Student Pocket Handbook Final

8/10/2019 Student Pocket Handbook Final

1/63

PocketHandbook


2/63

The AIChEPocket Handbook

Thomas R. Hanley, Editor

American Institute of Chemical Engineers3 Park Ave. 18th Floor

New York, New York 10016


3/63

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

Copyright 1985 by the American Institute of Chemical Engineers

ISBN 0-8169-0342-5

Reprinted, 1988, 1990, 1992, 1993, 2001, 2004, 2005, 2007,

2011


4/63

TABLE OF CONTENTS

Inorganic Chemistry ...................................................... 1

Organic Chemistry......................................................... 6Physical Chemistry........................................................ 10Fluid Flow....................................................................... 14Heat Transfer.................................................................. 18Distillation ...................................................................... 23Mass Transfer ................................................................. 26

Thermodynamics ........................................................... 29Kinetics and Reactor Design ........................................ 34Conversion Factors ....................................................... 40Physical Constants ........................................................ 44Greek Alphabet .............................................................. 48Mathematics ................................................................... 48Chemical Process Safety .............................................. 51Biochemical Engineering.............................................. 53


5/63

Foreword

The purpose of this handbook is to make readily avail-

able in a limited number of pages some of the more important chemical, biological, physical, safety, and mathe-matical data and concepts that are fundamental to the

practice of the chemical engineering 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 work on this Handbook.


6/63

INORGANIC CHEMISTRY

I. COMMON DEFINITIONS

Atomic numberthe number of protons in the nucleusof an atom.

Avogadros numberthe number of molecules(6.023 1023) in one gram-mole of a substance.

Equilibrium constants for the reaction aA bB cC dDwhere reaction is in solution,

([ ] refers to molarity)

where reaction is in the gas phase,

( p partial pressure)

Gram equivalent weight A. (nonredox reaction) the mass in grams of a

substance equivalent to 1 gram-atom of hydrogen,0.5 gram-atom of oxygen, or 1 gram-ion of the

hydroxyl ion. It can be determined by dividingthe molecular weight by the number of hydrogenatoms or hydroxyl ions (or their equivalent)supplied or required by the molecule in a givenreaction.

B. (redox reaction) the molecular weight in grams

divided by the change in oxidation state.Ion product of water ( K w)the product of thehydrogen ion and hydroxyl ion concentrations ingram-ions per liter;

K w [H ][OH ]

K p p cC p

d D

p a A p b

B

K c [C ]c[ D ]d

[ A ]a [ B ]b

1


7/63

Mass number the number of protons plus the number of neutrons in the nucleus of an atom.

Molality (m) (gram moles of solute)/(kilograms of solvent).

Molarity (M) (gram moles of solute)/(liters ofsolution).

Normality (N) (gram equivalents of solute)/(liters of solution).

Oxidation the loss of electrons by an atom or groupof atoms.

p Hthe negative logarithm (base 10) of the hydrogenion concentration in gram ions per liter;

Reduction the gain of electrons by an atom or groupof atoms.

Solubility product (S.P. or K sp )for the slightly solublesolid, A a B b , dissolving

A a B b (solid) aA (aq) bB (aq)where A is any cation and B is anyanion

S.P. or K sp [ A ]a [ B ]b a constant at a giventemperature

II. PROPERTIES OF CHEMICAL ELEMENTS

Atomic Atomic CommonName Symbol Number Weight Valence

Actinium Ac 89 (227) 3 Aluminum Al 13 26.9815 3 Americium Am 95 (243) 6,5,4,3 Antimony Sb 51 121.75 3,5

p H log 10[H ]

2


8/63


Argon Ar 18 39.948 0 Arsenic As 33 74.9216 3,5 Astatine At 85 (210) 1,3,5,7Barium Ba 56 137.34 2Berkelium Bk 97 (247) 4,3Beryllium Be 4 9.0122 2Bismuth Bi 83 208.980 3,5Boron B 5 10.811 3

Bromine Br 35 79.904 1,5Cadmium Cd 48 112.40 2Calcium Ca 20 40.08 2Californium Cf 98 (249) 3Carbon C 6 12.01115 4,2Cerium Ce 58 140.12 3,4Cesium Cs 55 132.905 1Chlorine Cl 17 35.453 1,3,5,7Chromium Cr 24 51.996 6,2,3Cobalt Co 27 58.9332 2,3Copper Cu 29 63.546 2,1Curium Cm 96 (247) 3Dysprosium Dy 66 162.50 3Einsteinium Es 99 (254) Erbium Er 68 167.26 3Europium Eu 63 151.96 3,2Fermium Fm 100 (253) Fluorine F 9 18.9984 1Francium Fr 87 (223) 1Gadolinium Gd 64 157.25 3

Gallium Ga 31 69.72 3Germanium Ge 32 72.59 4Gold Au 79 196.967 3,1Hafnium Hf 72 178.49 4Helium He 2 4.0026 0Holmium Ho 67 164.930 3

3


9/63


Hydrogen H 1 1.00797 1Indium In 49 114.82 3Iodine I 53 126.9044 1,5,7Iridium Ir 77 192.2 2,3,4,6Iron Fe 26 55.847 2,3Krypton Kr 36 83.80 0Lanthanum La 57 138.91 3Lawrencium Lw 103 (257)

Lead Pb 82 207.19 4,2Lithium Li 3 6.939 1Lutetium Lu 71 174.97 3Magnesium Mg 12 24.312 2Manganese Mn 25 54.9380 7,6,4,2,3Mendelevium Md 101 (256) Mercury Hg 80 200.59 2,1

Molybdenum Mo 42 95.94 6,5,4,3,2Neodymium Nd 60 144.24 3Neon Ne 10 20.183 0Neptunium Np 93 (237) 6,5,4,3Nickel Ni 28 58.71 2,3Niobium Nb 41 92.906 5,3Nitrogen N 7 14.0067 3,5,4,2Nobelium No 102 (254) Osmium Os 76 190.2 2,3,4,6,8Oxygen O 8 15.9994 2Palladium Pd 46 106.4 2,4Phosphorus P 15 30.9738 3,5,4Platinum Pt 78 195.09 2,4

Plutonium Pu 94 (242) 6,5,4,3Polonium Po 84 (210) 2,4Potassium K 19 39.102 1Praseodymium Pr 59 140.907 3,4Promethium Pm 61 (147) 3

4


10/63


Protactinium Pa 91 (231) 5,4Radium Ra 88 (226) 2Radon Rn 86 (222) Rhenium Re 75 186.2 7,6,4,

2, 1Rhodium Rh 45 102.905 2,3,4Rubidium Rb 37 85.47 1Ruthenium Ru 44 101.07 2,3,4,6,8

Samarium Sm 62 150.35 3,2Scandium Sc 21 44.956 3Selenium Se 34 78.96 2,4,5Silicon Si 14 28.086 4Silver Ag 47 107.870 1Sodium Na 11 22.9898 1Strontium Sr 38 87.62 2

Sulfur S 16 32.064 2,4,6Tantalum Ta 73 180.948 5Technetium Tc 43 (98) 7Tellurium Te 52 127.60 2,4,6Terbium Tb 65 158.924 3,4Thallium Tl 81 204.37 3,1Thorium Th 90 232.038 4Thulium Tm 69 168.934 3,2Tin Sn 50 118.69 4,2Titanium Ti 22 47.90 4,3Tungsten W 74 183.85 6,5,4,3,2Uranium U 92 238.03 6,5,4,3

Vanadium V 23 50.942 5,4,3,2

Xenon Xe 54 131.30 0Ytterbium Yb 70 173.04 3,2Yttrium Y 39 88.905 3Zinc Zn 30 65.37 2Zirconium Zr 40 91.22 4

5


11/63

III. COMMON ANIONS

Name Symbol Name Symbol

Arsenite AsO 3 Hydroxide OH

Arsenate AsO 4 Hypochlorite OCl Acetate C 2H3O2 Iodide IBicarbonate HCO 3 Iodate IO 3Bisulfate HSO 4 Molybdate MoO 4Bromate BrO 3 Nitrate NO 3Bromide Br Nitrite NO 2Carbonate CO 3 Oxalate C 2O4Chlorate ClO 3 Perchlorate ClO 4Chloride Cl Peroxide O 2Chromate CrO 4 Permanganate MnO 4Cyanamide CN 2 Phosphate PO 4Cyanide CN Sulfate SO 4Dichromate Cr 2O7 Sul de SDithionate S 2O6 Sul te SO 3Ferricyanide Fe(CN) 6 Thiocyanate CNSFerrocyanide Fe(CN) 6 Thiosulfate S 2O3Formate CHO 2

ORGANIC CHEMISTRY

Note: For conciseness the following symbols areused:

R H atom or saturated hydrocarbon group R hydrocarbon group only X halogen

n

an integer

I. GENERAL CLASSES OF COMPOUNDS

A. The straight and branched chain types of compounds

6


12/63

Type or Name General Formula

1. Alkane or paraf n(also saturatedhydrocarbons)

2. Alkene or ole n(unsaturatedhydrocarbons)

3. Alkyne

4. Alcohol

5. Ether

6. Aldehyde

7. Ketone

8. Carboxylic Acid

9. Grignard reagent

10. Acyl halide

7


13/63


11. Anhydride

12. Ester

13. Amide

14. Amine (base)

15. Nitrile

B. Cyclic Compounds

1. Cycloparaf n

8


14/63


II. PERTINENT NOTES

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

4. Naphthalenic

3. Aromatic

2. Cycloalkene

9


15/63

B. Mechanisms1. Free radical (unshared electron)

(no charge)

2. Carbonium ion (de cient in electrons)( positive charge)(carbon with six electrons)

3. Carbanion(excess of electrons)

(negative charge)(carbon with eight electrons)

PHYSICAL CHEMISTRY

1. Amagat s Law of Partial Volumes The volumeof a mixture of gases is equal to the sum of the par-tial volumes of each component gas. The partial

volume of a component gas is the volume whichthat component would occupy at the same temper-ature and pressure.

2. Boiling Point Elevation ( T b)The following equa-tions hold for a dilute solution of a nonionic non-

volatile solute.

where H v molal heat of vaporization K b molal boiling point elevation con-

stant m molality

M a solvent molecular weight

K b R (T bp )

2 M a

H v(1000)

T b K b m

10


16/63

R ideal-gas constant T bp solvent boiling point, absolute tem-

perature

3. Clausius Equation

where p pressureT absolute temperature

H m molal heat of vaporizationV molar vapor volumev molal liquid volume

4. Clausius-Clapeyron Equation Where the volumeof liquid can be ignored (or v 0) and where theideal-gas law holds (or V RT p ) the Clausiusequation becomes

and with H m constant, integration yields

The symbols are the same as in sections 2 and 3above.

5. Dalton s Law of Partial Pressures The pres-sure of a mixture of gases is equal to the sum ofthe partial pressures of each component gas.The partial pressure of a component gas is the

pressure which that component would exert if it alone occupied the volume at the same tem-

perature.

ln p2

p 1

H m R

cT 2 T 1T 1T 2 d

d ( ln p )

dT 1

p dp

dT

H m

RT 2

dp

dT

H m(V v ) T

11


17/63

6. Faraday s LawsFirst Law: The mass of a substance reacting

at the electrodes is directly proportional to thequantity of electricity passed through the solu-tion.

Second Law: The masses of different sub-stances produced during electrolysis are directly

proportional to their equivalent weights; 96,496coulombs of electricity 1 faraday electricity to

yield 1 gram equivalent of any substance.7. Freezing Point Depression ( T f ) The follow-

ing equations hold for a dilute solution of anonionic solute in which the solid phase is puresolvent.

where H f molal heat of fusion of solvent K f molal freezing point lowering con-

stant

m molality M a solvent molecular weight

R ideal-gas constant T f p solvent freezing point, absolute tem-

perature

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

K f R (T f p ) 2 M a

H f (1000)

T f K f m

12


18/63

of the phase rule applies to non-reactive sys-tems.

9. Graham s Law of Diffusion The rate of diffusionof a gas is inversely proportional to the square root of its density.

10. Henry 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 abovethe liquid.

11. Raoult s Law

where p a partial pressure of component A in vapor

x a mole fraction of A in liquid solution P a vapor pressure of pure liquid A

12. van t Hoff Reaction Isochore

at constant pressure

where H heat of reaction

K reaction equilibrium constant R ideal-gas constant T absolute temperature

If H is constant,

13. Molar Humidity moles vapor/mole vaporfree gas

Y y a

1 y a

p a P p a

ln a K 2 K 1b H

R cT 2 T 1T 1T 2 d

d ( ln K )

dT

H

RT 2

p a x a P a

13


19/63

Humidity pounds vapor/pound vapor-free gas

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

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

where p a partial pressure of component A ingas

P a vapor pressure of pure liquid A

P total pressure M a molecular weight of A M b molecular weight of B

y a mole fraction of a gas

FLUID FLOW

I. DEFINITIONS AND GENERAL EQUATIONS

Mass velocity

G V

H p 100Y

Y sat 100

p a ( P P a )

P a ( P p a )

H r 100 p a

P a

Y Y M a M b

14


20/63

Simple manometer equation

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

Average velocity,

Reynolds number, N Re

Mechanical energy balance

where 1 for turbulent ow ( N Re 4,000) 0.5 for laminar ow ( N Re 2,100)

Hydraulic radius

Equivalent diameter, D e

D e 4 (hydraulic radius, r H )

r H s , cross-sectional area

L p , the wetted perimeter

P a a

g

g c Z a

V 2a2 g c a W s

P b b

g

g c Z b

V 2b2 g c b H f

N Re DV DV

V q, volumetric flow rate

s , cross-sectional area

V

P a P b 32 L V

g c D 2

P a P b R m g

g c ( a b)

15


21/63

II. FRICTION

Skin friction

Fanning friction factor, f (ow in smooth pipes)

laminar

turbulent

Friction of valves and ttings (Add to length of pipe toget total equivalent length.)

Equivalent

Fittings and Valves resistance, pipe diameters

45-degree elbows 1590-degree elbows (standard radius) 3290-degree square elbows 60180-degree close return bends 75

Ts (used as elbow, entering run) 60Ts (used as elbow, entering branch) 90Couplings NegligibleUnions NegligibleGate valves (open) 7Globe valves (open) 300

Angle valves (open) 170

Friction loss from sudden expansion of cross sec-tion

H fe V 2a2 g c

a1 s as bb2

1 f . .5

4.0 log ( N Re f . .5) 0.4

f 16

DV 16

N Re

H fs 2 f LV 2

Dg c

16


22/63

Friction loss from sudden contraction of cross section

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

III. MEASUREMENT OF FLOWING FLUIDS

Venturi meter

(b is at throatof meter)

Ori ce meter, design equation ( N Re 20,000)

Pilot tube (manometer measures p s P )

IV. SYMBOLS USED

C u , C p coef cients of velocity D diameter g acceleration of gravity 32.2 ft /s 2 9.81 m/s 2

g c Newton s conversion factor 32.2 ft-lb m /(lb f -s2)1 m-kg/(N-s 2 )

H f head loss due to friction H fs head loss due to skin friction H fc head loss due to contraction of cross section

V C p

B 2 g c ( p s P )

V o 0.612 1 4 B

2 g c ( p a p b)

2 V sb V 2a C v B 2 g c ( p a p b)

H fc K cV

2b

2 g c

17


23/63

H fe head loss due to expansion of cross section K e expansion loss coef cient K c contraction loss coef cient L length of pipe P pressure

P a upstream pressure P b downstream pressure

p a , p b pressure in arms of manometer p s static pressure

R m manometer readings cross-sectional area V velocity

average velocityV a upstream velocityV b downstream velocityW s shaft work done by pump

Z elevation kinetic energy correction factor

ratio of diameter of ori ce to diameter of pipe

uid density, lb m /ft 3 a density of manometer uid

b density of uid above manometer kinematic viscosity viscosity

HEAT TRANSFER

I. CONDUCTION

Fourier s Law (constant k )steady state

q kA T

x

T R

V

18


24/63

unsteady state

Resistance in Series

Radial Heat Flow Through a Cylinder

where A m logarithmic mean area normal to heatow

r m logarithmic mean radius r m ( r o r i) ln [ r o r i]

II. CONVECTION

q hA T

where h k x , heat transfer coef cient k thermal conductivity of the uid x thickness of the laminar lm

III. COMBINED CONDUCTION AND CONVECTION

q UA avg ( T )

where U overall heat transfer coef cient T overall temperature difference

q k (2 r m ) L T

( r o r i )

k A m T

r

T

R A R B R C

q T

x A k A A

x B k B A

x C k C A

T t

k C p

x 2T

x 2

19


25/63

where A r reference area, usually the area of the solid through which heat isbeing conducted

h Fi , h Fo inside and outside fouling fac-tors

IV. RADIATION

where q 12 net radiation between surfaces 1 and2, Btu/hr

T 1, T 2 absolute temperature of surfaces 1,

2, R . A area of either surface, sq ft

Stefan-Boltzman Constant 1.712 10 9 Btu/hr-sq ft- R 4

F geometric view factor

V. EMPIRICAL, DIMENSIONLESS CORRELATION

Turbulent Flow in Clean Smooth Pipes

where N Re the Reynolds Number DG N Pr the Prandtl Number C p k

Laminar Flow in Clean Smooth Pipes

h i D

k1.86( N Re )

0.33 ( N Pr )0.33 ( w)

0.14 ( D L ) 0.33

h i D

k0.023( N Re )

0.8( N Pr )0.33 ( w)

0.14 [1 ( D L ) 0.7]

q12 AF (T 41 T

42)

1U

A r UA r

1

h i A i A r

x m

k m A m A r

1

h o A o A r

1

h Fi A i A r

1

h Fo A o A r

20


26/63

where the Reynolds and Prandtl Numbers are as de nedfor turbulence

VI. HEAT TRANSFER TO AND FROM FLUIDS FLOWINGNORMAL TO A SINGLE TUBE

where N Re the Reynolds Number D oG f

The subscript f calls attention to the fact that thecorrelation is based on the mean lm temperature,T f , which is de ned as the arithmetic mean of theaverage uid temperature and the wall tempera-ture.

VII. HEAT TRANSFER TO AND FROM FLUIDS FLOWINGPERPENDICULAR TO TUBE BANKS

(b and n depend on geometry)

where N Re

the Reynolds Number DGmax f

VIII. HEAT TRANSFER FROM CONDENSING VAPORS

Vertical Tubes

Horizontal Tubes

h avg 0.725 c k 3

f 2 f g

T o D o f d0.25

h avg 1.13 c k 3 f 2 f g

T o L f d0.25

h avg D o

k f b ( N Re )

n

h o D o k f

0.35 0.56( N Re )0.52

21


27/63

IX. NOTATION

A area, sq. ft.b empirical constant

C p speci c heat at constant pressure, Btu/lb- F D diameter, ft G mass velocity, lb m /sq ft-sec

Gmax mass velocity through minimum cross section intube bundle

g acceleration of gravity, 32.2 ft/sec 2

h

heat transfer coef cient, Btu/sq ft-hr- F k thermal conductivity, Btu/sq ft-( F/ft)-hr L length of tube or cylinder, ft q heat ow per unit of time, Btu/hr

R resistance r radius, ft T temperature, Ft time, hr

U over-all heat transfer coef cient, Btu/sq ft-hr F

x distance in direction of heat ow; thickness of layer, ft

latent heat of condensation or vaporization,

Btu/lb m viscosity,lb m /ft-sec

density, lb m /ft 3

Subscripts

avg average f lmi insideo outside

r reference

22


28/63

w wall m mean or log mean

DISTILLATION

I. FLASH (OR EQUILIBRIUM) DISTILLATION

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

II. DIFFERENTIAL (SIMPLE OR RAYLEIGH) DISTILLATION

When the relative volatility is constant y x

[1 ( 1) x ] can be substituted to give

For binary system following Raoult s Law

where p i partial pressure of component i

III. CONTINUOUS DISTILLATION (BINARY SYSTEM)WHERE CONSTANT MOLAL OVERFLOW IS ASSUMED

Total Material Balance

Fz F Dx D Bx B

F D B

(y x ) a(y x ) b

p a p b

lnW W o

1( 1)

ln c x (1 x o) x o(1 x ) d ln c1 x o1 x d

lnW W o

x

x o

dx y x

23


29/63

Operating Lines

1. Rectifying Section

Total material: V n 1 L n DComponent A : V n 1 y n 1 L n x n Dx D

2. Stripping Section

Total material: L m V m 1 BComponent A : L m 1 x m V m 1 y m 1 Bx B

3. Re ux RatioRatio of re ux to overhead product

4. Feed Condition Line

Type of Feed Slope 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 Ef ciency

E ME y n y n 1y * n y n 1

R D L D

V D D

y m 1 L m

L m B x m

Bx B L m B

y n 1 L n

L n D x n

Dx D L n D

24


30/63

where y n concentration of vapor above plate n

y n 1 concentration of vapor entering from plate below n

y* n concentration of vapor in equilibriumwith liquid leaving plate n

IV. NOTATION

relative volatility B moles of bottoms product D moles of overhead product F moles of feed L molar liquid down ow

R D ratio of re ux to overhead product V molar vapor up owW weight in still pot x mole fraction of the more volatile component in

the liquid phasey mole fraction of the more volatile component in

the vapor phase z D 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

25


31/63

MASS TRANSFER

I. DIFFUSION

1. Molecular Diffusion

2. Unidirectional Diffusion of a Gas A Through a SecondStagnant Gas B ( N B 0)

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

3. Equimolar Countercurrent Diffusion ( N B N A )(gases)

4. Unsteady State Diffusion

II. CONVECTION

1. Two-Film Theory

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

N A A

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

p At

D 2 p A

z 2

N A A

D RT

( p A 2 p A 1)

z 2 z 1

p B 1 p B 2

N A A

DP RT ( p B) lm

( p A 2 p A 1)

x 2 x 1

N A A

p A P

c N A A N B A d D RT p A z

26


32/63

2. Overall Coef cients

3. Transfer Unit

HTU height of a transfer unit

NTU number of transfer units

For dilute solutions (straight operating and equilib-rium line)

Z N TG H TG N TL H TL tower height

4. Dimensionless Group Equation (Sherwood)

( N Sh ) 0.023 ( N Re )0.8( N Sc )

1 3

N TG y 1 y 2

(y y*) lm

N TL x 2

x 1

dx x x

*

12

ln1 x 11 x

2

N TG y 2

y 1

dy

y* y12

ln1 y 21 y 1

H TL L

K L a

H TG G

K G a

1 K L

1 Hk G

1 k L

1 K G

1 k G

H k L

27


33/63

III. MOMENTUM, HEAT, AND MASS TRANSFER ANALOGY

where f Fanning friction factor

IV. NOTATION

A area perpendicular to direction of diffusiona interfacial area per unit volumeC concentration in liquid phased tube diameter

D molecular diffusivityG gas mass velocity, mass/(time)(area)

H Henry s Law constant, p i HC ih heat transfer coef cient

k lm coef cient of mass transfer K overall coef cient 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

N Re Reynolds number du N Sc Schmidt number D N Sh Sherwood number kd D

t timeT absolute temperatureu velocity

j M k cG

( N Sc )0.667

j H hC p G

cC p k d0.667

cw d0.140.5 f j H j D

28


34/63

lm logarithm mean average

Greek Letters

density viscosity

Subscripts

A, B components of mixtureG gas phase L liquid phase

i interface x mole fraction of liquidy mole fraction of gas

z length in direction of travel* equilibrium concentration

THERMODYNAMICS

I. DEFINITIONS

System an arbitrarily chosen portion of space which isunder consideration.

A. Closed system one in which matter does not passthrough its boundaries.

B. Open system one in which matter ows across itsboundaries.

C. Isolated system one in which there is no interchangeof energy or matter with the surroundings.

Boundaries the envelope separating the system fromthe surroundings.

Universe a system and its surroundings.

29


35/63

Total energy, E the sum of the various forms of energyof the system: e.g., U , internal energy; E k , kinetic en-ergy; E p , potential energy; Hence,

E U E p E k

II. FIRST LAW

In an isolated system E E 2 E 1 0

In a closed system E Q W

In an open system E g ( H E p E k) Q W

where the summed terms refer to leaving ( ) and enter-ing ( ) streamsIn a steady state open system

E system 0

Hence for the entering and leaving streams

H E k E p Q W

III. SECOND LAW

For any real process the total entropy of the universealways increases

S system S surroundings 0

IV. THERMODYNAMIC FUNCTIONS: DEFINITIONSAND RELATIONSHIPS

De nition of entropy

From First and Second Laws, with changes in E k ,

S dQ rev

T

30


36/63

E p , and composition negligible,

Also

P, V, T, S, U, H, G, A are state functions. Q and W are pathfunctions and have no total derivatives.

V. PERFECT-GAS RELATIONSHIPS

For any path:

For any path:

For monoatomic gas: C p 2.5 R and C v 1.5 R

For diatomic gas: C p 3.5 R and C v 2.5 R

Adiabatic ( Q 0) and reversible path for system with E p E k 0.

(per mole)

Isothermal path, ow or non ow

P 2 P 1

V 1V 2

W flow H [W nonflow ] ( per mole)

W nonflow U RT 1 1 c a P 2 P 1b

( 1)

1d( P 2 P 1) (V 1 V 2)

(T 2 T 1) ( 1)

U T 2

T 1

C v dT or ( U V )T 0

H T 2

T 1

C p dT or ( H P )T 0

C p ( H T ) p ; C v ( U T ) v; (C p C v)

dA dU d (TS ) SdT PdV

dG dH d (TS ) SdT VdP

dH dU d ( PV ) TdS VdP

dU dQ rev PdV TdS PdV

31


37/63

VI. CRITERIA FOR EQUILIBRIUM CHANGE

For system and surroundings: dS universe 0

For system alone: dG 0 when P , T constant dA 0 when V , T constant

VII. CHEMICAL THERMODYNAMICS

A. Fugacity ( f ) and Activity ( a )

(constant-temperature path)

and the limit of f P as P approaches 0 1.00

a f f 0

B. Equilibrium

Standard free energy at temperature T for thereaction

C. Cells

At standard conditions

G nF RT ln K a

RT lna r R a

s S

a a

A a b

B

RT ln K a

G rG R sG S aG A bG B

aA bB rR sS

G RT ln ( f 2 f 1) 2

1 VdP ( per mole)

W RT lnV 2V 1

RT ln P 1 P 2

( per mole)

32


38/63

At actual conditions

VIII. NOTATION

A U TS , Helmholtz work functiona activityC heat capacity

E total energy of the system E k kinetic energy of the system E p potential energy of the system

reversible voltage of cell F faradays per equivalent f fugacity

G H TS , Gibbs free energy g c Newton s conversion factor H U PV , enthalpy

h enthalpy per pound K equilibrium constant for the reaction as writ-

ten

K a equilibrium constant in terms of activity K f equilibrium constant in terms of fugacity K p equilibrium constant in terms of partial pres-

sure n number of equivalents for the reaction as

written P pressureQ heat, de ned as positive when absorbed by

system R gas constant S entropyT absolute temperature

G nF nF RT lna r R a

s S

a a A a b

B

33


39/63

U internal energy of the systemu velocityV volumev speci c volume

W work, de ned as positive when done by systemon surroundings

nal state minus initial state (C p C v)

Superscript

standard state

KINETICS AND REACTOR DESIGN

I. RATE OR REACTION

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

and where density remains unchanged

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

term, or r A k (T) f (C A , C B . . .)

A. Order, Molecularity, Elementary Reactions

Where the rate can be expressed as

r A dC Adt

r A 1

V dN adt

34


40/63

the reaction is ath order with respect to A andnth order overall; n a b

NOTE: a, b, . . . are empirically observed and arenot necessarily equal to the stoichiometric coef -cients. In the special case where a, b, . . . are thestoichiometric coef cients, 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

where E is the activation energy of the reaction

II. HOMOGENEOUS, CONSTANT FLUID DENSITY,BATCH KINETICS

A. Irreversible First-order Reaction

For the reaction A S products, with rate

the integrated form is

lnC AC A 0

ln (1 X A) kt

dC A

dt kC A or

dX A

dt k (1 X A)

k k oe E RT or ln

k 2 k 1

E

R c1T 1

1

T 2 d

r A kC a

A C b

B . . .

35


41/63

B. Irreversible Second-order Reaction

For the reaction A B S products, with rate

When M C B 0 C A 0 1, the integrated form is

When C A 0 C B 0 , the integrated form is

C. Irreversible nth-order Reaction

For the reaction with rate

the integrated form for n 1 is

D. Reversible First-order Reaction

For the reaction A R , K k 1 k 2 with rate

the integrated form is

ln X Ae X A

X Ae ln

C A C AeC A 0 C Ae

( k 1 k 2) t

dC Adt

dC Rdt k 1C A k 2C R

12

C 1 n A C 1 n

A 0 ( n 1) kt

dC Adt

kC n A

1

C A

1

C A 0

1

C A 0

X A1 X A

kt

lnC B C A 0C B 0 C A

ln M X A

M (1 X A)(C B 0 C A 0) kt

dC Adt kC AC B

36


42/63

E. Integration of Rate in General

For the reaction with rate

which is to be solved analytically or graphically.

III. BATCH REACTION WITH CHANGING FLUID DENSITY

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

tems),

where

The rate for any reactant A is then

Integrating in the general case

t C A 0 X A

0

dX A(1 A X A)( r A)

r a 1

V dN A

dt

C A 0

(1 A X A) dX A

dt

k f (C A , C B , . . .)

A V X A 1 V X A 0

V X A 0

C AC A 0

1 X A1 A X A

t C A 0 X A

0

dX A( r A )

C A

C A 0

dC A k f (C A , C B , . . .)

r A dC A

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

37


43/63

IV. FLOW REACTORS

A. Capacity Measures

Space time: time required to process one reactor volume of entering feed

mean residence time

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

In general

For irreversible rst-order reactions (isothermal)

For reversible rst-order reactions A rR

(isothermal)

where

C. Design Equation for Back-Mix (Ideal Stirred

N 1 k 2 k 2

(1 A)

k 1 A X A

N

N A N 2

ln (1 NX A)

12

k (1 A) ln (1 X A) A X A

C A 0 X A

0

dX A( r A)

orV

F A 0

X A

0

dX A( r A)

V

v

VC A 0 F A 0

(units of time)

38


44/63

Tank) Reactor

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

D. NOTATION

A, B, R, etc. substance A , etc.a, b, . . . exponents on concentration term of

empirical rate expressionC A concentration of A, moles A /volume

C A 0 initial concentration of A, moles A / volume

F A 0 feed rate of A or ow rate of A enteringthe reactor, moles A /time

K equilibrium constant k reaction rate constant, (conc 1 n )(time 1) n order of reaction

N A moles of A r A rate of reaction of any comoponent A,

moles A formed/time-volumeT temperaturet time

V volume of uid in batch reactor, vol-ume of uid in a ow reactor, or reactor

volume

C A entering

C A leaving (1

k per reactor) j

C A 0 X A

( r A) or

V

F A 0

X A

( r A)

39


45/63

v volumetric feed rate, volume of feed/ time

X A 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

Subscripts

e equilibrium value

CONVERSION FACTORS

Acceleration

1 ft /s 2 0.3048 m/s 2

0.6318 (mile/hr)/sec1.097 km/hr-s30.48 cm /s 2

1 rev/min2

2.778

104

rev/s2

0.001745 rad/s 2

0.01667 rev/min-s

Density

1 lb m /ft 3 16.02 kg/m 3

5.787 10 4 lb m /in3

0.01602 g/cc

Flow

1 ft 3 /min 4.719 10 4 m 3 /s0.1247 gal/s

40


46/63

0.4720 liter/s472 cc/s

Length

1 ft 0.3048 m1.894 10 4 mile1 3 yd12 in30.48 cm3.05 10 5 microns ( )

1 10 10 m10 8 cm1 10 4 microns ( )

Angle

1 rad 1 2 circle

0.1592 rev 0.637 quad57.3 deg3,438 min2.063 105 s

Mass

1 lb m 0.4536 kg4.464 10 4 long ton5 10 4 short ton4.536 10 4 metric ton0.4536 kg453.6 g0.0311 slug

Pressure

1 lb f / in2 abs 6.895 10 3 N/m 2

6.895 10 3 Pascal

41


47/63

0.06805 atm0.07031 kg/cm 2

2.036 in Hg @ 32 F2.307 ft H 2O @ 39 F70.307 g/cm 2

51.72 mm Hg @ 32 F51.72 torr

Power

1 ft-lb/min. 0.0226 W2.26 10 5 kW3.03 10 5 hp3.24 10 4 kg-cal/min0.001285 Btu/min

Temperature

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

Time

1 nanosecond 1 109

s

Velocity

1 ft /s 0.3048 m/s0.011364 mile/min0.6818 mile/hr

1.0973 km./hr 18.29 m/min30.48 cm/s

1 rev/min 0.1047 rad/s6 deg/s

42


48/63

Viscosity

1 centipoise 0.001 Pa-s0.001 N-s/m 2

0.01 g/cm-s6.72 10 4 lb m /ft-s2.42 lb m /ft-hr

Volume

1 ft 3 0.02832 m 3

0.03704 yd 3

0.80357 bushel (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 in 3

28.32 liters2.832 104 cm 3

2.832 104 ml59.8 pt (U.S. liq.)

Work and Energy

1 Btu 1054 J2.93 10 4 kW-hr 3.93 10 4 hp-hr 0.252 kg cal0.293 W-hr 10.41 liter-atm252 g cal778 ft-lb f 0.3676 ft 3-atm1.054 1010 ergs

43


49/63

Mole fraction ( x ) to mass fraction ( w )

Mass fraction ( w ) to mole fraction ( x )

where M i molecular weight of i

PHYSICAL CONSTANTS

Gas constants

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

1.987 Btu/lb m -mole- R8.314 joules/g-mole-K 1546 ft-lb f / lb m-mole- R10.73 (psi)-ft 3 /lb m -mole- R0.7302 atm-ft 3 /lb m -mole- R

Acceleration of gravity (standard)

g 32.17 ft/s 2 980.7 cm /s 2

Avogadro s number

N 6.023 10 23 molecules/g-mole

Boltzmann s constant

K 1.3805 10 16 erg/molecule-K

Newton s conversion constant

gc 32.17 lb m -ft/lb f -s2 1.000 kg-m/N-s 2

x Aw A M A

w A M A w B M B

w A x A M A

x A M A x B M B

44


50/63

Planck s constant

h 6.624 10 27 erg-s

Stefan-Boltzmann constant 1.355 10 12 cal/s-cm 2-K 4

1.712 10 9 Btu /hr-sq ft- R4

Velocity of light

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

Velocity of sound in dry air, 0 C and 1 atm

33,136 cm /s 1,089 ft /s

Heat of fusion of water at 1 atm, 0 C

79.7 cal /g

144 Btu /lb m

Heat of vaporization of water at 1 atm, 100 C

540 cal /g 972 Btu/lb m

Ton of refrigeration 12,000 Btu /hr

1 lb m -mole of perfect gas occupies 359 ft 3 at stan-dard conditions (32 F, 14.7 psi abs)

1 g-mole of perfect gas occupies 22.4 liters at 0 C and760 mm Hg

Thermochemistry

F 96,500 coulombs/gram equivalent

joules volts coulombs

coulombs amperes seconds

45


51/63

Dimensionless Groups

Name Symbol Formula

Fanning friction factor f pg cd 2 L V 2

Heat transfer factor j H (h c p G)( C p k )2 3Mass transfer factor j M ( k c G)( D)

2 3

Froude number N Fr V 2 gL

Graetz number N Gz wc p kLGrashof number N Gr L

3 2 g T 2

Nusselt number N Nu hd kPeclet number N Pe LV c p kPower number N Po Pg c n 3d 5Prandtl number N Pr c p kReynolds number N Re LV Schmidt number N Sc DSherwood number N Sh K c L D

Notation

c p speci c heat, Btu/ lb m - F D molecular diffusivity, sq ft/hr d diameter, ft G mass velocity, lb m /sq ft-hr

g acceleration of gravity, 32.2 ft/s2

g c conversion factor 32.2 ft-lb m /( lb f -s2 )

1 m-kg/(N-s 2)h heat transfer coef cient, Btu/sq ft-hr- F k thermal conductivity, Btu /sq ft-( F/ft)-hr

k c mass transfer coef cient, ft/hr L characteristic dimension, ft n rate of rotation, s 1

P power to agitator, ft-lb f /s p pressure drop, lb f /sq ft T temperature, FV uid velocity, ft /s

46


52/63

w mass ow rate, lb m /s coef cient of bulk expansion, F 1 density, lb m /ft 3

viscosity lb m

/ft-hr

Abbreviations

atm atmosphereBtu British thermal unit cal caloriecm centimeter cu cubicft foot, feet g gram

hp horsepower hr hour

in inchkg kilogram

km kilometer kW kilowatt lb m pound-masslb f pound-force

m meter min minute

ml milliliter pt pint qt quart

quad quadrant R degrees Rankine

rad radianrev revolution

s second yd yard

micron

47


53/63

GREEK ALPHABET

, alpha , eta , beta , theta

, gamma , iota , delta , kappa , epsilon , lambda , zeta M, mu, nu , tau, xi , upsilon

, omicron

, phi, pi , chi, rho , psi, sigma , omega

MATHEMATICS

Area of circle r 2

Circumference of circle 2 r

Surface of sphere 4 r 2

Volume of sphere (4 3) r 3

Volume of cone or pyramid 1 3 (base area)(height)

dx n nx n 1 dx

dax adx

a x 2

bx

c

0 x

b 2 b2 4ac2a

a 3 b 3 (a b )( a 2 ab b 2)

a 3 b 3 (a b )( a 2 ab b 2)

a 2 b 2 (a b )( a b )

48


54/63

Binomial series

Taylor series

f ( x ) f (a ) f (a ) x a

1! f (a )

( x a ) 2

2!

x n 2 y 2 (y 2 x 2)

( x y ) n x n n x n 1y n ( n 1)

2!

eax dx e ax

a

dx x

log e x ln x

x n dx x n 1 ( n 1) for n 1

udv uv vdu(u v ) dx udx vdx

d tan x sec 2 x dx

d cos x sin x dx

d sin x cos x dx

da x a x log ea dx

de ax ae ax dx

d cuv d

vdu udv

v2

d (uv ) udv vdu

d (u v ) du dv

49


55/63

MacLaurin series

Exponential series

log 10 x 0.4343 ln x , ln x 2.303 log 10 x

Arithmetic mean

Geometric mean

Harmonic mean

Logarithmic mean

Solution of

where P, Q are constants or functions of x

Integrating factor e Pdx IF

Solution y IF ( IF Q )dx C

dy

dx Py Q

a bln a b

2aba b

2 ab

a b2

3.1416, e 2.71828, i 2 1, i 2 1, i 4 1e x 1 x

x 2

2! x 3

3!

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

f (0) x 2

2!

50


56/63

CHEMICAL PROCESS SAFETYContributed by Joe Louvar

I. COMMON DEFINITIONS: GENERAL CONCEPTS

Chemical Process Safety The application of technologyand 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 Analysis, 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 featuresto reduce the potential for accidents.

Safety Design Features a) Inerting to control the concen-tration of a ammable gas to below the LFL, b) ground-ing and bonding to prevent static electricity chargingand discharging (spark) and potential re, c) installingrelief valves to prevent vessel ruptures, d) installingdouble block and bleeds to prevent the backup of reac-tive chemicals into a monomer storage tank, e) installingan explosion suppression system to prevent dust explo-sions, f) installing containment systems to catch the re-lease from relief valves, etc.

Safety Control Features a) Monitoring the temperatureand pressure to prevent abnormal conditions, b) addingreactor safeguards to prevent runaway reactions,c) adding redundant controls to decrease the frequencyof accidents, d) adding more reliable instruments to re-duce the frequency of plant accidents, etc.

51


57/63

II. COMMON DEFINITIONS: TERMS

Auto Ignition Temperature (AIT) A xed temperatureabove which a ammable 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 containsa liquid at a temperature above its atmospheric-

pressure boiling point. It is the explosive vaporizationof a large fraction of the vessel contents; possibly fol-

lowed by the combustion or explosion of the vaporizedcloud if it is combustible (similar to a rocket).De agration An explosion with a ame front moving in

the unburned gas at a speed below the speed of sound(1250 ft /s).

Detonation An explosion with a shock wave moving at a speed greater than the speed of sound in the unre-acted medium.

Flash Point (FP) The FP of a liquid is the lowest temperature at which it gives off enough vapor to form anignitable mixture with air.

Flammability Limits (LFL and UFL) A gas mixture willnot burn when the composition is lower than the lower

ammable limit (LFL). The mixture is also not com-bustible when the composition is above the upper am-mability limit (UFL).

Flammability Limits of Mixtures They are computedwith the following equations:

UFL MIXTURE 1

a a y iUFL i b

LFL MIXTURE 1

a a y i LFL ib

52


58/63

Lower Flammability Limit in the Presence of Mists LFL MISTS 0.1 LFL THEORETICAL

Mechanical Explosion An explosion due to the suddenfailure 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 belowthe minimum oxygen concentration.

Minimum Oxygen Concentration (MOC) It is estimatedusing the following equation:

Overpressure The pressure on an object as a result of an impacting shock wave.

Relief Valve A device that relieves the pressure within a vessel when the pressure approaches the maximumallowable working pressure (MAWP). All vessels havereliefs.

Risk This is the product of the frequency and the con-sequence of an accident scenario.

BIOCHEMICAL ENGINEERINGContributed by David Murhammer

I. COMMON DEFINITIONS: GENERAL CONCEPTS

Aerobes Organisms whose growth requires the pres-ence of air or oxygen.

Anabolism Metabolism involved with the biosynthesisof cellular components.

Anaerobes Organisms that grow in the absence of air or oxygen.

Biochemical Engineering The extension of chemicalengineering principles to biological systems with thegoal of producing useful products.

MOC ( LFL %) a Moles of Oxygen Moles of Fuel b

53


59/63

Bioreactor A vessel used for biological processes. Ex-amples include growing microorganisms and animalcells for the production of useful products.

Biotechnology The use or development of methods of direct genetic manipulation for a socially desirablegoal. Examples include the production of a particular chemical, production of better plants or seeds, andgene therapy.

Catabolism Metabolism involved with the breakdown of materials for the production of intermediates and energy.

Enzyme A catalytic protein (and in some cases RNA) produced by living cells.

Eukaryote A cell or organism with a membrane-boundnucleus and well-developed organelles. Examples in-clude yeast, animals, and plants.

Prokaryote A cell lacking a true nucleus. Examples in-clude bacteria 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 speci c types of living cells.

II. COMMON DEFINITIONS: TERMS

Antibiotics Substances of microbial origin that in verysmall amounts have antimicrobial activity.

Antibodies Glycoprotein molecules produced by B-lymphocytes in higher organisms in response to theintroduction of a foreign material (antigen). These mol-ecules react with antigens with great speci city.

Attachment Dependent Cells whose growth requiresattachment to a surface. Also referred to as Anchorage-Dependent.

Batch Culture A culture that once supplied with rawmaterials is run to completion.

54


60/63

ChemostatA bioreactor in which the continuous addi-tion of fresh medium and removal of efuent results inconstant nutrient, product, and cell concentrationswhen operated under steady state conditions.

Death PhaseThe portion of the growth curve in culturein which there is a net decline in the number of viable(live) cells.

Exponential (Log) Growth PhaseA period of growth ina culture in which the number of cells or cell mass in-creases exponentially, i.e., the growth rate is propor-tional to the population density:

where X cell number (cells /mL) or cell biomass(mg/mL), t is time, and is the specic growth rate (h 1).

Fed-Batch CultureA culture to which nutrients are pe-riodically added during the operation of the culture.

Growth YieldYield of biomass based on substrate (e.g.,glucose or oxygen) utilization:

where Y X S is the yield coefcient of biomass (X) basedon Substrate (S) and is usually given in terms of either (gm biomass/gm or mole substrate) or (cell number/gmor mole substrate).

K L aVolumetric mass transfer coefcient usually meas-

ured in h1

and often used to compare the efcienciesof bioreactors in supplying oxygen. The resulting oxy-gen transfer rate is then given by

dC L

dt K L a (C * C L),

Y X / S dX

dS ,

dX

dt X ,

55


61/63

where C L is the dissolved oxygen concentration withinthe bioreactor, t in time, and C * is the equilibrium dis-solved oxygen concentration (i.e., solubility) under thespeci ed 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 ltration 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

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

tion rate, K M is the Michaelis Constant and is equal tothe substrate concentration at v 1 2 vmax , and [ S ] isthe substrate concentration.

Perfusion Culture A bioreactor in which cells areretained, 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 tothe speci c growth rate ( ) by

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

PDT ln(2)

.

v vmax [ S ]

K M [ S ] ,

56


62/63

Power Number is given by

where P is the power input, is the density of the solu-tion being agitated, N is the rotational speed 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 concentrationon the speci c growth rate. This equation is given by

where is the speci c growth rate, m is the maximumspeci c growth rate when [ S ] W K s , [ S ] is the sub-strate concentration, and K s is the saturation constant or half-velocity constant and is equal to the substrateconcentration when 1 2 m .

Stationary Phase Phase in growth curve following theexponential growth phase in which there is no net growth. This phase is commonly associated with nutri-ent depletion.

m[ S ]

K s [ S ] ,

N P P

N 3 D 5 ,

57


63/63

American Institute ofChemical Engineers

3 Park AvenueNew York, NY10016-5991

203.702.7660800.242.4363www.aiche.org

Student Pocket Handbook Final

Documents

Transcript of Student Pocket Handbook Final