PFR vs. CSTR: Size and SelectivitySeries of Reactors10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. K. Dane Wittrup Lecture 9: Reactor Size Comparisons for PFR and CSTR This lecture covers reactors in series and in parallel, and how the choice of reactor affects selectivity versus conversion. PFR vs. CSTR: Size and Selectivity Material balance: CSTR PFR FV =AoX −rAA∫XVAF=AodX A0−rA “Levenspiel Plot” AX AoAFr− 1st or 2nd order reaction CSTR Volume • as X increases, decreases ACA −r decreases, for 1st and 2nd order, Aso FAo increases −rAPFR Volume Figure 1. General Levenspiel Plot. AoAFAr− oAFr− VCSTR AVPFR X X A So PFR is always a smaller reactor for a given conversion when kinetics are positive order. Figure 2. Levenspiel plots for a CSTR and a PFR for positive order reactions. Cite as: 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].Non-monotonically positive order kinetics arise: • Autocatalytic reactions (e.g. cell growth) • Adiabatic or non-isothermal exothermic reactions • Product inhibited reactions (some enzymes) Series of Reactors Example: 2 CSTRs FAo x2 v1 v2 1AF x1 2AF Figure 3. Schematic of two CSTRs in series. FVAo11= X −rA1 2nd reactor: 0 In + Out + Prod = Acc FFAA−+12rA2V2= Steady state 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Lecture 9 Prof. K. Dane Wittrup Page 2 of 6 Cite as: 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].FFAA=− V(A020FX22FA→ =0X2−X1) −rA2 Ao AFr− 2V 2X1V X 1X AoAFr− X Multiple CSTRs begin to approximate a single PFR 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Lecture 9 Prof. K. Dane Wittrup Page 3 of 6 Cite as: 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]. Figure 5. Reactor volumes for multiple CSTRs in series. Figure 4. Reactor volumes for 2 CSTRs in series.X AoAFr− AoAFr− VCSTR AX VPFR VCSTR VPFR Designed final conversion Final X X AoAFr− AoAFr− VCSTR AX VPFR VCSTR VPFR Final X Designed final conversion Figure 6. Levenspiel plots comparing CSTR and PFR volumes for changing kinetics. Left: The CSTR has the smaller volume. Right: The PFR eventually has the smaller volume. Choice of PFR vs CSTR depends on conversion. Choose the reactor that has the smallest volume Æreduce cost. Reactors: X FAo −rAV CSTRV PFRFinal X CSTR PFR Figure 7. To achieve the desired conversion with smaller reactor volumes, use a combination. In this case, use a CSTR then a PFR. By doing so, the reactor volume is less than the area underneath the curve. For competing parallel reactions, selectivity for desired product can dominate the choice. Example10.37 Chemical and Biological Reaction Engineering, Spring 2007 Lecture 9 Prof. K. Dane Wittrup Page 4 of 6 Cite as: 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]. A → D rk1D= Cα D = Desired, U = Undesired dA A →U rk2Uu= Cα ADefine “selectivity” rkSCDd()α12−αDU/== rkAUu If α>α, as C increases, 12 ASD increases /U-Favors PFR because C starts at C then drops whereas CSTR A Ao concentrations are always at lower C. AIf α1<α, as increases, 2C decreases ASD/U-CSTR favored If α1=α then 2kSdDU/=, no dependence on C kAu -Therefore no CSTR/PFR preference. Define a fractional yield dCkCα1φ==DdA −+dC12Adk CαAkuCαA Overall fractional yield AllDproducedΦ = AllAconsumed For a CSTR: Φ =φ Εxit CAΔCCA=−AA0C fFor a PFR: 1CΦ =AtφdCΔC∫ ACAA0 If 12α α= φ ΦACΔ fAC AC 0AC Figure 8. Fractional yield versus concentration. Selectivity does not depend on CA. 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Lecture 9 Prof. K. Dane Wittrup Page 5 of 6 Cite as: 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].If α12>α φ AC Figure 9. Fractional yield versus concentration when α1 > α2. CSTR PFR φ AC φ AC fAC 0AC fAC 0AC CSTRΦACΔ PFRΦACΔ Figure 10. Comparison of overall fractional yield for a CSTR and a PFR when α1 > α2. PFR is preferred because Φ >Φ, therefore the yield of D per mol A consumed PFR CSTRis higher. If α<α 12 φ AC φ AC fAC 0AC fAC 0AC CSTRΦACΔ PFRΦACΔ CSTR PFR Figure 11. Comparsion of overall fractional yield for a CSTR and a PFR when α1 > α2. ΦPFR<Φ CSTR10.37 Chemical and Biological Reaction Engineering, Spring 2007 Lecture 9 Prof. K. Dane Wittrup Page 6 of 6 Cite as: 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