I!-0W-TEMPERATURE DRY SCRUBBING
REACTION KINETICS AND MECHANISMS;
LIMESTONE DISSOLUTION AND SOLUBILITY
A Thesis Presented to
The Faculty of the College of Engineering and Technology
Ohio University
In Partial Fulfillment
of the Reculrernents for the Degree
Master of Science
-\h;·"'~ .". 1"\
by
Michael Maldei
June 1993 ACKNOWLEDGEMENTS
I would like to take the opportunity to thank my thesis advisor Dr. Mike Prudich for letting me work in this environmental area. Your patience regarding my language, your advise for my research and the freedom you left me in my studies are greatly appreciated.
Also I am grateful for the assistance of Dr. Ken Sampson, who has always taken the time to answer my questions regarding my research. Thanks for the organization of the many parties you hosted, which we enjoyed.
A special thank you belongs to my friend Petra stumm who encouraged me throughout the research. Thank you for the time you have taken to support me emotionally.
I would like to thank my grandparents for their encouragement and advise. Also, I wish to express my gratitude towards Sandip Chattopahyay for his support and being a friend. i
TABLE OF CONTENTS
LIST OF FIGURES • ..•..•...••. ... iii LIST OF TABLES .•.. ••..•. vi 1.0 INTRODUCTION ..•...... •..•. 1 1.1 HISTORY. ••..••..•. . ... 1 1.2 REMOVAL OF S02 iIN A COMMON LIME/LIMESTONE FGD PROCESS • . • . . . • . . • • . . . • . . . . 2 1.3 FACTORS AFFECTING THE REACTION RATE OF S02 REMOVAL ••••.••..•••.•...... 5 1.4 ADDITIVES FOR THE ENHANCEMENT OF THE REACTION BETWEEN SULFUR DIOXIDE AND LIMESTONE...... 6 1.5 EXPERIMENTAL APPROACH TO OBTAIN SOLUBILITIES AND DISSOLUTION RATES OF LIMESTONES . • • . . • . . . 7 2 • 0 LITERATURE REVIEW ..•..••...... 9 2.1 TECHNIQUES TO DETERMINE SOLUBILITIES AND DISSOLUTION RATES . . . . • . . . • . . . • . . . 9 2.2 LARGE SCALE TESTS ON THE APPLICATION OF ADDITIVES TO ENHANCE WET LIMESTONE FLUE GAS DESULFURIZATION (FGD) PERFORMANCE .• .. ..•... 15 3 . 0 MATERIALS • • • . . . • . . •. . 18 3.1 EQUIPMENT. •...... • .. 18 3.2 LIMESTONES ...... •...••..•... 20 3.3 ADDITIVES ..• . .. . .•... 23 3 . 4 SOFTWARE ...... 26 4 . 0 METHODS ..•...••...... 28 4.1 THEORY . •. .•...... 28 4.1.1 CARBONIC ACID/CARBONATE CHAIN ..•... 28 4.1.2 HYDRATION OF SULFUR DIOXIDE. . .•... 31 4.1.3 LIMESTONE DISSOLUTION...... •. 33 4.1.4 REACTION BETWEEN LIMESTONE AND SULFUR DIOXIDE 38 4.1.5 SOLVATION OF CITRIC ACID ...... •... 39 4.1.6 SOLVATION OF GLYCINE ...... •... 44 4.1.7 SOLVATION OF SODIUM SULFITE . 47 4.1.8 THEORETICAL APPROACH TO ESTIMATE LIMESTONE SOLUBILITIES ...... 48 4.2 EXPERIMENTS ...... •..... 52 4.2.1 INTRINSIC SOLUBILITY EXPERIMENTS 53 4.2.2 DISSOLUTION RATE EXPERIMENTS: FREE DRIFT METHOD ...... 54 4.2.3 DISSOLUTION RATE EXPERIMENTS: pH-STAT METHOD ...... 55 5.0 RESULTS AND DISCUSSION ...... •... 57 5.1 INTRINSIC SOLUBILITY EXPERIMENTS ••. 57 5.1.1 LIMESTONES ..•...... 57 5.1.2 ADDITIVES . 61 5.2 ESTIMATION OF LIMESTONE SOLUBILITY FROM FREE ENERGY CHANGES OF EQUILIBRIUM REACTIONS . . . 63 5.3 DISSOLUTION RATE EXPERIMENTS: FREE DRIFT METHOD. 66 5.3.1 LIMESTONES . 68 ii
5. 3.2 ADDITIVES .•••..••••••..•. 70 5.4 DISSOLUTION RATE EXPERIMENTS: pH-STAT METHOD 75 5.4.1 LIMESTONES . • • . . . • . . •• 76 5.4.2 ADDITIVES. •••.. •• ••. .•• 78 6.0 CONCLUSIONS AND RECOMMENDATIONS •••...•• 80 REFERENCES • . . • . • . . • . . . • •• ... 85 APPENDICES ••..•...•• ...... 89 APPENDIX A: LISTING AND RESULTS OF SEMIEMPIRICAL MODEL FOR THE ESTIMATION OF CALCIUM AND MAGNESIUM SOLUBILITIES ....•. .. 90 APPENDIX B: SOLUBILITIES OF of Ca 2 + , Mg2+ AND THE COMBINED VALUE FOR THE LIMESTONES MAXVILLE, CAREY, VANPORT, MISSISSIPPI AND BUCYRUS •.••..••.••. •. 102 APPENDIX C: SOLUBILITY OF MAXVILLE LIMESTONE AT VARIOUS ADDITIVE CONCENTRATIONS AND EXPERIMENTAL CONDITIONS ...... 112 APPENDIX D: EVALUATION PROGRAM FOR THE FREE DRIFT METHOD INCLUDING THE ADDITIVES CITRIC ACID AND GLYCINE . . . • ...... • 115 APPENDIX E: LIMESTONE DISSOLUTION RATES WITHOUT ADDITIVES OBTAINED USING THE FREE DRIFT METHOD ••...... • .. 121 APPENDIX F: MAXVILLE LIMESTONE DISSOLUTION RATES OBTAINED USING THE FREE DRIFT METHOD; ADDITIVES: CITRIC ACID, GLYCINE, SODIUM SULFITE .••.....•.... 127 APPENDIX G: LIMESTONE DISSOLUTION RATES WITHOUT ADDITIVES OBTAINED USING THE pH-STAT METHOD ...... •...... • 132 APPENDIX H: DISSOLUTION RATES OF MAXVILLE LIMESTONE OBTAINED USING THE pH-STAT METHOD; ADDITIVES: CITRIC ACID, GLYCINE ...... • 138 iii LIST OF FIGURES
Figure 1-1: Generic wet S02 removal process ...•. 3 Figure 3-1: Experimental set-up .••...... 18 Figure 3-2: Basket stirrer .....•...... 19 Figure 3-3: Equilibria among calcium and magnesium carbonates .•.•.••...... 23 Figure 4-1: Bicarbonate-carbonate equilibria as a function of solution pH • ...... 30 Figure 4-2: Bisulfite-sulfite distribution as a function of pH . • . . . . • • • . . . . • 32 Figure 4-3: Stochiometric factor as a function of pH and temperature ....•...... 38 Figure 4-4: variation in the stochiometric factor at various citric acid concentrations 43 Figure 4-5: Titration curve of glycine ...... 45 Figure 4-6: variation in mUltiplication factor at various glycine concentrations ..... 47 Figure 5-1: Repeatability test for free drift method 66 Figure 5-2: Effect of stirrer speed on observed dissolution rate ...... 67 Figure 5-3: Amount of HCl titratet as a function of time ...... •..... 75 Figure A-1: Calculated Ca2+ solubility for stone with ~~ = 0.5, ~~ = 0.5 . 96 Figure A-2: Calculated Ca 2+ solubility for stone with ~~ = 0.8, ~~ = 0.2 . 96 Figure A-3: Calculated Ca2+ solubility for stone with ~~ = 0.99, ~~ = 0.01 . 97 Figure A-4: Calculated Mg2+ solubility for stone with ~~ = 0.5, ~~ = 0.5 . 98 Figure A-5: Calculated Mg2+ solubility for stone with ~~ = 0.8, ~~ = 0.2 . 98 Figure A-6: Calculated Mg2+ solubility for stone with ~~ = 0.99, ~~ = 0.01 •••••• 99 Figure A-7: Calculated Ca2+ /Mg + solubility for stone with ~~ = 0.5, ~~ = 0.5 ... 100 Figure A-8: Calculated Ca2+/Mg2+ solubility for stone with ~~ = 0.8, ~~ = 0.2 .... 100 Figure A-9: Calculated Ca2+/Mg2+ solubility for stone with ~Ca = 0.99, ~Mg = 0.01 ·· 101 Figure B-1: Ca2+ solubility of Maxville limestone 103 Figure B-2: Ca2+ solubility of Carey limestone .. 103 Figure B-3: Ca 2+ solubility of Vanport limestone . 104 Figure B-4: Ca 2+ solubility of Mississippi limestone . 104 Figure B-5: Ca 2+ solubility of Bucyrus limestone . 105 Figure B-6: Mg2+ solubility of Maxville limestone 106 Figure B-7: Mg2+ solubility of Carey limestone .. 106 Figure B-8: Mg2+ solubility of Vanport limestone ... 107 Figure B-9: Mg2+ solubility of Mississippi limestone . 107 iv
Figure B-10: Mg2+ solubility of Bucyrus limestone 108 Figure B-11: Ca 2+ /Mg2+ solubility of Maxville limestone ••...... •.•..... 109 Figure B-12: Ca 2+ /Mg2+ solubility of Carey limestone . 109 Figure B-13: ca2+/Mg2+ solubility of Vanport limestone 110 Figure B-14: Ca 2+ /Mg2+ solubility of Mississippi limestone ...... ••••..... 110 Figure B-15: Ca 2+ /Mg2+ solubility of Bucyrus limestone 111 Figure C-1: Solubility of Ca 2+ and Mg2+ ions gained from the dissolution of Maxville limestone in distilled water as a function of citric acid concentration .. 113 Figure C-2: Solubility of Ca 2+ and Mg2+ ions gained from the dissolution of Maxville limestone in distilled water as a function of glycine concentration .... 113 Figure C-3: Solubility of Ca 2+ and Mg2+ ions gained from the dissolution of Maxville limestone in dist. water as a function of sodium sulfite concentration •.. 114 Figure E-1: Limestone dissolution rates at 30°C . 122 Figure E-2: Limestone dissolution rates at 60°C . 122 Figure E-3: Limestone dissolution rates at 90°C . 123 Figure E-4: Temperature dependency of Maxville dissolution rates ...•..... 124 Figure E-5: Temperature dependency of Carey dissolution rates ...••.... 124 Figure E-6: Temperature dependency of Vanport dissolution rates ...... 125 Figure E-7: Temperature dependency of Mississippi dissolution rates ...... •. 125 Figure E-8: Temperature dependency of Bucyrus dissolution rates ...•.•• 126 Figure F-l: Maxville limestone dissolution without additive ...... •... 128 Figure F-2: pH versus time curves for Maxville limestone with additive citric acid . 128 Figure F-3: pH versus time curves for Maxville limestone with additive glycine ... 129 Figure F-4: pH versus time curves for Maxville limestone with additive sodium sulfite 129 Figure F-5: Dissolution rates of Maxville limestone as a function of citric acid concentration ...... 130 Figure F-6: Dissolution rates of Maxville limestone as a function of glycine concentration 130 Figure F-7: Dissolution rates of Maxville limestone as a function of sodium sulfite concentration ....•... 131 Figure G-l: Limestone dissolution rates at 30°C . 133 Figure G-2: Limestone dissolution rates at 60°C . 133 v
Figure G-3: Limestone dissolution rates at 90°C • 134 Figure G-4: Temperature dependency of Maxville limestone dissolution rates .... 135 Figure G-5: Temperature dependency of Carey limestone dissolution rates .... 135 Figure G-6: Temperature dependency of Vanport limestone dissolution rates .... 136 Figure G-7: Temperature dependency of Mississippi limestone dissolution rates .... 136 Figure G-8: Temperature dependency of Bucyrus limestone dissolution rates .. 137 Figure H-1: Dissolution rates dependent on citric acid concentration ..••...... 139 Figure H-2: Dissolution rates dependent on glycine concentration ...... 139 vi
LIST OF TABLES
Table 3-1: Chemical analysis of limestones ..... 21 Table 3-2: Representative analyses from manufacturers ...••..... 21 Table 5-1: Calcium to magnesium ion ratio in parent limestone and in solution at equilibrium 59 Table 5-2: Solubilities of limestones reported by different investigators ...•..... 60 Table 5-3: Solubilities of Ca 2 + for Mississippi limestone obtained by model prediction and experiment ...... •....• 65 Table 5-4: Dissolution rates evaluated at pH = 5.5, using the free drift method ...... 69 Table 5-5: pH versus time values for the dissolution of Maxville limestone obtained using the free drift method ...... 71 Table 5-6: Dissolution rates obtained for Maxville limestone at 60°C without additive ... 78 1
1.0 INTRODUCTION
1.1 HISTORY
The discovery of fire by early man was a key event in the advancement of civilization. However, this discovery did not come with the knowledge that fire could produce by-products like 802. It has been known for a long time that the emission of 802 from the burning of large quantities of fossil fuel is creating environmental problems not to mention aggravating respiratory diseases in humans. This has called for concerted scientific attention to 802 removal from the air.
The first S02 removal from stack gases, in London in
1932, consisted of a simple water scrubbing process to absorb the 802 into solution. Some of the early processes for S02 removal were the Battersea Process in 1934 and the Sulfidine
Process developed in Germany prior to World War II. Since
1935, different absorbents like lime or limestone have been studied, mostly in small-scale pilot plants. Other processes have been introduced in the united states, Japan, and Germany as well as other countries in an attempt to meet governmental emission control requirements.
In the united States, a few years after the government initiated water pollution legislation in 1948, there was a public awakening to environmental problems which included air pollution. Prompted by government environmental activities, 2 the Environmental Protection Agency (EPA) was founded on
December 2, 1970. with the overhaul of the prior Clean Air
Act, the EPA strengthened its authority. In November 1990, with the revision of the Clean Air Act of 1970, the face of air quality regulation in the united states was changed dramatically.
Compliance standards for air emission controls are set by the EPA. Current standards dictate either near-term installation of flue gas desulfurization (FGD) systems or fuel switching. Many new and innovative FGD systems have been researched over the past decade. Most of these systems use
lime or limestone as sorbents. Since high limestone utilization is essential for the economic efficiency of FGD systems, a considerable amount of research has been done in this area.
1.2 REMOVAL OF S02 IN A COMMON LIME/LIMESTONE FGD PROCESS
In a common lime/limestone FGD process, S02 is removed
from the flue gas by contacting it with lime or limestone in an aqueous phase. Therefore, an aqueous slurry of lime or limestone is used to treat S02-bearing flue gases released
from a power plant. The S02 in the flue gas reacts with the
slurry to form calcium sulfite and calcium sulfate. The purified flue gas leaves through the smoke stack after passing through a mist eliminator to remove any slurry entrained in 3 the flue gas. This common process requires removing the reacted limestone and supplying fresh slurry. Figure 1-1 shows a typical wet FGD system.
MIST EUMINATOR
WATER
UMESTONE
Figure 1-1. Generic wet 802 removal process.
The basic parts of the 802 removal process, shown in the diagram above, are the ash collector, the mist eliminator, the reheater, and the tanks to hold the process water and the limestone slurry. Prior to entering the absorber, particulates in the flue gas are removed by the ash collector which can be a bag house or an electrostatic precipitator. In the absorber, the reaction between 802 and limestone takes place. The slurry is sprayed from the top of the absorber column while the flue 4 gas enters the absorber in countercurrent flow from the bottom and leaves through the top. The mist eliminator removes any remaining slurry from the scrubbed flue gas leaving the absorber column. The flue gas is then passed through the reheater before it exits through the stack. The tank that
holds the process water (which is partially recycled from the reacted slurry) is also a basic part of the process. Another important part is the tank that holds the limestone slurry. This tank serves the purpose of providing sufficient time for the limestone to dissolve in water.
The basic FGD process can be modified in many ways, one of which is to inject limestone particles directly into the furnace. In this high temperature zone the limestone is calcined to lime and becomes more reactive. Another modification would be to replace the absorber column with a fixed- or moving-bed reactor containing limestone particles.
In this modification the flue gas would need to be first humidified in order to insure an effective reaction between
the 802 and the limestone.
The focus of the current study is the kinetics of limestone dissolution in post-furnace scrubbing, where the
flue gas reacts with limestone at low temperatures «350°F).
In post-furnace scrubbing, the presence of a water layer surrounding the limestone particles is essential for the
absorption of 802 to occur. Therefore, attention is given to 5 the process chemistry in this water layer as regards factors which have an influence on the reaction rate between 502 and the absorbents. These factors include the solubilities and dissolution rates of limestones, which are investigated in this study.
1.3 FACTORS AFFECTING THE REACTION RATE OF S02 REMOVAL
The low temperature reaction of S02 with limestone is dependent on the relative humidity of the flue gas or an external supply of water in order for the S02 and CaC03 to dissolve. Therefore, when the limestone particles are surrounded by a thin film of water, the following steps are essential for S02 absorption: • transfer of S02 to the gas/liquid interface • solution of S02 in water at the interface ionization of dissolved S02 • 2- • transfer of HS03-, H+ and S03 ions from the interface into the liquid interior • dissolution of CaC03 ionization of dissolved calcium salts to form Ca2+ • 2 2- • reactions of ca + with S03 to form CaS03 • precipitation of CaS03*1/2 H20 oxidation of sulfite to sulfate • 2 2- • reaction of Ca + with S04 to form CaS04 • precipitation of CaS04*2 H20 • co-precipitation of Ca(S03)1-x(S04)x*1/2 H20 It has been found that gas-phase mass transfer, liquid-phase mass transfer and the dissolution of CaC03 are the most important rate-controlling mechanisms for S02 absorption
(Sada, Kumazawa, Butt, 1980). 6
Focusing our view on the dissolution rate of reagent grade CaC03 or limestone in water, it should be noted that the dissolution rate is dependent on a variety of factors. The pH value and the temperature of the liquid phase surrounding the limestone particles are important parameters. Also, the source of the limestone and the initial Ca2+ ion concentration present in the liquid phase are rate determining. The initial
Ca2+ ion concentration in solution is linked to the solubility of a limestone which represents the upper limit of concentration for this ion. In the case of a sUbsequent reaction of calcium ions with sulfite ions and the following precipitation of CaS03 , the initial amount of calcium ions will be diminished, allowing an increase in limestone dissolution rate. Additionally, limestone dissolution rates can be mass transport controlled.
1.4 ADDITIVES FOR THE ENHANCEMENT OF THE REACTION BETWEEN SULFUR DIOXIDE AND LIMESTONE
An additive is defined by Webster as "any of various substances added to a product, process or device to improve performance or quality." Additives can improve the performance of a FGD scrubber in many ways, one of which is the interaction of the additive with the process chemistry to yield an increased limestone dissolution rate and thereby an
S02 removal enhancement. Another advantage from the use of additives is the possibility of the reduction of gypsum 7 scaling in the absorber which occurs through nucleation. This precipitation of calcium sulfate caused by supersaturation in the liquid phase can be prevented by an additive which inhibits the natural oxidation of sulfite to sulfate.
Additives are also used to change the dewatering characteristics of the waste product. The economics involved in the use of additives seems to be promising compared to conventional methods to achieve the same performance enhancement.
Two important categories of additives are buffers and organic/inorganic deliquescents. Buffers like adipic acid, citric acid or glycolic acid are used to provide additional acidity at the limestone surface, thereby enhancing the limestone dissolution rate. organic/inorganic deliquescents are believed to increase or retain moisture at the limestone surface, thus enhancing 502 capture.
1.5 EXPERIMENTAL APPROACH TO OBTAIN SOLUBILITIES AND DISSOLUTION RATES OF LIMESTONES
Limestone dissolution rates were determined through the use of a spinning basket reactor. Two common methods to determine the limestone dissolution rate are the "free drift" and the "pH-stat" method. The "free drift" method implies that the pH of the solution will be allowed to drift to higher values when limestone particles are dissolved in it. From the 8 pH change per unit time and per unit area, the dissolution rate can be determined. In the "pH-stat" method, the solution pH is held at a constant value by adding the necessary amount of acid to the solution as the limestone dissolves. From the amount of acid titrated per unit time and from the surface area of the limestone sample, it is possible to calculate the dissolution rate.
Values for the solubility of different limestones are determined by dissolving the limestone powder in distilled water. The concentrations of calcium and magnesium ions in the water are then quantified by analysis with EDTA and EGTA.
These solubility experiments were performed at temperatures ranging from 30 to 90°C. 9
2.0 LITERATURE REVIEW
2.1 TECHNIQUES TO DETERMINE SOLUBILITIES AND DISSOLUTION RATES
Early research in the determination of calcite and aragonite solubilities and dissolution rates has primarily been performed by geochemists and oceanographic researchers.
These investigators determined calcite and aragonite equilibria in open seawater as well as under laboratory conditions. In seawater, the first direct studies of calcium carbonate dissolution were conducted by Peterson (1966) and
Berger (1967). Peterson suspended spheres of I celand Spar calcite at various depths in the Central Pacific Ocean, while
Berger studied the dissolution rate of biogenic calcite and aragonite using the same method. Under laboratory conditions,
Weyl (1958) examined the calcite dissolution rate by directing a jet of water at a crystal of Iceland Spar and found the rate of dissolution to be transport controlled. This phenomenon has been confirmed by other researchers investigating dissolution rates (Plummer and Wigley, 1976).
Dissolution rates have been commonly measured by two different methods, the 'pH-stat' and the 'free drift' method.
The pH-stat technique was developed by Morse in 1974 and is based on the maintenance of a constant degree of disequilibrium in the carbonate/carbonic acid system. This technique has been applied by Morse and Berner (1972), Berner and Morse (1974), Morse (1974), Plummer, Wigley and Parkhurst 10
(1978), Chan and Rochelle (1982), Toprac and Rochelle (1982) and Gage (1989). The a 1ternat i ve method, the free dri ft technique, is an approach to establish equilibrium between the carbonate species from an initial disequilibrium and an under or supersaturation of the solute. The free drift method has been used by Erga and Terjesen (1956), Sjoeberg (1976),
Plummer and Wigley (1976) and Plummer, Wigley and Parkhurst
(1978) to determine dissolution rates of calcite and aragonite, which are polymorphic forms of calcium carbonate.
Dissolution rate and solubility measurements have been conducted for a variety of biogenic, synthetic and geologic materials. These materials were either calcitic, aragonitic or contained other proportions of calcium and magnesium in a single phase. The kinetic behaviour of multiple phases which are often present in biogenic materials has also been studied.
Biogenic samples were used by Berger (1967), Morse and Berner
(1972) and Walter and Hanor (1978). Synthetic calcite found application in the experiments of Ingle et ale (1973) and
Sjoeberg (1976). Both synthetic calcite and geologic materials have been examined by Toprac and Rochelle (1982). They collected limestones like Ash Grove, Brassfield, Fredonia, Georgia Marble, Longview, Maysville, Pfizer and Stoneman to study their respective dissolution rates in a prepared solution. These dissolution rates were reported to be independent of limestone type or source. 11 Different solvents have been used by researchers to determine dissolution rates and solubilities. In seawater, the solubility of aragonite was measured by Berner (1976). Since the solubility determination of calcite in seawater is very complex, Berner (1976) performed additional experiments dissolving calcite and aragonite in distilled water and sUbsequently related their difference in solubility to the natural solvent. Pseudo-seawater, a solution of NaCl/CaCl2 , was selected by Berner and Morse (1974). This solution contained the same amount of calcium ions as present in seawater and was prepared to have an identical ionic strength. Since K+ and Cl- ions were not observed to form significant complexes with ca2+, Sjoeberg (1976) applied KCl in distilled water as solvent.
Solvents containing an initial amount of calcium ions were believed to have an effect on the dissolution rate (Sjoeberg, 1976). Sjoeberg quantified this effect by adding known amounts of analytical grade CaCl2 to the reactant solution. The reaction rate was found to decrease in proportion to the square root of increasing calcium ion concentration. This discovery lead to the identification of a disadvantage of the free drift method, the continuous change in the state of solvent saturation.
A factor which has an influence on the dissolution rate
of calcite was found to be the surface area (Sjoeberg, 1976). 12
In experiments using pure analytical CaC0 3 of different particle sizes, the dissolution rate per unit mass increased proportionally to the increase in calcite surface area.
Similar results were achieved by Rochelle and Toprac in 1982. They determined the particle-size distribution of naturally occuring limestones to be an influential parameter on their respective dissolution rates.
other parameters that are significant in controlling the chemistry of limestone dissolution are the ambient temperature, the solution pH and the atmospheric partial pressure of carbon dioxide. The ambient temperature determines the equilibrium constants between the chemical species in solution while the solution pH relates to the amount of hydronium ions which can react in the carbonate/carbonic acid system. The partial pressure of CO2 in the atmosphere indirectly influences the solution pH and defines the equilibrium pH under free drift conditions. Experiments leading to the quantification of these effects were performed by Plummer, Wigley and Parkhurst in 1978.
Limestone dissolution rates and solubilities are related to the solution pH and to the equilibria of the carbonate species. In those equilibria, the ions involved are specified in terms of their activities rather than their concentrations. The activities of electrolytes are dependent on the ionic strength of the solution and can be calculated from the Debye- 13 Hueckel formula. The application of the Debye-Hueckel theory of activity coefficients was reviewed by Garrels and Christ
(1967). They stressed the combined effects of the activities of several electrolytes in solution of a given electrolyte in regard to mineral equilibria.
Limestone dissolution in aqueous systems can be manipulated by introducing a small amount of certain chemicals into the system. Those additives either enhance or inhibit limestone dissolution and have attracted the interest of several investigators. Chan and Rochelle (1982) studied the influence of the additives adipic-, acetic-, acrylic- and sulfosuccinic acid on limestone dissolution rates. Their experimental results indicated an enhanced mass transfer of calcite due to a promoted acidity transport to the limestone surface. other carboxylic acids like glutaric, maleic or formic acid we1·e tested to compare their effectiveness in regard to S02 removal (Jarvis, Owens, stewart, 1986). The effects of the ions Na+, SO32 , thiosulfate and adipic acid on limestone dissolution were
investigated by Jarvis et ale (1988). An extension of this work includes the effect of sulfite ions in solution (Gage,
1989).
Dissolution rates are also influenced by impurities in the limestones and by the magnesium in solid solution with
calcium carbonate. Research focused on these factors for the 14 selection of limestone reagents in wet flue gas desulfurization (FGD) systems was performed by Jarvis, Roothaan, Meserole and Owens (1991). They concluded that limestones with lower concentrations of carbonate may be less desirable for reasons of transportation and waste disposal cost. Low-quality limestones also have higher concentrations of potential inhibitors like iron, silicon, magnesium, dissolved sulfite and aluminium complexes which could adversely affect scrubber operation. Magnesium availability as a solid solution with calcium carbonate and dolomitic content of limestones were also analysed. The dissolution rates of solid solution magnesium and the magnesium in dolomite were determined. Dolomite in limestones was determined to be inert under normal FGD system operating conditions whereas magnesium when present as a solid solution should improve FGD system performance.
However, since limestone properties like solubility or dissolution rate vary among limestones dependent on their source, there is a need for further research on the kinetics of dissolution of local Ohio limestones which is the sUbject of the present research. The data generated on physical and chemical properties of local Ohio limestones will be used in an existing computer program which models a granular limestone dry scrubbing reactor. 15
2.2 LARGE-SCALE TESTS ON THE APPLICATION OF ADDITIVES TO ENHANCE WET LIMESTONE FLUE GAS DESULFURIZATION (FGD) PERFORMANCE
The influence of formate ions in FGD systems on system performance and formate consumption rates at different operating conditions have been evaluated. The results of a test program conducted on the 0.4-MW mini-pilot wet limestone
FGD system at the Electric Power Research Institute's (EPRI)
High Sulfur Test Center (HSTC) were documented by Stohs, sitkiewitz and Owens in 1991. Tests were performed under natural-, inhibited-, and forced-oxidation conditions with concentrations of formate ion varied up to 4500 ppm. Attention was given to recycle slurry pH, process liquor composition, limestone grind and reaction tank volume. The results gained from this study on the formate ion additive showed an effect on S02 removal efficiency, limestone utilization, sulfite oxidation and on the waste solid's properties. It was found that the application of the formate ion under baseline
Chemistry conditions (no forced or inhibited oxidation) showed an increase in S02 removal efficiency of 28% at an additive level of 1000 ppm of formate ions. In this experiment, the slurry pH was maintained at a value of 5. o. A similar experiment, using a slurry with a pH of 5.5, resulted in an increase of S02 removal efficiency of 17%.
An investigation in the use of organic acid buffers for limestone wet scrubbing was made by Jankura, Milobowski, 16 Hallstrom and Novak in 1991. This study consisted of a group of experiments performed at the Michigan South Central Power Agency's 55-MW James R. Endicott power station. These experiments were made to develop design criteria for formic and dibasic acid buffers. A baseline increase from 90% to 95% S02 removal efficiency was reported at 500 ppm of either formic or dibasic acid buffer. To explain the increase in terms of the dissolution rate of limestones, they noted that certain additives may improve the wetting properties of the hydrophobic reagent solids thereby increasing the mass transfer of the solid dissolution at the interphase.
The additive Nalco~ 1243 was tested at Sherburne County
Generating station (SHERCO unit 3). This research for additive-enhanced desulfurization in FGD scrubbers was reported by Juip, Schabel, Lin, Dubin, Pickens and Byron in 1991. Previous evaluations showed lime savings of 35% at a 30 ppm additive catalyst dosage of N-1243. optimizing the dosage of the additive by an increase from 4 ppm to 8 ppm resulted in an additional lime savings of 12-20%. The lime savings in those large-scale tests were recognizable, because the sulfur dioxide removal was held constant during the testing. Juip et. ale (1991) stated that kinetically, the low solubility of the
limestone or CaC0 3 would be the rate-limiting step of S02 absorption. To overcome this, the additive N-1243, a
surfactant-based additive was believed to function by 17
increasing liquid-s02 gas and solids-gas sorption at the interface.
An overview of the use of additives in wet FGD systems was presented by Moser and Owens (1991). The concentration of additives required were discussed as well as how additives have to be introduced into the system. The combination of additives and cautions on additive use were also addressed.
The influence of additives on the dissolution rate of all different kinds of limestones cannot be exactly predicted. Therefore this investigation in the behaviour of Ohio limestones by use of additives is neccessary to better understand scrubber performance. 18
3.0 MATERIALS
3.1 EQUIPMENT
The experimental set-up used for the determination of solubilities and dissolution rates is shown in Figure 3-1. The central piece of equipment used during these experiments was the jacketed reactor which contained a liquid volume of up to
3 1.5 dm • The temperature of the liquid contents in the reactor was varied between 30 and 90°C by means of a constant temperature water bath which provided the water flow for the outer mantle of the reactor.
~._._------._------~--_._-_._--~-_._-_.------I
~------, J
@---- U
• to water bath
waterin • balance with Hel reservoir
Figure 3-1. Experimental set-up. 19
The basket stirrer, a pH electrode and a glass tube for the addition of Hel were inserted through the reactor cover.
The pH electrode was connected to a pH indicator, -recorder and -controller. Depending on the desired pH in solution, the pH controller activated the peristaltic pump which in turn delivered diluted hydrochloric acid through a glass tube into the reactor. The amount of HCl titrated per unit time was determined by weight loss from a reservoir of HCl placed on top of a balance.
The dimensions of the basket stirrer, employed in the free drift and pH-stat experiments are shown in Figure 3-2.
0-3/8"
2.5"
Figure 3-2. Basket stirrer. 20
The basket stirrer consisted of two threaded pipe nipples with end caps which were in horizontal position and opposite to each other. These pipe nipples were welded with short connection rods to the vertical axis of the stirrer. The opening of each end cap was covered by a fine mesh screen to keep the limestone particles inside the pipe nipples.
3.2 LIMESTONES
Five different limestones, including four local Ohio limestones, were used to obtain kinetic data for this study:
• Vanport limestone
• Maxville limestone
• Mississippi limestone
• Bucyrus limestone
• Carey limestone Vanport limestone was obtained from the Waterloo Coal Company,
Jackson, Ohio. Maxville limestone was collected from the
Maxville Quarries Inc., Logan, Ohio, while the Mississippi limestone was obtained from the Mississippi Lime Company,
Alton, Illinois. Samples of Carey and Bucyrus limestones were ordered from the quarries of the National Lime & stone Company at Carey and Bucyrus, Ohio, respectively. Limestones in the form of powder were used in the experiments for the determination of solubilities. Experiments to obtain dissolution rates were performed with particle sizes between
1.18 rom (16 mesh) and 1.00 mm (18 mesh). 21
Preliminary elemental analyses of some of these limestones provide information about the amount of calcium and magnesium present in representative samples. These analyses were performed according to ASTM, Part 05.05, Method D4326-84.
The content of calcium and magnesium was reported according to the amount of oxide present after ignition (Table 3-1).
Table 3-1. Chemical analysis of limestones. Source of limestone Mass-% of Mass-% of Ca/Mg CaO MgO mole ratio Vanport limestone 72.62 0.87 60.0 Maxville limestone 61.50 9.65 4.6 Carey limestone 56.44 39.93 1.0
Additional chemical analyses of the Ca/Mg content were available from the distributors of the limestones. Table 3-2 shows the results of these analyses and compares the Ca/Mg mole ratios. Since limestone composition is known to vary within each sample and within every delivery, an analysis can only be considered as an estimate for the given limestone source.
Table 3-2. Representative analyses from manufacturer. Source of limestone Mass-% of Mass-% of Ca/Mg CaC03 MgC03 mole ratio Carey limestone 54.5 45.0 0.73 Bucyrus limestone 80.0 17.0 2.85 Mississippi 97.8 to 0.4 to 62.5 to limestone 98.9 0.95 149.7 22
However, the close agreement of the data for Carey limestone in Tables 3-1 and 3-2 indicates that this estimate of the composition is typical for this particular limestone.
Another feature of the designated limestones is the amount of magnesium available in a soluble form. No analysis at Ohio University has been performed, thus far, to determine either the amount of soluble magnesium in solid solution or the amount of magnesium in relatively insoluble dolomite.
The five limestones identified were chosen because they represent two important stable equilibria among calcium and magnesium carbonates. The stable phases are referred to as calcite and dolomite, according to their Ca 2+ and Mg2+ content in the mineral. Figure 3-3 distinctively shows these phases represented in a double-logarithmic diagram, where the partial
2 2 pressure of CO2 in the air is the horizontal and the Ca + /Mg + concentration in the limestone is the vertical axis.
It should be mentioned that limestones occur not only in phases but naturally in polymorphic forms. Three forms of
CaC03 are known which are calcite, aragonite and vaterite. For a given temperature and pressure, the prevailing polymorphic form is those, which is the most thermodynamically stable one.
In addition to these polymorphic forms there are two hydrates of calcite, Trihydrocalcite CaC03 • H20 and Ikaite CaC03 • 6
H20, which occur naturally. 23
4
3 Calcite CaCO3
2 Dolomite I 1 CaMg(C03 )2 Brucite + 0 + Mg(OH)2 as CJ) -rQ.~ -1 ~ -2 Hydromagnesite -3 Mg (C0 2x 3 H 0 4 3)3(OH) 2 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 o log P CO2
Figure 3-3. Equilibria among calcium and magnesium carbonates. (Garrels and Christ, 1967)
3.3 ADDITIVES
Limestone particles in a wetted limestone flue gas desulfurization (FGD) process, like the Limestone Emission
Control (LEC) system, are surrounded by a thin layer of water.
This layer is provided either by condensation of water from humidified flue gas flowing across the particle or by direct spray injection of water on top of the limestone bed. Because of this layer of water there are two important interfaces: the gas/liquid interface between the flue gas and the water layer and the solid/liquid interface at the boundary between the 24 limestone particle and the water layer. The actual reaction chemistry between calcium carbonate and sulfur dioxide takes place in the water layer itself.
The reaction chemistry involved leads to criteria for the selection of additives, whi ch are expected to enhance the limestone dissolution rate or promote the absorption of S02 into the water layer surrounding the limestone particle. After considering this reaction chemistry, the following additives have been chosen to be used in the determination of solubilities and dissolution rate experiments:
• an organic acid: citric acid, C6Hg07
• an amino acid glycine, NH2-CH2-COOH
• sodium sulfite Na2S0 3
since organic acids are weak proton donors, their undissociated form predominates in an acidic environment which is present in the liquid bulk phase surrounding a limestone particle. Because of calcium carbonate dissolution at the solid/liquid interface, the pH of the fluid immediately next to the limestone surface maintains a higher value than the fluid at some distance away from this interface. For this reason, the organic acid close to the limestone surface is primarily in the dissociated form. This is expected to increase limestone dissolution rates because of the enhanced acidity transport to the limestone surface. 25
The unique property of amino acids is their amphoteric behaviour. These ampholytes can act either as an acid or a base, dependent on the pH of the solution in which they are dissolved. The isoelectric point, pI, is the pH-value at which an amino acid carries no net electric charge. Glycine has its isoelectric point at pH = 6.1 and thus it is there present in its zwitterionic form. At pH values higher than the isoelectric point, the zwitterion of glycine increasingly assumes its anionic form. At pH = pK2 = 9.78 the concentrations of the zwitterion form and the anionic form are equal while at higher pH values the anionic form dominates. At pH values lower than the isoelectric point the zwitterion reacts with a proton to assume its cationic form. At pH = pKl
= 2.35 the concentrations of the zwitterionic and the cationic form are equal. Lower pH values lead to an increased concentration of the cationic form.
Because of these properties, glycine is a potential candidate to enhance the 802 solution in the liquid bulk layer surrounding the limestone particle while at the same time promoting limestone dissolution at the particle surface. This is achieved by the amphoteric behaviour of glycine which allows a bUffering effect in both environments. At the limestone surface, glycine is expected to provide additional protons for limestone dissolution while in the liquid bulk layer glycine acts as an acceptor for protons thus allowing 26 more S02 to dissolve.
since sulfite ions are present in most desulfurization systems using limestone as a sorbent, it is important to understand their influence on limestone dissolution. There is a general agreement in the literature that sulfite ions at low concentrations enhance limestone dissolution while at higher concentrations limestone dissolution is inhibited. Also, it is common knowledge that the enhancement of limestone dissolution is very dependent on the limestone source. In the present research the effect of sodium sulfite on five selected limestones, including four local Ohio limestones, was quantified.
3.4 SOFTWARE
The free drift method produced experimental data in the form of pH versus time curves which were plotted by a chart recorder. These graphical data had to be converted into actual dissolution rates of the limestones used. This conversion was achieved by the development of a BASIC program which is listed in Appendix A. In the program, approximately 40-50 pH values versus time data points gained from the chart recorder serve as input values for each free drift experiment. Additional input information like reactor volume and temperature or the presence and amount of an additive are required. 27 In the absence of an additive, limestone dissolution rates were calculated by dividing the hydronium ion change between two data points by their time difference and by the limestone surface area. The limestone surface area for the amount of limestone used was obtained according to the equation:
6 m A ( 3-1) dp P
in which dp is the average particle diameter, m the mass of
limestone used and p the bulk density of limestone. The calculated dissolution rates were finally divided by a calculated stochiometric factor which accounted for the number of hydronium ions reacted per dissolved calcium ion. In free drift experiments including additives, an additional factor had to be determined. This factor was valid between two data points and expressed the proportion between the number of hydronium ions reacted in the presence and absence of an
additive. 28
4.0 METHODS 4.1 THEORY 4.1.1 CARBONIC ACID/CARBONATE CHAIN
When water is exposed to the atmosphere, carbon dioxide from the air dissolves in it. One molecule of aqueous carbon dioxide reacts with a molecule of water to form undissociated carbonic acid.
---+ t--- (4-1)
---+ t--- (4-2) since carbonic acid is known to be a weak acid and is mostly present in its undissociated form, the carbonate and the bicarbonate ions react with hydronium ions in two hydrolytic equilibrium reactions:
---+ t--- H30+ + HC03 (4-3)
---+ 2- t--- H30+ + C03 (4-4 )
Hydronium ions from the equations above, are in equilibrium with neutral water molecules as described by the ionic product of water.
---+ t--- ( 4-5)
Reactions 4-1 and 4-2 can be expressed by the law of mass action. Combining both yields:
= aH2C03 (aq) ( 4-6)
acO2 (g) 29
in which the activity of gaseous carbon dioxide can be replaced using Henry's law,
(4-7)
where Hc o 2 denotes the Henry constant and PC02 is the partial pressure of CO2 in air. Similarly for reactions 4-3 through 4- 5:
aHCo; • a H30 + a ·a ( 4-8) H2C03 (aq) H20
= aco;- • a H30 + (4-9) a HCO; • a H20
( 4-10)
From Equations 4-8 through 4-10, the mole fractions of
2 H2C03 , HC03- and C03 - can be calculated for a closed system in dependency on the solution pH. The mole fractions are obtained using the simplifications a, ::::: c, assuming that the activity coefficients are close to unity. Another simplification, a mo ~ 1, can be obtained from the product of the activity coefficient and the mole fraction of water. Figure 4-1 shows the results of those calculations at constant temperature. The
2 mole fractions of C03 -, HC03- and H2C03 at equilibrium have been normalized by dividing the amount of moles of each species by the sum of moles of the three chemical species. From Figure 4- 30
1 it can be shown that pure distilled water which has an initial pH of 7, when exposed to atmospheric air containing carbon dioxide will have a lower pH at equilibrium.
At pH 7 the normalized mole fraction of carbonic acid is approximately 0.2 while the value for the bicarbonate ion is
0.8. The normalized mole fraction for the carbonate ions is negligible. According to Equation 4-2, dissolving CO2 from the atmosphere disturbs the equilibrium by increasing the H2C0 3 concentration. The system responds to this disequilibrium by shifting the equilibrium of Equation 4-3 to the right, thereby lowering the solution pH.
1.0
Z 0 I- 0.8 U« Ct: u, W 0.6 ~ 0 ~
o 0.4 W N «~ ~ Ct: 0.2 0 Z
0.0 0 2 4 6 8 10 12 14 pH
Figure 4-1. Bicarbonate-carbonate equilibria as a function of solution pH. 31
The decrease of the solution pH will finally come to a halt when a dynamic equilibrium between CO2 entering and leaving the solution is reached.
4.1.2 HYDRATION OF SULFUR DIOXIDE
In order for a reaction between sulfur dioxide and limestone to occur in a limestone scrubber, sulfur dioxide has to be dissolved into water. At the gas/liquid interface, 502 from the flue gas is hydrated by water molecules to undissociated H250 3 :
+------+ ( 4-11)
+------+ (4-12)
Undissociated sulfurous acid reacts subsequently in two equilibrium reactions to bisulfite or sulfite ions thereby lowering the solution pH. The absorption rate is dependent on the pH of the liquid:
+------+ (4-13 )
+------+ (4-14)
Combining Equations 4-11 and 4-12 and applying the law of mass action for the equations above yields:
= YH2S03 (aq) • CH2S03 (aq)
PS02 (4-15) H so2 32
(4-16 )
= Yso;- · cso;- · YH • CH30 + 30+ (4-17) YHS03- • cHSo; • YH20 • CH20
The equilibrium curves for undissociated sulfurous acid, bisulfite and sulfite ions in the equations above, are given in Figure 4-2. The dependency is shown in terms of normalized mole fractions versus liquid phase pH. The normalization was achieved by dividing the amount of moles of each species of so 2 3 , HS0 3- and H2S03 by their sum of moles.
1.0
Z 0 I- 0.8 U -c ~ LL W 0.6 -.J 0 ~ o 0.4 W N -c-.J ~ ~ 0.2 0 Z
0.0 0 2 4 6 8 10 12 14 pH
Figure 4-2. Bisulfite-sulfite distribution as a function of pH. 33
From Figure 4-2 and the equilibrium reactions listed above, it can be recognized that the absorption of 502 in water is promoted at a high pH.
The actual reaction chemistry is more complicated, because the bisulfite ion enters into still another equilibrium reaction. Two equally charged H503- ions react via a condensation step to form the disulfite or 'pyrosulfite'
----t t--- (4-18 )
4.1.3 LIMESTONE DISSOLUTION
The two major constituents of limestone are calcitic and magnesian carbonates. Magnesium carbonate is often referred to as dolomite. Magnesium may also be present in a solid solution with calcium carbonate. Those mixed crystals make up a true homogeneous solution and can be expressed by:
----t t--- (4-19)
However, biogenic calcite can contain multiple phases of those mixed crystals which may vary in composition.
It is therefore practical to express the chemical reactions involved in the dissolution of limestones in terms of those major constituents. The solvation of limestone is described by: 34
CaC03 (s) t==::! CaC03 (aq) (4-20)
MgC03 ( s) t==::! MgC03 ( aq) (4-21) and sUbsequently the dissociation reactions:
2 2 CaC03 (aq) t==:! Ca + + C03 (4-22)
2 2 MgC03 (aq) t==:! Mg + + C03 - (4-23)
The law of mass action yields for the combined reactions
4-20, 4-22 and 4-21,4-23:
aCa 2 + • aco; (4-24 ) acac03 (s) and
a 2 + • aco;- Mg (4-25) aMgC03(S)
For the case of
aMgc03 (S) 1 (4-26) the solubility products of calcium and magnesium carbonate are defined by
(4-27) and (4-28)
similar to reactions 4-1 through 4-4, Equations 4-24 and
4-25 should be written in terms of their activity 35 coefficients:
= y Ca 2 + • CCa 2 + • Ycof- • ccof (4-29) aCaC03 (8)
= YMg 2 + • CCa 2 + • Ycof- • Cco; (4-30) aMgC03 (8)
In these equations, the activity of the solid phase has to be inserted. The activity of the solid phase would be 1 by definition if the limestone is assumed to be a pure solid.
This is seldom true for natural limestones. Therefore, the
CaC03 in a calcitic limestone which has a composition of (Cao.9sMgo.OS)C03 deviates from the activity of 1. Based on the assumption of ideal solution, the activity of CaC03 in this limestone is equal to its mole fraction.
The connection between limestone dissolution and the carbonic acid/carbonate chain is the carbonate ion. While limestone dissolves, an excess of carbonate ions is released, which has to be in equilibrium with bicarbonate ions and undissociated carbonic acid. To reestablish equilibrium, hydronium ions are necessary according to reactions 4-3 and 4-
4. During limestone dissolution, the solution pH thus increases.
The need of hydronium ions mentioned above is related to 36 another parameter, which is important for the free drift method. This parameter is the 'stochiometric factor', which defines how many hydronium ions will be necessary to reestablish an equilibrium state after initial disequilibrium caused by the dissolution of one calcium ion. The stochiometric factor is the product of the following theory:
From Figure 4-1 it can be noted that, at a pH of 4, the mole fraction of undissociated carbonic acid is nearly 1, while the fraction of bicarbonate and carbonate ions is negligible. For each calcium carbonate molecule dissolved in this environment, one carbonate ion is released and transferred into undissociated acid. Therefore two hydronium ions are necessary for this transfer.
The other extreme case is at a pH of approximately 13, where most of the chemical species are present as carbonate ions. Under these conditions, a carbonate ion released from the dissolution of limestone would not affect the equilibrium at all. Therefore no hydronium ion is necessary to maintain the equilibrium of the solution.
From those extreme cases, it can be seen that the value for the stochiometric factor lies between 0 and 2 for the pH interval from 0 to 14. The factor is calculated by finding first the normalized mole fractions of bicarbonate ions and carbonic acid in solution at a fixed pH. Here, the mole fractions are expressed in terms of concentrations rather than 37 activities, as a means of simplification:
1 VHCo; = (4-31)
1 (4-32) 1 +
where
(4-33)
(4-34)
and of course,
lO-pH (4-35)
From the mole fractions of bicarbonate and carbonic acid, the stochiometric factor can be found by:
(4-36)
This factor is shown in Figure 4-3 as a function of pH and temperature.
Looking at Figure 4-3 it is also obvious that a low pH shifts the equilibrium of the carbonate species towards undissociated carbonic acid. Therefore, the amount of 38 carbonate ions in the liquid phase is very small. Since the solubility product has to remain constant, a higher solubility of calcium and magnesium carbonate is expected.
2.0 --- ~~ n:: o " ~\ I ~~ U <{ ~ LL 1.5 ,t\90°C U o: 10°C ~ I- W ~ :2 ~~ o ~~ I1.0 ...... ~ U ~ o ~~ I- (f) ~~ ~
0.5 4 5 6 7 8 9 10 pH
Figure 4-3. Stochiometric factor, f s , as a function of pH and temperature.
4.1.4 REACTION BETWEEN LIMESTONE AND SULFUR DIOXIDE
In the liquid phase, dissolved calcium and sulfite ions
are reacted to form calcium sulfite. Simultaneously, calcium
ions can also react with bisulfite ions to form Ca(HS03) 2:
---+ t--- (4-37)
2 ---+ Ca + + HSO3 t--- (4-38)
The bisulfite and the sulfite ions might be oxidized, 39 resulting in the presence of sulfate ions:
t------+ (4-39)
t------+ ( 4-40)
These sulfate ions can react with dissolved calcium ions to
form aqueous calcium sulfate:
---+ t--- (4-41)
Finally, the aqueous calcium sulfite and sulfate are precipitated in a reaction involving water molecules:
---+ t--- (4-42)
---+ t--- (4-43)
As shown by the preceding equations, the pH in the liquid phase surrounding a limestone particle is not constant. The pH is maintained at a high value directly adjacent to the
limestone surface because the equilibrium reactions involved
in the dissolution of limestone are decreasing the hydronium
ion concentration. with increasing distance from the limestone
surface, the pH value decreases because the solution of S02 in water increases the hydronium ion concentration.
4.1.5 SOLVATION OF CITRIC ACID
citric acid is a polyprotic, organic acid because it
contains three carboxylic groups. It's formula can be 40
represented in the undissociated form by C6Hs0 7 or:
COOH I CH2 I HO-C-COOH I CH2 I COOH
Dependent on the solution pH, citric acid dissociates in water
2 3 and is present as C6Hg07 , C6H707-, C6H607 - or C6Hs07 -• The equilibrium reactions can be expressed by:
K1 ----+ H+ C6Hg07 t--- C6H707- + (4-44)
K2 2 - t------+ - H+ C6H707 C6H607 + (4-45 )
K3 2- ----+ 3- H+ C6H607 t--- C6Hs07 + (4-46 )
where K1 , K2 , K3 are the primary, secondary and tertiary dissociation constants and pKl = 3. 13, pK2 = 4. 76, pR3 = 6.4 their respective negative logarithms at These dissociation constants indicate a limited ionization in water, therefore citric acid is referred to as a weak polyprotic acid. For simplification, the steps of ionization can be written in terms of concentrations rather than activities. The
sUbscript 'g' refers here to the equilibrium concentration of each chemical species: 41
C- C + C6H7 O, ,g · H K = (4-47) 1 C C6HeO,,g
C 2- C + C6H 0i , g · H K = 6 (4-48) 2 C- C6 x,o,,g
C 3- C + C6HS07 ,g · H K3 (4-49 ) C 2- C6H6 07 ,g
The mole fractions of the anions at a specified pH can be calculated according to:
1 (4-50 ) 1 +
1 ( 4-51) 1 +
1 (4-52) 1 + +
1 (4-53) 1 +
The sum of all the anionic and neutral molecules at equilibrium, is equal to the initial amount of undissociated citric acid in solution: 42
(4-54)
Using the assumption that all of the citric acid initially present in the solution has been undissociated, the amount of hydronium ions delivered to the solution at pHI can be calculated at equilibrium to be:
n H + (pH!) = nC6H8~. 0 • [ 1IJ C6H8~ •g (pH!) • 0 +
lJ1 c &, o,-, g (pH1 )• 1 + 6 (4-55 ) C (pH ) • 2 + lJ1 6H6 ot,-g 1 C (pH ) • 3 lJ1 6HsO.,J,-g 1
A similar equation can be written for a second pH value, pH2 - The amount of hydronium ions provided for a pH change from pHI to pH2 is then given by
(4-56 )
Finally a mUltiplication factor is derived, which accounts for the ratio of hydronium ions provided in a pH interval between a solution with additive and a solution consisting only of water:
Iln + (citric acid) = H (4-57) IlnH + (H20)
The use of this factor is necessary to the evaluation of the dissolution rate of limestone in free drift experiments using citric acid as an additive. In those experiments, citric acid 43 acts as a buffer and the pH change per time is smaller than in experiments without additive. Nevertheless, the amount of hydronium ions provided per time may be even larger than in cases without additive. Therefore, the mUltiplication factor serves the purpose of relating the pH change per time to the actual dissolution rate of limestone. To obtain the actual dissolution rate, the apparent rate which was calculated without consideration of the additive, is mUltiplied with the factor. The multiplication factor is plotted in Figure 4-4 as a function of pH.
~-- ~------~-----~--- 100000 ~- "tI'~ ---_--..--- , ".. ,~ / .".....,.. - - - - - ,,' .//
,/"/ // 10000 / 1/ ,,'/ / ,"I I ,,,,'// 1000 ", / ", .// ,'/ ,,' / / ,,'// ,,'I 100 , ", II Additive conc.: ,,' / ",' / / ", // 5 mmoles/l " ./ 10 mmoles/l 10 ,,'/ ./ 15 mmoles/l ,"/ / 25 mmoles/l ,,'// ",~ tI',,~/... 1~i--r-...... ,r--r------,...... --_----..---_...... _-~ ...... --...... --_..---._.....--.---- 2 4 6 B 10 pH
Figure 4-4. Variation in the multiplication factor, fM,c' at various citric acid concentrations. 44
4.1.6 SOLVATION OF GLYCINE
Glycine, an a-amino acid dissolves in water in two equilibrium reactions with dissociation constants K1 and K2 :
The law of mass action yields for both reactions:
(4-59)
CH3N+-CH 2 -COOHg and
(4-60 )
From Equations 4-59 and 4-60 the mole fraction of the anionic, cationic and zwitterionic form of glycine at equilibrium can be calculated:
1 ( 4-61) 1 +
1 (4-62) 1 +
1 (4-63) 1 + 45
If the zwitterionic form of glycine is selected as a reference molecule, then the number of protons dissociated per molecule of glycine can be shown by Figure 4-5. At a very high pH, each reference molecule has delivered one proton to solution. In the opposite case, each reference molecule has accepted one proton and is therefore in its fully protonated, cationic form. The isoelectric point pI is the state where the reference molecule carries no net electric charge.
12
-~!_------~~~ ~~_c~s- -~ ~_coo B ~~Ir_u"1 I 0... pi
4
O-f-...... -r-~r--r--.---,r--r--r--r--r-..,..,.--r--.--....--r--.-~-,--r--r--r-'Ir--r-~--r-.,.....,.-r--r-r-r--r--r--r--r-r-1 -1.0 -0.5 0.0 0.5 1.0 H+ IONS DISSOCIATED/MOLECULE
Figure 4-5. Titration curve of glycine (Voet, 1990). 46
Adding up the number of moles of the cationic, anionic and neutral form at equilibrium yields the total amount of glycine which has been added to the solution.
n R N+-CR -COOH n R N+-CH. -COOH + n H N+-CH. -COO- + nH. N-CH. -COO- (4-64) 3 2 0 3 2 g 3 2 g 2 2 g
Choosing the cationic form of glycine as a reference state, the amount of hydronium ions which have been delivered to the solution at pHI is given by:
(4-65)
Writing an analogous equation for a second pH value, pH2 , and taking the difference of hydronium ions provided in this pH interval leads again to Equation 4-56.
(4-56)
The mUltiplication factor for the free drift method using glycine as additive, is similarly found as in Equation 4-57.
The factor is plotted in Figure 4-6 in dependency on the glycine concentration added to the solution.
t:.n + (glycine) = H (4-66 ) t:.nH + (H20) 47
100000000
10000000
0:::: 1000000 .-0 U 100000 ~ ~ 10000 a.... ~ --.J ::J 1000 Additive cone.: ~ 100 -- 5 mmoles/l - - 10 mmoles/l - - 15 mmoles/l 10 ------25 mmoles/l
1 2 4 6 8 10 12 pH
Figure 4-6. variation in multiplication factor, fM,G' at various glycine concentrations.
4.1.7 SOLVATION OF SODIUM SULFITE
Sodium sUlfite, Na2S03 dissociates in water into single positively-charged sodium and double negatively-charged sulfite ions:
(4-67)
In regard to the free drift method, evaluating the dissolution rates of limestones in a solution containing sodium sulfite is rather challenging because of the complexity of the reaction chemistry. The sulfite ions resulting from the ionization are 48 in equilibrium with bisulfite ions and undissociated sulfurous acid according to Equations 4-13 and 4-14. Eventually sulfur dioxide is released into the atmosphere.
Simultaneously, sulfite ions are reacting with calcium ions to calcium sUlfite, which was previously described by
Equation 4-37. Subsequently, the precipitation of calcium sulfite takes place (Equation 4-42). Finally the sulfurous acid/sulfite system is linked to the carbonic acid/carbonate chain by the following reaction:
+------0+ (4-68) where the equilibrium is normally far to the right.
4.1.8 THEORETICAL APPROACH TO ESTIMATE LIMESTONE SOLUBILITIES
Limestone solubility in an aqueous solution can be estimated if most of the ionic species present are known qualitatively. From this knowledge, the equilibrium reactions in which those ionic species interact are also usually understood. The equilibrium constants can be obtained from
(4-69)
where R is the ideal gas constant and ~Go is the free energy change of the reaction when all of its reactants and products are in their standard states. The equilibrium constant varies 49 with temperature as described by,
aHO 1 ss» = --- + ( 4-70) R TR if the reaction enthalpy dHo and the reaction entropy dSo are reasonably independent of temperature.
For the equilibrium reactions, the law of mass action provides the mathematical equations for subsequent solubility calculations. In regard to the dissolution of limestone, the equations necessary to estimate limestone solubilities were already mentioned in Equations 4-29 and 4-30.
In addition, the activity coefficient of a chemical species i in solution is defined as:
( 4-71)
Reviewing Equation 4-29 and writing Equations 4-6 and 4-8 through 4-10 in terms of their activity coefficients leads to:
y Ca 2+ • cca 2+ • Yco;- • cco~- = (4-29) acaco3 (8)
= yH2C03 (aq) • CH2CO) (aq) (4-72) PC02
HC02 50
(4-73 )
Y~- • C C0 2 - • YH 0+ • cH O· --3 3 3 3 (4-74)
= yH 0 · • CH30 ... • YOH- • COH 3 (4-75) (YH 0 • C ) 2 2 H20
The activity coefficients in those equations can be determined by computing the ionic strength of the aqueous solution according to:
(4-76)
where c j represents the concentration of each species in solution and Zi its respective charge. The activity of water can be approximated by the relation:
a = YHO' eRO = 1 - 0.017 · ~Ci (4-77 ) HO222 ~
where c·1 stands for the concentration of each dissolved cationic, anionic or neutral species.
The ionic strength is inserted in the Debye-Hueckel expression to determine the activity coefficients of each chemical species. The Debye-Hueckel theory considers the long- range electrostatic forces of charged ions on each other, resulting in lower activity coefficients. This expression is 51 valid for dilute solutions only, which is the case for the experimental work performed:
A • z1 · II Yi = exp (- (4-78 ) 1 + ai • B • II
In this case, A and B are characteristic constants dependent only on the dielectric constant, the density and the temperature of water. aj is a value dependent upon the 'effective diameter' of the ion in solution, while z refers to the ionic charge.
The calculation of limestone solubility is an iterative method: When the activity coefficients of the chemical species have been calculated, the concentrations of each ion can be found from Equations 4-29 and 4-72 through 4-75. These concentrations have to be inserted into the equation for the ionic strength (Equation 4-76) and subsequently into the
Debye-Hueckel equation to get updated activity coefficients. with these new coefficients, the calculations have to be repeatedly performed, until the values of the coefficients and the various ion concentrations converge. A BASIC program for this iterative method of estimating limestone solubilities has been written and is listed in Appendix A. 52 4.2 EXPERIMENTS
Five different limestones, Maxville, Carey, Bucyrus, Vanport and Mississippi limestone were employed in experiments to determine their solubility and to obtain their dissolution rates by the free drift and the pH-stat method. In all experiments, distilled water was used as the solvent. The effects of three potential additives, glycine, citric acid and sodium sulfite on solubilities and dissolution rates were investigated. The additives were mixed with the solvent prior to an experiment.
For solubility and dissolution rate experiments, two different limestone particle sizes were prepared. The solubility experiments were performed with a powder of each limestone having particle diameters smaller than 40 mesh «
0.01 mm). Dissolution rate experiments were conducted with particle diameters between 1.18 (16 mesh) and 1.00 mm (18 mesh) .
The pH meter used for all experiments was calibrated prior to each experiment. Selective buffers at pH values of 4,
7 and 10 were chosen to cover the pH range of interest. with the calibration of the pH meter, the chart recorder used in the free drift method was also adjusted. 53
4.2.1 INTRINSIC SOLUBILITY EXPERIMENTS
The reactor used for the determination of the limestone solubilities was filled with 1.25 liters of distilled water and was surrounded by an outer glass jacket. Water was circulated through the glass jacket in order to control the reactor temperature. Thereby the temperature at which the solubility of a particular limestone was measured could be set using the temperature controller for the water bath.
A plastic stirrer was mounted in the reactor through one of the four openings at the reactor lid. The pH and temperature electrodes were plugged into the top of the reactor and occupied two additional openings. The fourth opening allowed the exchange of carbon dioxide with the atmosphere. A thin polyethylene t.ube for the addition of hydrochloric acid or sodium hydroxide was inserted through the fourth opening and just penetrated the solvent surface in the reactor. The acid or base in the tube was transported by a peristaltic pump which in turn was operated by a pH controller connected with the pH meter. The solubility was measured at different pH values of the solvent, whose value remained constant during an experiment and was set at the pH controller.
The procedure below was followed for each experiment.
Upon reaching the desired temperature in the reactor, 0.625 g of limestone powder was added to the reactor contents. The pH 54 value of the solution was adjusted using the pH controller and
the system was operated for three hours. After this time, a
sample was removed and filtered through a 0.1 micron filter.
Subsequently, the sample was analyzed with EDTA (1,2 diaminoethanetetra-acetic acid) and EGTA ({Ethylenebis-
[oxyethylenenitrilo]}tetraacetic acid) to determine the concentration of calcium and magnesium ions present. These quantitative, titrimetric analytical techniques were documented by Jeffery, Bassett, Mendham and Denney in 1989.
These solubility determinations were carried out using a matrix of 15 experiments for each limestone. The temperature was varied between 30 and 90°C in steps of 15°C, while the pH was changed between pH 4 and pH 8 in steps of one unit.
Additional experiments were performed with the additives glycine, citric acid and sodium sulfite. The additive concentrations were 5, 10, 15 and 25 mmol/l of the substance
for a specified pH and temperature.
4.2.2 DISSOLUTION RATE EXPERIMENTS: FREE DRIFT METHOD
The free drift method made use of the same reactor
already applied to solubility type experiments although,
instead of the plastic stirrer, a spinning basket stirrer was
used. The two opposite baskets of the stirrer were filled with
2.25 g of limestone particles. 1.25 liters of distilled water were poured into the reactor. During these experiments, the pH 55 was allowed to drift from an initially low value of
approximately pH 4, to its equilibrium value. Each
experimental trial lasted between 6 and 12 hours. The pH of
the liquid phase was continously monitored and recorded using
a chart recorder which was connected to the pH meter.
Before an experiment was initiated, the pH value of the
liquid phase was adjusted to a value of close to pH 4 by the
addition of diluted hydrochloric acid. Upon starting an
experiment at a desired temperature, the spinning basket
stirrer was lowered into the liquid phase. The revolution
speed of the stirrer was set to a predetermined value, which was found prior to the experiments (Section 5. 3). At the
completion of the experiment, the recorded pH versus time
curve was evaluated and the dissolution rates determined by
the use of a BASIC program (Appendix D).
Free drift experiments were conducted without additives
at 30, 60 and 90°C for each of the five limestones. The
influence of the three additives was studied with Maxville
limestone at 60°C. The additive concentrations used were 5,
10, 15 or 25 mmol/l.
4.2.3 DISSOLUTION RATE EXPERIMENTS: pH-STAT METHOD
Preparations for the pH-stat method were quite similar to
those for the free drift method, since the same spinning 56 basket stirrer and the same particle size of limestone was used. The reactor was filled again with 1.25 liters of distilled water. In contrast to the free drift method, the pH was maintained constant during these experiments by means of the pH controller.
A beaker filled with hydrochloric acid of known concentration was put on a balance and the pH controller was set to the desired pH and activated. Simultaneously, the spinning basket reactor was moved into the liquid contents of the reactor and stirrer speed was adjusted. From the amount of hydrochloric acid titrated per time, the dissolution rate was determined according to Equation 4-79. The symbol S refers to the slope of the titrated acid versus time curve which for all experiments could be approximated by a linear function.
r = 1 S·C (4-79) 2 A .p
In Equation 4-79, c denotes the concentration while p represents the density of titrated hydrochloric acid. The A stands for the total area of the limestone surface in the experiments. The factor ~ results from the assumption for the pH-stat method that two hydronium ions are required to dissolve a single ion of calcium or magnesium.
Experiments were carried out with pure Maxville limestone at 60°C and pH 5. Additional runs were performed at the same conditions using the three additives at various concentrations. 57 5.0 RESULTS AND DISCUSSION
5.1 INTRINSIC SOLUBILITY EXPERIMENTS 5.1.1 LIMESTONES
The solubilities of the calcium carbonate and magnesium carbonate, present in the five limestones examined, are shown in Appendix B. Figures B-1 through B-5 exhibit the concentration of calcium ion in solution as a function of pH and temperature. Figures B-6 through B-10 display the magnesium ion concentration. Finally, the combined solUbility of calcium and magnesium carbonate is shown in Figures B-11 through B-15.
From the figures, a definite dependency of calcium and magnesium carbonate solUbility on the solution pH can be seen.
The calcium and magnesium ion concentrations increase with decreasing pH. This is in agreement with Equations 4-1 through
4-4 which describe the pH behaviour of the carbonate/carbonic acid chain. Decreasing the solution pH to a low value and maintaining the low value results, according to Le Chatelier's principle, in a new equilibrium between the chemical compounds in the carbonic acid Chain. At the new equilibrium, a high concentration of undissociated carbonic acid and a low concentration of carbonate ions will be present. As indicated by Equations 4-27 and 4-28 this leads to the conclusion that the concentrations of calcium and magnesium ions necessarily have to be increased in order to maintain the same solUbility 58 product in solution.
The effect of the temperature on limestone solubility is far less pronounced than the pH effect. At a pH of 8, there seems to be a slight decrease in calcium and magnesium carbonate solubility with increasing temperature, but this is not consistent with the temperature effect at low pH values.
The inconsistencies can be explained by the experimental error associated with solubility determinations. The standard deviation for these water chemistry determination was ± 2 x
10-4 mol/I.
The influence of the limestone type on the solubility of calcium and magnesium ions is theoretically related to the amount of calcium and magnesium originally present in the mineral and to the amount of impurities in the limestone.
Impurities in limestone lower the activity coefficients of calcium and magnesium ions in solution, thereby leading to an increase in their concentration.
However, Figures B-3, B-4 and B-5 in the Appendix B display a higher calcium ion solubility for Vanport,
Mississippi and Bucyrus limestones than for Maxville or Carey limestones (Figures B-1 and B-2). It should be noted here that since the calcium-to-magnesium ratio from Table 3-1 is higher for Vanport than for Maxville at comparable inpurities, the calcium ion solubility for Vanport is consistently higher. The 59 magnitude of the calcium-to-magnesium ratio in the parent limestone seems to be related to the Ca 2+ /Mg 2+ ratio in solution at equilibrium (Table 5-1). At pH 4, a significant dependency on the parent limestone can be noticed, while at higher pH values the experimental error exceeds the measured solubility ratios.
Table 5-1. Calcium-to-magnesium ion ratio in parent limestone and in solution at equilibrium.
Source of Ca 2 + /Mg2 + mole Ca2+ /Mg2 + mole ratio in limestone ratio parent solution at equilibrium, at limestone 60°C pH = 4 pH = 6 pH = 8
Maxville 4.6 3.8±2.6 6.0±8.7 5.1±22.6 Carey 1.0-1.2 1.1±O.3 O.9±0.6 1.4± 4.3 Vanport 60 6.0±4.4 7.8±9.2 11.0±80.0 Mississippi 103-247 9.5±8.1 8.2±8.7 4.7±11.4 Bucyrus 4.7 2.8±O.9 2.5±1.2 5.2±12.4
The magnesium ion concentrations in solution for the
Carey and Bucyrus limestones are greater than those observed for Maxville, Vanport and Mississippi limestones. This is in agreement with the initial magnesium content in the limestones. The combined calcium and magnesium ion concentrations in solution, especially at low pH, are found to be highest for Carey, Mississippi and Bucyrus limestones, while the combined concentrations for Vanport limestone is of comparable magnitude only at a low pH. 60
To compare some of the results of this study with those reported by previous investigators, Table 5-2 contains solubilities. Weast (1970) reported the solubility of natural calcite and aragonite in cold and hot water. It is assumed that these values are measured at the equilibrium pH, which should be around 8. Weast reported the solubility of natural calcite in cold water to be 1.39 x 104 molll and in hot water to be 1.79 x 104 mol/l. The solubility of natural aragonite was listed to be 1.52 x 104 molll in cold water and 1.89 x 104 molll in hot water.
Table 5-2. Solubilities of limestones reported by different investigators. Investigator Limestone Experimental Solubility condition in molll Weast (1970) nat. Calcite cold water 1.39 x 104 hot water 1.79 x 104 nat. Aragonite cold water 1.52 x 104 hot water 1.89 x 104 Baeckstroem Calcite goC 129.8 x 104 (1921) 35°C 76.4 x 104 Aragonite 9°C 145.8 x 104 35°C 87.5 x 104
This study Mississippi pH = 8, 30°C 9.27 X 104 pH = 8, 90°C 2.97 X 10-4
To show the large difference in reported values from previous investigators, additional data can be obtained from
Baeckstroem (1921), who determined the solubility of calcite at 9°C to be 129.8 x 104 moll I and at 35°C to be 76.43 x 10-4 mol/l. The solubility of aragonite was reported at the same 61 temperatures of 9°C and 35°C to be 145.8 x 104 molll and 87.5 x 104 molll, respectively.
However, the high amount of calcium containing
Mississippi limestone tested in this study at a pH of 8, has a combined ca2+/ Mg 2+ solubility of 9.2684 x 104 molll at 30°C and 2.9706 x 104 molll at 90°C, which is in between the values reported from Weast and Baeckstroem.
Boynton (1980) lists the equilibrium pH of limestones to be in the range from 8 to 9, while dolomite has a value about
9 to 9.2. It was found in this study that Maxville limestone has its equilibrium value near 8.0, while the other four limestones, including the dolomitic limestones Carey and
Bucyrus, reveal a lower equilibrium pH value. This value is near 7.5 and is therefore in disagreement with the pH value suggested by Boynton.
5.1.2 ADDITIVES
The combined solubility of calcium and magnesium ions in distilled water has been investigated by dissolving Maxville
limestone. Different concentrations of citric acid, glycine or sodium sulfite have been added to the solvent. The results of those experiments are presented in Appendix C.
Figure C-1 shows the combined calcium and magnesium ion concentration as a function of the amount of citric acid which 62 was added to the solvent (distilled water). For three experimental conditions, the ionic concentrations of calcium and magnesium increase significantly with increasing citric acid concentration. For example at T = 30°C and pH = 8 using no additive, the Ca2+/ Mg2+ solubility was measured to be about
5.4 x 104 mol/l. Adding an amount of 5 mmolll citric acid to the solvent yielded a Ca2+ IMg2+ solubility of 9 x 104 moll1.
Doubling the concentration of citric acid added resulted in a solubility of about 11.2 x 104 mol/I. It is recognized that the highest change in solubility occurs at a low additive concentration of 5 mmol per liter. At one experimental condition, 30°C and pH 4, there was nearly no change in solubility with increasing additive concentration.
From a theoretical viewpoint, the addition of a chemical should lead to an increase in solubility, because of a change in activity coefficients of calcium and magnesium. Another reason for an increased solubility is the formation of undissociated molecules from the reaction of calcium and magnesium ions with anions from the additive. Therefore, the expression 'intrinsic solubility' includes also the amount of ions dissolved due to undissociated complexes formed with the additive.
The addition of small amounts of glycine displayed an overall smaller change in solubility when compared to the experiments with citric acid. The only experimental condition 63 at which a clear increase in solubility could be identified was at 90°C and pH 4. At these experimental conditions the
Ca 2+ /Mg 2+ solubilities using glycine concentrations of 0, 5, 10
4 and 15 romol/l were 15.5 x 10 , 17.0 X 104 , 18.2 X 104 and 19.1
X 104 mol/I, respectively. In the other experiments, it was not possible to identify a clear trend.
Using sodium sulfite as an additive the change in
Ca2+/Mg2+ solubility caused by the additive was only slightly larger than in experiments using glycine as additive. A clear trend was found for the experimental condition of 90°C and pH
4. Here, the increase in sodium sulfite concentration led to an increase in calcium and magnesium ion solubility. The
Ca2+/Mg2+ solubilities using sodium sulfite concentrations of
4 4 4 0, 5, 10 and 15 mmol/l were 15.6 x 10 , 19.0 X 10 , 21.2 X 10 and 23.3 x 104 mol yL, respectively. In the other three experimental conditions seen in Figure C-3, the solubility changes only slightly. This is similar to the observations using glycine as the additive.
5.2 ESTIMATION OF LIMESTONE SOLUBILITY FROM FREE ENERGY CHANGES OF EQUILIBRIUM REACTIONS
As described in Chapter 4.1.8, the solubility of calcium and magnesium in limestone can be theoretically estimated.
This was done by an iterative calculation of equilibrium concentrations and by computing activity coefficients. The 64
BASIC code and the results of those estimations are listed in Appendix A.
Computational runs have been performed for three different types of limestone as regarding their calcium and magnesium content. It was assumed that the initial content of calcium in the limestone was 50 mol%, 80 mol% and 99 molt. The magnesium content was 50 mol%, 20 mol% and 1 mol%, respectively. No other impurity has been considered.
Comparing Figures A-l through A-3, it can be observed that at a high pH, the calcium ion concentration decreases slightly with increasing temperature. At a low pH the effect is reversed and the solubility of calcium ions decreases strongly with increasing temperature. Furthermore, it can be noted that there is a general increase of solubility with decreasing pH, but that this trend is especially noticable at low temperatures. Finally, the overall calcium ion concentration relates to the assumed initial mole fraction of calcium in the limestone.
In comparison to the experimental results obtained in this study, the modeling results show only a partial agreement. A comparison of the results for Mississippi limestone, which contains around 98 mass-% of CaC03 , indicates that at pH values larger than 6 the model predicts Ca 2+ ion solubilies lower than those observed experimentally (Table 65
5.3). At pH 5 and around 30 to 90°C, the model seems to agree reasonably well with the solubilities gained by the experiments. However, at low pH the model predictions are unsatisfactory over the entire temperature range studied.
Figures A-4 through A-6 show the solubility of magnesium ions in solution. Solubility trends similar to those observed for calcium ions are evident. Again, there is a relationship
Table 5-3. Solubilities of Ca 2+ for Missisippi limestone obtained by model prediction and experiment. Condition Model prediction: Experiment:
x 10-4 molll x 10-4 molll 30°C, pH = 8 5.4 7.9±2.0 60°C, pH = 8 3.1 4.7±2.0 90°C, pH = 8 1.9 2.6±2.0 30°C, pH = 6 8.0 14.3±2.0 60°C, pH = 6 4.1 17.3±2.0 90°C, pH = 6 2.3 19.1±2.0 30°C, pH = 4 66.0 26.4±2.0 60°C, pH = 4 31.0 24.5±2.0 90°C, pH = 4 16.0 25.2±2.0 between the mole fraction of magnesium assumed to be in the limestone and the magnesium ion solubility in solution. The combined solubilities of calcium and magnesium ions are displayed in Figures A-7 through A-g. For the three different computational runs, the calculated solubilities are the same. 66
5.3 DISSOLUTION RATE EXPERIMENTS: FREE DRIFT METHOD
A repeatability test for the free drift method was performed at a stirring rate of 750 rpm. In this test Maxville limestone was dissolved using the spinning basket reactor at
90°C. The results are shown in Figure 5-1 where the rectangles represent the first and the triangles the second experiment at the same conditions. The dissolution rate curves for both experiments are co-incident demonstrating good repeatability.
-2 ,,--.....
~ I en
x 6 -4 o 0 N 0 I 6 'i a 9 E ~J u 60 "0 -6 iD 1:1 0 x ~ Ch QtJA 8 en 6 ~ Q) 1fI~ ~ ~ - II 0 n ~ -8 u 0 [ E ~~ limestone Maxville o~ screen size -18/+ 16 0 ~ E 0 ~ sample LS890118A ~ # 6 0 temperature: 90°C ~
W -10 0 ~ ~ « 0 cr:: REPEATABIL TY TEST lqJ AT 750+/- 10 RPM 0 (9 0-12 ---.J 4 5 6 7 8 9 pH
Figure 5-1. Repeatability test for free drift method.
The experimental error for the free drift method was calculated at three pH values. At pH 4.5, 5.0 and 5.5 the 67 experimental error was determined to be ±O.4 x 10~, ±O.9 x 10~
6 and ±0.19 x 10- mmol x em? x S-I, respectively. Nevertheless, the reproducibility of the results obtained using the free drift method may be sensitive to the additive used.
To estimate the stirring rate at which the dissolution rate is no longer liquid-film mass-transfer controlled, experiments have been performed at varying stirrer speeds. The stirring rates ranged from 175 to 1400 rpm, while the solvent temperature was maintained at 90°C. A stirrer speed of 1000 rpm insures that the dissolution of Maxville limestone will be independent of stirrer speed. Figure 5-2 shows the combined results of these experiments.
-2 ~ I (f) 00000 175 1-10 RPM x ccccc 350 /-19 ~~M •• ~uu . Q Q Q -4 loA loA / IU ~r-M + .. a + + + + + N • + +A• 750 /-10 RPM I • • OOO~ p • • .g • ••••• 1 /-10 RPM • +A a •• • •• 1250; /-10 RPM E °Q)Oo •A • 0 • •• • •• 14001 1-10 RPM o -4il • 0 +:.,.. -6 0 +...,.-•• x 0 a't:JfJ _ ~ It • o ...... c.4 (f) 6 •• !I'& o + C+~ A· ••• Q) 0 - o C\.A .\\... 0 o a ~ ~ 6 ~.. -8 \J -- + ~ ~A6A·:.~ E 0 a <9+ 666· E o ~ +6"'A • <:» a o~ ~ • ~ . a ..t-4 ., W -10 ~ ~ ~. limestone Maxville A « • screen size °ib 0:::: -18/+16 ~ A • sample # : LS890118A ~ o temperature: 90°C 0-12 ---.J 4 5 6 7 8 9 pH
Figure 5-2. Effect of stirrer speed on observed dissolution rate. 68
5.3.1 Limestones
The results of free drift experiments without additives are shown in Appendix E. Figures E-l through E-3 are drawn to compare the dissolution rates of the five limestones used at either 30, 60 or 90°C. Figures E-4 through E-8 illustrate the dissolution rates of each single limestone at three different temperatures. For all limestones examined in this study, a general dissolution rate behaviour can be observed. The logarithm of the dissolution rate decreases in a linear fashion with increasing pH value of the solution. This is equivalent to a diagram which uses linear axes and in which the dissolution rate would decrease exponentially with increasing pH.
From the five limestones used in the free drift method the two dolomitic limestones, Carey and Bucyrus limestone, exhibit especially low dissolution rates at 30, 60 and 90°C which is shown in Table 5.4.
with increasing temperature the spread between the dissolution rates of the five limestones narrows. Considering a single limestone, a significant temperature effect can be seen only for a temperature difference of at least 60°C. 69 Table 5-4. Dissolution rates evaluated at pH = 5.5, using the free drift method. Temperature Limestone Dissolution rate
x 10-6 mmol/ (cm2 x s) 30°C Maxville O.10±O.19 Carey O.16±O.19 Vanport 0.50±0.19 Mississippi 5.01±0.19 Bucyrus O.18±O.19 60°C Maxville 2.51±O.19 Carey O.32±O.19 Vanport O.50±O.19 Mississippi O.40±O.19 Bucyrus O.10±O.19 90°C Maxville 1.41±O.19 Carey O.56±O.19 Vanport 2.00±O.19 Mississippi 2.51±O.19 Bucyrus 1.00±O.19
Dissolution rates of limestones have been studied by many investigators at varying experimental conditions. Plummer,
Wigley and Parkhurst (1978) used the free drift method to study the dissolution rate of calcite at 25°C for a pH near equilibrium, between 5.5 and 7. At a pH of 6.5 and only little
CO2 sparging they found the logarithm of the dissolution rate to be about -6.6 (non-logarithmic value: 2.51 x 10-7 mmol per cnr' per sec). At similar experimental conditions in the present study, Mississippi limestone at 30°C and a pH of 6.5 70 was found to have a logarithmic dissolution rate value of -7.1 (non-logarithmic value: 0.79 x 10-7 mmol per cm2 per sec).
Compared to the non-logarithmic value reported by Plummer et ale the dissolution rate obtained in the present study agrees reasonably well. The slight difference between those values may be caused by differences in the concentrations of limestone impurities.
5.3.2 ADDITIVES
The pH versus time curves obtained using the free drift method with the additives citric acid, glycine and sodium sulfite, are plotted in Figures F-2 through F-4. Figure F-1 shows a complete pH versus time curve for the dissolution of Maxville limestone without additive. The other drawings have a shortened x-axis for a better representation of the
important pH effects.
The pH versus time curve of 'pure' Maxville limestone has
the characteristic of a high slope at the beginning of dissolution. with advancing degree of dissolution and
increasing pH value, the slope is converging towards an equilibrium pH value of approximately 8.2, which is essentially reached after about 16 minutes (Table 5-5). Of course, this amount of time is dependent on the particle size of limestone used in the experiments which was in this case
the screen fraction between 1.00 and 1.18 mm. 71
Table 5-5. pH versus time values for the dissolution of Maxville limestone obtained using the free drift method.
Time 0 1 2 3 4 5 (min. ) pH 4.00 5.40 6.05 6.32 6.60 6.95
Time 6 7 8 9 10 11 (min. ) pH 7.28 7.50 7.66 7.87 8.02 8.20
Adding a small amount of citric acid to the solution leads to a different shape of pH versus time curves because of the buffer activity of citric acid. The time interval to reach an equilibrium pH is much longer, which is in agreement with the reported higher solubility of Maxville limestone using the additive citric acid. Also, from Figure F-2 it can be seen that the addition of citric acid yields a lower dissolution rate at low pH values when compared to the dissolution rate of
Maxville limestone in a solution without additive. The lower dissolution rate therefore results in a larger time interval to reach an equilibrium pH value.
A characteristic of the pH versus time curves using citric acid as an additive is the brief reversal of the pH drift direction. While an increase in solution pH is the by- product of limestone dissolution, the decrease in solution pH can be interpreted as limestone precipitation. This phenomenon is amplified with increasing citric acid concentration and might be caused by an initially high formation rate of 72 undissociated carbonic acid which only slowly escapes to the air. The reverse reaction of undissociated acid molecules to bicarbonate and carbonate ions is then favored by a progressively increasing pH. At a certain pH value, the reverse reaction of carbonic acid produces more hydronium ions than the dissolution of limestone uses. The pH drift trend is therefore reversed for a short time.
Adding glycine to the solution in which limestone is dissolved leads to pH versus time curves shown in Figure F-3. with increasing glycine concentration, the general trend is a reduction in pH change per unit time. This is understandable because the increase in glycine concentration provides a higher pH buffer capacity for the solution.
The addition of sodium sulfite to the solution generates the pH versus time curves which are exhibited in Figure F-4.
In the diagram there are three regions of particular interest.
The first region is located from 0 to 10 minutes where an increase in pH is followed by a pH reversal. Here, the size of the resulting peak is dependent on the additive concentration and is largest for the smallest sulfite concentration. The second region of interest includes the negative peaks with a sharp decrease in pH and following increase. The slope of the decrease and increase in pH once again seem to be related to the additive concentration. The third region of typical pH versus time curve behaviour is the positive peak which occurs 73 approximately at a pH of 4 .8. The sulfi te concentration determines the time after which this peak can be found.
The pH behaviour in the first region might be explained by a superposition of limestone dissolution using up protons with a dissociation reaction of sulfurous acid which reacts to bisulfite ions simultaneously releasing protons. Consequently, the amount of sulfurous acid present at the beginning of dissolution determines the size of the peak. with increasing additive concentration this peak decreases because of an increasing release of protons opposing the capture from limestone dissolution.
The second region is a result of Equation 4-68 in which the equilibrium is shifted strongly towards the side of the products. The reaction converts a major amount of carbonate ions to bicarbonate ions as long as bisulfi te ions are present. The sharp decrease in pH occurs, possibly, when bisulfite ions converted to sulfite ions are used up in subsequent reactions. It is likely that the decrease in pH is the result of the sudden reverse reaction of bicarbonate ions to carbonate ions. It should be noted here, that the evaluation of the pH versus time curve made after this effect has occurred, has been performed assuming that the additive is already consumed. Finally, the third region can be explained in a manner similar to that used in describing the phenomenon occurring in the pH versus time curves using citric acid as 74 additive.
The experiments for the free drift method have been evaluated with the BASIC program listed in Appendix D. The free-drift dissolution rates calculated using the program are shown in Figures E-l through E-8 and in Figures F-l through F
7. The dissolution rate of limestone in a solvent (distilled water) containing citric acid is initially high at a low pH value, but only slightly exceeding the dissolution rate of the limestone wit.hout; additive. This zone of increased dissolution rate is followed by a zone containing a drop in dissolution rate and eventually precipitation of limestone with the size of the disturbance dependent on citric acid concentration. At higher pH values, dissolution rates using citric acid are higher than without additive, especially around a pH of 6.8.
This is because at 60°C, a pK value of citric acid is located very close to that pH region of about 6.8.
The effect of the glycine is far less pronounced than in the case of citric acid. Limestone dissolution rates at pH values between 4 and 5.5 using the amino acid glycine as additive were found to be lower than limestone dissolution rates in a solution containing no additive. For pH values greater than 5. 5, the presence of glycine only slightly promotes the dissolution of limestone.
The reaction chemistry of the dissolution of limestone in 75 a solution containing sodium sulfite was found to be very complex. Therefore it was not possible to relate the whole pH versus time curve to actual dissolution rates. Nevertheless, a part of the pH versus time curve was evaluated after assuming that all bisulfite ions have been used up. The resulting dissolution rates are displayed in F-7.
5.4 DISSOLUTION RATE EXPERIMENTS: PH-STAT METHOD
From each pH-stat experiment, the experimental data obtained were plotted as the amount of Hel titrated per time.
An example is shown in Figure 5-3 where the titration curves are basically linear.
limestone Moxville 6 screen size -18/+16 sample # LS890118A sample wt. 2.25 g/1.25 I ,,--...., stirring rate : 1000 +/- 10 RPM en temperature : 30°C ""-.../ SLOPES: U ~S 0.00715413 PH 4 I4 ~S 0.00185988 PH 5 ~S 0.00147836 PH 6 Z ~S 0.000565797 PH 7 ~S 0.000261935 PH 7.4
0 00
o DDDDDD 'f;;;;;;""""""'t~;;;~~77f77f7;;;7;;7;~;77;;~~7;;;;;;;77;~777~ o 100 200 300 400 500 600 700 TIME (sec)
Figure 5-3. Amount of Hel titrated as a function of time. 76
The slopes of the linear curves have been determined by fitting a straight line through the experimental data. From these slopes, the dissolution rates were calculated according to Equation 4-79.
The experimental error for the pH-stat method was obtained at three different pH values. At pH 4.0, 5.0 and 6.0, the experimental error was calculated to be to.27 x 10~, to.15
5 X 10- and to. 03 x 10-5 mmol x em? x S-1 , respectively.
5.4.1 LIMESTONES
The pH-stat method was utilized to find the dissolution rates of Maxville, Carey, Vanport, Mississippi and Bucyrus limestones. As the name of the method implies, the pH was maintained constant at values of 4, 5, 6, 7. At pH values greater than 7 the equilibrium pH values, which are different for the five limestones, had to be considered. In most of those cases, a pH of close to 7.4 was maintained during the experiments.
Figures G-1 through G-3 in Appendix G represent the dissolution rates of those five limestones at 30, 60 and 90°C.
The effect of temperature on limestone dissolution rate is found to be rather small, while the limestone type is the dominating factor. For example, the dissolution rates of Carey and Bucyrus limestone are lower than the dissolution rates of 77 the other limestones at nearly all pH values investigated.
The temperature effect on each limestone type is shown in figures G-4 through G-8. For all five limestones, a change in temperature from 30 to 60°C results in the largest effect on limestone dissolution. In contrast to this, a temperature change from 60 to 90°C has only an insignificant influence on the dissolution rate of limestone.
Chan and Rochelle (1982) measured the dissolution of reagent grade CaC0 3 with N2 sparging in a solution containing
0.1 M CaCl2 • Using the pH-stat method they obtained dissolution rate constants at temperatures of 25 and 55°C.
These curves have a similar shape to those in the present study. Nevertheless a direct comparison is not possible because these rate constants need to be related to the actual dissolution rate via the dissolved limestone concentration.
The study of Plummer, Wigley and Parkhurst (1978) included experiments using the pH-stat and free drift methods. The free drift method was applied near the equilibrium pH while the pH-stat method was used at pH values far from equilibrium. At the pH where both methods overlap, the slopes of the rate of dissolution curves do not match each other. In the present study this problem could not be observed. However, dissolution rates at high pH values gained by the pH-stat method are higher than the rates gathered by the free drift 78 method (Table 5-6). This is due to the fact that the free drift method was initiated at a pH of 4. When the pH finally reached a value around 7.5, the calcium ion concentration in solution lead to a decrease in limestone dissolution rate.
Figure 5-6. Dissolution rates obtained for Maxville limestone at 60°C without additives.
pH = 4 pH = 6 pH = 8 Free drift 9 method 5.6 x 10-5 2.8 X 10-7 1.6 X 10- pH-stat 7 method 2.5 x 10-5 1.0 X 10-5 6.3 X 10-
5.4.2 ADDITIVES
The dissolution rates of Maxville limestone have been measured at 60°C in a solution containing the additive citric acid or glycine. As in the pH-stat experiments without additives, the dissolution rates were obtained by maintaining designated pH values. The additive sodium sulfite was found not to be suitable for evaluation in pH-stat experiments because of a high consumption rate of sulfite ions detected earlier by using the free drift method.
Figures H-l and H-2 in Appendix H summarize the results of the pH-stat experiments in which the additive concentration was varied from 5 to 25 mmol/l. The addition of 5 romol of citric acid leads to an increase in limestone dissolution rate, but only at a pH of 4. with increasing citric acid 79 concentration the dissolution rates are increased for all pH values, compared to the dissolution of Maxville limestone in water containing no additive. However, the spread of limestone dissolution rate data effected by the addition of citric acid is large at low pH values although it decreases with increasing solution pH.
The addition of small amounts of glycine produces similar effects in the spread of dissolution rate data. Nevertheless, glycine promotes the dissolution rate of Maxville limestone to a much lesser extent than does citric acid, and only at concentrations of 15 to 25 mmol/l with a solution pH greater than 5.
In the study of Chang and Brna (1986), citric acid in low concentrations was shown to improve 802 removal at the EPA
AEERL (Air and Energy Engineering Research Laboratory) limestone pilot plant for wet limestone fluegas desulfurization. At low additive concentrations, around 500 to
1000 ppm, citric acid was shown to be very effective for the capture of sulfur dioxide. In regard to the present study, it is not advisable to predict actual scrubber performance from the effect of citric acid on the dissolution rate of limestones. This is because sulfur dioxide was not included in the experimental conditions and renders the reaction chemistry very different from the studied one. 80
6.0 CONCLUSIONS AND RECOMMENDATIONS
The solubility values acquired from the experiments indicate a relationship between the molar percentages of CaC03
2 2 and MgC03 in the parent limestone and the Ca + and Mg + ion concentrations in solution at equilibrium. A high molar percentage of CaC03 in the parent limestone yields a high solubility of Ca2+ ions in solution at equilibrium. The same statement is valid for magnesium. The amount of impurity in the parent limestone was found not to be related to the combined Ca2+ and Mg2+ solubilities in distilled water.
The effect of temperature on limestone solubility in the range of 30 to 90°C was identified to be rather small in comparison to the pH effect between pH 4 and pH 8. On the average, a temperature increase from 30°C to 90°C resulted in a 50% increase in limestone solubility while a pH decrease from 8 to 4 yielded an enhancement in solubility of 250%.
The influence of the additive citric acid at concentrations in the range of 5 mmol/l to 25 mmol/l was found to increase the combined Ca2+ /Mg2+ solUbility of Maxville limestone by 50 to 100% dependent on the solution pH and temperature. Nevertheless, at 30°C and pH 4 no change in solubility was observed. The presence of glycine ions in solution in the same range of concentration affected the solubility of Maxville limestone by only a few percent. The 81 addition of sodium sulfite resulted in an increased Maxville
limestone solubility of about 10% at all experimental conditions.
Previous investigators of limestone solubility have often reported values without reporting the pH value at which the
solubilities were measured. In those cases it must be assumed that the pH at which the solubility was measured was the equilibrium pH of the solvent exposed to the atmosphere. Such
a pH would not be representative of values found in a wet flue gas desulfurization system. This is because the pH in a wet
scrubber is generally maintained at a value of about 5 while the equilibrium pH of limestone dissolved in distilled water
is about 8.
Limestone solubility is not likely to play a major role
in wet flue gas desulfurization because the amount of ions represented by the solubility value would be consumed rapidly
in a scrubbing operation. More likely, the dissolution rate would be the rate limiting factor for such processes.
The effect of temperature on limestone dissolution rate was investigated using the free drift and pH-stat method. Both methods showed that a difference in temperature from 30 to
90°C increases limestone dissolution rates by about a factor
of 10. The effect of the limestone source on dissolution rate was found to be very important. The five limestones studied 82 using the free drift method yielded a variation in their dissolution rates of about 10 to 100 times at 30°C and about
10 to 50 times at 60 and 90°C, due to the effect of limestone type on the dissolution rate. The variations in dissolution rates observed by the pH-stat method showed differences of about 10 to 50 times only.
The influence of the additive citric acid on Maxville
limestone dissolution rate was studied using the free drift method. The obtained results showed an increase in dissolution rate with increasing additive concentration at pH values
larger than 5. During the continuation of the experiments, the solvent appeared to be quickly oversaturated with respect to calcium and magnesium ions. While in this state, the pH trend reversed for a couple of minutes. The reversed pH trend was believed to be related to a precipitation of CaC03 and MgC03 from an oversaturation of the solvent. The pH-stat method using the same additive revealed a signifi~ant enhancement in
Maxville limestone dissolution rate only at a pH value of 4.
The effect of the additive glycine on Maxville limestone dissolution rates was investigated using the free drift and pH-stat method. The free drift method revealed no improvement
in dissolution rate at all pH values, while the pH-stat method
indicated a slight enhancement at glycine concentrations
exceeding 15 mmol/l. 83
The free drift method appeared to be a convenient technique to determine the dissolution rates of limestones in a solution containing no additive. When additives like citric acid or glycine were involved in the dissolution of limestone, the evaluation of the resulting pH versus time curves were more complicated, but still manageable. The free drift method was found to be of limited use for dissolution rate measurements when the additive sodium sulfite was tested.
The pH-stat method was successfully applied to limestone dissolution rate measurements in distilled water. The
influence of the additives citric acid and glycine on the dissolution rates of limestones could also be examined using the pH-stat method. This method was found not to be suitable for determining the dissolution rates of limestones in a solution containing sodium sulfate. This was due to the fact
that the initial assumption of two hydronium ions being
necessary to dissolve one Ca2+ or Mg2+ ion, did not apply.
Shortly after initiating an experiment the pH decreased from
a value of four to about 2.5. This decrease in pH was caused
by reaction chemistry involving the sulfate ion.
Dissolution rates obtained without additives using the pH-stat method were in agreement with those measured by the
free-drift method at pH values less than four. For higher pH
values, dissolution rates observed by the pH-stat method indicated higher dissolution rates than those obtained by the 84 free drift method at similar conditions. The reason for this difference in dissolution rates is the concentration of Ca2 + and Mg2+ ions in solution. This concentration keeps increasing throughout the free drift experiment. This is a clear disadvantage of the free drift method.
Further studies should be directed towards using specific ion electrodes for measuring limestone dissolution rates, instead of determining the calcium and magnesium ion concentration indirectly through the change in solution pH. Furthermore, it could be desirable to use a continuous sampling system, in combination with an ion chromatograph, to remove samples from the reactor in which the limestone dissolves. 85
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APPENDICES 90
APPENDIX A
LISTING AND RESULTS OF SEMIEMPIRICAL MODEL FOR THE ESTIMATION OF CALCIUM AND MAGNESIUM ION SOLUBILITIES 91 SEHIEMPIRICAL MODEL FOR THE CALCULATION OF CALCIUM AND MAGNESIUM ION SOLUBILITIES FROM DIFFERENT LIMESTONE TYPES:
1000 CLS 1010 DIM DH(15):DIM DS(15):DIM DG(15) 1020 PRINT"*** CALCULATION OF SOLUBILITY OF Ca2+ AND Mg2+ ***" 1030 PRINT 1040 PRINT"Ca-FRACTION IN THE MINERAL ="i:INPUT ACT1 1050 PRINT"Mg-FRACTION IN THE MINERAL ="i:INPUT ACT2 1060 PRINT 1070 PRINT"DO YOU WANT TO CREATE A DATA FILE"i:INPUT A$ 1080 PRINT 1090 PRINT"REACTIONS AND IONIC EQUILIBRIA:":PRINT 1100 PRINT" 1.) CaC03(s.) --- Ca2+ + C032-" 1110 PRINT" 2.) C032- + H+ --- HC03- 11 1120 PRINT" 3.) HC03- + H+ --- H2C03(aq.)" 1130 PRINT" 4.) H2C03(aq.) --- C02 (g.) + H20(l.)" 1140 PRINT" 5.) MgC03(s.) --- Mg2+ + C032-" 1150 PRINT" 6.) CaC03(aq.) --- Ca2+ + C032-" 1160 PRINT" 7.) MgC03(aq.) --- Mg2+ + C032-" 1170 PRINT" 8.) Ca2+ + HC03 --- (CaHC03)+" 1180 PRINT" 9.) Mg2+ + HC03 --- (MgHC03)+" 1190 PRINT"10.) H20 --- H+ + OH-" 1200 1205 IF A$ <> "Y" THEN 1240 1210 OPEN"O",#l,"A:\MODEL.DA1":OPEN"O",#2, "A: \MODEL.DA2" :OPEN"O",#3,"A:\MODEL.DA3" 1220 PRINT #l,"INTRINSIC SOLUBILITIES OF Ca2+":PRINT #1," " :PRINT #2,"INTRINSIC SOLUBILITIES OF Mg2+":PRINT #2," " :PRINT #3,"INTRINSIC SOLUBILITIES OF Ca2+/Mg2+" :PRINT #3," " 1231 PRINT #1," "i"PH=4.0 "i"PH=4.5 "j"PH=5.0 ",. "PH=5.5 UjUPH=6.0 , j"PH=6.5 ",. "PH=7.0 "j"PH=7.5 j"PH=8.0" 1232 PRINT #2," "j"PH=4.0 "j"PH=4.5 j"PH=5.0 ",. "PH=5.5 "i"PH=6.0 j"PH=6.5 " ,. "PH=7.0 "i"PH=7.5 j"PH=8.0" 1233 PRINT #3," "j"PH=4.0 "j"PH=4.5 j"PH=5.0 ",. "PH=5.5 "j"PH=6.0 j"PH=6.5 ",. "PH=7.0 "j"PH=7.5 j"PH=8.0" 1234 PRINT #1, "TEMP":PRINT #2, "TEMP":PRINT #3, "TEMP" 1240 FOR TEMP = 273+30 TO 273+90 STEP 10 1250 IF A$ = "Y" THEN PRINT #1,"":PRINT #1,TEMP-27 3 i " "i :PRINT #2,"":PRINT #2,TEMP-27 3 i " "i :PRINT #3,"":PRINT #3,TEMP-27 3 i " "i 1255 GOSUB 2070 1260 FOR PH = 4 TO 8 STEP .5 1270 GOSUB 1410 1280 PRINT 1290 PRINT"PH ="jPH,"TEMP ="jTEMP-273j"DEGREES CIt 92
1300 PRINT"INTRINSIC Ca2+ SOLUBILITY="iCONC5+CONC11 +CONC13 1310 PRINT"INTRINSIC Mg2+ SOLUBILITY="iCONC6+CONC12 +CONC14 1311 PRINT"INTRINSIC CA2+/MG2+ SOLU. =" i CONC5+CONC6+CONC11 +CONC12+CONC13 +CONC14 1320 IF A$ = "Y" THEN PRINT #1,USING"##.#AAAA"iCONC5 +CONC11+CONC13i :PRINT #2,USING"##.#AAAA"iCONC6 +CONC12+CONC14i 1321 IF A$ = lIy" THEN PRINT #3,USING"##.#AAAAliCONC5 +CONC6+CONC11+CONC12+CONC13+CONC14i 1330 NEXT 1340 NEXT 1350 END 1360 1370 1380 REM SUBROUTINE TO FIND Ca2+ AND Mg2+ CONCENTRATIONS
AT EQUILIBRIUM 1390 1400 1410 REM CaC03 (s.) Substance 1 1420 REM MgC03 (s.) Substance 2 1430 REM C02 (g. ) Substance 3 1440 REM H20(l.) Substance 4 1450 REM Ca2+ Substance 5 1460 REM Mg2+ Substance 6 1470 REM C032- Substance 7 1480 REM H+ Substance 8 1490 REM HC03- Substance 9 1500 REM H2C03 (aq.) Substance 10 1510 REM CaC03 (aq. ) Substance 11 1520 REM MgC03 (aq ,) Substance 12 1530 REM (CaHC03)+ Substance 13 1540 REM (MgHC03)+ Substance 14 1550 REM OH- Substance 15 1560 1570 A = .488335 + 7.37831E-04 * (TEMP-273) + 2.7193E-06 * (TEMP-273)A2 1580 B = .324084 + 1.59142E-04 * (TEMP-273) + 3.99458E-08 * (TEMP-273)A2 1590 1600 A05 = 5 A06 = 5.5 : AD? = 5.4 : ADa = 9 : A09 = 5.4 :A013 = 6 1610 B05 = .165 B06 = .2 B07 = 0 : B08 = 0 : B09 = 0 :B013 = 0 1620 A014 = 4 A015 = 3.5 1630 B014 = 0 B015 = 0 1640 1650 GAMMAS = 1 : Z5 = 2 93
1660 GAMMA 6 = 1 Z6 = 2 1670 GAMMA 7 = 1 Z7 = 1 1680 GAMMA8 = 1 Z8 = 1 1690 GAMMA9 = 1 Z9 = 1 1700 GAMMA10 = 1 1710 GAMMA13 = 1 Z13 = 1 1720 GAMMA14 = 1 Z14 = 1 1730 GAMMA15 = 1 Z15 = 1 1740 1750 ACTS = 10A(-PH) 1760 PRESS3 = .00039 1770 1780 CONC10 = PRESS3 / (K(4) * GAMMA10) 1790 CONC9 = CONC10 * GAMMA10 / (K(3) * GAMMA9 * ACT8) 1800 CONC7 = CONC9 * GAMMA9 / (K(2) * GAMMA7 * ACT8) 1810 FRAC7 = CONC7 / (CONC7 + CONC9 + CONC10) 1820 CONC5 = SQR(ACT1 * K(l) / (GAMMA5 * GAMMA5 * FRAC7 * «ACT2 * K(5) / (ACTl * K(l») + 1») / «4A(14-PH»/(330*(14-PH») lS30 CONC6 = SQR(ACT2 * K(5) / (GAMMA6 * GAMMA6 * FRAC7 * «ACT1 * K(l) / (ACT2 * K(5») + 1») / «4A(14-PH»/(330*(14-PH») 1840 CONC13 = K(S) * CONC5 * GAMMA5 * CONC9 * GAMMA9 / GAMMA13 1850 CONC14 = K(9) * CONC6 * GAMMA6 * CONC9 * GAMMA9 / GAMMA14 1860 CONC11 = CONC5 * GAMMA5 * CONC7 * GAMMA7 / K(6) 1870 CONC12 = CONC6 * GAMMA6 * CONC7 * GAMMA7 / K(7) 1880 ACT4 = 1 - .017 * (CONC5 + CONC6 + CONC7 + CONCS + CONC9 + CONC10 + CONC11 + CONC12 + CONC13 + CONC14 + CONC15) 1890 CONC15 = K(10) * ACT4 / (ACT8 * GAMMA15) 1900 1910 I = .5 * (CONC5 * Z5 A2 + CONC6 * Z6 A2 + CONC7 * Z7 A2 + (ACTS/GAMMA8) * Z8 A2 + CONC9 * Z9 A2 + CONC13 * Z13 A2 + CONC14 * Z14 A2 + CONC15 * Z15 A2) 1920 1930 GAMMA5 = 10A(-«A * Z5 A2 * SQR(I»/(l + A05 * B * SQR(I») + B05 * I) 1940 GAMMA6 = 10A(-«A * Z6 A2 * SQR(I»/(l + A06 * B * SQR(I») + B06 * I) 1950 GAMMA7 = 10A(-«A * Z7 A2 * SQR(I»/(l + A07 * B * SQR(I») + B07 * I) 1960 GAMMA8 = 10A(-«A * ZSA2 * SQR(I»/(l + A08 * B * SQR(I») + B08 * I) 1970 GAMMA9 = 10A(-«A * Z9 A2 * SQR(I»/(l + A09 * B * SQR(I») + B09 * I) 1980 GAMMA13 = 10A(-«A * Z13 A2 * SQR(I»/(l + A013 * B * SQR(I») + B013 * I) 1990 GAMMA14 = 10A(-«A * Z14 A2 * SQR(I»/(l + A014 * B * SQR(I») + B014 * I) 2000 GAMMA15 = 10A(-«A * Z15 A2 * SQR(I»/(l + A015 * B * SQR(I») + B015 * I) 2010 94
2020 IF ABS(OLD-I) < .000001 THEN RETURN 2030 OLD = I 2040 GOTO 1750 2050 2060 2070 REM SUBROUTINE TO FIND EQUILIBRIUM CONSTANTS AT
SPECIFIC TEMPERATURE 2080 2090 2100 R = 8.3143 2110 C = 2.302585 2120 2130 OHO(l) = -1207720 2140 OHO(2) = -1113688 2150 OHO(3) = -393780 2160 OHO(4) = -286020 2170 DH(5) = -543190 2180 OH(6) = -467160 2190 OH(7) = -677590 2200 OH(8) = o 2210 OH(9) = -692450 2220 OH (10) = -700120 2230 2240 050(1) = 92.95 2250 080(2) = 65.73 2260 050(3) = 213.82 2270 080(4) = 69.99 2280 08(5) = -53.17 2290 05(6) = -138.16 2300 OS(7) = -56.94 2310 OS(8) = o 2320 05(9) = 91.27 2330 OS(10) = 187.57 2340 2350 TO = 298 2360 T1 = 400 2370 T2 = 600 2380 2390 CPO(1) = 81.94 2400 CP1(1) = 97.13 2410 CP2(1) = 110.53 2420 2430 CPO(2) = 75.57 2440 CP1(2) = 90.18 2450 CP2(2) = 107.77 2460 2470 CPO(3) = 37.14 2480 CP1(3) = 34.29 2490 CP2(3) = 36.34 2500 2510 CPO(4) = 75.34 95 2520 CP1(4) = 41.32 2530 CP2(4) = 47.35 2540 2550 OT = .01 2560 2570 FOR I = 1 TO 4 2580 INT1 = 0 2590 INT2 = 0 2600 FOR T = TO TO TEMP STEP DT 2610 CP = CPO(I) * «T-T1) * (T-T2» I «TO-T1) * (TO-T2» + CP1(I) * «T-TO) * (T-T2» I «T1-TO) * (T1-T2» + CP2(I) * «T-TO) * (T-T1» I «T2-TO) * (T2-T1) ) 2620 INT1 = INT1 + CP * OT 2630 INT2 = INT2 + (ep/T) * OT 2640 NEXT 2650 OB(I) = OBO(I) + INT1 2660 05(1) = 050(1) + INT2 2670 NEXT 2680 2690 FOR I = 1 TO 15 2700 DG(I) = OB(I) - TE:MP * os (1) 2710 NEXT 2720 2730 OGR(1) = OG(5) + DG· (7) - DG(l) 2740 OGR(2) = OG(9) - DG, (7) - DG(8) 2750 DGR(3) = OG(10) - OG(9) - DG(8) 2760 OGR(4) = DG(3) + DG(4) - DG(10) 2770 OGR(5) = OG (6) + DG(7) - DG(2) 2780 2790 FOR I = 1 TO 5 2800 K(I) = EXP(-OGR(I)/(R * TEMP» 2810 NEXT 2820 2830 K(6) = 10A(-(-1228.732 - .299444*TEMP + 35512.75/TEMP + 485.818 * (LOG(TEMP)jC») 2840 K(7) = 10A(-(.991 + .00667 * TEMP» 2850 K(8) = 10A(1209.12 + .31294 * TEMP - 34765.05/TEMP - 478.782 * (LOG (TEMP) IC) ) 2860 K(9) = 10A(-59.215 + 2537.455jTEMP + 20.92298 * (LOG(TEMP)/C» 2870 K(10) = 10A(-283.971 + 13323/TEMP - 5.069842E-02*TEMP + 102.24447 * (LOG(TEMP)jC) - (1119669/(TEMP*TEMP») 2880 2890 PRINT:PRINT 2900 PRINT"TEMPERATURE ="iTEMP-273j"DEGREES C":PRINT 2910 FOR I = 1 TO 10 2920 PRINT"K"jIi" ="iK(I) ,"LOG K"iIi" ="iLOG(K(I»/C 2930 NEXT 2940 RETURN 96
~ I OLO '""-~ xLO S Q E~ cl{") .- IV) u c 8l!) Ir' +- '"" ~o () a c)
Figure A-l. Calculated Ca2 + solubility for stone with l/Ica=O • 5, t/!Mg==O. 5
"'t" I OLO ~ C',j Xl[) S Q E~ cL[) .- IV) (j c 8lO Ir' +- '\"' C"J o () a c)
Figure A-2. Calculated Ca2+ solubility for stone with l/Ica=O · 8, l/IMg== 0 . 2 97
"=t" I a lC) ~ xl(') S- o EO .S ~ <..) c:: 8lf) l~ + C'..l CJ (.)
Figure A-3. Calculated Ca 2+ solubility t/lca=O • 99 , for 1/;Mlg=O. 01 stone with 98
Figure A-4. Calculated Mg2+ solubility for stone with l/;ca=O • 5, t/;Mg==O. 5
Figure A-5. Calculated Mg2+ solubility for stone with t/;Ca=O • 8, t/;Mg==O. 2 99
""*"I 20 xlV") S o Eo .~ C'-.J c..) c: oyo + C'J C)) ~
Figure A-6. Calculated Mg2+ solubility for stone with '/Ica=O • 99, '/IMg=O. 01 100
o ci 1 '" a
Figure A-7. Calculated Ca2+/ Mg2+ solubility for stone with t/lca=O • 5, t/lMg==O. 5
o o "tI '" a
Figure A-8. Calculated Ca2+/Mg2+ solubility for stone with t/lca=O • 8, t/JMg==O. 2 101
a c:) 1 I'- a xU) S~ a E .S a Ol!) CI""')o u I +- ll) t"r' ~"("-.
>~ 8~ a
Figure A-9. Calculated Ca2+/ Mg2 + solubility for stone with 1/Ica=O • 99, tPMg=O. 01 102
APPENDIX B
SOLUBILITIES OF CA2 + , MG2 + AND THE COMBINED VALUE FOR THE LIMESTONES MAXVILLE, CAREY, VANPORT, MISSISSIPPI AND BUCYRUS 103
Figure B-1. Experimental Ca2 + solubility for Maxville limestone.
~ I o<-Q ~t") S- o E"¢ .S C'\l o c: o u C''\j IT- + C'\1a (J
Figure B-2. Experimental Ca2+ solubility for Carey limestone. 104
~ I 0<.0:t-r) S- o E~ .S C'\J U c c ~~ + C\Ja (.)
Figure B-3. Experimental Ca 2+ solubility for Vanport limestone.
~ I at{):IVJ S- o E~ .S C'\J U c o y~ + C\Ja ()
Figure B-4. Experimental Ca 2+ solubility for Mississippi limestone. 105
~ I 0<.0:NJ <. -0 E"'t- .s C'-,J o c: oyC"'l + ~ C) (.)
Figure B-5. Experimental Ca2+ solubility for Bucyrus limestone. 106
Figure B-6. Experimental Mg2+ solubility for Maxville limestone.
":t I 2~ xT- S- o E .S CD u c o (j \~ + C'..1 C)) ~
Figure B-7. Experimental Mg2+ solubility for Carey limestone. 107
~ I 2C"J x""'"- S o E .~ CXJ u c o o l"t + ('-.j CJ') ~
Figure B-8. Experimental Mg2 + solubility for Vanport limestone.
~ I o ~C"\j >< ,-- S- o E .S co
(J c: o o I"'i- + C\J o- ~ a
Figure B-9. Experimental Mg2+ solubility for Mississippi limestone. 108
-.::t I a C'\l x~ S a E .S CXJ U c: o u I~ + C"1 en ~
Figure B-10. Experimental Mg 2 + solubility for Bucyrus limestone. 109
Figure B-11. Experimental Ca 2+/ Mg2+ solubility for Maxville limestone.
Figure B-12. Experimental Ca 2+/ Mg2+ solubility for Carey limestone. 110
Figure B-13. Experimental Ca 2+/ Mg2+ solubility for Vanport limestone.
Figure B-14. Experimental Ca2+/Mg2+ solubility for Mississippi limestone. 111
Figure B-15. Experimental Ca2+jMg2+ solubility for Bucyrus limestone. 112
APPENDIX C
SOLUBILITY OF MAXVILLE LIMESTONE AT VARIOUS ADDITIVE CONCENTRATIONS AND EXPERIMENTAL CONDITIONS 113
r 30 o - x - I I I
0 0 -r-- :z I 0
u + ... z + o 0 0 U10- I c + - N cr> ~ c~ 00000 T 30°C. pH 4 <, 00000 T 30°C, pH 8 + ~~~~~ T 90°C pH 4 N o +++++ T 90°C: pH 8 UO-t-'1--r-r-r-.,.....,....,...-y--r--T~r--r-,.--,-.,.--r--r--r---r-T--.---,--r-or--r--r-r--r-T"'--r-T--.---,--r-or--r--r-r--r-T"'-,--oT--r--"r--r-~""T'--. I 15 10 15 o 5 10 1 2 2 CITRIC ACID CONe. IN MOL/L X 1 0-3
Figure C-l. Solubility of Ca 2+ and Mg2+ ions gained from the dissolution of Maxville limestone in distilled water as a function of citric acid concentration.
•I_30 00000 T 4 o _ 00000 T 8 ~~A~~ T 4 _ +++++ T x 8 --.J ~ --.J _- 020 ~ ..s -to-- I z - I I I ..:~ :zU _ o U10- I + o o ~ o o cr> ~ J <, + ... + + ~o ..I uO--+--r--r-r--r-~-r-T"'-,--,.--.---,--r-r--r-~-r--r---r-T--.---,--r-~.,--,---r--r-~--.---,--r-r--r-"--'---r-T"'--r-T~~~"'--' I o 15 GLYCINE CONC. IN MOL/L X 10-3
Figure C-2. Solubility of Ca 2+ and Mg2+ ions gained from the dissolution of Maxville limestone in distilled water as a function of glycine concentration. 114
... 00000 T I 30 30°C pH 4 a ccccc T 30°C: pH 8 AAAAA T 90°C. pH 4 +++ ... + T x = 90°C, pH = 8 --.J <, I .-.J T I 020 2 1 0
0 Z I 0 0 u z 010 °I + C'J + Q) ... ~ + a <, 0 + 0 N 0 0 0 0 5 10 15 20 25 SODIUM SULFITE CONe. IN MOL/L X 10-3
Figure C-3. Solubility of Ca 2+ and Mg2+ ions gained from the dissolution of Maxville limestone in distilled as a function of sodium sulfite concentration. 115
APPENDIX D
EVALUATION PROGRAM FOR THE FREE DRIFT METHOD INCLUDING THE ADDITIVE CITRIC ACID AND GLYCINE 116 The following BASIC program was written to evaluate free drift experiments, which provided pH values as a function of time. Those pH values had to be related to actual dissolution rates. The program is designed for the evaluation of five different limestones which can used in combination with or without the additives citric acid and glycine.
The theoretical basis for the evaluation of the pH/time data points is the formula,
V , id f • 1 ~qu~. M (0-1) Astone f s
in which every two successive pH values are inserted. The f M and f s in the equation above, are the mUltiplication and the stochiometric factor, respectively. The theoretical justification for those factors has been given in the previous chapter. Vliquid is the volume of the solvent, while the character
A denotes the total surface area of the limestone particles used.
The influence of temperature on both correction factors has been considered. Since the correction factors are derived from equilibrium constants, expressions for their temperature dependency can be found in the following program listing. 117 EVALUATION PROGRAM FOR THE FREE DRIFT METHOD INCLUDING THE ADDITIVES CITRIC ACID AND GLYCINE
10 CLS 110 DIM PH1(50) :DIM PH2(50) 120 DIM TI1(50) :DIM TI2(50) 130 DIM DELT(50) :DIM PH(50) 140 DIM STOCHIO(50):DIM RATE(50) 150 DIM LORATE(50) 160 DIM FACTOR(50) 170 PRINT"TEMPERATURE IN CELSIUS =U i : INPUT TEMP : PRINT 175 PRINT"VOLUME IN LITER =u i : INPUT VOLUME: PRINT 180 PRINT"HOW MANY VALUES ui:INPUT N : PRINT 190 PRINT"DO YOU WANT TO CREATE A DATA FILE"i:INPUT A$ : PRINT 191 PRINT"IS AN ADDITIVE PRESENT ui:INPUT B$ : PRINT: PRINT 195 196 IF B$ = "N" THEN 209 198 PRINT"CITRIC ACID [l]U 200 PRINT"GLYCINE [2]" 204 INPUT CHOICE:PRINT 206 PRINT"CONCENTRATION IN MMOLESjL Ui:INPUT CADDI :PRINT:PRINT 207 CADDI = CADDI * .001 208 209 FOR I = 1 TO N 210 PRINT"TIME IN SECONDS =ui:INPUT TI1(I) 212 PRINT"PH =ui:INPUT PH1(I):PRINT 220 IF I = 1 THEN 250 230 TI2(I-l) = TI1(I) 240 PH2(I-l) = PH1(I) 250 NEXT 260 265 A = 45.6825 270 FOR I = 1 TO N-l 275 FACTOR (I) = 1 280 DELT(I) = TI2(I) - TI1(I) 290 PH(I) = (PH1(I) + PH2(I»/2 300 PH = PH(I):GOSUB lOOO:STOCHIO(I) = SToeHIO 330 IF CHOICE = 1 THEN GOSUB 2500 340 IF CHOICE = 2 THEN GOSUB 3500 460 RATE(I) = «(10A(-PH1(I» - 10A(-PH2(I»)jDELT(I» jSTOCHIO(I»*lOOO*VOLUME*FACTOR(I)/A 470 REM LORATE(I) = LOG(RATE(I»/2.302585 480 NEXT 490 495 PRINT 118
500 PRINT" PH","STOCHIOM.","RATE","LOG RATE", "FACTOR" 510 PRINT"","FACTOR","(MMOLES/","(MMOLES/" 512 PRINT"","","CMA2*S)","CMA2*S)" 515 PRINT 520 FOR I = 1 TO N-l 530 PRINT USING"##.### "; PH (I) , : PRINT USING"##.#### "iSTOCHlO(I), : PRINT USING,,##.####AAAA "iRATE(I), : PRINT USING"###.#### "i LORATE(I), : PRINT USING"########.#"i FACTOR(I) 540 NEXT 550 : 560 IF A$ = "Y" THEN GOSUB 2000 980 END 990 991 1000 REM SUB R 0 UTI NE S T 0 CHI 0 1001 1002 REM SUBSTANCE 1 H+ 1004 REM SUBSTANCE 2 HC03 1005 REM SUBSTANCE 3 H2C03 1008 1010 K1 = 10A(-(6.57905 - .0124614 * TEMP + 1.34673E-04 * (TEMpA2») 1020 IF TEMP> 48 THEN K1 = 10A(-6.29) 1030 K2 = 10A(-(10.6205 - .0138682 * TEMP + 9.538541E-05 * (TEMpA2») 1040 IF TEMP> 70 THEN K2 = 10A(-10.12) 1048 1049 CONC1 = 10A(-PH) 1050 YSUBST2 = 1/(1 + K2/CONCl + CONC1/Kl) 1060 YSUBST3 = 1/(1 + K1*K2/(CONCI A2) + K1/CONC1) 1070 STOCHlO = YSUBST2 * 1 + YSUBST3 * 2 1100 RETURN 1120 1121 2000 REM SUB R 0 UTI NE DATA FILE 2001 2010 OPEN "O",#1,"A:CITRIC\MMOL25.DAT" 2020 FOR I = 1 TO N-1 2030 PRINT #l,PH(l),RATE(I): REM LORATE(I) 2040 NEXT 2050 CLOSE 1 2100 RETURN 2120 2121 2500 REM SUB R 0 UTI NE CIT RIC ACID 2501 2505 PH = PH2(I):GOSUB 3000:DELTA = DELTAl 2510 PH = PH1(I):GOSUB 3000:DIFF = DELTA - DELTA1 2515 IF PH1(l) = PH2(l) THEN 2540 2520 FACTOR(l) = 1 + DIFF/(10A(-PH1(I»-10A(-PH2(I») 119 2540 RETURN 2550 2551 3000 REM SUB R 0 U T INEF ACT 0 R
CIT RIC ACID 3001 3002 REM SUBSTANCE 4 C6H807,O 3003 REM SUBSTANCE 5 C6H807,G 3004 REM SUBSTANCE 6 C6H707-,G 3005 REM SUBSTANCE 7 C6H607 2-,G 3006 REM SUBSTANCE 8 C6H507 3-,G 3007 3010 K1 = 8.0727E-04 3020 K2 = 1.6795E-05 3030 K3 = 2.7484E-07 3040 3045 MOLES4 = CADDI * VOLUME 3050 CONCl = 10A(-PH) 3060 YSUBST5 = 1/(1 + K1/CONC1 + K1*K2/(CONC1 A2) + K1*K2*K3/(CONC1 A3» 3070 YSUBST6 = 1/(1 + K2/CONC1 + K2*K3/(CONC1 A2) + CONC1/K1) 3080 YSUBST7 = 1/(1 + CONC1/K2 + K3/CONC1 + (CONC1 A2)/(Kl*K2» 3090 YSUBST8 = 1/(1 + (CONC1 A2)/(K2*K3) + CONC1/K3 + (CONC1 A3)/(K1*K2*K3» 3100 DELTA1 = MOLES4 * (YSUBST6 * 1 + YSUBST7 * 2 + YSUBST8 * 3) 3120 RETURN 3130 3131 3500 REM SUB R 0 UTI N E GLYCINE 3501 3505 PH = PH2(I):GOSUB 4000:DELTA = DELTA1 3510 PH = PH1(I):GOSUB 4000:DIFF = DELTA - DELTA1 3520 FACTOR(I) = 1 + DIFF/(10A(-PH1(I»-10A(-PH2(I») 3540 RETURN 3550 3551 4000 REM SU B R 0 UTI N E F ACT 0 R GLYC I NE 4001 4002 REM SUBSTANCE 9 GLYCINE,O 4003 REM SUBSTANCE 10 H3N+ - CH2 - COOH,G 4004 REM SUBSTANCE 11 H3N+ - CH2 - COO-,G 4005 REM SUBSTANCE 12 H2N - CH2 - COO-,G 4007 4010 K1 = 10A(-2.35) 4020 K2 = 10A(-9.78) 4040 4045 MOLES9 = CADDI * VOLUME 4050 CONC1 = 10A(-PH) 4060 YSUBST10 = 1/(1 + K1/CONC1 + K1*K2/(CONC1 A2» 4070 YSUBST11 = 1/(1 + CONC1/K1 + K2/CONC1) 120 4080 YSUBST12 = 1/{1 + (CONClA2)/(Kl*K2) + CONC1/K2) 4100 DELTAl = MOLES9 * (YSUBSTll * 1 + YSUBST12 * 2) 4120 RETURN 121
APPENDIX E
LIMESTONE DISSOLUTION RATES WITHOUT ADDITIVES OBTAINED USING THE FREE DRIFT METHOD 122
-2 - - sample ~t. 2.25 c /1.25 I - screen < ize M -1t1+16 I - tempera ure 30°C (J1 - • stirring ate 1000 +-/- 10 RPM -4- N A • I - 0 • A 6 E .c. 0 A • ~.e 0. A u •• 0 0 A • -6 • • .DO en Ac:I.cP• A Q) - c·fi·c A • 0 . A • .A A • o - 0 I - 0 o •••A A • o !:( 0 Cl •• II . E - A - -8 Q A . - 0 o • A • E - 0 &) ...... - 0 A A 0 • - c . A . - c . 0 ~ - 0 . • lJ.J 0 A . Limes ones: 0 .. • • 0 • r-- 0 0 0 <{ -10 • 0 • 00000 ..,~ Moxvil e LS8901 18A - 0 AA 0::: o 0 c a a Carey 0 )0 • LS0492c7 0 A AAAAA Vanpo t LS0691C4 0 0 0 00 A C) ..... Missis sippi LS0691C8 ••••• Bucyri s LS0492E 6 o--.J -12 3.5 4.5 5.5 6.5 7.5 8.5 pH
Figure E-l. Limestone dissolution rates at 30°C.
-2 - - sample wt. 2.25 q /1.25 I ...... --... screen ( ize M -1 E1+16 I - tempera ure 60°C (J1 stirring ate 1000 ~/- 10 RPM -4 • N A • 0 0 I c. c· o ~ .0 0 A E ·0 0 A U • 0 • -6 . ~ 0 en . 0 Q) ... c· ~A 0 - •••• ...;a. 0 c 0 0 . "~'Iifb.A 0 !JAA E ...... A 0 -8 - A JAI 0 E • 0 . A 0 ""'--"'" .1fJ 0 .0 A ~ • ·0. 0 l..LJ Limes ones: ••• o. A ~ A r--- o • "- ° <:(-10 • • 00000 Maxvil '0 0 e LS89011 8A ... • A 0:::: [] 0 c [] [] Carey LS0492c 7 . A A A A A A . A Vanpo t LS0691C 4 A C) ••• •• Missis sippi LS0691C8 • •••• Bucyrt s LS0492~ 6 o--.J -12 3.5 4.5 5.5 6.5 7.5 8.5 pH
Figure E-2. Limestone dissolution rates at 60°C. 123
-2 - - sample wt. 2.25 ~ /1.25 I - screen ize M -1 1+16 I - tempera ure 90°C (f) - stirring ate 1000 i-/- 10 RPM - ~ ..... -4 A N 0 • - A o. I - OA • OA - . A E . 0 o~ • - • • 0 0 u • ·0 I • 0 ...., -6 0 (f) c - 0• • Q) ~ • A 0 - 0 ~. A 0 o - 0 q. A 00_ 0 o~ C • 0 E :J • 0 A -8 ... 0 • - 0 E c • • ,~ "--" . c •• - .a 6 c . .6 l...LJ 0 . °iiA Limes ones: A ~ 0 •• ...... 0 « -10 00000 Maxvil e LS89011 8A . 0 0:::: o 0 coo LS0492E7 0 A Carey • • 0 AAAAA Vanpo t LS0691C4 c C) .... - Missis sippi LS0691C8 • ••••• Bucyri S LS0492E6 S -12 3.5 4.5 5.5 6.5 7.5 8.5 pH
Figure E-3. Limestone dissolution rates at 90°C. 124
-2
~ 00000 30°C I Q QQQQ 60°C (f) ••••• 90°C -4 • - N a D I 0 C • Q E 0 • U 0 ~ 0 -6 •D 0 en • a (]) 0 • - o· 0 ~ .. • a 0 •• • 0 o 0 E -8 0 • .0 0 • 0 E 0 •• a "'--" 0 a a 0 • 0 W 0 •• 0 I- t'l • « -10 V o w. limestone Maxville • 0 0::: sample LS890118A bo # 00 • sample wit. 2.25 $/1.2P I 41 o screen size M -1 /+1 D stirrinq rate 1000 +/- 10 RPM o--.J -12 3.5 4.5 5.5 6.5 7.5 8.5 pH
Figure E-4. Temperature dependency of Maxville limestone dissolution rates.
-2
",--..... 00000 30°C , o 0 0 0 Q 60°C (f) ••••• 90°C -4 N I •Q •0 0 •a E 0 0 •0 U c 0 Q• 0 • 0 -6 0 (f) 0 o ~ Q) o 0 •c - 0 •c • 0 a 0 0 • Ca· o a. E -8 t'\ .., 0 0 E o 0 • <::» 0 0 • ( 0 0 • 0 0 0 0 • W 0 000 • I- aD ...• -10 v « limestone : Corey 0 50 o: sample LS049287 0 • N. 0000 sample WIt. : 2.25 $/1.2 5 I C) screen size M -1 /+1 ) stirrinc rate: 1000 +/- 10 RPM o--.J -12 3.5 4.5 5.5 6.5 7.5 8.5 pH
Figure E-5. Temperature dependency of Carey limestone dissolution rates. 125
-2
00000 30°C I 00000 60°C (f) ••••• 90°C -4 N D • 0 •• I 0 o 0 0 • E o 'po • • u o c 0 • -6 n.. (f) Cb • (]) % • 0 • o D 0 0 • ac a ~ • E -8 ·11 Ch ~ • 'Q t:I - E 0 jt "--'" a 0 0 • o 0 ~ • •• W 00 • I 0 • « -10 r't ... limestone Vanport 0 0:: 00 I sample # LS069104 0 0 0 sample wit. 2.25 ~/1.2 :> I 0 o screen size M -1 1+1 j g -12 stirrino rate 1000 +/- 10 RPM 3.5 4.5 5.5 6.5 7.5 8.5 pH
Figure E-6. Temperature dependency of Vanport limestone dissolution rates.
-2
00000 30°C I C C DO 0 60°C ••••• 90°C (f) .00 -4 .~ 0 N I • E D • 0 u C • 0 -6 - (f) 0 J • 0 (l) c • o c o • c 0• c:PtPCOODo 0 • E -8 .... o· Dc D ~ o·c E a ·0 <::» 0 0 ·i C 0 ~ W D C • I C 0 10 -. « -10 0 limestone Mississippi 0 o: sample # LS069108 • sample wit. 2.25 g/1.2P I C) screen size M -18/+1 D • g-12 stirrinq rote 1000 +/- 10 RPM 3.5 4.5 5.5 6.5 7.5 8.5 pH
Figure E-7. Temperature dependency of Mississippi limestone dissolution rates. 126
-2
00000 30°C I 0000 c 60°C (f) ••••• 90°C -4 N a 0 I .0 E •00· •a 00 a • u 0• 0 ~ • -6 o 0 • (f) q]o o 0 • Q) a 0 a 0 • o a o o a 0 • a g 0 • ~oo • E -8 '~- • 8 • E 0 • ~ OJ • 0 •• ctP. • W flgoo • t-- ct> -10 "'" -. « o o 0 cr: limestone Bucyrus c • sample # LS049286 Dc • sample wit. : 2.25 g/1.2D I (9 screen size M -1 1+1 p stirrina rate: 1000 +/- 10 RPM S -12 3.5 4.5 5.5 6.5 7.5 8.5 pH
Figure E-S. Temperature dependency of Bucyrus limestone dissolution rates. 127
APPENDIX F
MAXVILLE LIMESTONE DISSOLUTION RATES OBTAINED USING THE FREE DRIFT METHOD
ADDITIVES: CITRIC ACID GLYCINE SODIUM SULFITE 128
9
8
7
6
5
4--.i-,....,.--.-,.-,r--r-...,.-or--r--r--r---lr---,---,...--or--r--r--r-'"1r---,---,...--,.---,---r--r-'"1r---r---y-.,.----r---,.--r-r---r--,----r---T----r-~ o 5 10 15 20 TIME (min)
Figure F-l. Maxville limestone dissolution without additive.
Citric acid conc.: 5.5 +-+-+-+-+ 5 mmoles/l ~ 10 mmoles/l ...... 15 mmolesz'l ...... 25 mmoles/l
5.0
I 0...
Figure F-2. pH versus time curves for Maxville limestone with citric acid additive. 129
8
7
I 0.. 6
5 Glycine cone.: +-+-+-+-+ 5 mmolesjl ~ 10 mmoles/l ...-...... tHI 15 mmoles/l ...... 25 mmoles/l
20 40 60 80 100 TIME (min)
Figure F-3. pH versus time curves for Maxville limestone with glycine additive.
7
6
5 I 0...
4
Sulfite conc.: 3 +-+-+-+-+ 5 mmolesjl ~ 10 mmoles/l ...... 15 mmoles/l ...... -.. 25 mmoles/l 2-+-,-~....,....,....,...-r-,r--r-r-""""""""""'-"'''''''''''''''r-T-r'~,...,..-r~I''"''T'"'r~...... ,...-r-.--r-T''...,...... r--r-r''''''''''-''--'''''-r-T""~--yo-r-'T''''''I a 50 100 150 200 250 300 TIME (min)
Figure F-4. pH versus time curves for Maxville limestone with sodium sulfite additive. 130
8.0E-005 - Citric acid conc.: a a a a a 0 mmoles/l I ~ A A A A 5 mmoles/] U1 00000 10 mmoles/t x 6.0E-005 -. o ••• •• 15 mmoles/l 6 6 ••• 25 mmoles/l N I ~ U 4.0E-005 - 6
<, A • a U1 W DISSOLUTION -.J o 2.0E-005 - ~ ~ "'-../ W 0 .OE +000 ;---Miiil""------~-.,I;L,-_'l__a__G___Q_~a___a_~&QACI_A44:I~~~ f- « I I Ct:: .. . -2.0E-005 (/) PRECIPITATION U1 o -t--r--r-1,..,.-T'-r-"'T"'"""'r--r-r-r-T--,...... ,r--r-r-r--r-r--r--T'"-r-T--,...... ,--,-,...,....-r-r--r--T'"~...,..-,--r-,...,....-r-r--r-T'"~ - 4.0E- 005 I 4 8 pH
Figure F-5. Dissolution rates of Maxville limestone as a function of citric acid concentration.
8.0E-005 - Glycine cone.:
a a 0 a 0 0 mmoles/l I A A A A ~ 5 mrnolesZl (f) 00000 10 mmoles/l X 6.0E-005- ••• •• 15 mmoles/l 6666. 25 mmoles/l
4.0E-005 - o o DISSOLUTION 2.0E-005 - ... :'1. o 0"'· . ~~Ii". 4. 6 o <1 e \3\ ~a.-.. .__ o w ~ 0::: . -2.0E-005 PRECIPITATION if) (f) o - 4.0E- 005 -+-r--r-r--r-....-r--r-T"-r-r-,--y~r--r-T'-r--r-r-"'T"""'T'-r-T--,...... ,r--r-~-r-r--r--T'"-r-T--,...... ,r--r-r-r-T-r--r-r..,...., 4 pH
Figure F-6. Dissolution rates of Maxville limestone as a function of glycine concentration. 131
Sulfite cone.: 0 8.0E-OOS ooooe 0 mmoles/l ~ ~~AAA 5 mmoles/l -I • OA 00000 10 mmoles/l Ul ·oo~ ••••• 15 mmoles/l x 6.0E-005 • ..... 25 mmoles/l • 0 N C D I • • 0 ~ () 4.0E-005 <, a (f) DISSOLUTION W --.J 0 2.0E-005 ~ ~ "--""'" 0 W ~ Figure F-7. Dissolution rates of Maxville limestone as a function of sodium sulfite concentration. 132 APPENDIX G LIMESTONE DISSOLUTION RATES WITHOUT ADDITIVES OBTAINED USING THE PH-STAT METHOD 133 -2-.------r------r------r------.,r------.- - sample wt. 2.25 9/1 .25 I - screen size -18/+ 6 - temperatu e 30°C I - (f) - stirring ra e 1000 +v- 10 RPM -4-r------+------+------4------~~-----~- x - - N - ! I - • E - • u - @ • -6....,_r------t------+------+---~---+------1• • x - e.. - c •I (f) c (1) o E -8--t------t------+------+------4------f E "'--'" ~ Limes ones: ~ - 10 : 000 0 0 Maxvill 9 LS890118A : coo 0 0 Carey LS049:;; 87 C) - A A A A A Vanport LS069104 o - ••••• Mississippi LS069108 ---' ...... Bucyrus LS049~ 86 - 1 2 -t-r-r-r-r-r..,.-r-T-,-ir-,-,.....,--r--r-r__r_r-r-+-T__r~,....,..~r__r__r_+_r__r_r__r_r-r__,_,..._r_+_T__r~,....,..~r__r__r_I 3.5 4.5 5.5 6.5 7.5 8.5 pH Figure G-l. Limestone dissolution rates at 30°C. -2 - sample wt. 2.25 9/ 1.25 I ...--... screen size -18/+ 6 - temperatu e 60°C I (f) stirring ra e 1000 +/- 10 RPM -4 x N 8 I a.. i E .. i u 0 .. -6 - 0 x 0 (f) Q) 0 E -8 E "'--'" W t- Limes ones: -10 « 00000 ~ 0::: Maxvill LS8901 18A o 0 ceo Carey LS049:;; 87 C) A A A A A Vonpor t LS0691 04 o ••• •• Miss iss ippi LS0691 08 -..1 - ...... Bucyrus LS049~ 86 -12 3.5 4.5 5.5 6.5 7.5 8.5 pH Figure G-2. Limestone dissolution rates at 60°C. 134 -2-.,_r------...... ------r------r------r------, - sample wt. 2.25 9/1 .25 I - screen size -18/+ 6 - temperatu e 90°C I - en - stirring ro e 1000 +v- 10 RPM -4--1_..------+------+------+------+------1 x - - C"J - I I - .. i - • o E - o • • o -6--..------+------+------=~---+---~---t------tc ..... o - o II x - en - Q..) - o - o -8...... -_1------+------+------+------+------1 E - E - - W: Limes ones: ~ -10; 000 00 Moxvil13 LS890118A : 0 0 ceo Carey LS049~ 87 _AAAAA Vanport LS069 104 : ••••• Mississ ippi LS069108 : ••••• Bucyrus LS049~ 86 - 1 2 -+--r--T'-..--.,.--.y~...,.....,-.,--+-,--..,.....,...... ,r__"T"'...... __..___r_~i__r_....,__r__r-,--T""_r~_r_+~_r__T'__,__..,.-,.__r_..,...._r_+__r_1r__"T"'...... __r--r-....,__r_r_t 3.5 4.5 5.5 6.5 7.5 8.5 pH Figure G-3. Limestone dissolution rates at 90°C. 135 -2 ,--...... I U1 -4 x Ii N I 0 • • • E 0 u 0 -6 0 a x 0 0 (f) 00000 30 e Q) a a a a a 600 e 0 ·····90Oe • E -8 E "'-"'" W I- < -10 0::: limestone Maxville screen size -18/+16 (9 sample # LS890118A o sample wt. 2.25 g/1.2 j I --.J stirring rate 1000 +/- 10 RPM -12 3.5 4.5 5.5 6.5 7.5 8.5 pH Figure G-4. Temperature dependency of Maxville limestone dissolution rates. -2 ,--...... I U1 -4 x C"4 I •0 E ! o 0 -6 • x i 0 • (f) 00000 30°C 0 Q) o a a a a 60°C 0 ••••• so'c E -8 E "-"'" W I- « -10 ~ limestone Corey screen size -18/+16 (9 sample # LS049287 o sample wt. 2.25 g/1.2 :> I --.J stirring rate 1000 +/- 10 RPM -12 3.5 4.5 5.5 6.5 7.5 8.5 pH Figure G-5. Temperature dependency of Carey limestone dissolution rates. 136 -2 ",-...., U1 -4 x a N, • • • a E 0 ~ u 0 • -6 0 x o ' 0 U1 00000 30 e Q) a a a a a 600 e 0 ·····90oe E -8 E ""-'" w r- « -10 n::: limestone Vanport screen size -18/+16 G sample # LS069104 o sample wt. 2.25 g/1.2 b I --J stirring rate 1000 +/- 10 RPM -12 3.5 4.5 5.5 6.5 7.5 8.5 pH Figure G-6. Temperature dependency of Vanport limestone dissolution rates. -2 ",-..... I (f) -4 x ~ N, • 0 • c E 0 o • c -6 0 x ( (f) 00000 30°C Q) o a a a a 60 0 e 0 ••••• 900 e E -8 E <::» w .-« -10 fr:: limestone Mississippi screen size -18/+16 o sample # LS069108 o sample wt. 2.25 g/1.2 :> I --J stirring rate 1000 +/- 10 RPM -12 3.5 4.5 5.5 6.5 7.5 8.5 pH Figure G-7. Temperature dependency of Mississippi limestone dissolution rates. 137 -2 - - ...... -.... - - I - (J1 - -4- x - - N - • I - 0 - ij E - 0 u - 0 • ~ -6 - v x - 0 ~ - o (J1 - 00000 30°C Q) - ooooe 60°C 0 - ••••• 90°C -8 E - E - "--"" - W t- « -10 0:::: - limestone. Bucyrus - screen size -18/+ 16 c:> : sample # LS049286 o : sample wt. 2.25 g/1.26 I --J : stirring rate 1000 +/- 10 RPM -12 3.5 4.5 5.5 6.5 7.5 8.5 pH Figure G-8. Temperature dependency of Bucyrus limestone dissolution rates. 138 APPENDIX H DISSOLUTION RATES OF MAXVILLE LIMESTONE OBTAINED USING THE PH STAT METHOD ADDITIVES: CITRIC ACID GLYCINE 139 I _ Citric acid conc.: (f) _ 00000 0 mmol/l x 6.0E-005 - 5 mmoljl 6 6 A 6 6 10 mmoljl ••• •• 15 mmol/l ••••• 25 mmol/l x • 4.0E-005 (f) W o---.J ~ a ~ ~ I w 2.0E-005 - • ~ • ~ I (f) • <.n o o o O.OE+OOO I I I I I 3.5 4.5 5.5 6.5 7.5 8.5 pH Figure H-1. Dissolution rates dependent on citric acid concentration. pH Figure H-2. Dissolution rates dependent on glycine concentration.