CEE255A-L2- Ideal Flow Models

CEE255A-L2- Ideal Flow Models - CEE 255A Lecture 2 Reactor...

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Unformatted text preview: CEE 255A Lecture 2 Reactor Types and Ideal Flow Models Dr. Eric M.V. Hoek Civil & Environmental Engineering Reactor Types (a) Batch Reactor (b) MFR (CSTR) (c) MFR's in Series (d) Rectangular PFR (e) Tubular PFR (f) Serpentine PFR (g) Downflow PBR (h) Upflow PBR (i) Fluidized PBR Types of PhysicalChemical Reactors Accumulation = Inflow Outflow + Reaction General Mass Balance VdC/dt = Q0C0 QC kCn (a) Completely Mixed Batch Reactor (BR = CMBR) After initial reactants added, no reactants or products flow into or out of the reactor. Complete mixing occurs instantaneously and uniformly throughout the reactor. The reaction rate proceeds at the identical rate everywhere in the reactor. Reactants and products continuously flow into and out of the reactor. Complete mixing occurs instantaneously and uniformly throughout the reactor. (b) Completely Mixed Flow Reactor (MFR = CSTR = CSTFR = CMFR) The concentration and reaction rate are the same as in the effluent and identical everywhere in the reactor. Fluid moves through reactor as a plug does not mix with fluid elements in front or behind it. The reaction rate and concentration vary along the length of the reactor. The composition at any travel time/distance down the reactor is identical to the composition in a batch reactor after the same period of time has passed. (c) Plug Flow & Packed Bed Reactors (PFR, principles also apply to PBR) ContinuousFlow Reactors Sizing a MFR with the Reciprocal Rate of Reaction Analytically calculate the volume required to achieve 80% conversion of A given Q0 = 6 L/s and CA0 = 0.15 mol/L and the data below V = XFA0/(rA)exit; 1/(rA)exit = 800 Ls/mol V/FA0 = X 1/(rA)exit = 0.8800 Ls/mol = 640 Ls/mol V= FA0 X 1/(rA)exit = 640 Ls/mol (6 L/s 0.15 mol/L) = 560 L V/FA0 = 1/(rA)exitX Also, you can graphically determine the volume of CSTR required to achieve 80% conversion of A from: 1,000 X 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.85 The volume is based on the area under the curve r A , mol/L-s 0.005300 0.005200 0.005000 0.004500 0.004000 0.003300 0.002500 0.001800 0.001250 0.001000 1/(r A ), L-s/mol 189 192 200 222 250 303 400 556 800 1,000 1/(- r A ), L-s/mol 800 600 400 1/(rA) = 800 200 X = 0.8 0 0.0 0.2 0.4 0.6 0.8 1.0 Conversion, X ContinuousFlow Reactors Sizing a PFR with the Reciprocal Rate of Reaction Analytically calculate the volume required to achieve 80% conversion of A for Q0 = 6 L/s and CA0 = 0.1445 mol/L X V = FA0 0 dX/(rA) = FA0 X/(rA)x Let X = 0.1 and use the trapezoid rule V = (60.1445)(0.1)[(189+192)/2 +...+ (800+556)/2] = 225 L The volume is based on the area under the curve r A , mol/L-s 0.005300 0.005200 0.005000 0.004500 0.004000 0.003300 0.002500 0.001800 0.001250 0.001000 1/(r A ), L-s/mol 189 192 200 222 250 303 400 556 800 1,000 1/(- r A ), L-s/mol 1,000 800 X 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.85 600 400 200 0 0.0 0.2 0.4 0.6 0.8 1.0 Conversion, X ContinuousFlow Reactors Comparing MFR and PFR sizes 1,000 800 1/(- r A ), L-s/mol 600 V/FA0 - MFR 400 200 V/FA0 - PFR 0.0 0.2 0.4 0.6 0.8 1.0 0 Conversion, X Removal, R (or "Conversion, X") = 1 C/C0 1 C0 MFR: MFR = - 1 kC 1 C0 PFR: PFR = ln k C Comparison of PFR vs. MFR Performance C0 - 1 C = C0 ln C MFR PFR For 99.99% removal, the MFR retention time is ~1,000X larger than the PFR...Why do we use MFR/PFR Advantages & Disadvantages MFR Large open design allows easy maintenance Influent is instantaneously diluted, buffer against shock Ideal mixing can nearly be achieved in practice Mixing/aeration can consume be significant energy cost PFR Difficult to maintain and susceptible to shock loads Higher conversion per unit volume of reactor Difficult to achieve PFR conditions in real reactors Pressure drop in PFR/PBR can be significant energy cost Reactors in Series Reactors in Series (MFRMFR) X0 = 0 FA0 V1 X1=0.4; FA1 V2 X2=0.8 FAe MFF1: V1 = FA0(X1 X0) / (rA1) MFR2: V2 = FA0(X2 X1) / (rA2) Based on the molar flow rate used before, what is the total volume of reactors needed to achieve 80% conversion? Reactors in Series Reactors in Series (MFR-MFR) 1,000 800 1/(- r A ), L-s/mol 600 400 200 0 0.0 0.2 0.4 0.6 0.8 1.0 Conversion, X nMFRs in Series (1st order) X0 = 0 FA0 V1 (all tanks are the same size) X1; FA1 V2 X2; FA2 V3 X3; FA3 Xn-1; FAn-1 Vn Xn=0.8 FA,n (V1 = V2 = ...= Vn) Performance Eq' n : V = FA0 X (- rA ) Note : FA0 = C A0Q0 ; = V Q0 ; - rA = kC A Ci -1 CA -1 -1 = (1 + k i ) = (1 + k i ) C A0 Ci C0 C0 C1 Cn -1 -1 -1 -1 -n = = (1 + k 1 ) (1 + k 2 ) (1 + k n ) = (1 + k N ) ; i = N Cn C1 C2 Cn n For the same overall conversion, in all but the final tank, the rate of reaction will be quicker than in a single tank. Reactors in Series Modeling a PFR with nCSTRs in Series 1,000 800 1/(- r A ), L-s/mol 600 400 200 V/FA0 ( MFRs) = V/FA0 (1 PFR) 0 0.0 0.2 0.4 0.6 0.8 1.0 Conversion, X Tanks-in-Series (TIS) Model 1/ C n 0 1 n - MFRs = - 1 k Cn C 1 0 n - PFRs = ln k n C Ratio of n-MFR/ PFR R 90% 99% 99.9% 99.99% n=1 3.91 21.5 145 1090 n=2 1.88 3.91 8.87 21.5 n=3 1.5 2.37 3.91 6.69 n=5 1.27 1.64 2.16 2.88 n = 10 1.12 1.27 1.44 1.67 n = 100 1.01 1.02 1.04 1.05 Reactors in Series Reactors in Series (PFRPFR) X0 = 0 FA0 V1 X1=0.4; FA1 V2 X2=0.8 FAe PFR1: V1 = FA0 dX / (rA) X1 0 PFR2: V2 = FA0 dX / (rA) X2 X1 Vtotal = V1 + V2 = FA0 dX / (rA) + FA0 dX / (rA) X1 X2 0 X1 Vtotal = FA0 dX / (rA); PFRs in series do NOT change V X2 0 Reactors in Series Reactors in Series (PFRPFR) 1,000 800 1/(- r A ), L-s/mol 600 400 200 V/FA0 - PFR 0.0 0.2 0.4 0.6 0.8 1.0 0 Conversion, X Reactors in Series Reactors in Series (MFRPFR) X =0 MFR: 0 V1 = FA0X1 / (rA1) X2 FA0 PFR: V1 X1 X1 FA1 V2 X2=0.8 FAe V2 = FA0 dX / (rA) Reactors in Series (PFRMFR) PFR: V1 = FA0 dX / (rA) X1 0 V1 X1; FA1 X2=0.8 FAe MFR: X0 = 0 FA0 V2 V2 = FA0(X2 X1) / (rA2) Reactors in Series Reactors in Series (MFRPFR) 1,000 800 1/(- r A ), L-s/mol 600 400 200 V/FA0 - MFR 0.0 0.2 0.4 V/FA0 - PFR 0 0.6 0.8 1.0 Conversion, X Reactors in Series Reactors in Series (PFRMFR) 1,000 800 1/(- r A ), L-s/mol 600 400 V/FA0 - MFR 200 V/FA0 - PFR 0 0.0 0.2 0.4 0.6 0.8 1.0 Conversion, X Reactors in Series Reactors in Series (PFRMFRPFR) V1 X0 = 0 FA0 X1; FA1 X2 FA2 X3 FA3 V2 V3 PFR1: V1 = FA0 dX / (rA) X1 0 MFR: FA1 FA2 = rA2V2 V2 = (FA1 FA2) / (rA2) V2 = FA0(X2 X1) / (rA2) X3 Reactors in Series Reactors in Series (PFRMFRPFR) 1,000 800 1/(- r A ), L-s/mol 600 400 V/FA0 PFR1 200 V/FA0 PFR1 0 0.0 0.2 V/FA0 - MFR 0.4 0.6 0.8 1.0 Conversion, X MFR & PFR Reactors with Recycle 1 C0 MFR = - 1 kC 1 + R C0 / C + R PFR = ln k 1+ R Recycle has no effect on MFR residence time or reactor size, but can improve reaction kinetics. Recycle degrades PFR performance and requires larger reactor size and retention time. (a) MFR, 2nd order (b) MFR, 1st order (c) PFR, 1st order, R=1 (d) 3MFRs, 1st order Residence Time Distribution (RTD) The residence time is the "age" of a fluid element, or the time elapsed since it entered the reactor. Since fluid elements may take different "routes" through a reactor, they have different residence times. The residence time distribution (RTD) is a statistical distribution of residence times of all fluid elements leaving the reactor. The RTD is determined experimentally by injecting an inert chemical, molecule, or atom, called a tracer in the reactor at some time, t = 0, and measuring the changing concentration in the effluent stream with time. Accumulation = Inflow Outflow + Reaction VdC/dt = 0 QC 0 Pulse Tracer Response for Ideal Reactors C = C0e-t/ PFR MFR Conservative Tracer (dyes, salts, radioisotopes) Residence Time Distribution (RTD) soluble, nonreactive, nonadsorbing, detectable Reactor Pulse Input Ccurves Step Input Ccurves Reading/Review due Tue, Jan 13, 2:00 PM Homework Review MWH Chapters 15 Read MWH Chapter 6.16.5 Homework #1 (50 pts) due Tue, Jan 13, 2:00 PM Chapter 6, Problems 3, 4, 8, 11, 12 Extra Credit (+ 10 pts): Write out derivations for all performance equations for BR, PFR, and MFR for reaction orders of 0, 1, and 2. Create a table with columns for 0, 1, and 2 order reactions and rows for BR, PBR, and MFR reactors. Fill in the performance equations. Project Assignment #1 (5 pts) due Thu, Jan 15, 2:00 PM Submit your selected topic and abstract. ...
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This note was uploaded on 02/02/2012 for the course CEE 255A taught by Professor Erichoek during the Fall '11 term at UCLA.

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