Chapter 6

BITS, PILANI – K. K.BIRLA GOA CAMPUS MULTIPLE REACTIONS Chapter 6 PROF. SRINIVAS KRISHNASWAMY ASSOCIATE PROF. & HEAD OF DEPARTMENT DEPARTMENT OF CHEMICAL ENGINEERING BITS PILANI, K. K. BIRLA GOA CAMPUS Introduction After this chapter you will be able to focus on reactor selection and mole balances for multiple reactions  Seldom does 1 reaction occur in a reactor  Multiple reactions will occur (some desired / some undesired)  Economic success of a plant depends on minimizing undesired side reactions April 16, 2013 BITS, PILANI – K. K. BIRLA GOA CAMPUS 2 How we will go about it?  Describe basic types of multiple reactions  Define Selectivity and how it can be used to minimize unwanted side reactions  Choice of operating conditions and reactor type  Develop an algorithm to solve reaction engineering problems when multiple reactions are involved April 16, 2013 BITS, PILANI – K. K. BIRLA GOA CAMPUS 3 BIRLA GOA CAMPUS 4 . 2013 BITS. di and tri-ethanol amine PARALLEL REACTIONS (COMPETING REACTIONS) Two different pathways to form different products Oxidation of ethylene to ethylene oxide April 16. PILANI – K. K.Types of reactions SERIES REACTIONS (CONSECUTIVE REACTIONS) Reaction of ethylene oxide with ammonia to form mono. Types of reactions COMPLEX REACTIONS (CONSECUTIVE REACTIONS) Butadiene butadiene) from ethanol (ethylene, acetaldehyde, INDEPENDENT REACTIONS Crude oil to Gasoline April 16, 2013 BITS, PILANI – K. K. BIRLA GOA CAMPUS 5 Desired and Undesired Reactions A  D (kd) A  U (ku) ADU Minimize the formation of U and maximize U (objective) ECONOMIC INCENTIVE April 16, 2013 BITS, PILANI – K. K. BIRLA GOA CAMPUS 6 Possible reactions April 16, 2013 BITS, PILANI – K. K. BIRLA GOA CAMPUS 7 Selectivity and Yield Selectivity: Indication of preference of one product over another INSTANTANEOUS OVERALL For batch reactor it will be in terms of number of moles (Can we compare it for a CSTR?) April 16. 2013 BITS. K. PILANI – K. BIRLA GOA CAMPUS 8 . PILANI – K. BIRLA GOA CAMPUS 9 . K. 2013 BITS.Selectivity and Yield Yield: Ratio of the reaction rate of a given product to the reaction rate of the key reactant A INSTANTANEOUS OVERALL For batch reactor it will be in terms of number of moles (Can we compare it for a CSTR) SELECTIVITY & CONVERSION NOT THE BEST OF FRIENDS!! April 16. Selectivity and Yield . Selectivity and Yield . Selectivity and Yield . Selectivity and Yield . Selectivity and Yield . Selectivity and Yield . Problem (Product Distribution) . Solution . Solution . Solution . Solution . Solution . Problem (Good operating conditions) . Solution . Solution . Solution . Solution . Problem (Best Operating conditions) Based on previous example . Solution . 2013 BITS.Qualitative assessment April 16. K. BIRLA GOA CAMPUS 29 . PILANI – K. Qualitative assessment April 16. 2013 BITS. PILANI – K. BIRLA GOA CAMPUS 30 . K. Qualitative assessment . Qualitative assessment . Qualitative assessment . Contacting patterns . Contacting patterns . Problem . Solution . SOLUTION . Solution Selectivity and Yield desired product , rD=k1CA2CB undesired product , rU=k2CACB Selectivity parameter Run at high concentration of A. Use PFR. April 16, 2013 BITS, PILANI – K. K. BIRLA GOA CAMPUS 40 Parallel reactions A  D (kd) A  U (ku) desired product , rD=kDCA1 undesired product , rU=kUCA2 rA = rD + rU (1 and 2 are positive reaction orders) Objective: rD  and ru  = (kD/kU)CA1 - 2 April 16, 2013 BITS, PILANI – K. K. BIRLA GOA CAMPUS 41 Parallel reactions  Case 1: 1 > 2  Case 1: 1 < 2 Should the reaction be run at high or low temperatures? SD/U~ kD / kU = (AD / AU)e-[(ED  Case 1: ED > EU  Case 1: ED < EU April 16. BIRLA GOA CAMPUS 42 – EU) / RT] . PILANI – K. 2013 BITS. K. 2 &  1-2 are positive and negative April 16. K. BIRLA GOA CAMPUS 43 . 2013 BITS.Parallel reactions desired product . rU=k2CA2CB2 = (k1/k2)CA1 . rD=k1CA1CB1 undesired product .2CB1-2 Depends on whether 1 . PILANI – K. PILANI – K.5 A + B  S + U (k1) dCS/dt = dCU/dt = k1CA0.8 From the standpoint of favourable product distribution. BIRLA GOA CAMPUS 44 .5 CB1.DIY (Contacting Schemes) The desired liquid phase reaction A + B  R + T (k1) dCR/dt = dCT/dt = k1CACB0. K. order the contacting schemes from most desirable to least desirable April 16. 2013 BITS. PILANI – K.Parallel reactions (Problem) Determine the instantaneous selectivity. SD/U. K. for the liquid phase reactions Sketch the selectivity as a function of the concentration of A. 2013 BITS. Is there an optimum and if so what is it? April 16. BIRLA GOA CAMPUS 45 . BIRLA GOA CAMPUS 46 . 2013 BITS. K. PILANI – K.Parallel reactions (Solution) Write the equation for selectivity April 16. 2013 BITS. BIRLA GOA CAMPUS 47 . K.Parallel reactions (What else?)  Selectivity can be calculated  We can now calculate maximize selectivity reactor volume to  We can estimate the temperature at which we can operate the CSTR  We can estimate conversion  Can we increase conversion of desired product? April 16. PILANI – K. Irreversible First Order Reactions in series Rate Equations . Product Distribution .Qualitative discussion. Product Distribution (Series Reactions) .Qualitative discussion. Qualitative discussion.Product Distribution . Product Distribution .Qualitative discussion. Qualitative discussion.Product Distribution . Contacting Patterns . Contacting Patterns . 2013 BITS. K. PILANI – K.Series reactions Here the important variable is space time for a flow reactor and real time for a batch reactor  Case 1: R1 faster than R2  Case 1: R1 slower than R2 April 16. BIRLA GOA CAMPUS 56 . Series reactions April 16. BIRLA GOA CAMPUS 57 . PILANI – K. 2013 BITS. K. 2013 BITS.Series reactions April 16. PILANI – K. K. BIRLA GOA CAMPUS 58 . Series reactions Which gives April 16. BIRLA GOA CAMPUS 59 . 2013 BITS. PILANI – K. K. BIRLA GOA CAMPUS 60 .Series reactions April 16. 2013 BITS. PILANI – K. K. 2013 BITS.Series reactions April 16. BIRLA GOA CAMPUS 61 . PILANI – K. K. PILANI – K. BIRLA GOA CAMPUS 62 .Series reactions Reaction (1) Reaction (2) Species A: Species B: April 16. 2013 BITS. K. we see we arrive back at Equation 1 Now integrating Equation (2) Differentiating the RHS of Equation (2) Evaluating the constant of integration K1 when t = 0 then April 16. 2013 BITS. BIRLA GOA CAMPUS 63 . K.Series reactions Dividing by IF. PILANI – K. PILANI – K.Series reactions When do we stop the reaction to maximize B? What is Xopt? April 16. K. BIRLA GOA CAMPUS 64 . 2013 BITS. BIRLA GOA CAMPUS 65 . PILANI – K. K. 2013 BITS.Series reactions (Quantitative treatment PFR) April 16. Series reactions (Quantitative treatment) April 16. 2013 BITS. BIRLA GOA CAMPUS 66 . PILANI – K. K. Series reactions (Quantitative treatment MFR) April 16. 2013 BITS. K. PILANI – K. BIRLA GOA CAMPUS 67 . 2013 BITS. PILANI – K. K.Series reactions (Quantitative treatment MFR) April 16. BIRLA GOA CAMPUS 68 . PILANI – K.Series reactions (Quantitative treatment MFR) April 16. K. 2013 BITS. BIRLA GOA CAMPUS 69 . BIRLA GOA CAMPUS 70 . K.Series reactions (Quantitative treatment MFR) April 16. PILANI – K. 2013 BITS. Series reactions (Quantitative treatment MFR) April 16. PILANI – K. K. BIRLA GOA CAMPUS 71 . 2013 BITS. 2013 BITS. BIRLA GOA CAMPUS 72 .Series reactions (Quantitative treatment MFR) April 16. PILANI – K. K. Reaction Selection criteria  Selectivity  Yield  Temperature Control  Safety  Cost April 16. 2013 BITS. BIRLA GOA CAMPUS 73 . PILANI – K. K. with k1=0. PILANI – K.Finding the Selectivity For the elementary reaction. April 16. K. BIRLA GOA CAMPUS 74 .1 s-1 and k2=0. Plot the concentration of B and selectivity of B to C as a function of space time in a CSTR.2 s-1 with CAO= 2 mol/dm3. 2013 BITS. PILANI – K.Finding the Selectivity Species Balance on A & B April 16. BIRLA GOA CAMPUS 75 . K. 2013 BITS. PILANI – K. 2013 BITS. April 16. *) at which there is an acceptable molar flow rate of the desired product B from the CSTR. * is the minimum value of V (i. BIRLA GOA CAMPUS 76 .e.Finding the Selectivity Species Balance on C The space time. K. Algorithm for Multiple Reactions FOLLOW THE ALGORITHM April 16. K. 2013 BITS. BIRLA GOA CAMPUS 77 . PILANI – K. PILANI – K. 2013 BITS. BIRLA GOA CAMPUS 78 . K.April 16. 2013 BITS.Mole balance Reactor Type Batch Semi-batch (B added to A) CSTR Gas Phase Liquid Phase PFR PBR April 16. BIRLA GOA CAMPUS 79 . PILANI – K. K. 2013 BITS.Application of the algorithm Example: Liquid Phase Reaction Case 1: PFR (Mole balance for A. B. C and D) April 16. BIRLA GOA CAMPUS 80 . PILANI – K. K. K. 2013 BITS.Application of the algorithm Write the rate laws A+2B-->C 3C+2A-->D April 16. PILANI – K. BIRLA GOA CAMPUS 81 . Application of the algorithm SPECIES A SPECIES B SPECIES C SPECIES D April 16. 2013 BITS. BIRLA GOA CAMPUS 82 . K. PILANI – K. 2013 BITS.Application of the algorithm STOICHIOMETERY SPECIES A SPECIES B SPECIES C SPECIES D April 16. K. PILANI – K. BIRLA GOA CAMPUS 83 . PILANI – K.Application of the algorithm TIME TO USE POLYMATH k1A=0.0 at t=0: V=0. 2013 BITS. CCO=0. CBO=4. CDO=0 THINGS GETTING OUT OF HAND April 16. BIRLA GOA CAMPUS Vf=5 dm3 84 . K. CAO=4.5 k2C=2. 2013 BITS.1 April 16. BIRLA GOA CAMPUS 85 .Polymath Solution . K. PILANI – K. Application of the algorithm Case 2: CSTR : Liquid Phase SPECIES A SPECIES B SPECIES C SPECIES D April 16. PILANI – K. 2013 BITS. K. BIRLA GOA CAMPUS 86 . CC. This formulation leaves us with four equations and four unknowns (CA.Application of the algorithm We will specify V. CB. CBo along with the specific reaction rates kij. BIRLA GOA CAMPUS 87 . April 16. 2013 BITS. K. PILANI – K. and CD). CAo. 3055459 BITS.Polymath Solution .9839539 Cb Cc Cd 1. BIRLA GOA CAMPUS 88 .1900914 0.2 Nonlinear equations [1] f(Ca) = vo*(Cao-Ca)V*(k1a*Ca*Cb^2+2/3*k2c*Ca^2*Cc^3) = 0 [2] f(Cb) = vo*(Cbo-Cb)-V*(2*k1a*Ca*Cb^2) = 0 [3] f(Cc) = -vo*Cc+V*(k1a*Ca*Cb^2-k2c*Ca^2*Cc^3) = 0 [4] f(Cd) = -vo*Cd+V*(k2c*Ca^2*Cc^3)/3 = 0 Explicit equations [1] Cao = 4 [2] Cbo = 4 [3] k1a = 0. K.5 [4] k2c = 2 [5] V = 5 [6] vo = 5 April 16. 2013 Variable Ca Value 1.4883166 0. PILANI – K. Application of the algorithm Case 2: Semi Batch: Liquid Phase SPECIES A SPECIES B SPECIES C SPECIES D V=VO+vOt April 16. PILANI – K. BIRLA GOA CAMPUS 89 . K. 2013 BITS. Polymath Solution . PILANI – K.3 April 16. K. 2013 BITS. BIRLA GOA CAMPUS 90 . BIRLA GOA CAMPUS 91 . PILANI – K. 2013 BITS.Multiple reactions: Gas Phase (PFR) April 16. K. 2013 .Multiple reactions: Gas Phase (PFR) SPECIES A SPECIES B SPECIES C rB = r1B rC = r1C + r2C rD = r2D BITS. PILANI – K. BIRLA GOA CAMPUS 92 SPECIES D April 16. K. k1ACACB2 Reaction (1) A + 2B -> C r1A/-1 = r1B/-2 = r1c/1 r1B = 2r1A r1C = -r1A Reaction (2) 2A + 3B -> D r2A/-2 = r2C/-3 = r2D/1 r2A = (2/3)r2C r2D = -(1/3)r2C April 16. 2013 BITS.Multiple reactions: Gas Phase (PFR) RELATIVE RATES r2C = .k2CCA2CC3 r1A = . K. PILANI – K. BIRLA GOA CAMPUS 93 . BIRLA GOA CAMPUS 94 . K.Multiple reactions: Gas Phase (PFR) Species A Species B Species C Species D (1) (2) (3) (4) April 16. 2013 BITS. PILANI – K. Multiple reactions: Gas Phase (PFR) Stoichiometry Combine Species A Species B Species C Species D April 16. K. BIRLA GOA CAMPUS 95 . 2013 BITS. PILANI – K. PILANI – K.Polymath Solution Initial Conditions Use the Polymath ordinary differential equation solver April 16. BIRLA GOA CAMPUS 96 . K. 2013 BITS. Multiple reactions: Gas Phase (CSTR) All equations apply as do initial conditions A: B: C: D: Total: FT = FA + FB + FC + FD Use the Polymath nonlinear equation solver April 16. PILANI – K. BIRLA GOA CAMPUS 97 . K. 2013 BITS. all the equations mentioned in last few slides apply. BIRLA GOA CAMPUS 98 . K. B. 2013 BITS. April 16. PILANI – K.Practice Problem  Write the net rates of formation for A. C and D (Reactions are elementary) In a CSTR for gas phase. Clarke April 16. Arthur C. PILANI – K. K. a PFR. BIRLA GOA CAMPUS 99   . and a PBR. a semi-batch reactor. a CSTR.Objective Assessment of Chapter   Define different types of selectively and yield Choose the appropriate reactor and reaction system that would maximize the selectivity of the desired product given the rate laws for all the reactions occurring in the system Describe the algorithm used to design reactors with multiple reactions Apply the CRE algorithm to size reactors in order to maximize the selectivity and to determine the species concentrations in a batch reactor. in systems with multiple reactions The only way of finding the limits of the possible is by going beyond them into the impossible. 2013 BITS.