l O 3 z IL j -4 v0 * • ••1 —ii 1 '•5 3 cj < •J O 0 CO 3 ro 3 -t- h - 3 3 -r u 00 CL 2 o < 1 U l 3 F \\ 1 W J— •—< O' < Ci< II ■v h- o to a z H 3 o x c r r r IV 2 X < CO • O o F 3 U l + 3 -1 3 3 3 3 3 U 3 u 3 u Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 242 OJ - CM 0 ■tf r—4 M 0 CM 0 OJ CO ;\1 ■ 1 1 | 1 1 t I 1 i 1 1 I 1 1 1 1 i I 1 1 1 1 1 1 1 1 1 i 1 1 1 1 I O ' o T—1 CM ro .n to Is- r~ ro CO CO CO dv O' •O' o o o o •-H ^ AJ CM ro n n . 0 :0 ro to : 0 . 0 ro (0 ! 0 0 CO ro sT sT sf- <}• sT r-H r-H r—4r“ 4 ih rH r—4 r—4 r—4 r—4 r—4 r—4 r-H -■ r—4 4—4 r-H r-H • X 3 3 3 O •- IU y JO 3 \O 4-4 3 r—4 X #> XO Is- O (?) 3 •> r-H 0 s H 4— \X •* 3 ♦ H ;7 r-« 3 —4 1— o X X m I IU 3 X \ 1- 3 < • X 10 H- • 3 3 r-H 0 s < X CO 4- !|J r 4-4 r—r 4— 1 3 \ 3 X 1- O' (?) X 2 ) J •—« 3 3 a a 3 IJ 3 o . X LU 3 3 •■5 < 3 a 4—4 'V vO a © 3 ^ ) X 44- 0j tO 3 a in tO 3 ro XX D’J 4-4 3 X » a » • a to o 3 o X X X a CO X 3 r :n r-4 - •> 3 ■O' O o h- a » o o X r r-H X < z • XXX *—« 3 co (?) r—4 o 4—4 3 0 X 4— o n u j 3 ■7 3 's i r—44-4 #- r—4 0 X * ►h XX X 3) IL < 3 O '•> r- 3 X #» a 3 #• »• 3 XI :u © X 4—4 X 3 o r Is- O » ■3 ■x & a . 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Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced 14 FORMAT( 1 HO, 1UX*@ND SOLIDS OUT CORRECTION FOR SULFATE BALANCE®) 143 15 FORMA T ( 1 HO » 1 j X »©ERROR IN SULFATE BALANCE = @r F 1 1 r 5 » t? < 1 4 4 16 FORMAT! 1 HO, 1 OX»©PER CENT ACID REACTED = @»F1 1.5/1H »1 OX. 14b • 4 ~ < L C) X uJ i r- X r—4 a LU j o < o l—J . i i o < : a LU r—Hr—H sT J a 3 UJ X 1 2 .u ,—4 i P u X 10 X Z u X) CVJ 10 D. UJ F —rto r 1— i P u u UUJ LU r—H — <$> II 1 «. r r-H ! ■T * r u L ■— 4-4 < ■i *-4 X >" X 3 to . a (9 _J tO F 1— rH o X —4 TF •T L V V D 3 CO < r-4 r-H J v> t 2 X to X h— X 7 J - > J r-4 to 0 O J _J 7> l l r J J 1 ♦ r - 4—* '4 X i 3 rs -"■r 'U sT o -■ o r—4 a X X in • CO ■o o 10 X ■ cvj L —« a X i P 0 jo ll l l • o Lto tL —< X F o t.0 < a < o X to — X r-H 4-4 o O :u - I 19 (J t.0 to 2 u '•T X < D F O 2 L 4-4 J h* < X w> — r-H r—4 3 J -T (0 F < F -« X F O 2 o 2 Ir HI 3 n r—4 LO IL r—4 pH a — 1 » * i 613 FORMAT ( 1 HO « 1 OX » 5>AA VALUE ACCOUNT I MG FOR CALC I TE AND ACID F U M IN G Preweighed plastic bottle with 100c.c or 150c.c. of NaOH s o l u t i o n I Q u e n c h i ng <- S a m p ! e ▼ Wei ghi ng V Soli ds Fi 1 teri ng Liquor ▼ Washed with V o l u m e d i s t i l l e d n o t e d w a t e r I Dri ed at 110°C Analysed for S07 + + ▼ and Ca wei ghed At A1can Works L a b o r a t o r y Analysed for CaF2> CaSO^,:aS0 C a C O ^ SiO 2 ’ and S i 0 o i______2_ FIGURE AIV.1 Initial Solids Out Samples Handling S c h e m e Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Preweighed plastic 2 46 bottle with 500c.c. of NaOH solution ;• Quenchin c P ng 1 Wei ghgh i ng i Solids crushed in b o t t l e r • L i q u o r S o l i d s Fi1trati on V Washing with V o l u m e d i s t i l l e d n o t e d w a t e r V Wei gh i ng Analysed for SO. j a n dj ^ Cr a ++ j l 1 D r y i n g at 9 0 ° C Wei ghi ng v D r y i n g at At Alcan Works 2 0 0 ° C L a b o r a t o r y Wei ghi ng ______{Analysed for CaF 2, C a S O ^ , j C a C 0 3 , Si 02 and R2^3 FIGURE AIV.2; Modified Solids Out Samples Handling S c h e m e Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ro -r=- the sample. s am ple. reactor in the solids out. reactor in the solids out.t To determine the amount of soluble CaSO. in the in the solids out.in the solids out. To calculate the amountTo of determine impurities the'total leaving amount the’ of soluble SOT in CaCOo due and to the this amount To transformation. calculate of SOT the in amount the of sample silica liquor leaving the To calculate theTo amount calculate of CaSO, the amount leaving of_CaS0, the reactor transformed to To calculate the amount of CaF? leaving the reactor 2 % R 2°3 %S i 0 ^ 0 i %S % C a C 0 3 %CaF %CaF % C a S 0 4 Constituent Purpose S 0 4 (g./l.) Ca++(g./l.) out s a m p l e S a m p l e Solids TABLE AIV.l; Utility of Sample Analysis Sample of AIV.l; Utility TABLE solids out s a m p l e L i q u o r of of s olids descrion pti Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 8trS P u r p o s e 1 i qu 1 o i r . qu 1 o i r . To determine the amount of fluorine in the sludge To determine the amount of silica in the sludge the scrubber. To determine the amount of H2S04 in the sludge. s c r u b b e r . reactor into the scrubber. To calculate the amount of SiF,To entering determine the the amount of Si02 in the sludge solids. To calculate the amount of H^SO, vaporTo determine entering the amount of CaSO^ in the sludge. To calculate the amount of fluorine leaving the . « S i 0 2 % C a S 0 4 F " ( g . / g . ) S0~(g./g.) Si02(g./g.) F'C g . / l . ) SO^g./l-.) Si02(g./1.) Constituent 1 i quo r1 i S a m p l e s a m p l e s 1 udge 1 s s i u d g e s a m p l e e f f 1 u e n t S c r u b b e r TABLE AIV.l; AIV.l; Continued TABLE liq u i d of S o l i d s of descrion pti Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. >■— ro vo so; l i q u o r 2 4 . 94 3 8 . 3 5 ' content of 9 3 . 9 2 3 8 . 3 8 9 4 . 3 0 sol id s % C a S 0 ^ in Expected values 5.70 6.58 11.67 8 8. 3 0 sol id s % C a F £ in • soj soj l i q u o r 25.50 3 8 . 9 4 3 8 . 1 7 content of 9 3 . 0 0 9 5 . 3 5 s ol id s % C a S 0 ^ in Reported values 5.34 6.17 s olids % C a F 2 in TABLE AIV.2. Analysis of Synthetic Samples 12 11.66 95.75 3 s a m p l e Syntheti c Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE AIV.3. Results.of Solids Out Sample 250 Analysis S a m p l e Wht. of Wht. of sample V o l u m e N o . s a m p l e solids after of l i q u o r t a k e n d r y i n g at (calculated) (g •) 200'°c‘ (g.) c c . 1 1 A - 1 4 8 1 . 3 2 59. 54 4 9 8 . 4 11A-15 93.78 7 0 . 7 7 4 9 8 . 2 1 1 A - 1 6 84.80 62.78- 497.7 1 1 A - 1 7 9 5 . 1 1 79 . 21 4 9 6 . 8 11A-18 92.47 7 0 . 3 5 4 9 6 . 9 11A-19 95.84 7 4 . 0 6 4 9 6 . 9 1 2 A - 1 4 77.58 60 .74 4 9 9 . 3 12A-15 92.86 7 4. 36 499 .3 1 2 A - 1 6 86.91 68.60 499 .3 1 2 A - 17 8 2 . 1 1 65. 20 499 .6 1 2 A - 1 8 82. 26 64.52 499.5 1 2 A - 1 9 82.70 65.17 499 .4 1 3 A - 1 6 76 .81 5.6.04 4 9 8 . 3 1 3 A - 17 83.62 61.50 497.3 13A-18 90.27 67 .39 4 9 4 . 9 1 3 A - 1 9 8 0 . 1 5 5 9 . 2 8 4 9 8 . 0 13A-20 81.83 6 0 . 2 0 4 9 5 . 3 13A-21 85. 24 64.02 493.4 1 4 A - 1 6 7 0 . 1 0 5 0. 94 4 9 7 . 6 14A-17 87.37 67 .04 4 9 4 . 3 14A-18 87 .93 67 .88 4 9 5 . 1 1 4 A - 1 9 9 1 . 1 2 7 0 . 6 1 4 9 9 . 2 14A-20 83.00 6 2 . 8 2 4 9 9 . 2 14A-21 89 .40 68.56 497.6 ' 1 5 A - 1 6 89 .70 72.21 497 .0 1 5 A - 1 7 83.54 68.98 497.7 1 5 A - 1 8 7 6 . 5 0 59 .65 497 .6 1 5 A - 1 9 9 0 . 0 8 72.67 4 9 8 . 7 1 5 A - 2 0 80 . 28 6 3 . 3 6 4 9 9 .3 1 5 A - 2 1 82. 21 '65.10 4 9 8 . 4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 251 TABLE AIV.3; Contd. S a m p l e l i q u o r .solids analysis N o . a n a l y s i s (g./i . ) • (g./i . ) „ ++ so; Ca C a F 2 C a S O ^ C a C O g Si 02 R 2°3 Total 1 1 A - 1 4 41 .76 0 .46 22 .1 70 .98 1. 51 0 .72 0 . 3 7 95 .68 1 1 A - 1 5 44 .17 0.48 20.9 78.10 1. 04 0 .77 0 . 3 2 101 .13 1 1 A - 1 6 41 .71 0 .46 18 .5 7 7 . 4 0 1. 51 0 .75 0 . 4 0 98 16 1 1 A - 1 7 45 .09 0 .46 17 .5 7 8 . 5 7 0. 90 0 .75 0 . 2 8 98 00 1 1 A - 1 8 42 .68 0 .46 20 .2 7 5 . 1 8 0 .99 0 .77 0 . 2 9 97 53 11A-19 43.61 0 .46 18 2 7 5 . 5 3 1.75 0.76 0.26 96 50 1 2 A - 1 4 23 .79 0 .32 9 1 NA 1. 40 0 .83 NA 1 2 A - 1 5 29 .40 0 .51 9 .8 NA 2. 18 0 .76 NA 1 2 A - 1 6 26 .20 0 47 10 4 NA 1. 04 0 .82 NA 1 2 A - 1 7 26 .30 0 45 10 3 NA 1. 04 0 .83 NA 1 2 A - 1 8 20 .85 0 43 8 9 NA 1. 32 0 .79 NA 1 2 A - 1 9 21 .13 0 38 7 8 NA 1. 00 0 .94 NA 1 3 A - 1 6 26 .34 0 47 15 2 7 9 . 97 0. 94 1 00 NA 97 11 1 3 A - 1 7 30 .82 0 42 17 0 83.82 0.94 0 79 NA 102 55 1 3 A - 1 8 • 15 .23 0 41 16 3 8 3 . 47 0. 76 0 78 NA 101 31 1 3 A - 1 9 24 . 13 0 38 16 4 79 .62 0. 94 0 79 NA 97 74 1 3 A - 2 0 22 . 18 0 44 15 6 8 2 . 4 2 2. 54 0 84 NA 101 4 1 3 A - 2 1 25 .74 0 37 16 4 8 1 . 0 2 0. 76 0 79 NA 98. 97 1 4 A - 1 6 19 .64 0 37 21 3 NA 1. 04 0 92 NA 14A-17 17.04 0 50 21 7 7 1 . 6 8 0. 94 0 80 NA 95. 12 1 4 A - 1 8 28 .87 0 44 19 8 74.01 0.94 0 72 NA 95. 47 1 4 A - 1 9 21 .29 0 34 18. 5 NA 0- 76 0 92 NA 1 4 A - 2 0 21 . 26 0. 40 19 5 NA 0. 94 0 78 NA 1 4 A - 2 1 22 .81 0. 44 18. 2 76 .46 0. 84 0 75 NA 96. 25 1 5 A - 1 6 17 .60 0 44 12. 8 NA 0. 94 0 82 NA 1 5 A - 17 16 .01 0 41 13. 8 NA 0. 84 0. 81 NA 1 5 A - 1 8 13 .74 0. 38 14. 4 NA 0. 94 0. 84 NA 1 5 A - 1 9 13 .28 0 43 11 8 NA 0. 66 0. 81 NA 15A-20 11.54 0. 39 13. 2 NA 0. 84 0. 82 NA 1 5 A - 2 1 19 .31 0. 36 12. 3 NA 0. 84 0. 78 NA Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 252 TABLE AIV.4; Scrubber Liquor Samples Analysis S a m pl e Liquor Analysis No. (g./i.) • F"(Average S0 = S i 0 2 of all rep!i cates) 1 1 A - 1 4 2.46 0 . 1 0 0 .04 1 1 A - 1 5 2.41 0 . 0 8 0 . 0 5 1 1 A - 1 6 2.76 0 . 1 2 0 . 0 7 1 1 A - 1 7 2.79 0 . 1 2 0 . 0 7 1 1 A - 1 8 . 2.79 0.. 11 0 . 0 5 1 1 A - 1 9 2.76 0 . 1 1 0 . 0 7 1 2 A - 1 4 2.61 0 . 1 7 0 . 0 2 1 2 A - 1 5 2.58 0 . 1 6 0 . 0 2 1 2 A - 1 6 2.62 0 .15 0 . 0 2 1 2 A - 1 7 2.62. 0 . 1 5 0 . 0 2 1 2 A - 1 8 2.64 0 . 1 6 0 . 0 2 1 2 A - 1 9 2.66 0 .17 0 . 0 2 1 3 A - 1 6 2.46 0 . 0 8 0 . 0 2 1 3 A - 1 7 2.4 8 0 . 0 8 0 . 0 5 1 3 A - 1 8 2.44 0 . 0 8 0 . 0 2 1 3 A - 1 9 2.50 0 . 0 7 0 .04 1 3 A - 2 0 2.50 0 . 0 9 0 . 0 3 1 3 A - 2 1 2.46. 0 . 0 8 0 . 0 3 1 4 A - 1 6 2.26 0 . 0 6 0 . 0 5 1 4 A - 1 7 2.32 0 . 0 1 0 . 1 1 1 4 A - 1 8 2. 22 0 . 0 7 0 . 0 5 1 4 A - 1 9 2.28 0 .07 0 . 0 9 1 4 A - 2 0 2.34 0 . 0 7 0 . 1 2 1 4 A - 2 1 2.24 0 .07 0 . 1 2 1 5 A - 1 6 2.40 0 . 1 6 0.02. 1 5 A - 1 7 2.55 0 . 1 7 0 . 0 4 1 5 A - 1 8 2.00 0 . 1 7 0 . 0 3 1 5 A - 1 9 2.50 0 . 1 3 0.04. 1 5 A - 2 0 2.35 0 . 1 6 0 . 0 4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE AIV.4. Contd. S a m p l e Li qu o r ' An a l y s is N o . ( g./i.) F” (Average S 0 = Si 09 o f all repli cates) 1 5 A - 2 1 2 . 3 5 0 . 1 6 0 . 0 4 1 6 A - 1 6 2.55 0.28 0.04 1 6 A - 1 7 2 . 3 0 0 . 2 7 0 . 0 5 1 6 A - 1 8 2 . 7 0 0 . 2 7 0 . 0 3 1 6 A - 1 9 2 . 6 5 0 . 2 3 0 . 0 5 « 1 6 A - 2 0 2 . 6 0 0 . 2 2 0 . 0 4 16A-21 2.30 0.29 0 . 0 5 1 7 A - 16 2 . 5 7 0 . 3 2 0 . 0 8 1 7 A - 1 7 2.70 0.36 0.11 1 7 A - 1 8 2 . 8 2 0 . 3 4 0 . 0 7 17A-19 2.87 0.33 0.11 1 7 A - 2 0 2 . 8 2 0 . 3 2 0 . 0 9 1 7 A - 2 1 2 . 6 7 0 . 3 2 0 . 1 1 1 8 A - 1 6 2 . 4 5 0 . 1 7 0 . 0 4 1 8 A - 1 7 2 . 9 8 0 . 2 2 0 . 0 5 1 8 A - 1 8 2 . 7 6 0 . 2 2 0 . 0 4 18A-19 2.52 0.18 0.05 1 8 A - 2 0 2 . 7 0 0 . 2 0 0 . 0 4 1 8 A - 2 1 2 . 6 2 0 . 2 0 0 . 0 5 1 9 A - 1 6 2 . 6 8 0 . 3 2 0 . 0 1 8 1 9 A - 1 7 2 . 4 8 0 . 2 6 0 . 0 1 8 1 9 A - 1 8 2 . 5 0 0 . 2 6 0 . 0 1 8 1 9 A - 1 9 2 . 4 7 0. 26 0 . 0 1 9 19A-20 2.62 0.24 0 .0 1 8 1 9 A - 2 1 2 . 6 4 0 . 2 7 0 . 0 1 8 IF- 16 2.54 0.18 0.021 IF- 17 2 . 6 8 0 . 1 9 0 . 0 2 0 IF- 18 2 . 5 9 5 0. 20 0 . 0 2 0 IF- 19 2 . 5 7 0 . 1 9 0 . 0 1 9 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE AIV.4. Contd. S a m p l e Liquor Analysis N o . : ( g . / i . ) F"(Average so I S i 0 2 o f all repli cates) 1 F - 2 0 2 . 7 2 0 . 2 1 0 . 0 1 9 I F - 21 2 . 7 0 0 . 2 0 0 .019 2 F - 1 6 2 . 6 5 0 . 2 2 0 . 0 1 8 2 F - 1 7 2 . 7 5 0 . 2 5 0 . 0 1 9 2 F - 1 8 2 . 8 0 0 . 2 6 0 . 0 2 0 2 F - 1 9 2 . 8 5 0 . 2 5 0 . 0 2 1 2 F - 2 0 2 . 8 6 0 . 2 7 0 .021 2 F - 2 1 • 2 . 6 9 0 . 2 2 0 . 0 2 0 3 F - 1 6 2 . 7 1 0 . 3 0 0 . 0 1 9 3 F - 1 7 2 . 7 5 0 . 3 0 0 . 0 1 9 3 F - 1 8 2 . 7 0 0 . 2 9 0 . 0 1 9 3 F - 1 9 2 . 7 4 0 . 2 8 0 . 0 1 9 3 F - 2 0 2 . 7 2 0 . 2 7 0 . 0 1 9 3 F - 2 1 2 . 6 9 0 . 2 8 0 . 0 2 0 4 F - 1 6 2 . 6 1 0 . 1 7 0 . 0 2 0 4 F - 1 7 2 . 7 4 0 .19 0 . 0 2 0 4 F - 1 8 2 . 6 4 0 . 1 7 0 . 0 1 9 4 F - 1 9 2 . 6 2 0 . 1 7 0 . 0 1 9 4 F - 2 0 2 . 6 8 0 . 1 7 0 .020 4 F - 2 1 2 . 8 2 0 . 1 9 0 . 0 2 1 5 F - 1 6 2 . 8 0 0 . 2 4 0 . 0 2 0 5 F - 1 7 2 . 7 4 0 . 2 4 0 . 0 2 0 5 F - 1 8 2 . 8 4 0 . 2 3 0 . 0 2 0 5 F - 1 9 2 . 7 1 0 . 2 4 0 . 0 2 0 5 F - 2 0 2 . 7 8 0 . 2 3 0 . 0 2 0 5 F - 2 1 2 . 8 4 0 . 2 4 0 . 0 2 0 6 F - 1 6 2 . 6 8 0 . 1 8 0 . 0 2 1 6 F - 1 7 2 . 7 6 0 . 1 8 0 . 0 2 1 6 F - 1 8 2 . 7 2 0 . 1 8 0 . 0 20 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 255 TABLE AIV . 4 . Contd. S a m p l e Liquor Analysis No. ( g/1 •) F~(Average S 0 4 S i 0 g o f al 1 repli cates) 6 F - 1 9 2 . 7 1 0 . 1 8 0 . 0 2 0 6 F - 2 0 2 . 7 6 0 . 1 9 0 . 0 2 1 6 F - 2 1 2 . 7 1 0 . 1 8 0 . 0 2 1 7 F - 1 6 2 . 6 2 0 . 2 3 0 . 0 1 8 7 F -17 2 . 7 8 0 . 2 7 0 . 0 1 9 7 F - 1 8 2 . 7 2 0 . 2 6 0 . 0 1 8 . 7F-19 2.72 0 . 2 5 0 . 0 1 9 7F-20 • 2.69 0 . 2 4 0 . 0 1 9 7 F - 2 1 2 . 5 8 0 . 2 3 0 . 0 1 9 8 F - 1 6 2 . 6 7 0 . 1 2 0 . 0 2 0 8 F - 1 7 2 . 7 1 0 . 1 3 0 . 0 2 0 8 F - 1 8 2 . 7 4 0 .11 0 . 0 2 1 8 F - 1 9 2 . 7 8 0 . 1 4 0 . 0 2 1 8 F - 2 0 2 . 8 0 0 . 1 4 0 . 0 2 1 8 F - 2 1 2 . 8 0 0 . 1 3 0 . 0 2 2 9 F - 1 6 2 . 6 7 0 . 2 2 0 . 0 2 1 9 F - 1 7 2 . 6 6 0 .19 0 . 0 2 0 9 F - 1 8 2 . 6 3 0 . 1 7 0 . 0 2 1 9 F - 1 9 2 . 6 1 0 . 1 5 0 . 0 2 0 9 F - 2 0 2. 53 0 . 1 8 0 . 0 2 0 9 F - 2 1 2 . 6 9 0 . 1 9 0 . 0 2 1 1 0 F - 1 6 2 . 6 6 0 . 3 0 0 . 0 1 9 1 0 F - 1 7 2 . 6 2 0 . 3 5 0 . 0 1 9 1 0 F - 1 8 2 . 6 4 0 . 2 9 0 . 0 1 8 10 F- 19 2 . 6 3 0 . 3 1 0 . 0 1 9 1 0 F - 2 0 2 . 6 9 0 . 4 2 0 . 0 1 8 10 F — 21 2 . 6 1 0 . 3 2 0 . 0 1 8 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Ch S i 0 2 1 . 0 6 4 0 . 0 0 2 4 5 0 . 3 1 4 0 . 0 0 . 0 0 . 4 6 7 0 . 1 3 8 0 . 3 0 1 0 . 6 9 4 (%) Solids Portion C a S 0 4 9 4 . 7 0 9 9 . 0 • S i 0 g 0 i S • 0 . 0 0 0 1 6 0.00637 93,51 0.00051 99.73 0.00062 54.74 0.000670.00043 99.0 82.50 0.00025 99.0 0 . 0 0 0 0 5 F" 0 . 0 0 3 7 0 0 . 0 0 2 9 1 0 . 0 0 3 7 3 0.0038 0.00031 99.0 0 . 0 0 0 5 4 0 . 0 0 5 1 6 Liquid Portion (g7g. of Liquid) 0 . 9 4 9 1 7 0 . 9 6 6 6 5 0 . 7 3 4 4 0.8763 0.00482 0 . 8 8 7 0 0 . 8 8 5 1 so4= In S I u d g e F r a c ton i Li qui d quid Li 0 . 7 5 2 9 8 0.73836 0.97726 0.00176 0.94848 0.91692 0.00310 0.97150 . 9 3 8 2 0.8252 In S l u d g e F r a c t i o n Solids 0.02615 0.9738 0 . 2 6 1 4 0.07146 0.92853 0 . 0 5 1 5 0.1060 0.8940 0 . 0 2 8 5 0 0 . 0 6 1 7 7 0.0528 0.9472 2F 3F 5F7F 0 . 2 4 7 0 R un N o » 10F 1 9A 16A 17A 1 8A TABLE AIV.5; Analysis AIV.5; Sludge TABLE Gas Line Transfer Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 257 TABLE AIV.6, Si0^ Content Of Solids^Of Solids Out Sample Where Only The Scrubber Effluent Analysis Was Done S a m p l e %S i 0 2 Sample % S i 0 2 S a m p l e % S i 0 g No . N o . No - 1 6 A - 1 6 0 . 1 2 1 9 A - 1 9 . 0.86 4F-16 0 . 7 7 1 6 A- 17 0 . 2 0 1 9 A - 2 0 0 . 8 4 4 F - 1 7 0 .69 1 6 A - 1 8 0 . 4 4 19 A — 21 0 . 8 5 4 F - 1 8 0 . 6 7 1 6 A - 1 9 0 . 2 4 1 F — 16 0 .79 4 F - 1 9 0 . 7 1 1 6 A - 2 0 0 . 1 5 1 F - 1 7 0 . 7 9 4 F - 2 0 0 . 7 2 1 6 A - 2 1 0 . 4 1 1 F — 18 0 . 7 8 4 F - 2 1 0 . 7 1 1 7 A - 1 6 0 . 8 0 1 F — 19 0 .83 5 F -1 6 0 . 7 9 1 7 A - 1 7 0 .79 1 F - 20 0 . 7 9 5 F - 1 7 0 .80 1 7 A - 1 8 0 . 8 0 1 F — 21 0 . 7 7 5 F - 1 8 0 .79 1 7 A - 1 9 0 .78 2F-16 0.78 5 F - 1 9 0 .80 1 7 A - 2 0 0 . 8 1 2 F - 1 7 0 . 8 0 5 F - 2 0 0 .79 1 7 A - 2 1 0 .80 2 F - 1 8 0.7.6 5 F - 2 1 0 .81 18A-16 0.91 2F-19 0 .76 6F-16 0 . 7 7 1 8 A - 1 7 0 . 7 6 .2F-20 0 .75 6F-17 0 .76 1 8 A - 1 8 0.70 2F-21 0.75 6F-18 0 .77 1 8 A - 1 9 0 .79 3 F - 1 6 0 . 7 7 6 F - 1 9 0 .78 1 8 A - 2 0 0 . 7 6 3 F - 1 7 0 . 7 7 6 F - 2 0 0 .76 1 8 A - 2 1 0 . 7 8 3 F - 1 8 0 .76 6 F - 2 1 0 .76 19A-16 0.83 3F-19 0 . 7 5 7 F - 1 6 0 .76 1 9 A - 1 7 0 . 8 9 3 F - 2 0 0 . 7 5 7 F - 1 7 0 .76 1 9 A - 1 8 0 . 8 8 3 F - 2 1 0 . 7 6 7 F - 1 8 0 .76 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 258 TABLE AIV.6, Contd. S a m p l e % S i 0 2 S a m p l e % S i 0 2 No. N o . 7 F - 1 9 0 . 7 5 9 F - 1 8 0 . 7 8 7 F - 2 0 0 . 7 6 9 F - 1 9 0 . 7 8 7 F - 2 1 0 . 7 5 9 F - 2 0 0 . 7 6 8 F - 1 6 0 . 7 3 9 F - 2 1 0 . 7 9 8 F - 1 7 0 . 7 5 1 0 F - 1 6 0 . 7 8 8 F - 18 0 . 7 3 1 0 F - 1 7 0 . 8 1 8 F - 1 9 0 . 7 4 1 0 F - 1 8 0 . 8 0 8 F - 2 0 0 . 7 6 1 0 F - 1 9 0 . 8 0 8 F - 2 1 0 . 7 4 1 0 F - 2 0 0 . 7 8 9 F - 1 6 0 . 7 6 1 0 F - 2 1 0 . 8 1 9 F - 1 7 0 . 7 5 4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 259 1 .0 9 2 . 6 9 0 . 7 5 4 . 2 9 0 . 6 9 - 1 . 2 2 - 3 . 3 6 - 0 . 3 2 - 2 . 9 3 F I u o rna i Balances (a) 2 . 1 1 2 . 4 4 (%) 3 . 5 7 - 1 . 6 4 - 5 . 1 3 - 4 . 0 5 - 5 . 0 4 Sul faSul t e in M a s s E r r o r * - 2 . 3 6 - 4 . 9 4 - 4 . 1 3 - 5 . 2 5 2 . 6 9 - 8 . 5 2 - 0 . 6 0 -10.31 -3.18 -10.86 -0.97 0.16 C a l curn i 5 . 9 8 6 . 8 5 1 3 . 6 4 7 . 5 4 2 2 . 2 1 1 9 . 4 62 2 . 0 4 - 3 . 9 4 2 0 . 0 3 - 6 . 2 1 2 0 . 1 9 S i 0 2 (b) 4 (%) s o 2 7 7 . 5 6 8 0 . 4 2 7 5 . 8 7 7 7 . 0 9 6 5 . 0 7 6 6 . 5 4 h 6 3 . 8 066.09 64.92 2 3 . 1 0 6 5 . 6 1 62.42 27.25 -12.02 Conversions 8 5 . 4 7 7 1 . 6 2 85.638 4 . 5 8 8 3 . 4 9 83.83 76.2387.29 75.73 80.04 5.31 5.90 -5.57 neq. 3.59 -3.73 -1.37- 3.22 C a F g 7 4 . 8 7 7 0 . 7 5 7 3 . 5 4 ‘ 7 1 . 5 4 Solids Out Flow Correction Flow Out Solids Analysis Assuming CaCOg Formation During No During Filtration; Formation CaCOg Assuming Analysis 19 17 15 14 16 18 17 19 18 16 1415 6 9 . 0 9 6 9 . 9 5 N o . S a m p l e Average 85.06 A v e r a q e 12A 11A R u n No. TABLE AIV.7 Mass Balances and Conversions Using the Reported Solids Out Solids Reported the Using Conversions and AIV.7 Balances TABLE Mass (b) neg. indicates more SiOgleaving in solids than entered in spar. (a) A negative sign indicates accumulation. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. * ■ a> £T •r* r H o CO CMCM r-> to CM CD O CMCM to S- CO CM r H CO CO * o CO o O r H CD o ••••••••• ••• a 3 r-H L O LO CO CO f—H o CO CM c r— 1 fd Ll. p— fd CO cu to + J CM r-H L O C M *3* o C M r H S- o £E S- 3 «d* CM LO t o r-H <3 * r^. CD CO CO s- •i— LO CO to r-H to o to r ^ t-H CDCO t o LlJ O ••«•••••*••* r— o CO <=3- COCO LO CO <3 - o fd 1 r-H 1 o CD r-*. CO r H CM C D r—1 C D CO CDCD cr> CD CO r H o CD • CD • to c o •r— to ■s CO CO t o «=J* r H CO LO o rv. 00 r H LOCM r-H t o CO CM CD t o CO o o LO CO t— 1 to LO LO CO LO to H c d 0 0 r H CM <3- Ll . •♦•••••••••••• fd LO CM o CM CO CMCM LO CO CO a \ 0 0 o CO - o r*-. c «=c CO 3 o r H c c z : i-H Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. * CD c • r * t o r ^ . CMLOCO t o S- LO CO r H LO t o r H CD o •••••• o 3 « s f p H CM <3* pH c : r — 1 p H 1 1 f d U. t r— f d 0 0 CD t o -f-> p H t-H o CO o CO t o fd pH CM o CT> t-H CO f d ___ ’ M- •••••• s : r — f —1 CM CO c-H CO r-H 3 1 1 1 1 £= 00 •r— S- o E s - 3 LO to LO CO S- •p~ CO <=3* CO CM LO CM LUO ••••• r— o O r H p H CM CO rd 1 1 o o o LO <=d- r H to O J cr> r - s LO t-H r ^ . cr> o • •••••• •r— CO o CM pH o CO 00 pH (/) c . o •1“ t o CT> O 't r H r-* . CO CO CM s - o CM *=3* CM r H CM p H CD _ ' 00 ••*•••• > CM •sd* <=3* LO CO CO O'! LO c n r COCO CO 0 0 CO CO o o CM CO <5j- o t-H to CM CM LO <3* CO CO LO 0 0 Ul. •••••• • fd cn t o o o o o i>. 0 0 CO r^. CD r— CD Q_ • cr> £ o fd c • < 3 o in Z i-H Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 262 ■ 6 . 4 5 1 4 . 7 1 1 4 . 0 0 1 5 . 1 4 1 4 . 4 8 3 7 . 0 8 3 1 . 2 6 2 8 . 6 3 4 8 . 6 8 1 4 . 4 6 4 3 . 6 1 4 4 . 8 0 Si 1i ca 1i Si (%) 1 .5 6 0 . 3 3 0 . 7 5 0 . 4 1 4 .63 4 - 3 . 7 6 - 1 . 5 6 - 0 . 8 6 - 1 . 2 9 t F I u o rne i Error in Mass Balances (a) - 4 . 6 9 - 5 . 0 9- 7 . 3 7 - 8 . 8 5 5 . 5 2 - 1 . 8 7 - 8 . 2 2 - 9 . 9 9 - 7 . 9 7 2 . 8 6 neg. - 6 . 7 3 8 . 3 6 - 7 . 7 3 16 .6216 1 9 . 9 6 1 7 . 5 7 2 3 . 3 9 - 7 . 3 5 2 2 . 6 3 Si02 (b) Ca1cium .18.69 -4.64 4 (%) s o 2 7 8 . 1 5 7 6 . 3 1 7 6 . 6 4 6 3 . 5 9 6 4 . 7 3 2 1 . 4 4 6 4 . 7 1 1 6 . 0 6 h Conversions 8 5 . 4 7 83.83 77.52 7.39 -6.12 8 4 . 2 5 85.82 80.84 9.07 86.12 76.99 8.59 7 2 . 6 7 6 5 . 4 8 7 0 . 8 48 5 . 1 1 6 4 . 0 8 7 1 . 3 7 6 9 . 5 1 6 7 . 4 5 6 0 . 4 8 C a F 2 6 9 . 4 4 6 5 . 0 5 ■ 7■ 4 . 6 2 Solids Out Flow Rate Corrected to Force a Sulfate Balance Sulfate a Force to Corrected Rate Flow Out Solids Analysis Assuming CaCOg Formation During Filtration; During Formation CaCOg Assuming Analysis No. 17 15 18 19. 87.69 80.60 18 14 16 14 16 17 15 S a m p l e .19 A v e r a g e A v e r a g e 12A 11A R un No. TABLE AIV.8 Mass Balances and Conversions Using Reported Solids Out Solids Reported Using Conversions and Balances AIV.8 Mass TABLE (b) neg. indicates more Si02 leaving in solids than entered in spar. (a) A negative sign indicates accumulation. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. - fd p « LOCO COCO c n rH H r H CD LO o 0 0 o CO 0 0 c o CO CM P O rH CM <0 -I— •••••• * ••••• CD r— LO CO r H LOCOCO CD c o c n CD O O • r— E o 3 LO LOLO CM c n CD CO P o CD LO r H • r cn CM COCD r-H LO COCOLO P s*. U • •••♦• ***••• LU r— CO 'd - CM C h r-H cn CO o r H P p . LO rd CM x— 1 CM o t-H rH CD PLO to £o • *f— to ,- - LO CO LO p CO P O o LO co CTi CO CM r-H CO 0 0 CO CO o c o c n rH O r H CM cn LO p p o LO CO r H LOLO CO P CO LU •• -« ••••••••••• rd CO CM CO o CM r H T—1 'd * 0 0 p CO p . CO P o p - p CD p p p p CD LO c o LOLO LOLO QJ r — CD CD O. • CDCD £ o CO p CO cn o rH to CD p 0 0 CDO r H fd 03 z z r H r H r-H r H CM CM s - rH r H r H r H CM CM $ *. CO QJ CD > > c < <=£ c • CO Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced TABLE AIV.8 Continued i— •r— s CD CO r • LU o r— i Q CO c O•p“ CO o - S - s e U OS-C CO CO O - S - r • CO CO fd s a CD e S-. CO CO fd c o > Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced TABLE AIV.9 Continued j ) j/ • c c 00 o •r— •r— LxJ — r CO zs c id £ - Q TABLE AIV.9 Continued r~“ r ' •r* O C r— 0 LU S c/> oc td c O Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced TABLE AIV.10 Continued r— •r— LU CO S O ■r— OO z s - S CO 0 z s CO - S f t r f t r 0 S-. sz f t r to CO < CO M*3 Or^. ^ r CO *=3" CM > CD 0 L C TABLE AIV.10 Continued .#r- •i— r*" - r U L s: o O C C D O O CD (/) (O c c Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced TABLE AIV.11 Continued • o r— 'r- CO r— LxJ : s •r— CO to o c s~ to - Q ) 0 C > CD o o t c 3 c CO CO TABLE AIV.ll Continued •i— r-* O 0 0 •r— a U L r— Q C o 3 c rtf £ - O c r £ O QJ S- O CO £ £ £ z _ o • ^ 0 0 O M C O •i— O O O O »r— LU r— i 0 0 r—* n ♦ - 4 ■ i— •r- CO 4-> rtf 3 rtf 3 £ a rtf cu rtf M C M C M C H r O C O C •'tf* n c o c o O o 0 0 ^ r ^ r 1 f— O H r n c n r O L O o o o H r H r H r • * • • • • • • « • • • • • • • • • • • • • • • • • • • • • • • • • • • • • « • • • # • • • • » • • • H r H r H r o o cn O C 0 0 O L O C O M C O C O C M C O C H r o o O C O C • M C O L M C O L cn n c O L M C M C O L O L n c ■ H r H r CD LO O 0 0 O L • # n c o «tf* H r o O C M C M C O C O C O C O C O C O C H r o o o O C *tf* O C O C O C c O L HrH r rH • • • * • • * • • • • • • • • • M C o n c n c o O L O L O C 0 0 O L O C 0 0 O L •tf* r**. 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CO 00 CO a> CD CD c n CD CL • rd fd £ O CO r-- c o cn o r H E LO r-^ CO cn O rH e fd z r-H r-H tH t-H CVJ CVJ CD r H rH H r H CVJ CVJ CD 00 > > ct E «=c <=£ 3 o r-H CO C £ z t-H rH Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced TABLEAIV.11 Continued 1 o •P“ oo r— LU : s — r • CD — L C d c c E fd o SZ > CD to c to u o z s to - s rd rd O dLO rd rd 3 3 O E CD H h • • • • • • * • • • • • • • • • • • • • • • • • • • • • • • • • • • ♦ • • • • 0 0 . ^ r H r o OCO CO r-H o o n c Ocoo o c CO - - . r-* r-H 0 0 r-H - r-n r-n CM CM MCO 0 0 CM CO 0 0 --.CO . - r- rH z s c CD n c »—i LO n c n c CO 0 0 r-n. CM CO CO ) a n c • t n c c < H n c »H n c - Oin00 0 n i CO r-n o c o c n c r-H LO o c CO o c CM i o o n c CO r-n CO <3- CM 0 0 o rH - h • • CM o O00 0 CO 0 0 OCO CO CO 0 0 . - r CO ML - LO r-H LO CM o rH CM o o c 0 0 0 0 CM o o t CO rH rH SZ CD > o • • CM rH n c 0 0 n c LO OCO t CO Or-. - r CO CO CM CO n c ^ r . ^ r LO CO iH H i • • • • C < C < o H r <3* n c DCD > > CD CD > o dfd rd , •CO o t rH r-H CO H t rH r-H CO MLO CM CO - CM r-H o t 0 0 H rH rH rH GO • • • * • • CO CM f-H CO rH CO o CO rH CO H i H r CO CM CO CM o . - r CO 0 0 rH CO r ^ O o n c rH 0 0 OLO CO n c n c H t H t CO r-n n c LO rH H t CO rH O C —t—1 t— O CO rH Li- OCO CM CO n c rH r-n . - - r rH r-H r-n n c H t rH rH rH SZ n c CD CO MCM CM tH n c n c CO 3"*=i* " *3 O00CO 0 0 CO r-n CO CO CO r-n rH rH r-n HrH rH - -n r r-n rH • ' o c CO t— H r o o rH CM f-H o c 0 0 o t rH 0 0 • I tH r-n rH CD n c fd r ^ CVJ O r ^ . c n CO rH c n CVJ CO n *- 0 CVJ CO CDCD rH O LOLO CO LOLO 10 • 1— •••••••••••• u £ 0 3 0 0 LO LO rH O CVJ CVJ CVJ rH s - ■ r- r-H rH rH f-H r H r H c o COCOCO < 0 CO s - O •••••••••• • • UJ 1— rH rH rH r H r H r-H rH rH r H rH rH i H rd O CVJ O CVJ CD T-H CO CO O t o O CVJ CD CO «-H CO LO c o 0 0 CO 0 t-H •f— • to g 0 • r - CO <■—. CO CO cvj CVJ . CVJ CO * 3 - CO s~ 0 CVJ CVJ CVJ LO •5 j- c n t-H LOCO CVJ CO 0 ) ___ ' CO ••••* • • ••••• > CVJ LO CO cn rH t-H CO t o CO CO n - CO c r e CO COCO cn cn CO c o COCO COCOCO 0 0 rtf* t o CO LO LO n - CO COCO 0 «d- cn cvj CO CO O CO c n CVJ r - - . 0 t^J- r-* . rH rH CO Li ••«••••••••••• ft * r - . c n rH rH LO CO CO COCO n * . n -s COCO 0 c o CO 0 0 CD cn COCO CO 0 0 CO 0 0 CO 0 0 CO c 3 0 Ll_ U. 2 : CVJ CO Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. without prohibited reproduction Further owner. copyright the of permission with Reproduced TABLE AIV.ll Continued . cc r— • n • 00 CJ> •1“ O U L r— CO =5 c cd c L C £ < o $- to o c s a s a L- s. O LO (/) s a c a ) Q LO d ✓ — 2 —s *— o s v Vf- s v O O V o • ^ o 00 00 •r- r-H o r— Lu O V o •r— CO r~■ •r— * r OO •P" +•> co fd 3 3 E CD n c o o o fC CM CM MCM C CM r-H < H r o o r-H o c O C O L o c o c O O o t O O D V M C o 3 • • • • • • • • • ♦ • • • • • « • • ♦ • • • • • • • • - • • • • • • • • • • • • • * * • • • • • • • ♦ • • • .°° H r*- o CO o d O C O C *d“ rH MCM C CM r*- ^ r OCO C CO 00 rH tH H r rH tH CM H t «H H r rH CM H r CM Mr-. CM to H r H r 00 O O L H r o c O L O L O V • H r O V O C o v O C n }- • LU cn * vo CT) 00 O C 00 o v H t vo 00 O V < CM H r CM ML O V LO CM CM 3 3 • • • • • • • o VO • - • - M C o •Sf* O C LO 00 tH 00 o •sfr •Sf* o H r H r M C nCO C cn tH o cn o v O C CM H r O C cn rH CM OCM LO CO cn tH CTi LO *• TABLE AIV.ll Continued *r— 0 s LU •r— f— CD p— ) / ( DC c CO 3 c c S- V) <0 0 CL) - i L- u. O fO 0 fO l N ,*-*N - ^— z T Z --- - O O • k - ' r— to <4- Ucn -U •r— r— O C Z to •r— CO O r— •r— •r— O 0 0 0 - U =5 - r o LO o c cn t-H cn r—l LO CO t-H . - r Oco CO t-H LO - - t-H f-H t-H • Ch • o c >- r> cn 0 0 0 0 «st- cn - t-H f-H 0 0 t-H t-H r-N. 0 0 OCO CO 3 o c - U • • • • • • • • • • * - r O C t-H O C cn CO CM CO CO t-H 00 O C f-H CO r^s cn LO CO cn cn f-H 0 LO CO 0 0 t-H LO co CO CO t t-H t-H M C M C LO t-H 0 0 -H r-H OCO CO O OCO CO CM O H r LO nCM cn CO CM co 0 O H r <3- H r OC CO CO 00 CO 1 c cn cn 0 0 DCD CD Sw > TABLE AIV -11 Continued —• r— S - T «r- J U CO o r— 0 0 SZ SZ CO s- s. LO CD S- LO o o o r • S- 13 c: rd CD £ Q. _ » : z : z __ _ o o • - - •r- O i-H r— 0 0 •f— 00 O 00 r— •r— O c r O O O r— 4- L 4-> 3 TABLE AIV.ll Continued S •r- — r *r— co U L o r— : a O C O CD i / i CO i / i i / i CO c c 19^3 Born in Bannia, Italy 1963 Completed High School at St. Mary’s College, Sault Ste. Marie, Ontario, Canada 1967 Received the Degree of Bachelor of Applied Science in Chemical Engineering from the University of Windsor, Windsor, Ontario, Canada. 1972 Candidate for the Degree of Doctor of Philosophy in Chemical Engineering at the University of Windsor, Windsor, Ontario, Canada 281 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. X I— l • • • • CVJ rH rH a H X U_ rH rH ■n r ■ 4 •H X a < UJ < H o : o o o < > O z o X o O o o X z O o o z l • r • * ! © UJ o cc UJ U- J- CL < C9 UJ ir CO o 137 138 llJ a a a X a > i i 7 3 2 238