Lecture 4 Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of chemical reactions and the design of the reactors in which they take place. Lecture 4 – Tuesday 1/18/2011 Block 1 Size CSTRs and PFRs given –rA=f(X) Block 2 Reaction Orders Arrhenius Equation Block 3 Stoichiometric Table Definitions of Concentration Calculate the Equilibrium Conversion, Xe 2 Review Lecture 2 Reactor Differential Algebraic Integral X X Batch N A0 V CSTR PFR dX t N A0 rAV 0 dX r AV dt dX FA0 rA dV t FA0 X rA X V FA0 0 dX rA X PBR 3 dX FA0 rA dW X W FA 0 0 dX rA W Review Lecture 2 FA 0 rA X Review Lecture 2 Area = Volume of PFR FA 0 rA V X1 X1 0 FA 0 d X rA Review Lecture 2 moles of A reacted up to point i Xi moles of A fed to first reactor Only valid if there are no side streams 6 Review Lecture 2 7 Review Lecture 2 Two steps to get Step 1: Rate Law rA gC i Step 2: Stoichiometry Ci hX Step 3: Combine to get rA f X rA f X Review Lecture 3 Power Law Model α order in A rA kCACB β order in B OverallRectionOrder α β 2A B 3C A reactor follows an elementary rate law if the reaction orders just happens to agree with the stoichiometric coefficients for the reaction as written. e.g. If the above reaction follows an elementary rate law rA k AC2ACB 9 2nd order in A, 1st order in B, overall third order Review Lecture 3 k Ae E = Activation energy (cal/mol) E RT T k A k R = Gas constant (cal/mol*K) T T = Temperature (K) A = Frequency factor (same units as rate constant k) order) (units of A, and k, depend on overall reaction 10 T 0 k 0 A 1013 Review Lecture 3 Mole Balance Rate Laws These topics build upon one another 11 Stoichiometry Review Lecture 3 rA f X Step 1: Rate Law Step 2: Stoichiometry Step 3: Combine to get 12 rA gCi Ci hX rA f X We shall set up Stoichiometry Tables using species A as our basis of calculation in the following reaction. We will use the stochiometric tables to express the concentration as a function of conversion. We will combine Ci = f(X) with the appropriate rate law to obtain -rA = f(X). b c d A B C D a a a A is the limiting Reactant. 13 NA NA 0 NA 0 X For every mole of A that react, b/a moles of B react. Therefore moles of B remaining: N B 0 b b N B N B 0 N A 0 N A 0 X a N A 0 a Let ΘB = NB0/NA0 Then: 14 b N B N A 0 B X a c c NC NC 0 N A 0 X N A 0 C X a a Species Symbol Initial Change Remaining A A NA0 -NA0X NA=NA0(1-X) B B NB0=NA0ΘB -b/aNA0X NB=NA0(ΘB-b/aX) C C NC0=NA0ΘC +c/aNA0X NC=NA0(ΘC+c/aX) D D ND0=NA0ΘD +d/aNA0X ND=NA0(ΘD+d/aX) Inert I NI0=NA0ΘI ---------- NI=NA0ΘI FT0 NT=NT0+δNA0X N i 0 Ci 00 Ci 0 yi 0 and d c b 1 Where: i a a a N A0 C A00 C A0 y A0 15 δ = change in total number of mol per mol A reacted Note: If the reaction occurs in the liquid phase or if a gas phase reaction occurs in a rigid (e.g. steel) batch reactor Then V V0 N A N A 0 1 X CA CA 0 1 X V V0 16 N B N A 0 b b CB B X CA 0B X V V0 a a etc. Suppose rA kA CA2 CB Batch: V V0 rA k A CA 0 2 b 1 X B X a Equimolar feed: B 1 Stoichiometric feed: b B a 17 2 if rA kA CA2 CB then rA CA 0 3 b 1 X B X ConstantVolume Batch a 2 and we have r f X A 18 1 rA X Calculating the equilibrium conversion for gas phase reaction,Xe Consider the following elementary reaction with KC=20 dm3/mol and CA0=0.2 mol/dm3. Xe’ for both a batch reactor and a flow reactor. 2A B 2 CB rA k A CA K C 19 Calculate Xe CA0 0.2 mol dm 3 KC 20 dm3 mol dX rAV dt NA 0 Step 2: rate law, rA k AC2A k BCB Step 1: 20 2 CB rA k A CA KC kA KC kB Calculate Xe Symbol Initial Change Remaining A NA0 -NA0X NA0(1-X) B 0 ½ NA0X NA0 X/2 Totals: NT0=NA0 NT=NA0 -NA0 X/2 @ equilibrium: -rA=0 CBe Ke 2 CAe 21 C Be 0C KC 2 Ae NAe CAe CA 0 1 X e V Xe CBe CA 0 2 Calculating the equilibrium conversion for gas phase reaction Solution: At equilibrium Stoichiometry Constant volume Batch Species A B 22 2 C Be rA 0 k A C Ae K C C Be KC 2 C Ae A B/ 2 V V0 Initial NA0 0 NT0=NA0 Change -NA0X +NA0X/2 Remaining NA=NA0(1-X) NB=NA0X/2 NT=NA0-NA0X/2 Xe CA0 Xe 2 Ke 2 2 CA 0 1 X e 2CA 0 1 X e 2K e C A 0 Xe 2200.2 8 2 1 Xe X eb 0.703 23 Flow System Stochiometric Table Species Symbol Reactor Feed Change 24 Reactor Effluent A A FA0 -FA0X FA=FA0(1-X) B B FB0=FA0ΘB -b/aFA0X FB=FA0(ΘB-b/aX) Where: i Fi0 Ci0 0 Ci0 y i0 FA 0 CA 0 0 CA 0 yA 0 Flow System Stochiometric Table Species Symbol Reactor Feed Change C C FC0=FA0ΘC +c/aFA0X FC=FA0(ΘC+c/aX) D D FD0=FA0ΘD +d/aFA0X FD=FA0(ΘD+d/aX) Inert I FI0=A0ΘI ---------- FT0 FA 0 and C A 0 0 FI=FA0ΘI FT=FT0+δFA0X Where: i Fi 0 Ci 0 0 Ci 0 yi 0 25 Reactor Effluent CA 0 yA0 d c b 1 a a a FA Concentration – Flow System C A Species Symbol Reactor Feed Change Reactor Effluent A A FA0 -FA0X FA=FA0(1-X) B B FB0=FA0ΘB -b/aFA0X FB=FA0(ΘB-b/aX) C C FC0=FA0ΘC +c/aFA0X FC=FA0(ΘC+c/aX) D D FD0=FA0ΘD +d/aFA0X FD=FA0(ΘD+d/aX) Inert I FI0=FA0ΘI ---------- FI=FA0ΘI FT0 Where: 26 i Fi 0 C C y i0 0 i0 i0 FA 0 CA 0 0 CA 0 y A 0 Concentration – Flow System C A FT=FT0+δFA0X and FA d c b 1 a a a Concentration Flow System: C A Liquid Phase Flow System: CA FA FA 0 1 X 0 FA 0 CA 0 1 X Flow Liquid Phase N A 0 b b CB B X CA 0B X 0 a a NB etc. We will consider CA and CB for gas phase reactions in the next lecture 27 Heat Effects Isothermal Design Stoichiometry Rate Laws Mole Balance 28 End of Lecture 4 29