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Lecture 2 Kjemisk reaksjonsteknikk Chemical Reaction Engineering Department of Chemical Engineering Review of Lecture 1 Definition of Conversion, X Design Equations in Terms of X Size CSTRs and PFRs given –rA= f(X) Conversion for Reactors in Series 1 - 13/04/2015 General Mole Balance System Volume, V FA0 GA FA Department of Chemical Engineering General Mole Balance on System Volume V In Out Generation FA 0 FA r dV A Accumulation dN A dt 2 2 - 13/04/2015 Reactor Mole Balance Summary Reactor Batch Differential Integral t dN A rAV dt NA N A0 dN A rAV NA t Department of Chemical Engineering FA 0 FA V rA CSTR PFR Algebraic dFA rA dV V FA FA 0 FA dFA drA V 3 3 - 13/04/2015 Consider the generic reaction a AbB c C d D Chooselimit ingreact antA as basis of calculat ion b c d A B C D a a a Department of Chemical Engineering Define conversion, X molesA react ed X molesA fed 4 4 - 13/04/2015 Batch Moles A Moles A Moles A remaining init ially react ed NA N A0 N A0X dN A 0 N A0dX Department of Chemical Engineering dN A dX N A0 rA V dt dt 5 5 - 13/04/2015 Reactor Mole Balances in terms of conversion Reactor Differential Algebraic Integral X X Batch N A0 V CSTR Department of Chemical Engineering 6 PFR dX t N A0 rAV 0 dX r AV dt dX FA 0 rA dV t FA 0 X rA X V FA0 0 dX rA X PBR FA 0 dX rA dW X W FA 0 0 dX rA W 6 - 13/04/2015 Batch reactor Department of Chemical Engineering 7 - 13/04/2015 Continuous stirred tank reactor (CSTR) Department of Chemical Engineering 8 - 13/04/2015 Continuous stirred tank reactor (CSTR) Department of Chemical Engineering 9 - 13/04/2015 Plug flow reactor (PFR) Department of Chemical Engineering 10 - 13/04/2015 Plug flow reactor (PFR) Department of Chemical Engineering 11 - 13/04/2015 Levenspiel Plots Department of Chemical Engineering 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: FA 0 g(X) rA 12 12 - 13/04/2015 Levenspiel Plots Department of Chemical Engineering 13 13 - 13/04/2015 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) 1 FA 0 x 4 1 V dX FA 0 r 3 r ( 0 ) r ( X / 2 ) r ( X ) A A A A 0 X Department of Chemical Engineering Other numerical methods are: Trapezoidal Rule (uses two data points) Simpson’s Three-Eight’s Rule (uses four data points) Five-Point Quadrature Formula 14 14 - 13/04/2015 Reactors in Series Given: rA as a function of conversion, one can also design any sequence of reactors: moles of A reacted up to point i Xi moles of A fed to first reactor Department of Chemical Engineering Only valid if there are no side streams. Molecule Flow rate of species A at point i: FAi FA0Xi 15 15 - 13/04/2015 Reactors in Series Department of Chemical Engineering 16 16 - 13/04/2015 Reactors in Series Reactor 1: FA1 FA0 FA0 X1 FA0 FA1 FA0 FA0 FA0 X 1 FA0 X 1 V1 rA1 rA1 rA1 Department of Chemical Engineering 17 FA 0 rA V1 X 17 - 13/04/2015 Reactors in Series Reactor 2: X2 FA 0 V2 dX rA X1 Department of Chemical Engineering FA 0 rA V2 X 18 18 - 13/04/2015 Reactors in Series Reactor 3: FA2 FA3 rA3V3 0 FA0 FA0 X 2 FA0 FA0 X 3 rA3V3 0 V3 Department of Chemical Engineering 19 FA 0 X 3 X 2 rA 3 V3 FA 0 rA X 19 - 13/04/2015 Reactors in Series Department of Chemical Engineering 20 20 - 13/04/2015 Space time is the time necessary to process one reactor volume of fluid at entrance conditions. Department of Chemical Engineering Important Definitions V 0 S-1 Space velocity: SV = v0/V (s-1)=1/ Space velocity is normally given at the standard conditions (STP). Liquid hourly space velocity (LHSV= v0,liquid/V) Gas hourly space velocity (GHSV) = v0,gas/V 21 - 13/04/2015