CHEE 321: Chemical Reaction Engineering Module 5: Multiple Reactions (Chapter 6, Fogler) Course (Content) Organization Isothermal, Ideal Reactor (Single Reaction) Design Output Mole Balance Rate Law Design Algorithm (Module-1) (Module-2) (Module-3) • Reactor Volume In – Out + Con = Acc n 1. GMBE, 2. Rate Law • Reaction Time (rA) = kCA FA,in-FA,out+(rA)V = dCA/dt 3. Stoich 4.Combine • Rate Constant Analysis of Rate law (Module-4) Kinetics: How to obtain k and rxn order • Conversion Multiple Reactions • Product Composition (Module-5) Selectivity, Yield Non-Isothermal Reactor Design Output (Module-6) • Energy Balance • Temperature Profile dT/dz = ? • Heat Transfer Rate • Heat Removal • Equilibrium Reactions • Heating Requirement T -T =? • Multiple Steady State in out Topics to be covered in this Module • Types of multiple reactions • Introduction to selectivity and yield • Qualitative Analyses (Parallel and Series Reactions) – Maximizing the reactor operation for single reactant systems – Maximizing the reactor operation for two reactant systems • Algorithm for Reactor Design of Multiple Reactions – Mole Balance – Net Rates of Reactions – Stoichiometry Multiple Reactions Types of Multiple Reactions 1. Series Reactions ⎯ABC → ⎯k1 2 k⎯ → ⎯ Use molar flow rates and concentrations; 2. Parallel Reactions DO NOTuse conversion! ⎯ABk1 → ⎯ ⎯ACk2 → ⎯ 3. ParallelComplex Reactions: Series and ⎯ABC →k1 ⎯ + +ACD ⎯k2 → ⎯ Cannot use stoichiometric tables to relate 4. Independent change in CB to change in CA ⎯ACk1 → ⎯ ⎯B k2 →D ⎯ Selectivity and Yield Desired Reaction: Instantaneous Global kD A ⎯→⎯ D rD ~ FD Selectivity SDU = SDU = r F Undesired Reaction: U U k U rD A⎯⎯→U FNDD Yield YD = YD == kU2 −rA DU⎯⎯→ FFNNA00−−AAA • What should be the criterion for designing the reactor ? • Is it necessary that reactor operates such that minimum amount of undesired products are formed ? D S Total Cost E P Reactor D A A R Cost System U A T O R U Reactant Conversion Instantaneous vs. Global Yield • For a CSTR: SSDUDU= YYDD= For proof, see Fogler Ex. 6-1 (pg 308) • For a PFR, concentrations and rxn rates are changing along reactor length: rdFDD instantaneous yield: YD == −−rdFA A D formed FD global yield YD == A reacted (FFA0 − A ) −1 CA YY = dC′ for v=v : DD∫C A 0 A0 ()CCAA0 − Series Reactions Batch reactor, isothermal, incompressible , t=0 CA=CA0 From Fogler website http://www.engin.umich.edu/~cre/06chap/frames_learn.htm Series Reactions See Appendix A3 Series Reactions What about byproduct C? This can be calculated by integration, or by stoichiometry dC C = k C , t = 0 C = 0 dt 2 B C You would have the same set of equations for an isothermal PFR, replacing t with τ ; see Fogler Ex. 6-4 Parallel Reactions: Selectivity for Single Reactant Systems eaction)Example (parallel r k Desired Reaction: ⎯A D →D ⎯ αD rDDA= k C α Undesired Reaction: kU U ⎯A →U ⎯ rUUA= k C ??AWhat is the net rate of reaction of r k Cα D k S =D = DA = D C α( DU− α ) DU α U A rU kUA C k U .Let us examine some reactor operating scenarios to maximize selectivity , 6.2Fogler Parallel Reactions: Selectivity for Single Reactant Systems Case 1: αD-αU >0 rD kD α()DU− α SDU= = CA High CA favors D rU kU How can we accomplish this? • For gas phase reactions, maintain high pressures • For liquid-phase reactions, keep the diluent to a minimum • Batch or Plug Flow Reactors should be used • CSTR should NOT be chosen Parallel Reactions: Selectivity for Single Reactant Systems Case 2: αD-αU < 0 rD kD S = = Low CA favors D DU α()UD− α rU kUA C How can we accomplish this? C • low pressuresoperate at For gas phase reactions, A0 • For liquid-phase dilute reactions, the feed CA • preferredCSTR is CA Reactant concentration at low levelmaintained Parallel Reactions: Selectivity for Single Reactant Systems Case 3: αD-αU = 0 Concentration cannot be used operating parameter for selectivity maximization What now? r k A D D AexpD E− [D RT / ] D SDU= = = =expE [ −DU ( E − ) RT / ] r k A U U AexpU E− [U RT / ] U (a) If ED > EU • temperatureOperate reactor at highest possible of these discussions None / strategies examine yield. Both must be considered (b) If E > E U D in reactor design! • Operate reactor at lowest possible temperature Parallel Reactions: Selectivity for wo ReactantT Systems Example kD α1 β 1 Desired Reaction: ABD+ ⎯⎯→ rDDAB k= C C α β Undesired Reaction: kU 2 2 ABU+ ⎯⎯→ rUUAB k= C C rD kD α()()1 α− 2 β 1− 2 β SDU= =CCAB rU kU Parallel Reactions: Selectivity for Two Reactant Systems Case 1: α >α ; β > β 1 2 1 2 Let, a = α1-α2; b = β1 - β2 rD kD a b SDU= = CCA B rU kU For high SDU, maintain both A & B as high as possible How can we accomplish this? • Use Batch reactor • Use Plug Flow reactor Parallel Reactions: Selectivity for wo ReactantT Systems Case 2: α1>α2; β1 < β2 Let, a = α1-α2; b = β2 - β1 k a ABD+ ⎯⎯→D α1 β 1 rD kD CA rDDAB k= C C SDU= = b k α β rU kU CB ABU+ ⎯⎯→U 2 2 rUUAB k= C C For high SDU high and of B lowA, maintain concentration of How can we accomplish this? See Fogler Figure 6.3 • slowlywhere B is fed Use semi-batch reactor • continuouslyB being fed of with side streams ubular reactor TUse • fAUse series of small CSTR with each reactorand B to first only to ed Parallel Reactions: Selectivity for Two Reactant Systems Case 3: α1<α2; β1 < β2 Let, a = α2-α1; b = β2 - β1 rkDD1 SDU == ab rkCCUUAB For high SDU, maintain both concentration of A and B low How can we accomplish this? • For gas phase reactions, operate at low pressures • For liquid-phase reactions, dilute the feed • CSTR is preferred Parallel Reactions: Selectivity for Two Reactant Systems Case 4: α1<α2; β1 > β2 Let, a = α2-α1; b = β1 - β2 b rD kD CB SDU == a rU kU CA For high SDU, maintain concentration of B high and of A low How can we accomplish this? • Use semi-batch reactor where A is fed slowly • Use Tubular reactor with side streams of A being fed continuously • Use series of small CSTR with B fed only to first and A to each reactor Same as Case 2, with A and B switched… Why Semi-Batch Reactors? B heat C A A, B • B is slowly fed to A contained • Product C is continuously in the reactor. removed • Unwanted products can be • Higher conversion for minimized reversible reactions can be • exothermic reaction can be obtained carried out at controlled rate Semi-Batch Reactors - GMBE 1. GMBE on a molar basis Input - Output + Gen = Accu. For Species A FB0 B dN Constant 0− 0 +r ( V ) = A v0 A dt Density Systems VV= + vt For Species B 00 dNB FrVBB0 −+0() = Constant dt Flowrate Semi-Batch Reactors - GMBE 2. GMBE on a concentration Basis F B0 B v0 For Species A (no inflow) dN 0− 0 +r ( V ) = A NVC[]A = A A dt d() V C dC dV ()r V= A =V A +C A dt dt A dt dC dC v ()rV=+ VA vC ⇒ A =−()rC0 A dt 0 A dtA V A Constant flow Similarly for Species B and density []FvC= dNB BB000 FrVBB0 −+0() = dV dt = v NVC[]B = B 0 dC v dt B =−()rCC0 ( − ) dtBBB V 0 Modification to the CRE Algorithm for Multiple Reactions Fogler, 6.4 • Mole balance on every species (not in terms of conversion) • Rate Law: Net Rate of reaction for each species, e.g., rA = Σ riΑ • Stoichiometry a) Liquid Phase, incompressible: CA=NA/V=FA/v0 b) Gas Phase use Variable volumetric flowrate; ideal gas • Combine – More difficult: set of algebraic or differential equations for A, B, … Design Equation for Reactors – Multiple Reactions Gas-Phase Liquid Phase NOTE the design equations are EXACTLY Batch as for a single reaction but… Semi-Batch (B fed) Balances must be written for all components CSTR PFR PBR What are the assumptions for each reactor type? Net Rate of Reaction For N reactions, the net rate of formation of species A is: For a given reaction iai A + bi B → ci C + di D NOTE: You can use stoichiometric coefficients to relate relative rates of reaction of species for a specific reaction only Example: Net Rate of Reaction • The following reactions follow elementary rate law: Write net rates of formation of A, B and C Fogler, 6.4.2; see Ex. 6-5 Example: Multiple Gas Phase Reactions in an Isothermal PFR The complex gas phase reactions take place in a PFR. The feed is equal molar in A and B with FA0 = 10 mol/min and the volumetric flow rate is 100 dm3/min. The reactor volume is 1,000 dm3, there is no pressure drop, the 3 total entering concentration is CT0 = 0.2 mol/dm and the rate constants are: S Plot FA, FB, FC, FD and CD / as a function of V Taken from http://www.engin.umich.edu/~cre/06chap/frames_learn.htm Gas Phase Multiple Reactions - Algorithm 1. Mole Balance A Remember, unlike single-reactions, B for multiple reactions mole balance for each species must be written C D rA, rB, rC, rD are all NET rates of reactions Example (cont’d) 2. Rate Laws Species A ⇒ ⇒ Species B Species C Species D Example (cont’d) 3. Stoichiometry 4. Combine ⇒ Solution Also, see example 6-10 What you should know… • Qualitative Analyses (Parallel and Series Reactions) – Maximizing the reactor operation for single reactant systems – Maximizing the reactor operation for two reactant systems – Consideration of selectivity and yield • Algorithm for Reactor Design of Multiple Reactions – Mole Balance – Net Rates of Reactions – Stoichiometry – Be able to write the set of equations for the system – usually cannot be solved without computer programs – be able to sketch the expected qualitative behaviour.