Lecture 9: Reactor Size Comparisons for PFR and CSTR

10.37 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 V= PFR FAo XA −rA V=∫ XA 0 FAo dX A −rA “Levenspiel Plot” • as X A increases, C A decreases FAo − rA 1st or 2nd order reaction −rA decreases, for 1st and 2nd order, F so Ao increases −rA Figure 1. General Levenspiel Plot. XA PFR Volume CSTR Volume FAo − rA FAo − rA VCSTR XA VPFR XA Figure 2. Levenspiel plots for a CSTR and a PFR for positive order reactions. So PFR is always a smaller reactor for a given conversion when kinetics are positive order. 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 v1 x1 FA1 v2 FA2 x2 Figure 3. Schematic of two CSTRs in series. V1 = FAo X1 −rA1 0 2nd reactor: In + Out + Prod = Acc FA1 − FA2 + rA2 V2 = Steady state 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. K. Dane Wittrup Lecture 9 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]. FA2 = FA0 − X 2 FA0 FAo − rA → V2 = FA0 −rA2 V1 ( X 2 − X1 ) V2 X1 Figure 4. Reactor volumes for 2 CSTRs in series. X2 X Multiple CSTRs begin to approximate a single PFR FAo − rA X Figure 5. Reactor volumes for multiple CSTRs in series. 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. K. Dane Wittrup Lecture 9 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]. FAo − rA FAo − rA VPFR VCSTR VPFR VCSTR X XA Designed final conversion Final X 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: CSTR FAo −rA VCSTR VPFR PFR X Final X 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. Example A→ D rD = kd C Aα1 A →U α2 D = Desired, U = Undesired rU = ku C A 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. K. Dane Wittrup Lecture 9 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]. SD /U = Define “selectivity” If α1 > α 2 , as C A rD kd (α1 −α 2 ) = CA rU ku increases, S D /U increases -Favors PFR because C A starts at C Ao then drops whereas CSTR concentrations are always at lower C A . If α1 < α 2 , as C A increases, S D /U decreases -CSTR favored If α1 = α 2 then S D /U = kd , no dependence on C A ku -Therefore no CSTR/PFR preference. Define a fractional yield φ= kd C αA1 dCD = − dC A kd C αA1 + ku C αA 2 Overall fractional yield For a CSTR: Φ= Φ = φ Εxit C All D produced All A consumed A ΔC A = C A − C A 0 For a PFR: If Φ= 1 ΔC A ∫ C At CA 0 f φ dC A α1 = α 2 φ ΦΔC A C Af C A0 CA Figure 8. Fractional yield versus concentration. Selectivity does not depend on CA. 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. K. Dane Wittrup Lecture 9 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 α1 > α 2 φ CA Figure 9. Fractional yield versus concentration when α1 > α2. CSTR PFR φ φ Φ PFR ΔC A Φ CSTR ΔC A C Af C Af C A0 CA C A0 CA Figure 10. Comparison of overall fractional yield for a CSTR and a PFR when α1 > α2. PFR is preferred because Φ PFR >Φ CSTR , therefore the yield of D per mol A consumed is higher. If α1 < α 2 Φ CSTR ΔC A φ C Af C A0 Φ PFR ΔC A φ C Af CA C A0 C A CSTR PFR Figure 11. Comparsion of overall fractional yield for a CSTR and a PFR when α1 > α2. Φ PFR <Φ CSTR 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. K. Dane Wittrup Lecture 9 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 YYYY].