L5-1 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. Relate all V(  ) to XA Put together Review: Derive –r A = f(X A ) Relate all rj to Cj  j ≡ stoichiometric coefficient  for products, ⊖ for reactants Relate all Cj(XA) to V(  ) Batch: Flow: Batch: Flow: Batch & Flow: Now that C j is in terms of X A, we can write the rate law in terms of X A

L5-2 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. Review: Stoichiometric Tables Species Feed rate (mol/time) Change in reactor (mol/time) Effluent rate from reactor (mol/time) AF A0 -F A0 X A F A = F A0 (1–X A ) B F B0 =   F A0 B F A0 X A F B = F A0 (   + B X A ) C F C0 =  C F A0 C F A0 X A F C = F A0 (  C + C X A ) D F D0 =  D F A0 D F A0 X A F D = F A0 (  D + D X A ) I F I 0 =  I F A0 ---FI =FI0FI =FI0 TotalF T0  F A0 X A F T = F T0 +  F A0 X A F A0 F B0 F C0 F D0 F I 0 FAFBFCFDFIFAFBFCFDFI j ≡ stoichiometric coefficient  for products, ⊖ for reactants InOut

L5-3 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. L5: Reactor Design Recipe and Reactor Scale-Up (Sizing) Goal: Develop an algorithm that combines reactor design equations with reaction rates for the design of different reactors

L5-4 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. The Logic of Isothermal Reactor Design InOut - + Generation = Accumulation 1. Set up mole balance for specific reactor 2. Derive design eq. in terms of X A for each reactor BatchCSTRPFR 3. Put C j is in terms of X A and plug into r A 4. Plug r A into design eq and solve for the time (batch) or volume (flow) required for a specific X A Today and next week! (We will always look conditions where Z 0 =Z)

L5-5 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. Batch Reactor Operation (1) Batch Volume is constant, V=V 0 Mole balance Rate law Stoichiometry (put C A in terms of X) Combine A → B -r A = kC A 2 2 nd order reaction rate Calculate the time required for a conversion of X A in a constant V batch reactor

L5-6 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. Batch Reactor Operation (2) Calculate the time required for a conversion of X A in a constant V batch reactor Evaluate Rearrange to get like variables together k is constant for an isothermal reaction Time required to achieve X A for 2 nd order rxn Integrate A → B -r A = kC A 2 2 nd order reaction rate

L5-7 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. Batch Reactor Operation (3) Batch Volume is constant, V=V 0 Calculate the time required for a conversion of X A in a constant V batch reactor Mole balance Rate law Stoichiometry (put C A in terms of X) Combine A → B -r A = kC A 1 st order reaction rate Mole balance as a function of conversion

L5-8 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. Batch Reactor Operation (4) Calculate the time required for a conversion of X A in a constant V batch reactor Evaluate to solve for time Rearrange to get like variables together k is constant for an isothermal reaction Time required to achieve X A for 1 st order rxn Integrate Mole balance as in terms of X A : A → B -r A = kC A 1 st order reaction rate Remember: Confused about the integration? See the next slide

L5-9 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. Batch Reactor Operation (4) Calculate the time required for a conversion of X A in a constant V batch reactor Integrate A → B -r A = kC A 1 st order reaction rate 0=ln(1) Remember:

L5-10 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. Typical Cycle Time for a Batch Polymerization ActivityTime (h) 1. Charge feed to the reactor and agitate (t f ) Heat to reaction temperature (t e )0.2 – Carry out reaction (t R )(varies) 4. Empty and clean reactor (t c )0.5 – 1.0 Total time excluding reaction3.0 – 6.0 Total Cycle Time t t = t f + t e + t R + t c Total Cycle Time t t for a batch process is much longer than the reaction time because it takes time to set up, heat, and clean the reactor each time it is used

L5-11 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. CSTR Operation (1) Calculate the CSTR volume required to get a conversion of X A Mole balance Rate law Stoichiometry (put C A in terms of X) Combine A → B -r A = kC A Liquid-phase 1 st order reaction rate Put F A0 in terms of C A0 Volume required to achieve X A for 1 st order rxn (    )

L5-12 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. Scaling CSTRs Space time  (residence time) required to achieve X A for 1 st order irreversible rxn Chemical engineers are involved in scaling up a laboratory scale reaction to the pilot plant scale or full-scale reactor If one knows the volume of the pilot-scale reactor required to achieve X A, how is this information used to achieve X A in a larger reactor? k in the small reactor is the same as k in the bigger reactor Want X A in the small reactor to be the same as X A in the bigger reactor  0 in the small reactor must be different from  0 in the bigger reactor Suppose for a 1 st order irreversible liquid-phase reaction: Separate variables we will vary from those held constant So the reactor volume V must be proportional to the volumetric flow rate  0 How?

L5-13 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. Scaling CSTRs with Spacetime  A → B -r A = kC A So if you know the spacetime  required to get a conversion of X A in a CSTR, you can use that to achieve the same X A in a different size CSTR 1 st order reaction rate What  is required to achieve a specific X A ? CSTR relationship between  and X A for 1 st order liquid-phase rxn (isothermal and V = V 0 ) Space time  (residence time) required to achieve X A for 1 st order irreversible rxn Rearrange to get X A in terms of 

L5-14 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. Damköhler Number, Da Estimates the degree of conversion that can be obtained in a flow reactor First order irreversible reaction: 1 st order irreversible reaction Second order irreversible reaction: 2 nd order irreversible reaction How is X A related to Da in a first order irreversible reaction in a flow reactor? Substitute From previous slide:

L5-15 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. If Da<0.1 for this 1st order irreversible rxn in a flow reactor, then Damköhler Number, Da Estimates the degree of conversion that can be obtained in a flow reactor Relate X A to Da for a 1 st order irreversible rxn in a flow reactor: If Da>10 for this 1st order irreversible rxn in a flow reactor, then 1 st order irreversible rxn

L5-16 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. Sizing CSTRs for 2 nd Order Rxns Mole balance Rate laws Stoichiometry Combine or Calculate the CSTR volume required to get a conversion of X A A → B -r A = kC A 2 Liquid-phase 2 nd order reaction rate In terms of conversion? In terms of space time? In terms of X A as a function of Da? 2 nd order liquid irreversible reaction

L5-17 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. CSTRs in Series C A0  0 C A1  C A2     Effluent of reactor 1 is input for reactor 2, no change in  A first order reaction is carried out isothermally using 2 CSTRs that are the same size, and  and k are the same in both reactors (      & k 1 = k 2 = k) Relate C A2 to C A1, k, &  1. Mole balance CSTR 2 2. Rate law CSTR 2 3.Stoichiometry CSTR 2 4.Combine for CSTR 2 Determine V 1 for 1 st CSTR using our standard procedure. For 2 nd CSTR: Skip this step for now.

L5-18 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. CSTRs in Series, C A1 C A0  0 C A1  C A2  A first order reaction is carried out isothermally using 2 CSTRs that are the same size, and  and k are the same in both reactors (      & k 1 = k 2 = k) What is C A1 in terms of  and k? We know for a single CSTR: Put X A for 1 st CSTR in terms of C A1 : Substitute: Solve for C A1 :    Effluent of reactor 1 is input for reactor 2, no change in 

L5-19 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. CSTRs in Series, C A2 C A0  0 C A1  C A2     Effluent of reactor 1 is input for reactor 2 A first order reaction is carried out isothermally using 2 CSTRs that are the same size, and  and k are the same in both reactors (      & k 1 = k 2 = k) Relate C A2 to k &  Substitute 1 st order irreversible rxn with V 1 = V 2,     and k 1 = k 2

L5-20 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. n CSTRs in Series C A0  0 C A1  C A2     For n identical CSTRs, then: How is conversion related to the # of CSTRs in series? Put C An in terms of X An (X A at the last CSTR): 1 st order irreversible liquid phase rxn run in n CSTRs with identical V,  and k 1 st order irreversible liquid-phase rxn run in n CSTRs with identical V,  and k Rate of disappearance of A in the nth reactor:

L5-21 Slides courtesy of Prof M L Kraft, Chemical & Biomolecular Engr Dept, University of Illinois at Urbana-Champaign. Isothermal CSTRs in Parallel F A0 F A01 F A02 same T, V,  Subscript i denotes reactor i F A01 = F A02 = … F A0n Volume of each CSTR Molar flow rate of each CSTR Mole Balance Conversion achieved by any one of the reactors in parallel is the same as if all the reactant were fed into one big reactor of volume V