10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. William H. Green Lecture 8: The Plug Flow Reactor rA = −k [ A] 2 X A FAo = −rAV X A FAo nd VCSTR = (2 order reaction) 2 2 k [ A]0 (1− X A ) treact . = VBatch XA k [ A]0 (1− X A ) ( [ A] ) = ? FAo = 0 moles A VBatch = time FAo [ A]0 = VBatch [ A]0 treact + td ⎡ ⎤ XA ⎢t d + ⎥ k [ A]0 (1 − X A ) ⎦⎥ ⎣⎢ Assume XA=90% If treact>td then VBatch = 2FAo ⋅ 0.9 [ A]0 k [ A]0 (1− 0.9 ) VCSTR = 0.9FAo k [ A]0 2 ≤ 1.8FAo k [ A]0 2 Figure 1. Three tanks in series. [ A]CSTR = [ A]in + rA [ ] [ A]in If rA = − k A [ A]out = 1+ Da V v0 [ A]in = 1+ kV v0 If n CSTRs are in series: each volume = V n Cite as: William Green, Jr., 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]out = [ A]in ⎛ kV ⎞ 1+ ⎜ ⎟ ⎝ nv0 ⎠ n Æimproves productivity: concentration of A in 1st one is higher than would be in one large CSTR = [ A]0 e [ A]out Batch − kV v0 kV = 3 ⇒ 95% conversions v0 [ A]0 out = [ A]CSTR ⎛ 3⎞ ⎜1+ ⎟ ⎝ n⎠ series n N 1 10 100 XA .75 .93 .948 PFR Figure 2. Diagram of a plug flow reactor. Plug Flow Reactor (behaves like an infinite number of infinitely small CSTRs) FAin − FAout + rA ( ΔV ) = 0 CSTR ⎛ FAin − FAout ⎞ ⎜ ⎟ = −rA ΔV ⎝ ⎠ dFA = −rA design equation for PFR dV dFA = r ( C A ,CB ,...) dV = −kC ACB (for example) FA = C Av0 dFA F F = −k A B dV v0 v0 dY = F ( t ,Y ) where t is replaced by V. This can be expressed as: dt Example: ZZZ A + B YZ ZX ZC k k rev 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. William H. Green Lecture 8 Page 2 of 4 Cite as: William Green, Jr., 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]. ⎛ kFA FB krev FC ⎞ + ⎜− ⎟ v02 v0 ⎟ ⎜ ⎛ FA ⎞ d ⎜ ⎟ ⎜ kFA FB krev FC ⎟ FB = ⎜ − + ⎟ dV ⎜⎜ ⎟⎟ ⎜ v0 ⎟ v02 FC ⎠ ⎝N ⎜ kF F k F ⎟ Y ⎜⎜ + A2 B − rev C ⎟⎟ v0 v0 ⎠ ⎝ F ( t ,Y ) z Figure 3. Diagram of a plug flow reactor showing flow in the z-direction. dV = area ⋅ dz Mass flow rate is constant ( v ρ A ) = const. ρ = ∑ CiWi dρ =0 dz d ( vρ A) dv dA dρ + Av =0 = ρ A + ρv dz dz dz dz For a liquid, Rearrange: ⎛ 1 dA 1 d ρ ⎞ dv = −v ⎜ + ⎟ dz ⎝ A dz ρ dz ⎠ dA dρ =0 = 0 and for a liquid For a normal pipe dz dz dv = 0 ⇒ v = v0 Therefore: dz (We can’t assume this for gases!) For a PFR: dFA = rA dV FA = v [ A] d ( vC A ) dV = rA For liquids, v is constant so we can take it out of the differential. 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. William H. Green Lecture 8 Page 3 of 4 Cite as: William Green, Jr., 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]. v dC A , for liquids area dz dC A area = rA dz v0 rA = Instead of treact we have zreact! area ⋅length v0 XA area ⋅ z = = v0 k [ A]0 (1− X A ) t pipe = t PFR Flow is driven by the pressure drop across the pipe. P0 Pfinal Figure 4. Diagram of a pipe showing pressure upstream and downstream. PV = NRT P ∑ Ci = RT ⎫ Fi ⎪ ⎬ turns F's into concentrations ∑n Fn ⎪⎭ ρ = ∑ CiWi , Wi is molecular weight of i. P Ci = RT v= mass flowrate ← const. ρ (z) 10.37 Chemical and Biological Reaction Engineering, Spring 2007 Prof. William H. Green Lecture 8 Page 4 of 4 Cite as: William Green, Jr., 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].