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MIT 10 37 - Exam 1 Review

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10 37 Chemical and Biological Reaction Engineering Spring 2007 Exam 1 Review In Out Production Accumulation Accumulation 0 at steady state FA0 FA rAV 0 FA0 A 0 0 FA A For a liquid phase with constant density 0 For A B the reaction moles are the same so For A 2 B 0 0 moles extent of reaction for a reactant and for a product N rxns N i N i 0 i n n n 1 Suppose A B C XA N A0 N A N A0 N A N A0 1 X A Thermodynamics Suppose Ke e k1 ZZZ X A B YZZ Z 2C k 1 G RT G G f products G f reactants Kc B C A has units You need to use standard states such as 1M to make it dimensionless Enzyme Catalysis Energy without enzyme with enzyme S P Reaction Progress Figure 1 Energy diagram for a reaction with and without enzyme Cite as William Green Jr and K Dane Wittrup course materials for 10 37 Chemical and Biological Reaction Engineering Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY E S U ES ES E P Pseudo steady state approximation d ES 0 dt ES f other species Cell Growth cells N volume N N0e t Monod kinetics max S KS S YA B A B Rate Constants k T Ae Ea RT Given k1 and k2 you can calculate k and a different temperature CSTRs V FA0 X A rA Incorporates changing volumetric flow rate If the reaction is 1st order and it consists of liquids with constant density XA k 1 X A V volume 0 volumetric flow rate k 1 k Da k Damk hler number ratio of kinetic effect to volumetric effect or XA 2nd order reaction ratio of reaction rate to dilution rate 10 37 Chemical and Biological Reaction Engineering Spring 2007 Exam1 Review Page 2 of 10 Cite as William Green Jr and K Dane Wittrup course materials for 10 37 Chemical and Biological Reaction Engineering Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY XA kC A0 1 X A 2 Da kC A0 XA 1 2 Da 1 4 Da 2 Da For constant density and 1st order reaction dN A dt dC A C A0 C A rA dt FA0 FA rAV Let C C A A C A0 t t Nondimesionalize dC A 1 Da C A 1 dt Solve given C A 0 at t 0 1 1 e 1 Da t C A 1 Da Tanks in series 1st order reaction C A n C A 0 1 Da n Reactor Design Equations FA0 X A rA dN A Batch rAV dt N A V A If V changes then V must remain in the differential CSTR PFR V dX A rA Adz FA0 PBR Pressure drop consideration If A g 2 B g Use 0 0 conservation of mass 10 37 Chemical and Biological Reaction Engineering Spring 2007 Exam1 Review Page 3 of 10 Cite as William Green Jr and K Dane Wittrup course materials for 10 37 Chemical and Biological Reaction Engineering Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY Introduce ideal gas law Pm FT RT FT FT 0 1 X m P P FT RT nRT Reactor volume positive order reactions VCSTR FAo rA VPFR area under curve XA Figure 2 Levenspiel plot for a CSTR and a PFR for positive order reactions Selectivity CSTR inst overall C A C Af C A0 CA Figure 3 Fractional yield versus concentration Overall yield times concentration difference shown for a CSTR CSTR k1 k2 A P C k3 A U k1 A k3 A V FA0 A Non ideal reactors Residence time distribution E t 10 37 Chemical and Biological Reaction Engineering Spring 2007 Exam1 Review Page 4 of 10 Cite as William Green Jr and K Dane Wittrup course materials for 10 37 Chemical and Biological Reaction Engineering Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY reactor t C t E t must have a pulse trace E t C t C t dt 0 E t 1 0 tm tE t dt 0 Mean residence time tm for an Ideal CSTR Ideal PFR 2 t tm E t dt 2 0 Variance 2 for an Ideal CSTR 2 Ideal PFR 0 V E t t f t t t dt f t 0 0 property of a dirac delta function 0 For a CSTR E t e t Example 1 z L FA0 FA FB FC Figure 4 Schematic of a PFR with inflow of A and outflow of A B and C r1 r2 A B C r1 k1C A r2 k2CB YB moles of B produced moles of A in FB L FA0 Mole balance on B 1 dFB rB r1 r2 k1C A k2CB Axs dz FB CB 0 FA0 C A0 0 10 37 Chemical and Biological Reaction Engineering Spring 2007 Exam1 Review Page 5 of 10 Cite as William Green Jr and K Dane Wittrup course materials for 10 37 Chemical and Biological Reaction Engineering Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 0 dCB k1C A k2CB Axs dz 0 dC A k1C A Axs dz dC A k1 Axs dz CA 0 k A ln C A 1 xs z 0 Initial condition at z 0 gives ln C A0 0 k A C A C A0 exp 1 xs z 0 k A kA dCB k2 Axs CB 1 xs C A0 exp 1 xs dz 0 0 0 Axs 0 z z time call it This is the time it takes for something to flow to the end of the reactor of length z 0 G V velocity Axs dCB k2CB k1C A0 e k1 d k Integrating factor e 2 d CB ek2 k1C A0 e k2 k1 d kC k k CB ek1 1 A0 e 2 1 k2 k1 Initial condition z 0 CB 0 B kC 0 1 A0 k2 k1 kC CB 1 A0 e k1 e k2 k2 k1 1 dFC r2 Axs dz 1 dFA r1 Axs dz 1 dFB r1 r2 Axs dz 10 37 Chemical and Biological Reaction Engineering Spring 2007 Exam1 Review Page 6 of 10 Cite as William Green Jr and K Dane Wittrup course materials for 10 37 Chemical and Biological Reaction Engineering Spring 2007 MIT OpenCourseWare http ocw mit edu Massachusetts Institute of Technology Downloaded on DD Month YYYY 1 dFA dFB dFC 0 Axs dz dz dz FA0 FA FB FC FC FA0 FA FB F find A C B Figure 5 Graphs of flow rates of A B and C as a function of residence time dCB k1C A0 k1e k1 k2 e k2 0 d k2 k1 k1e k1 k2 e k2 ln k1 k1 ln k2 k2 k ln 1 k1 k2 k2 k ln 1 …


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