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Lecture 2 Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of chemical reactions and the design of the reactors in which they take place. 1 Lecture 2 – Tuesday 1/15/2013 Review of Lecture 1 Definition of Conversion, X Develop the Design Equations in terms of X Size CSTRs and PFRs given –rA= f(X) Conversion for Reactors in Series Review the Fall of the Tower of CRE 2 Review Lecture 1 Reactor Mole Balances Summary The GMBE applied to the four major reactor types (and the general reaction AB) Reactor Differential Algebraic Integral NA Batch dN dt A N A0 CSTR PFR V dF A dV t r AV dN rA NA A rAV FA 0 FA rA FA V FA 0 FA dF A dr A 3 PBR dF A dW FA rA t W FA 0 dF A V FA rA W Review Lecture 1 CSTR – Example Problem Given the following information, Find V 0 10 dm 3 C A0 FA0 0C A0 Liquid phase 0 FA 0C A 4 0 10 dm min V ? C A 0 . 1C A 0 FA C A 3 min Review Lecture 1 CSTR – Example Problem (1) Mole Balance: V FA0 FA rA 0C A0 0C A (2) Rate Law: r A kC A (3) Stoichiometry: CA 5 FA FA 0 rA 0 C A 0 C A rA Review Lecture 1 CSTR – Example Problem (4) Combine: V 0 C A 0 C A kC A (5) Evaluate: C A 0 . 1C A 0 10 dm V V 6 3 C A 0 0 . 1C A 0 min 0 . 23 min 900 2 .3 1 0 .1C 391 dm A0 3 10 1 0 . 1 0 . 23 0 . 1 dm 3 Define conversion, X Consider the generic reaction: aAbB c C d D Chose limiting reactant A as basis of calculation: A b a B c C a Define conversion, X X moles A reacted moles A fed 7 d a D Batch Moles A Moles A Moles A remaining initially reacted NA dN A dN A dt 8 N A0 0 N A 0 dX N A0 dX dt r AV N A0 X Batch dN A dt r AV t 0 X 0 N A0 t t X X Integrating, X t N A0 0 dX r AV The necessary t to achieve conversion X. 9 CSTR Consider the generic reaction: aAbB c C d D Chose limiting reactant A as basis of calculation: A b a B c C a Define conversion, X X moles A reacted moles A fed 10 d a D CSTR Steady State dN dt Well Mixed 11 0 FA 0 FA V r A rA A dV rAV CSTR Moles A Moles A Moles A leaving entering reacted FA FA0 FA V V 12 FA 0 FA0 r A FA0 X dV 0 F A 0 F A 0 X rA FA0 X rA CSTR volume necessary to achieve conversion X. PFR dF A dV rA FA FA0 FA0 X Steady State dF A 0 F A 0 X dX dV 13 rA FA0 PFR V 0 X 0 V V X X Integrating, X V FA0 r 0 dX A PFR volume necessary to achieve conversion X. 14 Reactor Mole Balances Summary in terms of conversion, X Reactor Differential Algebraic Integral X X Batch N A0 dX dt r AV 0 V CSTR PFR t N A0 FA 0 rA dV r AV t FA 0 X rA X dX dX V F A 0 dX rA 0 X 15 PBR FA 0 dX dW X rA W 0 F A 0 dX r A W Levenspiel Plots Reactor Sizing Given –rA as a function of conversion, -rA= f(X), one can size any type of reactor. We do this by constructing a Levenspiel plot. Here we plot either (FA0/-rA) or (1/-rA) as a function of X. For (FA0/-rA) vs. X, the volume of a CSTR and the volume of a PFR can be represented as the shaded areas in the Levenspiel Plots shown as: FA0 rA 16 g(X ) Levenspiel Plots FA 0 rA X 17 CSTR FA 0 Area = Volume of CSTR rA FA0 X1 V r A X 1 X1 18 PFR 19 Levenspiel Plots 20 Numerical Evaluations of Integrals The integral to calculate the PFR volume can be evaluated using method as Simpson’s One-Third Rule: (See Appendix A.4) X V 1 r 0 rA ( X 2 ) FA0 A dX 1 4 1 FA0 3 r ( 0 ) r ( X / 2 ) r ( X ) A A A x 1 rA 1 rA ( X 1 ) 1 rA ( 0 ) 21 0 X1 X2 Other numerical methods are: Trapezoidal Rule (uses two data points) Simpson’s Three-Eight’s Rule (uses four data points) Five-Point Quadrature Formula Reactors in Series Given: rA as a function of conversion, one can also design any sequence of reactors in series by defining X: Xi total moles of A reacted up to point i moles of A fed to first reactor Only valid if there are no side streams. Molar Flow rate of species A at point i: FAi FA 0 FA 0 X i 22 Reactors in Series 23 Reactors in Series Reactor 1: F A1 F A 0 F A 0 X 1 V1 F A 0 F A1 r A1 FA 0 rA 24 FA0 FA0 FA0 X 1 rA1 V1 X1 X FA0 X 1 r A1 Reactors in Series Reactor 2: X2 V2 FA0 r X1 dX A V2 FA0 rA X1 25 X2 X Reactors in Series Reactor 3: F A 2 F A 3 rA 3V 3 0 F A 0 F A 0 X 2 F A 0 F A 0 X 3 rA 3V 3 V3 0 F A 0 X 3 X 2 rA 3 V3 FA 0 rA 26 X1 X X2 X3 Reactors in Series 27 Reactors in Series Space time τ is the time necessary to process 1 reactor volume of fluid at entrance conditions. 28 V 0 KEEPING UP The tower of CRE, is it stable? 29 Reaction Engineering Mole Balance Rate Laws These topics build upon one another. 30 Stoichiometry Heat Effects Isothermal Design Stoichiometry Rate Laws Mole Balance CRE Algorithm 31 Mole Balance Rate Laws Be careful not to cut corners on any of the CRE building blocks while learning this material! 32 Heat Effects Isothermal Design Stoichiometry Rate Laws Mole Balance 33 Otherwise, your Algorithm becomes unstable. End of Lecture 2 34