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Calculations Formulas Definitions
Calculations Formulas Definitions 1
ChemE Calculations Formulas Deﬁ Deﬁ nitions nitions American Institute of Chemical Engineers 120 Wall Street, 23rd FL. New York, NY 10005 www.aiche.org/students The AIChE Email: email@example.com Student Customer Service: 1.800.242.4363 203.702.7660 (Outside U.S.) Pocket Handbook © 2014 AIChE 9865-14 • 04.14 G41784AICHE_CVR.indd 1 5/2/14 8:21 AM13282AICEtext 4/12/04 12:20 PM Page 58G37759AICEtext_28535AICEtext 10/11/13 4:08 PM Page p1 The AIChE Pocket Handbook Thomas R. Hanley, Editor American Institute of Chemical Engineers 120 Wall Street, 23rd Floor New York, New York 10005G41784AICEtext_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 0-8169-0342-513282AICEtext 4/12/04 12:20 PM Page p3 TABLE OF CONTENTS Inorganic Chemistry...................................................... 1 Organic Chemistry......................................................... 6 Physical Chemistry........................................................ 10 Fluid Flow....................................................................... 14 Heat Transfer.................................................................. 18 Distillation ...................................................................... 23 Mass Transfer ................................................................. 26 Thermodynamics ........................................................... 29 Kinetics and Reactor Design ........................................ 34 Conversion Factors ....................................................... 40 Physical Constants ........................................................ 44 Greek Alphabet .............................................................. 48 Mathematics ................................................................... 48 Chemical Process Safety .............................................. 51 Biochemical Engineering.............................................. 5313282AICEtext 4/12/04 12:20 PM Page p413282AICEtext 4/12/04 12:20 PM Page p5 Foreword The purpose of this handbook is to make readily avail- able in a limited number 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 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.13282AICEtext 4/12/04 12:20 PM Page p613282AICEtext 4/12/04 12:20 PM Page 1 INORGANIC CHEMISTRY I. COMMON DEFINITIONS Atomic number—the number of protons in the nucleus of an atom. Avogadro’s number—the number of molecules 23 (6.023 10 ) in one gram-mole of a substance. Equilibrium constants for the reaction aA bB cC dD where reaction is in solution, c d [C ] [D] K ([ ] refers to molarity) c a b [A] [B] where reaction is in the gas phase, c d p p C D K ( p partial pressure) p a b p p A B 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 dividing the molecular weight by the number of hydrogen atoms or hydroxyl ions (or their equivalent) supplied or required by the molecule in a given reaction. B. (redox reaction) the molecular weight in grams divided by the change in oxidation state. Ion product of water (K )—the product of the w hydrogen ion and hydroxyl ion concentrations in gram-ions per liter; K [H ][OH ] w 113282AICEtext 4/12/04 12:20 PM Page 2 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 of solution). Normality (N)—(gram equivalents of solute)/(liters of solution). Oxidation—the loss of electrons by an atom or group of atoms. pH—the negative logarithm (base 10) of the hydrogen ion concentration in gram ions per liter; pH log [H ] 10 Reduction—the gain of electrons by an atom or group of atoms. Solubility product (S.P. or K )—for the slightly soluble sp solid, A B , dissolving a b A B (solid) aA (aq) bB (aq) a b where A is any cation and B is any anion a b S.P. or K [A ] [B ] a constant at a given sp temperature II. PROPERTIES OF CHEMICAL ELEMENTS Atomic Atomic Common Name 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 213282AICEtext 4/12/04 12:20 PM Page 3 Atomic Atomic Common Name Symbol Number Weight Valence Argon Ar 18 39.948 0 Arsenic As 33 74.9216 3,5 Astatine At 85 (210) 1,3,5,7 Barium Ba 56 137.34 2 Berkelium Bk 97 (247) 4,3 Beryllium Be 4 9.0122 2 Bismuth Bi 83 208.980 3,5 Boron B 5 10.811 3 Bromine Br 35 79.904 1,5 Cadmium Cd 48 112.40 2 Calcium Ca 20 40.08 2 Californium Cf 98 (249) 3 Carbon C 6 12.01115 4,2 Cerium Ce 58 140.12 3,4 Cesium Cs 55 132.905 1 Chlorine Cl 17 35.453 1,3,5,7 Chromium Cr 24 51.996 6,2,3 Cobalt Co 27 58.9332 2,3 Copper Cu 29 63.546 2,1 Curium Cm 96 (247) 3 Dysprosium Dy 66 162.50 3 Einsteinium Es 99 (254) — Erbium Er 68 167.26 3 Europium Eu 63 151.96 3,2 Fermium Fm 100 (253) — Fluorine F 9 18.9984 1 Francium Fr 87 (223) 1 Gadolinium Gd 64 157.25 3 Gallium Ga 31 69.72 3 Germanium Ge 32 72.59 4 Gold Au 79 196.967 3,1 Hafnium Hf 72 178.49 4 Helium He 2 4.0026 0 Holmium Ho 67 164.930 3 313282AICEtext 4/12/04 12:20 PM Page 4 Atomic Atomic Common Name Symbol Number Weight Valence Hydrogen H 1 1.00797 1 Indium In 49 114.82 3 Iodine I 53 126.9044 1,5,7 Iridium Ir 77 192.2 2,3,4,6 Iron Fe 26 55.847 2,3 Krypton Kr 36 83.80 0 Lanthanum La 57 138.91 3 Lawrencium Lw 103 (257) — Lead Pb 82 207.19 4,2 Lithium Li 3 6.939 1 Lutetium Lu 71 174.97 3 Magnesium Mg 12 24.312 2 Manganese Mn 25 54.9380 7,6,4,2,3 Mendelevium Md 101 (256) — Mercury Hg 80 200.59 2,1 Molybdenum Mo 42 95.94 6,5,4,3,2 Neodymium Nd 60 144.24 3 Neon Ne 10 20.183 0 Neptunium Np 93 (237) 6,5,4,3 Nickel Ni 28 58.71 2,3 Niobium Nb 41 92.906 5,3 Nitrogen N 7 14.0067 3,5,4,2 Nobelium No 102 (254) — Osmium Os 76 190.2 2,3,4,6,8 Oxygen O 8 15.9994 2 Palladium Pd 46 106.4 2,4 Phosphorus P 15 30.9738 3,5,4 Platinum Pt 78 195.09 2,4 Plutonium Pu 94 (242) 6,5,4,3 Polonium Po 84 (210) 2,4 Potassium K 19 39.102 1 Praseodymium Pr 59 140.907 3,4 Promethium Pm 61 (147) 3 413282AICEtext 4/12/04 12:20 PM Page 5 Atomic Atomic Common Name Symbol Number Weight Valence Protactinium Pa 91 (231) 5,4 Radium Ra 88 (226) 2 Radon Rn 86 (222) — Rhenium Re 75 186.2 7,6,4, 2,1 Rhodium Rh 45 102.905 2,3,4 Rubidium Rb 37 85.47 1 Ruthenium Ru 44 101.07 2,3,4,6,8 Samarium Sm 62 150.35 3,2 Scandium Sc 21 44.956 3 Selenium Se 34 78.96 2,4,5 Silicon Si 14 28.086 4 Silver Ag 47 107.870 1 Sodium Na 11 22.9898 1 Strontium Sr 38 87.62 2 Sulfur S 16 32.064 2,4,6 Tantalum Ta 73 180.948 5 Technetium Tc 43 (98) 7 Tellurium Te 52 127.60 2,4,6 Terbium Tb 65 158.924 3,4 Thallium Tl 81 204.37 3,1 Thorium Th 90 232.038 4 Thulium Tm 69 168.934 3,2 Tin Sn 50 118.69 4,2 Titanium Ti 22 47.90 4,3 Tungsten W 74 183.85 6,5,4,3,2 Uranium U 92 238.03 6,5,4,3 Vanadium V 23 50.942 5,4,3,2 Xenon Xe 54 131.30 0 Ytterbium Yb 70 173.04 3,2 Yttrium Y 39 88.905 3 Zinc Zn 30 65.37 2 Zirconium Zr 40 91.22 4 513282AICEtext 4/12/04 12:20 PM Page 6 III. COMMON ANIONS Name Symbol Name Symbol Arsenite AsO Hydroxide OH 3 Arsenate AsO Hypochlorite OCl 4 Acetate C H O Iodide I 2 3 2 Bicarbonate HCO Iodate IO 3 3 Bisulfate HSO Molybdate MoO 4 4 Bromate BrO Nitrate NO 3 3 Bromide Br Nitrite NO 2 Carbonate CO Oxalate C O 3 2 4 Chlorate ClO Perchlorate ClO 3 4 Chloride Cl Peroxide O 2 Chromate CrO Permanganate MnO 4 4 Cyanamide CN Phosphate PO 2 4 Cyanide CN Sulfate SO 4 Dichromate Cr O Sulﬁde S 2 7 Dithionate S O Sulﬁte SO 2 6 3 Ferricyanide Fe(CN) Thiocyanate CNS 6 Ferrocyanide Fe(CN) Thiosulfate S O 6 2 3 Formate CHO 2 ORGANIC CHEMISTRY Note: For conciseness the following symbols are used: 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 com- pounds 613282AICEtext 4/12/04 12:20 PM Page 7 Type or Name General Formula 1. Alkane or parafﬁn (also saturated hydrocarbons) 2. Alkene or oleﬁn (unsaturated hydrocarbons) 3. Alkyne 4. Alcohol 5. Ether 6. Aldehyde 7. Ketone 8. Carboxylic Acid 9. Grignard reagent 10. Acyl halide 713282AICEtext 4/12/04 12:20 PM Page 8 Type or Name General Formula 11. Anhydride 12. Ester 13. Amide 14. Amine (base) 15. Nitrile B. Cyclic Compounds 1. Cycloparafﬁn 813282AICEtext 4/12/04 12:20 PM Page 9 Type or Name General Formula 2. Cycloalkene 3. Aromatic 4. Naphthalenic II. PERTINENT NOTES A. Markovnikov’s (Markownikoff’s) Rule for the addition of acids to acids to oleﬁns: the negative group of the acid adds to the carbon atom having the fewest hydrogen atoms. 913282AICEtext 4/12/04 12:20 PM Page 10 B. Mechanisms 1. Free radical (unshared electron) (no charge) 2. Carbonium ion (deﬁcient 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 volume of 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 which that component would occupy at the same temper- ature and pressure. 2. Boiling Point Elevation (T )—The following equa- b tions hold for a dilute solution of a nonionic non- volatile solute. T K m b b 2 R(T ) M bp a K b H (1000) v where H molal heat of vaporization v K molal boiling point elevation con- b stant m molality M solvent molecular weight a 1013282AICEtext 4/12/04 12:20 PM Page 11 R ideal-gas constant T solvent boiling point, absolute tem- bp perature 3. Clausius Equation H dp m dT (V v) T where p pressure T absolute temperature H molal heat of vaporization m V molar vapor volume v molal liquid 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 RTp) the Clausius equation becomes d( ln p) H 1 dp m 2 dT p dT RT and with H constant, integration yields m p H T T 2 m 2 1 ln c d p R T T 1 1 2 The symbols are the same as in sections 2 and 3 above. 5. Dalton’s Law of Partial Pressures—The pres- sure of a mixture of gases is equal to the sum of the 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. 1113282AICEtext 4/12/04 12:20 PM Page 12 6. Faraday’s Laws First Law: The mass of a substance reacting at the electrodes is directly proportional to the quantity 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; 96,496 coulombs of electricity 1 faraday electricity to yield 1 gram equivalent of any substance. 7. Freezing Point Depression (T )—The follow- f ing equations hold for a dilute solution of a nonionic solute in which the solid phase is pure solvent. T K m f f 2 R (T ) M f p a K f H (1000) f where H molal heat of fusion of solvent f K molal freezing point lowering con- f stant m molality M solvent molecular weight a R ideal-gas constant T solvent freezing point, absolute tem- fp perature 8. Gibbs Phase Rule—At equilibrium the number of independent variables (F) required to spec- ify the system 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 1213282AICEtext 4/12/04 12:20 PM Page 13 of the phase rule applies to non-reactive sys- tems. 9. Graham’s Law of Diffusion—The rate of diffusion of 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 above the liquid. 11. Raoult’s Law p x P a a a where p partial pressure of component A in a vapor x mole fraction of A in liquid solution a P vapor pressure of pure liquid A a 12. van’t Hoff Reaction Isochore d ( ln K ) H at constant pressure 2 dT RT where H heat of reaction K reaction equilibrium constant R ideal-gas constant T absolute temperature If H is constant, K H T T 2 2 1 ln a b c d K R T T 1 1 2 13. Molar Humidity—moles vapor/mole vaporfree gas y p a a Y 1 y P p a a 1313282AICEtext 4/12/04 12:20 PM Page 14 Humidity—pounds vapor/pound vapor-free gas M a Y Y M b Relative Saturation—ratio of partial pressure of vapor to partial pressure of vapor at saturation (vapor pressure) p a H 100 r P a Percentage of Saturation—ratio of vapor con- centration to vapor concentration at saturation (ratio of molar humidity to saturated molar humidity) p (P P ) Y a a H 100 100 p Y P (P p ) sat a a where p partial pressure of component A in a gas P vapor pressure of pure liquid A a P total pressure M molecular weight of A a M molecular weight of B b y mole fraction of a gas a FLUID FLOW I. DEFINITIONS AND GENERAL EQUATIONS Mass velocity G V 1413282AICEtext 4/12/04 12:20 PM Page 15 Simple manometer equation g P P R ( ) a b m a b g c Hagen-Poiseuille equation (laminar ﬂow in long hori- zontal tube) 32 L V P P a b 2 g D c Average velocity, V q, volumetric flow rate V s, cross-sectional area Reynolds number, N Re DV DV N Re Mechanical energy balance 2 2 P g V P g V a a b b Z W Z H a s b f g 2g g 2g a c c a b c c b where 1 for turbulent ﬂow (N 4,000) Re 0.5 for laminar ﬂow (N 2,100) Re Hydraulic radius s, cross-sectional area r H L , the wetted perimeter p Equivalent diameter, D e D 4 (hydraulic radius, r ) e H 1513282AICEtext 4/12/04 12:20 PM Page 16 II. FRICTION Skin friction 2 2 f LV H fs Dg c Fanning friction factor, f (ﬂow in smooth pipes) 16 16 laminar f DV N Re 1 . .5 turbulent 4.0 log (N f ) 0.4 Re . .5 f Friction of valves and ﬁttings (Add to length of pipe to get total equivalent length.) Equivalent Fittings and Valves resistance, pipe diameters 45-degree 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 Angle valves (open) 170 Friction loss from sudden expansion of cross sec- tion 2 2 V s a a H a1 b fe 2 g s c b 1613282AICEtext 4/12/04 12:20 PM Page 17 Friction loss from sudden contraction of cross section 2 K V c b H fc 2 g c Values of K are given on page 6-18, Perry’s Chemical c Engineers’ Handbook, 7th ed., Don W. Green, ed., McGraw-Hill Book Co., New York, NY, 1997. III. MEASUREMENT OF FLOWING FLUIDS Venturi meter 2g ( p p ) (b is at throat c a b s 2 2V V C b a v of meter) B Oriﬁce meter, design equation (N 20,000) Re 2g ( p p ) 0.61 c a b V o 4 B 21 Pilot tube (manometer measures p P) s 2g ( p P) c s V C p B IV. SYMBOLS USED C , C coefﬁcients of velocity u p D diameter 2 2 g acceleration of gravity 32.2 ft /s 9.81 m/s 2 g Newton’s conversion factor 32.2 ft-lb /(lb -s ) c m f 2 1 m-kg/(N-s ) H head loss due to friction f H head loss due to skin friction fs H head loss due to contraction of cross section fc 1713282AICEtext 4/12/04 12:20 PM Page 18 H head loss due to expansion of cross section fe K expansion loss coefﬁcient e K contraction loss coefﬁcient c L length of pipe P pressure P upstream pressure a P downstream pressure b p , p pressure in arms of manometer a b p static pressure s R manometer reading m s cross-sectional area V velocity V average velocity V upstream velocity a V downstream velocity b W shaft work done by pump s Z elevation kinetic energy correction factor ratio of diameter of oriﬁce to diameter of pipe 3 ﬂuid density, lb /ft m density of manometer ﬂuid a density of ﬂuid above manometer b kinematic viscosity viscosity HEAT TRANSFER I. CONDUCTION Fourier’s Law (constant k) steady state kAT T q x R 1813282AICEtext 4/12/04 12:20 PM Page 19 unsteady state 2 T k T x 2 t C p x Resistance in Series T q x x x A B C k A k A k A A B C T R R R A B C Radial Heat Flow Through a Cylinder k(2 r ) LT k A T m m q (r r ) r o i where A logarithmic mean area normal to heat m ﬂow r logarithmic mean radius m r (r r )ln [r r ] m o i o i II. CONVECTION q hAT where h kx, heat transfer coefﬁcient k thermal conductivity of the ﬂuid x thickness of the laminar ﬁlm III. COMBINED CONDUCTION AND CONVECTION q UA (T ) avg where U overall heat transfer coefﬁcient T overall temperature difference 1913282AICEtext 4/12/04 12:20 PM Page 20 A x 1 r 1 m 1 1 1 U UA A A A A A i m o i o r h k h h h i m o Fi Fo A A A A A r r r r r where A reference area, usually the area r of the solid through which heat is being conducted h , h inside and outside fouling fac- Fi Fo tors IV. RADIATION 4 4 q AF (T T ) 12 1 2 where q net radiation between surfaces 1 and 12 2, Btu/hr T , T absolute temperature of surfaces 1, 1 2 2, R. A area of either surface, sq ft Stefan-Boltzman Constant 1.712 9 4 10 Btu/hr-sq ft-R F geometric view factor V. EMPIRICAL, DIMENSIONLESS CORRELATION Turbulent Flow in Clean Smooth Pipes h D i 0.8 0.33 0.14 0.7 0.023(N ) (N ) ( ) [1 (DL) ] Re Pr w k where N the Reynolds Number DG Re N the Prandtl Number C k Pr p Laminar Flow in Clean Smooth Pipes h D i 0.33 0.33 0.14 0.33 1.86(N ) (N ) ( ) (DL) Re Pr w k 2013282AICEtext 4/12/04 12:20 PM Page 21 where the Reynolds and Prandtl Numbers are as deﬁned for turbulence VI. HEAT TRANSFER TO AND FROM FLUIDS FLOWING NORMAL TO A SINGLE TUBE h D o o 0.52 0.35 0.56(N ) Re k f where N the Reynolds Number D G Re o f The subscript f calls attention to the fact that the correlation is based on the mean ﬁlm temperature, T , which is deﬁned as the arithmetic mean of the f average ﬂuid temperature and the wall tempera- ture. VII. HEAT TRANSFER TO AND FROM FLUIDS FLOWING PERPENDICULAR TO TUBE BANKS h D avg o n b(N ) (b and n depend on geometry) Re k f where N the Reynolds Number DG Re max f VIII. HEAT TRANSFER FROM CONDENSING VAPORS Vertical Tubes 3 2 0.25 k g f f h 1.13 c d avg T L o f Horizontal Tubes 3 2 0.25 k g f f h 0.725 c d avg T D o o f 2113282AICEtext 4/12/04 12:20 PM Page 22 IX. NOTATION A area, sq. ft. b empirical constant C speciﬁc heat at constant pressure, Btu/lb-F p D diameter, ft G mass velocity, lb /sq ft-sec m G mass velocity through minimum cross section in max tube bundle 2 g acceleration of gravity, 32.2 ft/sec 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 time, Btu/hr R resistance r radius, ft T temperature, F t time, hr U over-all heat transfer coefﬁcient, Btu/sq ft- hrF x distance in direction of heat ﬂow; thickness of layer, ft latent heat of condensation or vaporization, Btu/lb m viscosity,lb /ft-sec m 3 density, lb /ft m Subscripts avg average f ﬁlm i inside o outside r reference 2213282AICEtext 4/12/04 12:20 PM Page 23 w wall m mean or log mean DISTILLATION I. FLASH (OR EQUILIBRIUM) DISTILLATION Fz yV xL (component material balance) F F V L (over-all material balance) II. DIFFERENTIAL (SIMPLE OR RAYLEIGH) DISTILLATION x W dx ln W y x o x o When the relative volatility is constant y x [1 ( 1)x] can be substituted to give x(1 x ) 1 x W 1 o o ln ln c d ln c d W ( 1) x (1 x) 1 x o o For binary system following Raoult’s Law (yx) p a a (yx) p b b where p partial pressure of component i i III. CONTINUOUS DISTILLATION (BINARY SYSTEM) WHERE CONSTANT MOLAL OVERFLOW IS ASSUMED Total Material Balance F D B Fz Dx Bx F D B 2313282AICEtext 4/12/04 12:20 PM Page 24 Operating Lines 1. Rectifying Section Total material: V L D n1 n Component A: V y L x Dx n1 n1 n n D L Dx n D y x n1 n L D L D n n 2. Stripping Section Total material: L V B m m1 Component A: L x V y Bx m1 m m1 m1 B L Bx m B y x m1 m L B L B m m 3. Reﬂux Ratio Ratio of reﬂux to overhead product L V D R D D D 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 Efﬁciency y y n n1 E ME y* y n n1 2413282AICEtext 4/12/04 12:20 PM Page 25 where y concentration of vapor above plate n n y concentration of vapor entering from n1 plate below n y* concentration of vapor in equilibrium n with 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 downﬂow R ratio of reﬂux to overhead product D V molar vapor upﬂow W weight in still 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 z mole fraction of the more volatile component in D 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 2513282AICEtext 4/12/04 12:20 PM Page 26 MASS TRANSFER I. DIFFUSION 1. Molecular Diffusion N p N N p A A A B D A c d A P A A RT z 2. Unidirectional Diffusion of a Gas A Through a Second Stagnant Gas B (N 0) B ( p p ) N DP A A A 2 1 A RT ( p ) x x B lm 2 1 in which ( p ) is the log mean of p and p B lm B B 2 1 3. Equimolar Countercurrent Diffusion (N N ) B A (gases) ( p p ) N D A A A 2 1 A RT z z 2 1 4. Unsteady State Diffusion 2 p p A A D 2 t z II. CONVECTION 1. Two-Film Theory N A k ( p p ) k (C C ) G AG Ai L Ai AL A k ( p p ) k (C C ) G AG A L A AL 2613282AICEtext 4/12/04 12:20 PM Page 27 2. Overall Coefﬁcients 1 1 H K k k G G L 1 1 1 K Hk k L G L 3. Transfer Unit HTU—height of a transfer unit G H TG K a G L H TL K a L NTU—number of transfer units y 2 dy 1 1 y 2 N ln TG y y 2 1 y 1 y * 1 x 2 1 x dx 1 1 N ln TL x x 2 1 x 2 x * 1 For dilute solutions (straight operating and equilib- rium line) y y 1 2 N TG (y y ) lm * Z N H N H tower height TG TG TL TL 4. Dimensionless Group Equation (Sherwood) 0.8 13 (N ) 0.023 (N ) (N ) Sh Re Sc 2713282AICEtext 4/12/04 12:20 PM Page 28 III. MOMENTUM, HEAT, AND MASS TRANSFER ANALOGY 0.5 f j j H D where f Fanning friction factor 0.667 0.14 C h p w j c d c d H C G k p k c 0.667 j (N ) M Sc G IV. NOTATION 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, p HC i i 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 N Reynolds number du Re N Schmidt number D Sc N Sherwood number kdD Sh t time T absolute temperature u velocity 2813282AICEtext 4/12/04 12:20 PM Page 29 lm logarithm mean average Greek Letters density viscosity Subscripts A, B components of mixture G gas phase L liquid phase i interface x mole fraction of liquid y mole fraction of gas z length in direction of travel * equilibrium concentration THERMODYNAMICS I. DEFINITIONS System—an arbitrarily chosen portion of space which is under consideration. A. Closed system—one in which matter does not pass through its boundaries. B. Open system—one in which matter ﬂows across its boundaries. C. Isolated system—one in which there is no interchange of energy or matter with the surroundings. Boundaries—the envelope separating the system from the surroundings. Universe—a system and its surroundings. 2913282AICEtext 4/12/04 12:20 PM Page 30 Total energy, E—the sum of the various forms of energy of the system: e.g., U, internal energy; E , kinetic en- k ergy; E , potential energy; Hence, p E U E E p k II. FIRST LAW In an isolated system E E E 0 2 1 In a closed system E Q W In an open system E g(H E E ) Q W p k where the summed terms refer to leaving () and enter- ing () streams In a steady state open system E 0 system Hence for the entering and leaving streams H E E Q W k p III. SECOND LAW For any real process the total entropy of the universe always increases S S 0 system surroundings IV. THERMODYNAMIC FUNCTIONS: DEFINITIONS AND RELATIONSHIPS Deﬁnition of entropy dQ rev S T From First and Second Laws, with changes in E , k 3013282AICEtext 4/12/04 12:20 PM Page 31 E , and composition negligible, p dU dQ PdV TdS PdV rev Also dH dU d(PV) TdS VdP dG dH d(TS) SdT VdP dA dU d(TS) SdT PdV C (HT ) ; C (UT ) ; (C C ) p p v v p v P, V, T, S, U, H, G, A are state functions. Q and W are path functions and have no total derivatives. V. PERFECT-GAS RELATIONSHIPS T 2 For any path: H C dT or (HP) 0 p T T 1 T 2 For any path: U C dT or (UV ) 0 v T T 1 For monoatomic gas: C 2.5 R and C 1.5 R p v For diatomic gas: C 3.5 R and C 2.5 R p v Adiabatic (Q 0) and reversible path for system with E E 0. p k ( 1) (P P ) (V V ) (T T ) 2 1 1 2 2 1 ( 1) RT P 1 2 W U ca b 1d (per mole) nonflow 1 P 1 W H [W ] ( per mole) flow nonflow Isothermal path, ﬂow or nonﬂow P V 2 1 P V 1 2 3113282AICEtext 4/12/04 12:20 PM Page 32 V P 2 1 W RT ln RT ln ( per mole) V P 1 2 VI. CRITERIA FOR EQUILIBRIUM CHANGE For system and surroundings: dS 0 universe For system alone: dG 0 when P, T constant dA 0 when V, T constant VII. CHEMICAL THERMODYNAMICS A. Fugacity ( f ) and Activity (a) 2 G RT ln ( f f ) VdP ( per mole) 2 1 1 (constant-temperature path) and the limit of fP as P approaches 0 1.00 a ff 0 B. Equilibrium Standard free energy at temperature T for the reaction aA bB ∆ rR sS G rG sG aG bG R S A B r s a a R S RT ln RT ln K a a b a a A B C. Cells At standard conditions G nF RT ln K a 3213282AICEtext 4/12/04 12:20 PM Page 33 At actual conditions r s a a R S G nF nF RT ln a b a a A B VIII. NOTATION A U TS, Helmholtz work function a activity C heat capacity E total energy of the system E kinetic energy of the system k E potential energy of the system p reversible voltage of cell F faradays per equivalent f fugacity G H TS, Gibbs free energy g Newton’s conversion factor c H U PV, enthalpy h enthalpy per pound K equilibrium constant for the reaction as writ- ten K equilibrium constant in terms of activity a K equilibrium constant in terms of fugacity f K equilibrium constant in terms of partial pres- p 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 3313282AICEtext 4/12/04 12:20 PM Page 34 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 (C C ) p 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 ﬂuid is 1 dN a r A V dt and where density remains unchanged dC A r A dt Frequently, the rate can be described as a temperature- dependent term times a concentration-dependent term, or r k (T) f (C , C . . .) A A B A. Order, Molecularity, Elementary Reactions Where the rate can be expressed as 3413282AICEtext 4/12/04 12:20 PM Page 35 a b r kC C . . . A A 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 1 n 1 k (conc) (time) From Arrhenius’s Law the variation with temper- ature is k E 1 1 2 ERT k k e or ln c d o k R T T 1 1 2 where E is the activation energy of the reaction II. HOMOGENEOUS, CONSTANT FLUID DENSITY, BATCH KINETICS A. Irreversible First-order Reaction For the reaction AS products, with rate dC dX A A kC or k(1 X ) A A dt dt the integrated form is C A ln ln (1 X ) kt A C A0 3513282AICEtext 4/12/04 12:20 PM Page 36 B. Irreversible Second-order Reaction For the reaction A BS products, with rate dC A kC C A B dt When M C C 1, the integrated form is B0 A0 C C M X B A0 A ln ln (C C ) kt B0 A0 C C M(1 X ) B0 A A When C C , the integrated form is A0 B0 1 1 1 X A kt C C C 1 X A A0 A0 A C. Irreversible nth-order Reaction For the reaction with rate dC A n kC A dt the integrated form for n 1 is 1n 1n C C (n 1) kt A A0 D. Reversible First-order Reaction 1 For the reaction A R, K k k with rate ∆ 1 2 2 dC dC R A k C k C 1 A 2 R dt dt the integrated form is X X C C Ae A A Ae ln ln (k k )t 1 2 X C C Ae A0 Ae 3613282AICEtext 4/12/04 12:20 PM Page 37 E. Integration of Rate in General For the reaction with rate dC A r k f (C , C , . . .), A A B dt X C A A dX dC A A t C A0 (r ) k f (C , C , . . .) A A B 0 C A0 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), C 1 X A A C 1 X A0 A A where V V X X A 1 A 0 A V X A 0 The rate for any reactant A is then 1 dN C dX A A0 A r k f (C , C , . . .) a A B V dt (1 X ) dt A A Integrating in the general case X A dX A t C A0 (1 X )(r ) A A A 0 3713282AICEtext 4/12/04 12:20 PM Page 38 IV. FLOW REACTORS A. Capacity Measures Space time: time required to process one reactor volume of entering feed mean residence time V VC A0 (units of time) v F A0 B. Design Equation for Plug Flow (Ideal Tubular) Reactor In general X X A A dX dX A V A C or A0 (r ) F (r ) A A0 A 0 0 For irreversible ﬁrst-order reactions (isothermal) k (1 ) ln (1 X ) X A A A A 1 For reversible ﬁrst-order reactions A rR ∆ 2 (isothermal) X N A A A k ln (1 NX ) 1 A 2 N N where k 2 N 1 (1 ) A k 2 C.Design Equation for Back-Mix (Ideal Stirred 3813282AICEtext 4/12/04 12:20 PM Page 39 Tank) Reactor C X X V A0 A A or (r ) F (r ) A A0 A For a ﬁrst-order reaction in j equal-sized backmix reac- tors in series C entering A j (1 k per reactor) C leaving A D. NOTATION A, B, R, etc. substance A, etc. a, b, . . . exponents on concentration term of empirical rate expression C concentration of A, moles A/volume A C initial concentration of A, moles A/ A0 volume F feed rate of A or ﬂow rate of A entering A0 the reactor, moles A/time K equilibrium constant 1n 1 k reaction rate constant, (conc )(time ) n order of reaction N moles of A A r rate of reaction of any comoponent A, A moles A formed/time-volume T temperature t time V volume of ﬂuid in batch reactor, vol- ume of ﬂuid in a ﬂow reactor, or reactor volume 3913282AICEtext 4/12/04 12:20 PM Page 40 v volumetric feed rate, volume of feed/ time X fraction of reactant A converted, dimen- A sionless Greek Symbols measure of density change with reaction, dimen- A sionless space time based on entering feed, time Subscripts e equilibrium value CONVERSION FACTORS Acceleration 2 2 1 ft/s 0.3048 m/s 0.6318 (mile/hr)/sec 1.097 km/hr-s 2 30.48 cm /s 2 4 2 1 rev/min 2.778 10 rev/s 2 0.001745 rad/s 0.01667 rev/min-s Density 3 3 1 lb /ft 16.02 kg/m m 4 3 5.787 10 lb /in m 0.01602 g/cc Flow 3 4 3 1 ft /min 4.719 10 m /s 0.1247 gal/s 4013282AICEtext 4/12/04 12:20 PM Page 41 0.4720 liter/s 472 cc/s Length 1 ft 0.3048 m 4 1.894 10 mile 13 yd 12 in 30.48 cm 5 3.05 10 microns () 10 1 Å 10 m 8 10 cm 4 1 10 microns () Angle 1 rad 12 circle 0.1592 rev 0.637 quad 57.3 deg 3,438 min 5 2.063 10 s Mass 1 lb 0.4536 kg m 4 4.464 10 long ton 4 5 10 short ton 4 4.536 10 metric ton 0.4536 kg 453.6 g 0.0311 slug Pressure 2 3 2 1 lb /in abs 6.895 10 N/m f 3 6.895 10 Pascal 4113282AICEtext 4/12/04 12:20 PM Page 42 0.06805 atm 2 0.07031 kg/cm 2.036 in Hg @ 32F 2.307 ft H O @ 39F 2 2 70.307 g/cm 51.72 mm Hg @ 32F 51.72 torr Power 1 ft-lb/min. 0.0226 W 5 2.26 10 kW 5 3.03 10 hp 4 3.24 10 kg-cal/min 0.001285 Btu/min Temperature F 1.8(C) 32 K C 273 R F 459 Time 9 1 nanosecond 1 10 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 4213282AICEtext 4/12/04 12:20 PM Page 43 Viscosity 1 centipoise 0.001 Pa-s 2 0.001 N-s/m 0.01 g/cm-s 4 6.72 10 lb /ft-s m 2.42 lb /ft-hr m Volume 3 3 1 ft 0.02832 m 3 0.03704 yd 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.) 3 3 1.728 10 in 28.32 liters 4 3 2.832 10 cm 4 2.832 10 ml 59.8 pt (U.S. liq.) Work and Energy 1 Btu 1054 J 4 2.93 10 kW-hr 4 3.93 10 hp-hr 0.252 kg cal 0.293 W-hr 10.41 liter-atm 252 g cal 778 ft-lb f 3 0.3676 ft -atm 10 1.054 10 ergs 43G22046AICEtext_28535AICEtext 9/16/11 9:50 AM Page 44 Mole fraction (x) to mass fraction (w) x M A A w A x M x M A A B B Mass fraction (w) to mole fraction (x) w M A A x A w M w M A A B B where M molecular weight of i i PHYSICAL CONSTANTS Gas constants R 0.0821 atm-liter/g-mole-K 1.987 g-cal/g-mole-K 1.987 Btu/lb -mole- R m 8.314 joules/g-mole-K 1546 ft-lb /lb -mole- R f m 3 10.73 (psi)-ft /lb -mole- R m 3 0.7302 atm-ft /lb -mole- R m Acceleration of gravity (standard) 2 2 g 32.17 ft/s 980.7 cm /s Avogadro’s number 23 N 6.023 10 molecules/g-mole Boltzmann’s constant 16 K 1.3805 10 erg/molecule-K Newton’s conversion constant 2 2 g 32.17 lb -ft /lb -s 1.000 kg-m/N-s c m f 4413282AICEtext 4/12/04 12:20 PM Page 45 Planck’s constant 27 h 6.624 10 erg-s Stefan-Boltzmann constant 12 2 4 1.355 10 cal/s-cm -K 9 4 1.712 10 Btu /hr-sq ft-R Velocity of light 10 c 186,000 miles/s 3 10 cm /s Velocity of sound in dry air, 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 /lb m Heat of vaporization of water at 1 atm, 100C 540 cal /g 972 Btu/lb m Ton of refrigeration 12,000 Btu /hr 3 1lb -mole of perfect gas occupies 359 ft at stan- m 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 volts coulombs coulombs amperes seconds 4513282AICEtext 4/12/04 12:20 PM Page 46 Dimensionless Groups Name Symbol Formula 2 Fanning friction factor f pg d2LV c 23 Heat transfer factor j (hc G)(C k) H p p 23 Mass transfer factor j (k G)(D) M c 2 Froude number N V gL Fr Graetz number N wc kL Gz p 3 2 2 Grashof number N L T Gr g Nusselt number N hdk Nu Peclet number N LVc k Pe p 3 5 Power number N Pgn d Po c Prandtl number N c k Pr p Reynolds number N LV Re Schmidt number N D Sc Sherwood number N K LD Sh c Notation c speciﬁc heat, Btu/lb -F p m D molecular diffusivity, sq ft/hr d diameter, ft G mass velocity, lb /sq ft-hr m 2 g acceleration of gravity, 32.2 ft/s 2 g conversion factor 32.2 ft-lb /(lb -s ) c m f 2 1 m-kg/(N-s ) h heat transfer coefﬁcient, Btu/sq ft-hr-F k thermal conductivity, Btu/sq ft-(F/ft)-hr k mass transfer coefﬁcient, ft/hr c L characteristic dimension, ft 1 n rate of rotation, s P power to agitator, ft-lb /s f p pressure drop, lb /sq ft f T temperature, F V ﬂuid velocity, ft /s 4613282AICEtext 4/12/04 12:20 PM Page 47 w mass ﬂow rate, lb /s m 1 coefﬁcient of bulk expansion, F 3 density, lb /ft m viscosity lb /ft-hr m Abbreviations atm atmosphere Btu British thermal unit cal calorie cm centimeter cu cubic ft foot, feet g gram hp horsepower hr hour in inch kg kilogram km kilometer kW kilowatt lb pound-mass m lb pound-force f m meter min minute ml milliliter pt pint qt quart quad quadrant R degrees Rankine rad radian rev revolution s second yd yard micron 4713282AICEtext 4/12/04 12:20 PM Page 48 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 2 2 a b (a b)(a b) 3 3 2 2 a b (a b)(a ab b ) 3 3 2 2 a b (a b)(a ab b ) 2 b 2b 4ac 2 a x bx c 0 x 2a 2 Area of circle r Circumference of circle 2r 2 Surface of sphere 4r 3 Volume of sphere (43) r Volume of cone or pyramid 13 (base area)(height) dax adx n n1 dx nx dx 4813282AICEtext 4/12/04 12:20 PM Page 49 d(u v) du dv d(uv) udv vdu u vdu udv dc d 2 v v ax ax de ae dx x x da a log a dx e 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 log x ln x e x ax e ax 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 2 (x a) x a f (x) f (a) f (a) f '(a) 1! 2! 4913282AICEtext 4/12/04 12:20 PM Page 50 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! 2 4 3.1416, e 2.71828, i 21, i 1, i 1 log x 0.4343 ln x, ln x 2.303 log x 10 10 Arithmetic mean a b 2 Geometric mean 2ab Harmonic mean 2ab a b Logarithmic mean a b ln ab Solution of dy Py Q dx where P, Q are constants or functions of x Pdx Integrating factor e IF Solution y IF (IF Q)dx C 5013282AICEtext 4/12/04 12:20 PM Page 51 CHEMICAL PROCESS SAFETY Contributed by Joe Louvar I. COMMON DEFINITIONS: GENERAL CONCEPTS Chemical Process Safety—The application of technology 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 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 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 storage tank, e) installing an 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 temperature and pressure to prevent abnormal conditions, b) adding reactor safeguards to prevent runaway reactions, c) adding redundant controls to decrease the frequency of accidents, d) adding more reliable instruments to re- duce the frequency of plant accidents, etc. 5113282AICEtext 4/12/04 12:20 PM Page 52 II. COMMON DEFINITIONS: TERMS 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 explosive vaporization of a large fraction of the vessel contents; possibly fol- lowed by the combustion or explosion of the vaporized cloud if it is combustible (similar to a rocket). Deﬂagration—An explosion with a ﬂame 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 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 Mixtures—They are computed with the following equations: 1 LFL MIXTURE y i a b a LFL i 1 UFL MIXTURE y i a b a UFL i 5213282AICEtext 4/12/04 12:20 PM Page 53 Lower Flammability Limit in the Presence of Mists— LFL 0.1 LFL MISTS 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 shock wave. 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- sequence of an accident scenario. BIOCHEMICAL ENGINEERING Contributed 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 biosynthesis of cellular components. Anaerobes—Organisms that grow in the absence of air or oxygen. Biochemical Engineering—The extension of chemical engineering principles to biological systems with the goal of producing useful products. 5313282AICEtext 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. Biotechnology—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 gene 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-bound nucleus 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 speciﬁc types of living cells. II. COMMON DEFINITIONS: TERMS 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. 5413282AICEtext 4/12/04 12:20 PM Page 55 Chemostat—A bioreactor 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 curve in culture in which there is a net decline in the number of viable (live) cells. Exponential (Log) Growth Phase—A period 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 population density: dX X, dt where X cell number (cells/mL) or cell biomass 1 (mg/mL), t is time, and is the speciﬁc growth rate (h ). Fed-Batch Culture—A culture to which nutrients are pe- riodically added during the operation of the culture. Growth Yield—Yield of biomass based on substrate (e.g., glucose or oxygen) utilization: dX Y , X/S dS where Y is the yield coefﬁcient of biomass (X) based XS on Substrate (S) and is usually given in terms of either (gm biomass/gm or mole substrate) or (cell number/gm or mole substrate). K a—Volumetric mass transfer coefﬁcient usually meas- L 1 ured in h and often used to compare the efﬁciencies of bioreactors in supplying oxygen. The resulting oxy- gen transfer rate is then given by dC L K a(C * C ), L L dt 5513282AICEtext 4/12/04 12:20 PM Page 56 where C is the dissolved oxygen concentration within L the bioreactor, t in time, and C* is the equilibrium dis- solved oxygen concentration (i.e., solubility) 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 v [S] max v , K [S] M where v is the reaction rate, v is the maximum reac- max tion rate, K is the Michaelis Constant and is equal to M 1 the substrate concentration at v ⁄2v , and [S] is max 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 (N )—A dimensionless number com- p monly used to determine the amount of power intro- duced to the bioreactor as a result of agitation. The 5613282AICEtext 4/12/04 12:20 PM Page 57 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 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 concentration on the speciﬁc growth rate. This equation is given by [S] m , K [S] s where is the speciﬁc growth rate, is the maximum m speciﬁc growth rate when [S]W K , [S] is the sub- s strate concentration, and K is the saturation constant s or half-velocity constant and is equal to the substrate 1 concentration when ⁄2 . m Stationary Phase—Phase in growth curve following the exponential growth phase in which there is no net growth. This phase is commonly associated with nutri- ent depletion. 5713282AICEtext 4/12/04 12:20 PM Page 5813282AICEtext 4/12/04 12:20 PM Page 58ChemE Calculations Formulas Deﬁ Deﬁ nitions nitions American Institute of Chemical Engineers 120 Wall Street, 23rd FL. New York, NY 10005 www.aiche.org/students The AIChE Email: firstname.lastname@example.org Student Customer Service: 1.800.242.4363 203.702.7660 (Outside U.S.) Pocket © 2014 AIChE 9865-14 • 04.14 Handbook
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