ChemE Defi nitions

American Institute of Chemical

120 Wall Street, 23rd FL. New York, NY 10005 www.aiche.org/students The AIChE Email: [email protected] Customer Service: 1.800.242.4363 Student 203.702.7660 (Outside U.S.) Pocket

© 2014 AIChE 9865-14 • 04.14 Handbook

G41784AICHE_CVR.indd 1 5/2/14 8:21 AM 13282AICEtext 4/12/04 12:20 PM Page 58 G37759AICEtext_28535AICEtext 10/11/13 4:08 PM Page p1

The AIChE Pocket Handbook

Thomas . Hanley, Editor

American Institute of Chemical Engineers 120 Wall Street, 23rd Floor New York, New York 10005 G41784AICEtext_28535AICEtext 4/30/14 12:02 PM Page p2

The AIChE Pocket Handbook is a publication of AIChE and its Student Chapters Committee.

Reprinted, 1988, 1990, 1992, 1993, 2001, 2004, 2005, 2007, 2011, 2013, 2014

Copyright © 1985 by the American Institute of Chemical Engineers

ISBN 0-8169-0342-5 13282AICEtext 4/12/04 12:20 PM Page p3


Inorganic ...... 1 ...... 6 ...... 10 Flow...... 14 Transfer...... 18 ...... 23 Transfer ...... 26 ...... 29 Kinetics and Reactor Design ...... 34 Conversion Factors ...... 40 Physical Constants ...... 44 ...... 48 ...... 48 Safety ...... 51 Biochemical ...... 53 13282AICEtext 4/12/04 12:20 PM Page p4 13282AICEtext 4/12/04 12:20 PM Page p5


The purpose of this handbook is to make readily avail- able in a limited of pages some of the more im- portant chemical, biological, physical, safety, and mathe- matical data and concepts that are fundamental to the practice of the profession. With these principles you should be able to solve many chemical engineering problems.

Good Luck!

AIChE would like to thank Professors David Murhammer, Chuck Coronella, Galen Suppes, and Joseph F. Louvar for their on this Handbook. 13282AICEtext 4/12/04 12:20 PM Page p6 13282AICEtext 4/12/04 12:20 PM Page 1



Atomic number—the number of in the nucleus of an . Avogadro’s number—the number of (6.023 1023) in one - of a substance. Equilibrium constants for the reaction aA bB cC dD where reaction is in ,

d [C ] [D] K ([ ] refers to molarity) c [A]a[B]b

where reaction is in the ,

c d p C p D p Kp a b ( partial ) p A p B

Gram — A. (nonredox reaction) the mass in of a substance equivalent to 1 gram-atom of , 0.5 gram-atom of , or 1 gram- of the hydroxyl ion. It can be determined by dividing the molecular weight by the number of hydrogen or hydroxyl (or their equivalent) supplied or required by the in a given reaction. B. ( reaction) the molecular weight in grams divided by the change in .

Ion of (Kw)—the product of the hydrogen ion and hydroxyl ion in gram-ions per liter;

Kw [H ][OH ]

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Mass number—the number of protons plus the number of in the nucleus of an atom. (m)—(gram moles of solute)/( of ). Molarity (M)—(gram moles of solute)/(liters of solution). Normality (N)—(gram equivalents of solute)/(liters of solution). Oxidation—the loss of by an atom or of atoms. pH—the negative ( 10) of the hydrogen ion in gram ions per liter;

pH log10[H ]

Reduction—the of electrons by an atom or group of atoms.

Solubility product (S.P. or Ksp)—for the slightly soluble

, Aa Bb , dissolving Aa Bb (solid) aA (aq) bB (aq) where A is any cation and B is any anion a b S.P. or Ksp [A ] [B ] a constant at a given


Atomic Atomic Common Number Weight Ac 89 (227) 3 Aluminum Al 13 26.9815 3 Am 95 (243) 6,5,4,3 Sb 51 121.75 3,5

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Atomic Atomic Common Name Symbol Number Weight Valence Ar 18 39.948 0 As 33 74.9216 3,5 At 85 (210) 1,3,5,7 Ba 56 137.34 2 Bk 97 (247) 4,3 Be 4 9.0122 2 Bi 83 208.980 3,5 B 5 10.811 3 Br 35 79.904 1,5 Cd 48 112.40 2 Ca 20 40.08 2 Cf 98 (249) 3 C 6 12.01115 4,2 Ce 58 140.12 3,4 Cesium Cs 55 132.905 1 Cl 17 35.453 1,3,5,7 Cr 24 51.996 6,2,3 Co 27 58.9332 2,3 Cu 29 63.546 2,1 Cm 96 (247) 3 Dy 66 162.50 3 Es 99 (254) — Er 68 167.26 3 Eu 63 151.96 3,2 Fermium Fm 100 (253) — F 9 18.9984 1 Fr 87 (223) 1 Gd 64 157.25 3 Ga 31 69.72 3 Ge 32 72.59 4 Au 79 196.967 3,1 Hf 72 178.49 4 He 2 4.0026 0 Ho 67 164.930 3

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Atomic Atomic Common Name Symbol Number Weight Valence Hydrogen H 1 1.00797 1 In 49 114.82 3 I 53 126.9044 1,5,7 Ir 77 192.2 2,3,4,6 Fe 26 55.847 2,3 Kr 36 83.80 0 La 57 138.91 3 Lw 103 (257) — Pb 82 207.19 4,2 Li 3 6.939 1 Lu 71 174.97 3 Mg 12 24.312 2 Mn 25 54.9380 7,6,4,2,3 Md 101 (256) — Hg 80 200.59 2,1 Mo 42 95.94 6,5,4,3,2 Nd 60 144.24 3 Ne 10 20.183 0 Np 93 (237) 6,5,4,3 Ni 28 58.71 2,3 Nb 41 92.906 5,3 N 7 14.0067 3,5,4,2 No 102 (254) — Os 76 190.2 2,3,4,6,8 Oxygen O 8 15.9994 2 Pd 46 106.4 2,4 P 15 30.9738 3,5,4 Pt 78 195.09 2,4 Pu 94 (242) 6,5,4,3 Po 84 (210) 2,4 K 19 39.102 1 Pr 59 140.907 3,4 Pm 61 (147) 3

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Atomic Atomic Common Name Symbol Number Weight Valence Pa 91 (231) 5,4 Ra 88 (226) 2 Rn 86 (222) — Re 75 186.2 7,6,4, 2,1 Rh 45 102.905 2,3,4 Rb 37 85.47 1 Ru 44 101.07 2,3,4,6,8 Sm 62 150.35 3,2 Sc 21 44.956 3 Se 34 78.96 2,4,5 Si 14 28.086 4 Ag 47 107.870 1 Na 11 22.9898 1 Sr 38 87.62 2 S 16 32.064 2,4,6 Ta 73 180.948 5 Tc 43 (98) 7 Te 52 127.60 2,4,6 Tb 65 158.924 3,4 Tl 81 204.37 3,1 Th 90 232.038 4 Tm 69 168.934 3,2 Sn 50 118.69 4,2 Ti 22 47.90 4,3 W 74 183.85 6,5,4,3,2 U 92 238.03 6,5,4,3 V 23 50.942 5,4,3,2 Xe 54 131.30 0 Yb 70 173.04 3,2 Y 39 88.905 3 Zn 30 65.37 2 Zr 40 91.22 4

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Name Symbol Name Symbol

ϵ AsO3 OH ϵ Arsenate AsO4 OCl Acetate C2H3O2 I HCO3 Iodate IO3 ෇ Bisulfate HSO4 Molybdate MoO4 Bromate BrO3 NO3 Bromide Br Nitrite NO2 ෇ ෇ Carbonate CO3 C2O4 ෇ ClO3 ClO4 ෇ Cl O2 ෇ Chromate CrO4 Permanganate MnO4 ෇ ϵ Cyanamide CN2 PO4 ෇ CN SO4 ෇ ෇ Dichromate Cr2O7 Sulfide S ෇ ෇ Dithionate S2O6 Sulfite SO3 ϵ Fe(CN)6 Thiocyanate CNS ෇෇ ෇ Fe(CN)6 S2O3 Formate CHO2


Note: For conciseness the following symbols are used: R H atom or saturated group Rhydrocarbon group only X n an


A. The straight and branched chain types of com- pounds

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Type or Name General

1. or paraffin (also saturated )

2. or olefin (unsaturated hydrocarbons)






8. Carboxylic

9. Grignard

10. Acyl halide

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Type or Name General Formula

11. Anhydride



14. (base)


B. Cyclic Compounds

1. Cycloparaffin

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Type or Name General Formula

2. Cycloalkene

3. Aromatic

4. Naphthalenic


A. Markovnikov’s (Markownikoff’s) Rule for the of to acids to olefins: the negative group of the acid adds to the carbon atom having the fewest hydrogen atoms.

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B. Mechanisms 1. Free (unshared ) (no charge)

2. (deficient in electrons) ( positive charge) (carbon with six electrons)

3. (excess of electrons) (negative charge) (carbon with eight electrons)


1. Amagat’s Law of Partial —The of a of is equal to the sum of the par- tial volumes of each component gas. The partial volume of a component gas is the volume which that component would occupy at the same temper- ature and pressure.

2. Elevation (Tb)—The following equa- tions hold for a dilute solution of a nonionic non- volatile solute.

Tb Kbm 2 R(Tbp) Ma Kb Hv(1000)

where Hv molal heat of

Kb molal elevation con- stant m molality

Ma solvent molecular weight

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R ideal-

Tbp solvent boiling point, absolute tem- perature 3. Clausius Equation

dp H m dT (V v) T

where p pressure T absolute temperature

Hm molal heat of vaporization V molar volume v molal volume 4. Clausius-Clapeyron Equation—Where the volume of liquid can be ignored (or v 0) and where the ideal-gas law holds (or V RT͞p) the Clausius equation becomes d( ln p) 1 dp Hm 2 dT p dT RT

and with Hm constant, integration yields p2 Hm T2 T1 ln c d p1 R T1T2

The symbols are the same as in sections 2 and 3 above. 5. ’s Law of Partial —The pres- sure of a mixture of gases is equal to the sum of the partial pressures of each component gas. The of a component gas is the pressure which that component would exert if it alone occupied the volume at the same tem- perature.

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6. Faraday’s Laws First Law: The mass of a substance reacting at the is directly proportional to the of passed through the solu- tion. Law: The of different sub- stances produced during are directly proportional to their equivalent ; 96,496 of electricity 1 faraday electricity to 1 gram equivalent of any substance.

7. Point Depression (Tf)—The follow- ing equations hold for a dilute solution of a nonionic solute in which the solid phase is pure solvent.

Tf Kf m 2 R (Tf p) Ma Kf Hf (1000)

where Hf molal heat of fusion of solvent

Kf molal freezing point lowering con- stant m molality

Ma solvent molecular weight R ideal-gas constant

Tfp solvent freezing point, absolute tem- perature

8. Gibbs —At equilibrium the number of independent variables (F ) required to spec- ify the is equal to the number of compo- nents (C ) minus the number of phases (P) plus two, or symbolically F C P 2. This form

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of the phase rule applies to non-reactive sys- tems. 9. Graham’s Law of —The rate of diffusion of a gas is inversely proportional to the of its . 10. ’s Law—At a constant temperature, the con- centration of a gas dissolved in a liquid is directly proportional to the partial pressure of the gas above the liquid. 11. Raoult’s Law pa xa Pa

where pa partial pressure of component A in vapor

xa of A in liquid solution

Pa of pure liquid A 12. van’t Hoff Reaction Isochore

d ( ln K ) H at constant pressure 2 dT RT

where H heat of reaction K reaction R ideal-gas constant T absolute temperature If H is constant, K2 H T2 T1 ln a b c d K1 R T1T2 13. Molar —moles vapor/mole vaporfree gas

ya pa Y 1 ya P pa

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Humidity—pounds vapor/ vapor-free gas

Ma Y Y Mb

Relative Saturation— of partial pressure of vapor to partial pressure of vapor at saturation (vapor pressure)

pa Hr 100 Pa

Percentage of Saturation—ratio of vapor con- centration to vapor concentration at saturation (ratio of molar humidity to saturated molar humidity)

Y pa (P Pa) H p 100 100 Ysat Pa (P pa)

where pa partial pressure of component A in gas

Pa vapor pressure of pure liquid A P total pressure

Ma molecular weight of A

Mb molecular weight of B

ya mole fraction of a gas



Mass G V␳

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Simple manometer equation

g ␳ ␳ Pa Pb Rm ( a b) gc

Hagen-Poiseuille equation (laminar flow in long hori- zontal tube)

32 V ␮ P P a b 2 gc D

Average velocity, V

q, V s, cross-sectional

Reynolds number, NRe

DV␳ DV N Re ␮ ␯

Mechanical balance

2 2 Pa g V a Pb g V b Z W Z H ␳ a ␣ s ␳ b ␣ f a gc 2gc a b gc 2gc b

where ␣ Ӎ 1 for turbulent flow (NRe 4,000)

␣ 0.5 for laminar flow (NRe 2,100) Hydraulic

s, cross-sectional area rH Lp, the wetted perimeter

Equivalent diameter, De

De 4 (hydraulic radius, rH)

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Skin friction

2 2 f LV Hfs Dgc Fanning friction factor, f (flow in smooth pipes)

16␮ 16 laminar f DV␳ NRe 1 . .5 turbulent 4.0 log (NRe f ) 0.4 f. .5

Friction of valves and fittings (Add to of to get total equivalent length.)

Equivalent Fittings and Valves resistance, pipe diameters 45- elbows 15 90-degree elbows (standard radius) 32 90-degree square elbows 60 180-degree close return bends 75 T’s (used as elbow, entering run) 60 T’s (used as elbow, entering branch) 90 Couplings Negligible Unions Negligible Gate valves (open) 7 Globe valves (open) 300 valves (open) 170

Friction loss from sudden expansion of cross sec- tion

2 2 V a sa Hfe a1 b 2 gc sb

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Friction loss from sudden contraction of

2 KcV b Hfc 2 gc

Values of Kc are given on page 6-18, Perry’s Chemical Engineers’ Handbook, 7th ed., Don W. Green, ed., McGraw-Hill Book Co., New York, NY, 1997.


Venturi meter

2g ( p p ) (b is at throat s 2 c a b 2V V C b a v B ␳ of meter)

Orifice meter, design equation (NRe 20,000)

0.61 2gc ( pa pb) V o B ␳ 21 ␤4

Pilot tube (manometer measures ps P)

2gc ( ps P) V C p B ␳


Cu , Cp coefficients of velocity D diameter g of 32.2 ft /s2 9.81 m/s2 2 gc ’s conversion factor 32.2 ft-lbm /(lbf -s ) 1 m-kg/(N-s2 )

Hf head loss due to friction

Hfs head loss due to skin friction

Hfc head loss due to contraction of cross section

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Hfe head loss due to expansion of cross section

Ke expansion loss coefficient

Kc contraction loss coefficient L length of pipe P pressure

Pa upstream pressure

Pb downstream pressure

pa, pb pressure in arms of manometer

ps static pressure

Rm manometer reading s cross-sectional area V velocity V velocity

Va upstream velocity

Vb downstream velocity

Ws shaft work done by Z elevation ␣ correction factor ␤ ratio of diameter of orifice to diameter of pipe 3 ␳ fluid density, lbm /ft

␳a density of manometer fluid

␳b density of fluid above manometer ␯ kinematic ␮͞␳ ␮ viscosity



Fourier’s Law (constant k) kAT T q x R

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unsteady state

T k 2T x ␳ 2 t Cp x

Resistance in

T q xA xB xC

kA A kB A kC A T RA RB RC Radial Heat Flow Through a Cylinder ␲ k(2 rm) L T k Am T q (ro ri ) r

where Am logarithmic area normal to heat flow

rm radius

rm (ro ri)͞ln [ro ͞ri]


q hAT

where h k͞x, coefficient k of the fluid xthickness of the laminar film

III. COMBINED CONDUCTION AND CONVECTION q UAavg ( T ) where U overall heat transfer coefficient T overall temperature difference

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A x 1 r 1 m 1 1 1 U UAr Ai Am Ao Ai Ao hi km ho hFi hFo Ar Ar Ar Ar Ar

where Ar reference area, usually the area of the solid through which heat is being conducted

hFi, hFo inside and outside fac- tors


␴ 4 4 q12 AF (T 1 T 2) where q12 net radiation between 1 and 2, Btu/hr T1, T2 absolute temperature of surfaces 1, 2, R. A area of either , sq ft ␴ Stefan-Boltzman Constant 1.712 109 Btu/hr-sq ft-R 4 F geometric view factor


Turbulent Flow in Clean Smooth Pipes

hiD 0.023(N )0.8(N )0.33(␮͞␮ )0.14[1 (D͞L)0.7] k Re Pr w

where NRe the DG͞␮

NPr the Cp ␮͞k

Laminar Flow in Clean Smooth Pipes

h D i 0.33 0.33 0.14 0.33 1.86(N ) (N ) ( ␮͞␮ ) (D͞L) k Re Pr w

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where the Reynolds and Prandtl are as defined for


h D o o 0.52 0.35 0.56(NRe) kf

where NRe the Reynolds Number DoG͞␮f The subscript f calls attention to the fact that the correlation is based on the mean film temperature,

Tf , which is defined as the mean of the average fluid temperature and the wall tempera- ture.


havg Do n b(NRe) (b and n depend on ) kf ͞␮ where NRe the Reynolds Number DGmax f


Vertical Tubes

3 2 k ␳ g ␭ 0.25 c f f d havg 1.13 ␮ To L f Horizontal Tubes

3 2 k ␳ g ␭ 0.25 c f f d havg 0.725 ␮ To Do f

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A area, sq. ft. b empirical constant

Cp specific heat at constant pressure, Btu/lb-F D diameter, ft

G mass velocity, lbm /sq ft-sec Gmax mass velocity through minimum cross section in tube bundle g acceleration of gravity, 32.2 ft/sec2 h heat transfer coefficient, Btu/sq ft-hr-F k thermal conductivity, Btu/sq ft-(F/ft)-hr L length of tube or cylinder, ft q heat flow per unit of , Btu/hr R resistance r radius, ft T temperature, F t time, hr U over-all heat transfer coefficient, Btu/sq ft- hrF x in direction of heat flow; thickness of layer, ft ␭ of or vaporization,


␮ viscosity,lbm /ft-sec 3 ␳ density, lbm /ft

Subscripts avg average f film i inside o outside r reference

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w wall m mean or log mean



FzF yV xL (component material balance) F V L (over-all material balance)


W x dx ln Ύ Wo y x xo

When the relative ␣ is constant y ␣x͞ [1 (␣ 1)x] can be substituted to give

W 1 x(1 xo) 1 xo ln ln c d ln c d Wo (␣ 1) xo(1 x) 1 x

For binary system following Raoult’s Law

(y͞x) p ␣ a a (y͞x)b pb

where partial pressure of component i


Total Material Balance F D B


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Operating Lines 1. Rectifying Section Total material: Vn1 Ln D Component A: Vn1 yn1 Ln xn DxD

L Dx n D yn1 xn Ln D Ln D

2. Stripping Section Total material: Lm Vm1 B Component A: Lm1 xm Vm1 ym1 BxB

L Bx m B ym1 xm Lm B Lm B

3. Reflux Ratio Ratio of reflux to overhead product


4. Feed Condition

Type of Feed of feed line Superheated vapor (downward to left) Saturated vapor 0 (horizontal) Liquid and vapor (upward to left) Saturated liquid (vertical) Cold liquid (upward to right)

5. Murphree Plate Efficiency

yn yn1 E ME y*n yn1

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where yn concentration of vapor above plate n yn1 concentration of vapor entering from plate below n

y*n concentration of vapor in equilibrium with liquid leaving plate n


B moles of bottoms product D moles of overhead product F moles of feed L molar liquid downflow

RD ratio of reflux to overhead product V molar vapor upflow W weight in pot x mole fraction of the more volatile component in the liquid phase y mole fraction of the more volatile component in the vapor phase

zD mole fraction of the more volatile component in the feed

Subscripts B bottoms product D overhead product F feed m any plate in stripping section of column m 1 plate below plate m n any plate in stripping section of column n 1 plate below plate n o original charge in still pot

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NA pA NA NB D pA c d A P A A RT z

2. Unidirectional Diffusion of a Gas A Through a Second

Stagnant Gas B (NB 0)

( p p ) N DP A2 A1 A A RT ( pB)lm x2 x1

in which ( p ) is the log mean of p and p B lm B2 B1

3. Equimolar Countercurrent Diffusion (NB NA) (gases)

( p p ) N D A2 A1 A A RT z2 z1

4. Unsteady State Diffusion

2 pA pA D 2 t z


1. Two-Film

NA k ( p p ) k (C C ) A G AG Ai L Ai AL

kG ( pAG pA) kL (CA CAL)

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2. Overall Coefficients

H 1 1 KG kG kL

1 1 1 KL HkG kL

3. Transfer Unit HTU—height of a transfer unit


NTU—number of transfer units

y2 dy 1 1 y2 N TG Ύ ln y y 2 1 y1 y1 *

x2 dx 1 1 x1 N TL Ύ ln x x 2 1 x2 x1 *

For dilute (straight operating and equilib- rium line)

y y N 1 2 TG (y y*)lm

Z NTG HTG NTL HTL tower height 4. Dimensionless Group Equation (Sherwood)

0.8 1͞3 (NSh) 0.023 (NRe) (NSc)

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0.5 f jH jD where f Fanning friction factor

␮ 0.667 0.14 h Cp ␮w jH c d c d CpG k ␮

kc j (N )0.667 M G Sc


A area perpendicular to direction of diffusion a interfacial area per unit volume C concentration in liquid phase d tube diameter D molecular diffusivity G gas mass velocity, mass/(time)(area)

H Henry’s Law constant, pi HCi h heat transfer coefficient k film coefficient of mass transfer K overall coefficient of mass transfer L liquid mass velocity, mass/(time)(area) N moles of a substance per unit time p partial pressure P total pressure R gas constant

NRe Reynolds number du␳͞␮

NSc ␮͞␳D

NSh kd͞D t time T absolute temperature u velocity

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lm logarithm mean average

Greek Letters ␳ density ␮ viscosity

Subscripts A, B components of mixture G gas phase L liquid phase i x mole fraction of liquid y mole fraction of gas z length in direction of travel * equilibrium concentration



System—an arbitrarily chosen portion of which is under consideration. A. —one in which does not pass through its boundaries. B. Open system—one in which matter flows across its boundaries. C. —one in which there is no interchange of energy or matter with the surroundings.

Boundaries—the envelope separating the system from the surroundings. —a system and its surroundings.

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Total energy, E—the sum of the various forms of energy

of the system: e.g., U, ; Ek, kinetic en-

ergy; Ep, ; Hence,

E U Ep Ek

II. FIRST LAW In an isolated system E E2 E1 0

In a closed system E Q W

In an open system E g(H Ep Ek) Q W

where the summed terms refer to leaving () and enter- ing () streams In a steady state open system Esystem 0 Hence for the entering and leaving streams

H Ek Ep Q W


For any real process the total of the universe always increases Ssystem Ssurroundings 0


Definition of entropy dQ rev S Ύ T

From First and Second Laws, with changes in Ek,

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Ep, and composition negligible, dU dQrev PdV TdS PdV Also

dH dU d(PV) TdS VdP dG dH d(TS) SdT VdP dA dU d(TS) SdT PdV

Cp (H͞T )p; Cv (U͞T )v; ␥ (Cp͞Cv) P, V, T, S, U, H, G, A are state functions. Q and W are path functions and have no total .



For any path: H Ύ Cp dT or (H͞P)T 0



For any path: U Ύ Cv dT or (U͞V )T 0


For monoatomic gas: Cp 2.5 R and Cv 1.5 R

For diatomic gas: Cp 3.5 R and Cv 2.5 R Adiabatic (Q 0) and reversible path for system with

Ep Ek 0. ͞ ͞ ␥ ͞ ␥͞(␥1) (P2 P1) (V1 V2) (T2 T1) RT P (␥1)͞␥ W U 1 ca 2 b d nonflow ␥ 1 (per mole) 1 P1 ␥ Wflow H [Wnonflow] ( per mole) Isothermal path, flow or nonflow

P V 2 1 P1 V2

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V2 P1 W RT ln RT ln ( per mole) V1 P2

VI. CRITERIA FOR EQUILIBRIUM CHANGE For system and surroundings: dSuniverse 0 For system alone: dG 0 when P, T constant dA 0 when V, T constant


A. ( f ) and Activity (a)

2 ͞ G RT ln ( f2 f1) Ύ VdP ( per mole) 1 (constant-temperature path) and the of f͞P as P approaches 0 1.00 ͞ a f f0 B. Equilibrium Standard free energy at temperature T for the reaction aA bB ∆ rR sS


r s a a R S RT ln a b RT ln Ka a A a B

C. Cells At standard conditions

G⑀ nF RT ln Ka

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At actual conditions

r s a R a S G ⑀nF ⑀ nF RT ln a b a A a B


A U TS, Helmholtz work a activity C E total energy of the system

Ek kinetic energy of the system

Ep potential energy of the system ⑀ reversible voltage of F faradays per equivalent f fugacity G H TS,

gc Newton’s conversion factor H U PV, h enthalpy per pound K equilibrium constant for the reaction as writ- ten

Ka equilibrium constant in terms of activity

Kf equilibrium constant in terms of fugacity

Kp equilibrium constant in terms of partial pres- sure n number of equivalents for the reaction as written P pressure Q heat, defined as positive when absorbed by system R gas constant S entropy T absolute temperature

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U internal energy of the system u velocity V volume v specific volume W work, defined as positive when done by system on surroundings final state minus initial state

␥ (Cp͞Cv)




The rate of reaction of any component A based on unit volume of fluid is

1 dNa r A V dt

and where density remains unchanged

dCA r A dt

Frequently, the rate can be described as a temperature- dependent a concentration-dependent term, or

rA k (T) f (CA, CB . . .)

A. Order, , Elementary Reactions Where the rate can be expressed as

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a b rA kC A C B . . . the reaction is ath order with respect to A and nth order overall; n a b NOTE: a, b, . . . are empirically observed and are not necessarily equal to the stoichiometric coeffi- cients. In the special case where a, b, . . . are the stoichiometric coefficients, the reaction is elementary: unimolecular (n 1), bimolecular (n 2), trimolecular (n 3) B. Rate Constant k and Temperature Dependency of a Reaction

k (conc)1 n(time)1 From Arrhenius’s Law the variation with temper- ature is

k E 1 1 E͞RT 2 k koe or ln c d k1 R T1 T2

where E is the energy of the reaction


A. Irreversible First-order Reaction For the reaction A S products, with rate

dCA dXA kC or k(1 X ) dt A dt A

the integrated form is

CA ln ln (1 XA) CA0

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B. Irreversible Second-order Reaction For the reaction A B S products, with rate

dCA kC C dt A B ͞ When M CB0 CA0 1, the integrated form is

CB CA0 M XA C C kt ln ln ( B0 A0) CB0 CA M(1 XA) When CA0 CB0 , the integrated form is

1 1 1 XA kt CA CA0 CA0 1 XA C. Irreversible nth-order Reaction For the reaction with rate

dC A n kC dt A

the integrated form for n 1 is

1n 1n C A C A0 (n 1) kt D. Reversible First-order Reaction

1 ͞ For the reaction A ∆ R, K k1 k2 with rate 2

dCA dCR k C k C dt dt 1 A 2 R

the integrated form is

XAe XA CA CAe k k t ln ln ( 1 2) XAe CA0 CAe

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E. Integration of Rate in General For the reaction with rate

dCA r k f (C , C , . . .), A dt A B

XA dX CA dC A A t CA0 Ύ Ύ ( rA ) k f (CA, CB , . . .) 0 CA0

which is to be solved analytically or graphically.


Where density change is proportional to the frac- tional conversion of any reactant A (isothermal sys- tems),

C 1 X A A ⑀ CA0 1 A XA


V V ⑀ XA 1 XA 0 A V XA 0

The rate for any reactant A is then

1 dNA CA0 dXA r k f (C , C , . . .) a ⑀ A B V dt (1 A XA) dt

Integrating in the general case

XA dX A t CA0 Ύ (1 ⑀ X )(r ) 0 A A A

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A. Capacity Measures Space time: ␶ time required to process one reactor volume of entering feed mean

V VCA0 ␶ (units of time) v FA0

B. Design Equation for Plug Flow (Ideal Tubular) Reactor In general

XA XA dXA V dXA ␶ CA Ύ or Ύ 0 (r ) F (r ) 0 A A0 0 A

For irreversible first-order reactions (isothermal) ␶ ⑀ ⑀ k (1 A) ln (1 XA) A XA

1 For reversible first-order reactions A ∆ rR 2 (isothermal)

⑀ ⑀ A XA N A k ␶ ln (1 NX ) 1 2 A N N


k2 N 1 (1 ⑀A) k2

C. Design Equation for Back-Mix (Ideal Stirred

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Tank) Reactor

C X V X ␶ A0 A A or ( rA) FA0 ( rA)

For a first-order reaction in j equal-sized backmix reac- tors in series

C entering A j (1 k␶ per reactor) CA leaving

D. NOTATION A, B, R, etc. substance A, etc. a, b, . . . exponents on concentration term of empirical rate

CA concentration of A, moles A/volume CA0 initial concentration of A, moles A/ volume FA0 feed rate of A or flow rate of A entering the reactor, moles A/time K equilibrium constant k constant, (conc1n)(time1) n order of reaction

NA moles of A

rA rate of reaction of any comoponent A, moles A formed/time-volume T temperature t time V volume of fluid in , vol- ume of fluid in a flow reactor, or reactor volume

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v volumetric feed rate, volume of feed/ time

XA fraction of reactant A converted, dimen- sionless

Greek Symbols

⑀A measure of density change with reaction, dimen- sionless ␶ space time based on entering feed, time


e equilibrium value


Acceleration 1 ft/s2 0.3048 m/s2 0.6318 (mile/hr)/sec 1.097 km/hr-s 30.48 cm /s2

1 rev/min2 2.778 104 rev/s2 0.001745 /s2 0.01667 rev/min-s Density

3 3 1 lbm /ft 16.02 kg/m 4 3 5.787 10 lbm /in 0.01602 g/cc Flow 1 ft3/min 4.719 104 m3/s 0.1247 /s

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0.4720 liter/s 472 cc/s Length 1 ft 0.3048 m 1.894 104 mile 1͞3 yd 12 in 30.48 cm 3.05 105 microns (␮) 1 Å 1010 m 108 cm 1 104 microns (␮) Angle 1 rad 1͞2␲ 0.1592 rev 0.637 quad 57.3 deg 3,438 min 2.063 105 s Mass

1 lbm 0.4536 kg 4.464 104 long ton 5 104 short ton 4.536 104 metric ton 0.4536 kg 453.6 g 0.0311 Pressure

2 3 2 1 lbf /in abs 6.895 10 N/m 6.895 103

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0.06805 atm 0.07031 kg/cm2 2.036 in Hg @ 32F 2.307 ft H2O @ 39 F 70.307 g/cm2 51.72 mm Hg @ 32F 51.72

Power 1 ft-lb/min. 0.0226 W 2.26 105 kW 3.03 105 hp 3.24 104 kg-cal/min 0.001285 Btu/min

Temperature F 1.8(C) 32 K C 273 R F 459


1 nanosecond 1 109 s

Velocity 1 ft/s 0.3048 m/s 0.011364 mile/min 0.6818 mile/hr 1.0973 km./hr 18.29 m/min 30.48 cm/s 1 rev/min 0.1047 rad/s 6 deg/s

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Viscosity 1 centipoise 0.001 Pa-s 0.001 N-s/m2 0.01 g/cm-s 4 6.72 10 lbm /ft-s

2.42 lbm /ft-hr

Volume 1 ft3 0.02832 m3 0.03704 yd3 0.80357 (U.S.) 7.481 gal (U.S.) 6.229 gal (British) 25.714 qt (dry, U.S.) 29.92 qt (liq., U.S.) 1.728 103 in3 28.32 liters 2.832 104 cm3 2.832 104 ml 59.8 pt (U.S. liq.)

Work and Energy 1 Btu 1054 J 2.93 104 kW-hr 3.93 104 hp-hr 0.252 kg cal 0.293 W-hr 10.41 liter-atm 252 g cal

778 ft-lbf 0.3676 ft3-atm 1.054 1010

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Mole fraction (x) to mass fraction (w)

xA MA wA ϭ xA MA ϩ xB MB Mass fraction (w) to mole fraction (x)

wA͞MA xA ϭ wA͞MA ϩ wB͞MB

where Mi ϭ molecular weight of i


R ϭ 0.0821 atm-liter/g-mole-K ϭ 1.987 g-cal/g-mole-K

ϭ 1.987 Btu/lbm-mole-ЊR ϭ 8.314 /g-mole-K

ϭ 1546 ft-lbf /lbm-mole-ЊR 3 ϭ 10.73 ()-ft /lbm-mole-ЊR 3 ϭ 0.7302 atm-ft /lbm-mole-ЊR Acceleration of gravity (standard)

g ϭ 32.17 ft/s2 ϭ 980.7 cm /s2 Avogadro’s number

N ϭ 6.023 ϫ 1023 molecules/g-mole Boltzmann’s constant

K ϭ 1.3805 ϫ 10Ϫ16 /molecule-K Newton’s conversion constant

2 2 gc ϭ 32.17 lbm-ft /lbf -s ϭ 1.000 kg-m/N-s

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Planck’s constant h 6.624 1027 erg-s


␴ 1.355 1012 cal/s-cm2-K4 1.712 109 Btu /hr-sq ft-R4

Velocity of c 186,000 miles/s 3 1010 cm /s

Velocity of in dry , 0C and 1 atm 33,136 cm /s 1,089 ft /s

Heat of fusion of water at 1 atm, 0C

79.7 cal /g 144 Btu /lbm

Heat of vaporization of water at 1 atm, 100C

540 cal /g 972 Btu/lbm

Ton of refrigeration 12,000 Btu /hr

3 1lbm-mole of perfect gas occupies 359 ft at stan- dard conditions (32F, 14.7 psi abs) 1 g-mole of perfect gas occupies 22.4 liters at 0C and 760 mm Hg

Thermochemistry F 96,500 coulombs/gram equivalent joules coulombs coulombs

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Dimensionless Groups Name Symbol Formula

2 Fanning friction factor f pgcd͞2L␳V 2͞3 Heat transfer factor jH (h͞cpG)(Cp␮͞k) 2͞3 Mass transfer factor jM (kc ␳͞G)(␮͞␳D) 2 Froude number NFr V ͞gL Graetz number NGz wcp͞kL 3 2 2 NGr L ␳ ␤gT͞␮ NNu hd͞k Peclet number NPe LV␳cp͞k 3 5 number NPo Pgc͞␳n d Prandtl number NPr cp␮͞k Reynolds number NRe LV␳͞␮ Schmidt number NSc ␮͞␳D Sherwood number NSh Kc L͞D


cp specific heat, Btu/lbm-F D molecular diffusivity, sq ft/hr d diameter, ft

G mass velocity, lbm /sq ft-hr g acceleration of gravity, 32.2 ft/s2 2 gc conversion factor 32.2 ft-lbm/(lbf-s ) 1 m-kg/(N-s2) h heat transfer coefficient, Btu/sq ft-hr-F k thermal conductivity, Btu/sq ft-(F/ft)-hr

kc mass transfer coefficient, ft/hr L characteristic , ft n rate of rotation, s1

P power to agitator, ft-lbf /s

p pressure , lbf /sq ft T temperature, F V fluid velocity, ft /s

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w mass flow rate, lbm /s ␤ coefficient of bulk expansion, F1 3 ␳ density, lbm /ft

␮ viscosity lbm /ft-hr

Abbreviations atm Btu cal cm centimeter cu ft , feet g gram hp horsepower hr in inch kg km kilometer kW kilowatt

lbm pound-mass

lbf pound- m meter min ml milliliter pt pint qt quart quad quadrant R degrees Rankine rad rev revolution s second yd yard ␮ micron

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, ␣ , ␩ , ␤ , ␪ , ␥ , ␫ , ␦ , ␬ , ⑀ , ␭ lambda , ␨ M, ␮ , ␯ , ␶ , ␰ , ␷ , , ␾ , ␲ pi , ␹ , ␳ , ␺ psi , ␴ , ␻


a2 b2 (a b)(a b) a3 b3 (a b)(a2 ab b2) a3 b3 (a b)(a2 ab b2) 2 2 2 b b 4ac a x bx c 0 x 2a Area of circle ␲r 2 of circle 2␲r Surface of sphere 4␲r 2 Volume of sphere (4͞3)␲ r 3 Volume of or pyramid 1͞3 (base area)(height) dax adx

n n1 dx nx dx

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d(u v) du dv d(uv) udv vdu

u vdu udv d c d v v2

ax ax de ae dx

x x da a logea dx d sin x cos x dx d cos x sin x dx

2 d tan x sec x dx ͐(u v) dx ͐udx ͐vdx ͐udv uv ͐vdu

n n1 ͐x dx x ͞(n 1) for n 1 dx Ύ loge x ln x x

ax ax e ͐e dx a

Binomial series

n(n 1) n n n1 (x y) x n x y 2!

n2 2 2 2 x y (y x )

Taylor series

x a (x a)2 f (x) f (a) f (a) f (a) 1! 2!

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MacLaurin series

2 x x f (x) f (0) f (0) f (0) 1! 2!

Exponential series

2 3 x x x e 1 x 2! 3!

␲ 3.1416, e 2.71828, i 21, i2 1, i4 1 log10 x 0.4343 ln x, ln x 2.303 log10 x a b 2 2ab

Harmonic mean 2ab a b Logarithmic mean a b ln a͞b Solution of

dy Py Q dx

where P, Q are constants or functions of x e ͐Pdx IF

Solution y IF ͐(IF Q)dx C

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Chemical Process Safety—The application of and management practices a) to prevent accidents in plants, and/or b) to reduce the potential for accidents. Process Safety Management—An OSHA regulation that emphasizes the management of safety within plants. This is an especially important and effective regulation that has 14 elements: 1) Employee Participation, 2) Process Safety Information, 3) Operating Procedures, 4) Process Hazards , 5) Mechanical Integrity, 6) Management of Change, 7) Incident Investigation, 8) Hot Work Permits, 9) Employee Training 10) Pre- Startup Review, 11) Emergency Planning, 12) Contrac- tors, 13) Audits, and 14) Trade Secretes. Safety Technology—Design features and control features to reduce the potential for accidents. Safety Design Features—a) Inerting to control the concen- tration of a flammable gas to below the LFL, b) ground- ing and bonding to prevent static electricity charging and discharging (spark) and potential fire, c) installing relief valves to prevent vessel ruptures, d) installing double block and bleeds to prevent the backup of reac- tive chemicals into a monomer , e) installing an suppression system to prevent dust explo- sions, f) installing containment to catch the re- lease from relief valves, etc. Safety Control Features—a) Monitoring the temperature and pressure to prevent abnormal conditions, b) adding reactor safeguards to prevent runaway reactions, c) adding redundant controls to decrease the of accidents, d) adding more reliable instruments to re- duce the frequency of plant accidents, etc. 51 13282AICEtext 4/12/04 12:20 PM Page 52


Auto Ignition Temperature (AIT)—A fixed temperature above which a flammable mixture is capable of extract- ing enough energy from the environment to self-ignite. Boiling Liquid Expanding Vapor Explosion (BLEVE)—A BLEVE occurs when a vessel ruptures which contains a liquid at a temperature above its atmospheric- pressure boiling point. It is the vaporization of a large fraction of the vessel contents; possibly fol- lowed by the or explosion of the vaporized if it is combustible (similar to a ). Deflagration—An explosion with a flame front moving in the unburned gas at a below the (1250 ft /s). Detonation—An explosion with a moving at a speed greater than the speed of sound in the unre- acted medium. (FP)—The FP of a liquid is the lowest tem- perature at which it gives off enough vapor to form an ignitable mixture with air. Flammability Limits (LFL and UFL)—A gas mixture will not burn when the composition is lower than the lower flammable limit (LFL). The mixture is also not com- bustible when the composition is above the upper flam- mability limit (UFL). Flammability Limits of —They are computed with the following equations:

1 LFLMIXTURE yi a a b LFLi 1 UFLMIXTURE yi a a b UFLi

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Lower Flammability Limit in the Presence of Mists— Ϸ LFLMISTS 0.1 LFL THEORETICAL Mechanical Explosion—An explosion due to the sudden failure of a vessel containing a nonreactive gas at a high pressure. Minimum Oxygen Concentration (MOC)—A mixture of gas will not burn if the oxygen concentration is below the minimum oxygen concentration. Minimum Oxygen Concentration (MOC)—It is estimated using the following equation: Moles of Oxygen MOC (LFL%) a b Moles of Fuel Overpressure—The pressure on an object as a result of an impacting . Relief Valve—A device that relieves the pressure within a vessel when the pressure approaches the maximum allowable working pressure (MAWP). All vessels have reliefs. Risk—This is the product of the frequency and the con- of an accident scenario.


Aerobes— whose growth requires the pres- ence of air or oxygen. involved with the of cellular components. Anaerobes—Organisms that grow in the absence of air or oxygen. —The extension of chemical engineering principles to biological systems with the goal of producing useful products. 53 13282AICEtext 4/12/04 12:20 PM Page 54

Bioreactor—A vessel used for biological processes. Ex- amples include growing microorganisms and animal cells for the production of useful products. —The use or development of methods of direct genetic manipulation for a socially desirable goal. Examples include the production of a particular chemical, production of better plants or seeds, and . —Metabolism involved with the breakdown of materials for the production of intermediates and energy. —A catalytic (and in some cases RNA) produced by living cells. Eukaryote—A cell or with a membrane-bound nucleus and well-developed . Examples in- clude yeast, animals, and plants. Prokaryote—A cell lacking a true nucleus. Examples in- clude and blue-green algae. Virus—A noncellular entity that consists minimally of protein and DNA or RNA and that can replicate only af- ter entry into specific types of living cells.


Antibiotics—Substances of microbial origin that in very small amounts have antimicrobial activity. Antibodies—Glycoprotein molecules produced by B- lymphocytes in higher organisms in response to the introduction of a foreign material (antigen). These mol- ecules react with antigens with great specificity. Attachment Dependent—Cells whose growth requires attachment to a surface. Also referred to as Anchorage- Dependent. Batch Culture—A culture that once supplied with raw materials is run to completion.

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Chemostat—A in which the continuous addi- tion of fresh medium and removal of effluent results in constant nutrient, product, and cell concentrations when operated under steady state conditions. Death Phase—The portion of the growth in culture in which there is a net decline in the number of viable (live) cells. Exponential (Log) Growth Phase—A of growth in a culture in which the number of cells or cell mass in- creases exponentially, i.e., the growth rate is propor- tional to the density:

dX ␮ X, dt

where X cell number (cells /mL) or cell biomass (mg/mL), t is time, and ␮ is the specific growth rate (h1). Fed-Batch Culture—A culture to which nutrients are - riodically added during the of the culture. Growth Yield—Yield of biomass based on substrate (e.g., or oxygen) utilization:

dX Y , X/S dS

where YX͞S is the yield coefficient of biomass (X) based on Substrate (S) and is usually given in terms of either (gm biomass/gm or mole substrate) or (cell number/gm or mole substrate).

KLa—Volumetric mass transfer coefficient usually meas- ured in h1 and often used to compare the efficiencies of in supplying oxygen. The resulting oxy- gen transfer rate is then given by

dCL K a(C * C ), dt L L

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where CL is the dissolved oxygen concentration within the bioreactor, t in time, and C* is the equilibrium dis- solved oxygen concentration (i.e., ) under the specified conditions. Lag Phase—The portion of the growth curve between in- oculation and the beginning of cell growth. Media Sterilization—Removal of undesired microorgan- isms from the media through filtration or heat to pre- vent their growth during the course of a bioreactor run. Michaelis-Menton Kinetics—Common type of enzyme ki- netics given by

vmax[S] v , KM [S]

where v is the reaction rate, vmax is the maximum reac-

tion rate, KM is the Michaelis Constant and is equal to 1 the substrate concentration at v ⁄2vmax , and [S] is the substrate concentration. Perfusion Culture—A bioreactor in which cells are retained, medium is added continuously or semi- continuously, and spent medium containing toxic metabolites is removed. Population Doubling Time (PDT)—The time required for the viable cell population to double. This term is com- monly used for animal cell cultures, and is related to the specific growth rate (␮) by

ln(2) PDT ␮ .

Power Number (Np)—A dimensionless number com- monly used to determine the amount of power intro- duced to the bioreactor as a result of agitation. The

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Power Number is given by P N , P 3 5 ␳N D

where P is the power input, ␳ is the density of the solu- tion being agitated, N is the of the im- peller, and D is the impeller diameter. Monod Equation—An equation commonly used to model the effect of the rate-limiting substrate concentration on the specific growth rate. This equation is given by

␮m[S] ␮ , Ks [S]

where ␮ is the specific growth rate, ␮m is the maximum

specific growth rate when [S] W Ks, [S] is the sub-

strate concentration, and Ks is the saturation constant or half-velocity constant and is equal to the substrate 1 concentration when ␮ ⁄2␮m. Stationary Phase—Phase in growth curve following the phase in which there is no net growth. This phase is commonly associated with nutri- ent depletion.

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