Analysis of Reaction Rate Data Methods

L9b-1 Review: Analysis of Rate Data Goal: determine reaction order, , and specific reaction rate constant, k Data collection is done in the lab so we can simplify BMB, stoichiometry, and fluid dynamic considerations Want ideal conditions well-mixed (data is easiest to interpret) Constant-volume batch reactor for homogeneous reactions: make concentration vs time measurements during unsteady-state operation Differential reactor for solid-fluid reactions: monitor product concentration for different feed conditions during steady state operation Method of Excess Differential method Integral method Half-lives method Initial rate method Differential reactor More complex kinetics Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.

L9b-2 Review: Method of Half-lives Half-life of a reaction (t1/2): time it takes for the concentration of the reactant to drop to half of its initial value dC dt A products r = A = kC A kC A A ln (t1/2) 1 1 1 = t ( ) 1 1 k 1 C C A A0 Slope = 1- 1 2 = C C at t = t A A0 1 2 1 2 k 1 1 = 12 t ( ) 1 1 C A0 ln CA0 1 Plot ln(t1/2) vs ln CA0. Get a straight line with a slope of 1- 2 k 1 ( ) ( ) = + ln t ln 1 lnC 12 A0 ( ) 1 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.

L9b-3 Review: Method of Initial Rates When the reaction is reversible, the method of initial rates can be used to determine the reaction order and the specific rate constant Very little product is initially present, so rate of reverse reaction is negligible A series of experiments is carried out at different initial concentrations Initial rate of reaction is determined for each run Initial rate can be found by differentiating the data and extrapolating to zero time By various plotting or numerical analysis techniques relating -rA0 to CA0, we can obtain the appropriate rate law: = A0 r kC A0 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.

L9b-4 Review: Differential Catalyst Bed r A: rate of reaction per unit mass of catalyst Conversion of reactants & change in reactant concentration in the bed is extremely small flow in - flow out + rate of gen = rate of accum. + = F F r W 0 L A0 Ae A F F C C A0 Ae 0 A0 Ae = = r A W W FAe FA0 When constant flow rate, 0 = : CA0 Cp Fp ( ) Product concentration 0 p C W C C 0 A0 Ae = = r A W The reaction rate is determined by measuring product concentration, Cp W Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.

L9b-5 Review: Multiple Rxns & Selectivity 1) Parallel / competing rxns k1 k2 2) Series rxns A C B B k1 Desired product A k1 k2 3) Complex rxns A+B C+D A+C E k2 C instantaneous rate selectivity, SD/U rate of formation of D S rate of formation of U instantaneous yield, YD (at any point or time in reactor) D r r = = D r r rate of formation of D rate of consumption of A D U = = Y U D A overall rate selectivity, D U S overall yield, Y N N D Fi nal nal moles of desired product moles of undes D = = D U S F at exit D = Fi ir ed pr od ct u Y flow U D F F A0 A F F Exit E x molar flow rate of desired product molar flow rate of undesir D at tfinal = = D U S N batch D = Y it ed pr oduct D U N N A0 A Maximize selectivity / yield to maximize production of desired product Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.

Review: Maximizing SD/U for Parallel Rxns ( ) ( A B U A Specific rate of desired reaction kD increases: L9b-6 E E D RT U What reactor conditions and configuration maximize selectivity? ) A D 1 2 1 2 = D U S e C C a) If ED > EU b) If ED < EU more rapidly with increasing T less rapidly with increasing T Use lower temperature(not so low that the reaction rate is tiny) Use higher temperature To favor production of the desired product Now evaluate concentration: a) 0 b) 0 1 2 1 2 1 2 1 2 Use large CA Use small CA c) 0 d) 0 1 2 1 2 1 2 1 2 Use large CB Use small CB Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.

L9b-7 Concentration Requirements & Reactor Selection How do concentration requirements play into reactor selection? U kD D A+B kU CA 0 CB 0 CA0 0 CB0 0 CSTR: concentration is always at its lowest value (that at outlet) PFR PFR (or PBR): concentration is high at the inlet & progressively drops to the outlet concentration Semi-batch: concentration of one reactant (A as shown) is high at t=0 & progressively drops with increasing time, whereas concentration of B can be kept low at all times CB 0 Batch: concentration is high at t=0 & progressively drops with increasing time CA(t) CB(t) CA Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.

kD L9b-8 D High CA favors undesired product formation (keep CA low) High CA favors desired product formation A+B kU U PFR/PBR Side streams feed low CA Semi-batch reactor slowly feed A to large amt of B CA CSTRs in series Batch reactor High CB favors desired product formation CA When CA & CB are low (end time or position), all rxns will be slow High CB PFR/PBR CA CA High P for gas-phase rxn, do not add inert gas (dilutes reactants) CA 0 CB CA0 0 CB0 0 CSTR PFR/PBR w/ side streams feeding low CB CB Semi-batch reactor, slowly feed B to large amount of A CB CSTRs in series High CB favors undesired product formation (keep CB low) High CA PFR/PBR w/ high recycle PFR/PBR CB CB Dilute feed with inerts that are easily separated from product Low P if gas phase Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign. B consumed before leaving CSTRn

L9b-9 Different Types of Selectivity D r r rate of formation of D rate of formation of U = = D U S instantaneous rate selectivity, SD/U U S overall rate selectivity, D U F F Exit E x molar flow rate of desired product molar flow rate of undesir D = = D U S it ed pr oduct U N N Fi nal nal moles of desired product moles of undes D = = D U S Fi ir ed pr od ct u U D r r rate of formation of D rate of consumption of A instantaneous yield, YD (at any point or time in reactor) = = Y D A Y overall yield, D N F Evaluated at outlet Evaluated at tfinal D D = Y = Y batch flow D D N N F F A0 A A0 A Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.

L9b-10 Series (Consecutive) Reactions k1 k2 Time is the key factor here!!! A U D (desired) (undesired) Spacetime for a flow reactor Real time t for a batch reactor To maximize the production of D, use: CSTRs in series Batch or or PFR/PBR n and carefully select the time (batch) or spacetime (flow) Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.

L9b-11 Concentrations in Series Reactions -rA = k1CA rB,net = k1CA k2CB k1 k2 A C B How does CA depend on ? dF dV dC dV k1 A A = = = k C k C C C e 1 A 0 1 A A A 0 How does CB depend on ? B k C d V ( 1 d ) ( dF dC d V k1 B = = = k 2 B C k C e 2 B k C Substitute 1 A 0 1 A0 V 0 ) ( ) dC dC d k k B B 1 1 = + = k C e 2 B k C 2 B k C k C e A0 1 A0 ( ) k2 Use integrating factor (reviewed on Compass) k k d C e 1 2 e e k B d ( ) = k k C 1 A0 k C 2 1 = 1 A0 k C e B k 2 1 = C C C C C A0 A B Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.

L9b-12 Reactions in Series: Cj & Yield k1 = C C e B A A0 C A k k 1 2 e e k = C 1 A0 k C B k 2 1 = C C C C C A0 A B opt The reactor V (for a given 0) and that maximizes CB occurs when dCB/dt=0 ( 1 2 1 d k k ) 1 A0 k C dC k k B 1 2 = k e + = k e 0 2 k k 1 1 = ln opt k k 1 2 2 V = = 0 opt so V opt 0 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.

L9b-13 What reactor/reactors scheme and conditions would you use to maximize the selectivity parameters for the following parallel reaction? kD E/R 300 T 2000 T A+C D desired kU1 0.5 = U r 10 e C C = D r 8 00e C C A C A C 1 A+C U1 undesired RT E Need to maximize SD/U1 ( ) k T = Ae ( ) E E D U1 D r r A A D U D U D = T 1 1 = S e C C D U1 A C U1 U1 ( ) 2000 300 T 1700 T ( ) Plug in numbers: 800 10 0.5 1 1 1 C C 0.5 = D U S e C = D U S 80e C A A 1 1 To maximize the production of the desired product, the temperature should be a) As high as possible (without decomposing the reactant or product) b) Neither very high or very low c) As low as possible (but not so low the rate = 0) d) Doesn t matter, T doesn t affect the selectivity e) Not enough info to answer the question ED > EU, so use higher T Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.

L9b-14 What reactor/reactors scheme and conditions would you use to maximize the selectivity parameters for the following parallel reaction? kD 300 T 2000 T A+C D desired kU1 0.5 = U r 10 e C C = D r 8 00e C C A C A C 1 A+C U1 undesired RT E Need to maximize SD/U1 ( ) k T = Ae ( ) E E D U1 D r r A A D U D U D = T 1 1 = S e C C D U1 A C U1 U1 ( ) 2000 300 T 1700 T ( ) Plug in numbers: 800 10 0.5 1 1 1 C C 0.5 = D U S e C = D U S 80e C A A 1 1 To maximize the production of the desired product, CA should be a) As high as possible b) Neither very high or very low c) As low as possible d) Doesn t matter, CA doesn t affect the selectivity e) Not enough info to answer the question D < U1, so high CA favors undesired product formation (keep CA low) Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.

L9b-15 What reactor/reactors scheme and conditions would you use to maximize the selectivity parameters for the following parallel reaction? kD 300 T 2000 T A+C D desired kU1 0.5 = U r 10e C C = D r 800e C C A C A C 1 A+C U1 undesired Need to maximize SD/U1 ( ) E E D U1 D r r A A D U D U D = T 1 1 = S e C C D U1 A C U1 U1 ( ) 2000 300 T 1700 T ( ) Plug in numbers: Since ED>EU1, kD increases faster than kU1 as the temperature increases Operate at a high temperature to maximize CD with respect to CU1 800 10 0.5 1 1 1 C C 0.5 = D U S e C = D U S 80e C A A 1 1 D< U1, keep CA low to maximize CD with respect to CU1 rD and rU1 are 1st order in CC, so changing CC does not influence selectivity HOWEVER, high CC will increase the reaction rate and offset the slow reaction rate that is caused by low CA (that s a good thing) What reactor should we use? Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.

L9b-16 What reactor/reactors scheme and conditions would you use to maximize the selectivity parameters for the following parallel reaction? A+C D desired kU1 kD 300 T 2000 T 0.5 = U r 10e C C = D r 800e C C A C A C 1 A+C U1 undesired Need to maximize SD/U1 1700 T 0.5 = D U S 80e C A 1 ED>EU1, operate at a high temperature to maximize CD with respect to CU1 D< U1, keep CA low to maximize CD with respect to CU1 rD and rU1 are 1st order in CC, so changing CC does not influence selectivity HOWEVER, high CCwill increase the reaction rate and offset the slow reaction rate that is caused by low CA(that s a good thing) What reactor should we use? CA C PFR Semi-batch reactor slowly feed A to large amount of C A High CC PFR/PBR w/ side streams feeding low CA Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.

L9b-17 How does the selection of reactor/reactors scheme and conditions change if D can react with C and form another undesired product? A+C D desired A+C U1 undesired kD kU1 kU2 D+C U2 undesired = 300 T 8000 T 2000 T 6 0.5 = U r 10e C C U r 10 e C D C C = D r Need to maximize SD/U1 and SD/U2 800e C C A C A C 1 2 ED>EU1, operate at a high T 1700 T D< U1, keep CA low High CC increases rxn rate & offsets slow rxn from low CA 0.5 = D U S 80e C A 1 2000 T 6000 T 0.5 800e C C D r r 4 0.5 1 A C = = 8 10 = D U S e C C S A D D U2 8000 T 2 U2 6 10 e C D C C Since ED<EU21, kD increases slower than kU2 as T increases operate at low T to maximize CD D> U2, keep CA high to maximize CD rD, rU1 & rU2 are all 1st order in CC, so changing CC does not influence selectivity, but high CC will offset the rate decrease due to low CA Low CD reduces the production of U2 Conflicts with maximizing SD/U1! Conflicts with maximizing SD/U1! Conflicts with producing the product D!!! Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.

L9b-18 kD kU1 kU2 A+C D desired A+C U1 undesired D+C U2 undesired 6000 4 8 10 e = 1700 T Maximize SD/U1 & SD/U2 0.5 0.5 1 T = D U S 80e C D U S C C A A D 1 2 ED>EU1, operate at a high T ED<EU2, operate at low T D> U2, keep CA high Low CD reduces production of U2 D< U1, keep CA low Want to maximize CD High CC increases rxn rate & offsets slow rate caused by low CA Consider relative magnitude of SD/U1 and DD/U2 as a function of position in PFR PFR w/ side streams feeding low CA PFR 2, low T C PFR, high T A High T, CC is initially high, CA is low high SD/U1 Initially CD=0 rU2=0. Both gradually increase down reactor Initially high SD/U2 (because CD is low), but SD/U2 gradually decreases down reactor At some distance down the reactor, significant amounts of D have formed SD/U2 becomes significant with respect to SD/U1 At this point, want low T, high CA & low CC Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.

L9b-19 If a CSTR were used with CA = 1 mol/L and CD= 1 mol/L, at what temperature should the reactor be operated? kD A+C U1 undesired kU1 kU2 A+C D desired D+C U2 undesired = 300 T 8000 T 2000 T 6 0.5 = U r 10e C C U r 10 e C D C C = D r Need to maximize SD/(U1+U2) 800e C C A C A C 1 2 2000 T CA=1 CD=1 0.5 800e C C D r + A C = = D U S ( ) + U 300 T 1 2 8000 T U r U r 1 2 6 + 10e C C 10 e C D C C A C 2000 T 800e 10 2000 T 0.5 ( ) 1 80e = S = S D + D + 300 T 8000 T 300 T 8000 T 6 10 10 10 10 U U U U ( ) 1 ( ) 1 1 2 5 1 2 + e e + e 10 e Plot SD/(U1+U2) vs temperature to find the temperature that maximizes SD/(U1+U2) Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.

L9b-20 If a CSTR were used with CA = 1 mol/L and CD= 1 mol/L, at what temperature should the reactor be operated? A+C D desired A+C U1 undesired kD kU1 kU2 D+C U2 undesired = 300 T 8000 T 2000 T 6 0.5 = U r 10e C C U r 10 e C D C C = D r 800e C C A C A C 1 2 Need to maximize SD/(U1+U2) 600K 4 2000 T 3.5 80e = S D + 300 T 8000 T 3 U U 5 1 2 + e 10 e 2.5 SD/(U1+U2) 2 1.5 1 0.5 0 0 200 400 Temperature (K) 600 800 1000 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.

L9b-21 Calculate the yield of forming B in a CSTR and PFR when the conversion of A is 90% and CA0 = 4 mol/L. The following reactions occur in the reactor: kB B B r k 2L min What is the expression for the yield of B for a CSTR? F Y F F mol kC = = 1 min 1 = A B C r k C A C = k C A C B 0 C C B = = B Y Y = (overall yield) B B B C C C C A0 0 A 0 A0 A A0 A We know CA0 and CA when XA=0.9. How do we get CB? In - Out + Gen. = Accum. dN F F r V dt 0 C r Use the mole balance on A to find (at 90% conversion) In - Out + Gen. = Accum. + A A0 A V F r F B 0 C V B = B r + = + = F B r V 0 B B0 B B 0 = mol L min C mol = B 2 C B = B r 2L min = B B d N dt0 = A C C r V = A0 0 A 0 A C C V A0 A = = = C C r C C r A0 A A A0 A A r 0 A Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.

L9b-22 Calculate the yield of forming B in a CSTR and PFR when the conversion of A is 90% and CA0 = 4 mol/L. The following reactions occur in the reactor: mol kB kC = = B r k 2L min 1 min 1 = A B C r k C A C = k B C A C C C C mol = + r B r C r B A0 A What is rA? = Y = = A 2L min C B B C C r A0 A A Plug -rA back into expression for mol L min C 1 m in 1 = + r 2 C = + r k k C A A A B C A min C C C CA0 = 4 mol/L, and at XA=0.9, CA= 0.4 mol/L A0 A A0 A = = mol L min r + A 2 C A mol L mol L 4 0. 4 = = 1.5 min Residence time for XA = 0.9 mol L min 1 mol L + 2 0.4 mi n mol mi ( ) 2L 1.5min B r n = Y = Y = Y 0.83 B B B C C mol L mo L l A 0 A 4 0. 4 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.

L9b-23 Calculate the yield of forming B in a CSTR and PFR when the conversion of A is 90% and CA0 = 4 mol/L. The following reactions occur in the reactor: kB B B r k 2L min r k = + kC mol 1 min 1 = C r k C A C = = = 1 k A B C A C mol L min = + r 2 C k C A A A B C A min What is the expression for the yield of B for a PFR? F Y F F Use the mass balance to get CB dF r dV dV CB B C 0 B0 Use the mole balance on A to find (at 90% conversion) dF r dV dV = + d L B 0 C C (overall yield) B = = B Y Y = B B B C C C C A0 0 A 0 A0 A A0 A B 0 dC d mol L min mol mi dC dC d mol L min B B B = = = = 2 B r B r B mol L min ( ) = dC 2 d = n = 0 C 2L C C 2 0 B B B0 dC d dC mol L min 1 min 1 dC d A 0 dC A A = + 2 C A = r = = r A A A A min CA dC mol 1 A = d A A0 0 2 C ( ) A + 2mol L C min A C Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.

L9b-24 Calculate the yield of forming B in a CSTR and PFR when the conversion of A is 90% and CA0 = 4 mol/L. The following reactions occur in the reactor: kB B B r k 2L min = + mol kC = = 1 min 1 A B = C r k C 1 min A C = k C A C mol L min = + r 2 C r k k C A A A B C A C mol B = Y = C 2L m B Use mole balance on A to find (at XA = 0.9) mol 2 L ln m ol 2 L mol 1 L mo mol 0. L L m i n 2 L min = C C B in A0 A + C CA A0 dC mol L 1 1 ( ) A = = d 0 A0 0 min min C + + 2 C C A A mol L + 2 4 CA0 = 4 mol/L CA = 0.4 mol/L = ln = 0.92 min l mi n + 2 4 Yield was better in the CSTR, but the residence time was longer ol 0 .92m C B r B = = = Y Y Y 0 .5 1 B B B mol L mol L C C C C A0 A A0 A 4 0.4 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois, Urbana-Champaign.