PHEN 612 SPRING 2008 WEEK 1 LAURENT SIMON

PHEN 612 SPRING 2008 WEEK 1 LAURENT SIMON

Chapter 1 * 1.1 Rate of reactions r A A+B->C Species A, B, and C We are interested in the rate of disappearance of A The rate of reaction, ra, is the number of moles of A reacting per unit time per unit volume (mole/s.m 3 ). * Elements of Chemical Reaction Engineering Fourth Edition by H. Scott Fogler, Prentice Hall, 2006

Chapter 1 For heterogeneous system, r A [mole/s.g catalyst). The rate law for r is independent of the type of reactor used: f(t,p,type of catalyst, position) The rate law is an algebraic expression (ex: -r A = k.c A ) > based on experiments. Convention: r A : rate of formation or generation of A; -r A : rate of disappearance of A

Chapter 1 1.2 The general mole balance equation Fo Accumulation = input output + generation ( ) d N dt G F = F F + G o If one assumes uniformity in the control volume: G =r.v (moles/time = moles/(time.volume).volume

Chapter 1 In general: Δ Gi = riδvi r 1 r 2 r i V Total rate of generation: In the limit: G V = rdv M M G = Δ G = r ΔV i i i i= 1 i= 1 ( ) d N dt d N = F F + G o V ( ) dt = Fo F + rdv We need to estimate the time (batch) or reactor volume (continuous flow) necessary to convert a desired amount of reactants into product.

Chapter 1 1.3 Batch reactors: Constant volume, no flow in, no flow out ( ) d N dt = rv t 1 = N N A0 A1 dn A rv A Time t 1 is the time necessary to reduce the # of moles from N A0 to N A1. Also the time to form N B1 moles of B 1.4 Continuous-flow reactors: CSTR; PFR; PBR

Chapter 1 1.4.1Continuous stirred tank reactor F (CSTR) 0 V ( ) d N dt = Fo F + rdv Assuming steady-state operation: d(n )/dt = 0 No spatial variation in the reaction rate (i.e., perfect mixing): F0 F V = r Remember: F =C v F V = C v 0 0 r C v

Chapter 1 1.4.1 Tubular reactor F 0 ΔV ΔG V V+ΔV F V ( ) d N dt = Fo F + rdv Input-output + generation = 0 F F r V V V +ΔV + Δ = 0 F V +ΔV FV ΔV = r df dv = r V 1 F df = = F F 0 1 r F 1 0 df r V 1 is the volume necessary to reduce the entering molar flow rate from F 0 to F 1

Chapter 1 1.4.3 Packed-bed reactor F 0 ΔW ΔG F W W+ΔW W ( ) ' d N dt = Fo F + rdw Input-output + generation = 0 F F r W ' W W +ΔW + Δ = 0 F W +ΔW FW ' = r ΔW df ' dw = r W F0 F1 df df 1 = = ' ' r F r F 1 0 W 1 is the catalyst necessary to reduce the entering molar flow rate F 0 to F 1

Chapter 1 1.5 Industrial reactors Liquid-phase reactions (Batch and CSTR) Gas-phase reactions (PFR and PBR). Fluidized-bed reactors are also used.

Chapter 2 * Conversion and reactor sizing 2.1 Defining conversion aa+bb->cc+dd A: basis of calculation A+(b/a)B->(c/a)C+(d/a)D per mole of A basis A is the limiting reactant X A = (moles of A reacted)/(moles of A fed) *Elements of Chemical Reaction Engineering Fourth Edition by H. Scott Fogler, Prentice Hall, 2006

Chapter 2 2.2 Batch reactor design equation t=0--->n A0 ; t--->n A0 X N A = N A0 -N A0 X= N A0 (1-X) N A0 dx dt = rv A In terms of concentration, we use N A = C A V ---> dc A /dt = r A t = N X A0 0 dx rv A

Chapter 2 2.5 CSTRs in series X i = (total moles of A reacted up to point i)/ (moles of A fed to the first reactor) F A1 F A2 F A0 i=1 X 1 i=2 Two CSTRs in series: V 1 V 2 X 2 Should we use 2 reactors: V 1 and V 2 Or ust one reactor V 1 +V 2? Reactor 1: input output + generation = 0 F A0 F A1 + r A1 V 1 = 0 But F A1 = F A0 F A0 X 1 As a result V 1 = F A0 (1/-r A )X 1 Reactor 2: input output + generation = 0 F A1 F A2 + r A2 V 2 = 0 As a result V 2 = F A0 (1/-r A )(X 2 X 1 )

Chapter 3 * Rate laws and Stoichiometry Basic definitions Homogeneous reaction: one phase Heterogeneous reaction: more than one phase Irreversible reaction: Reversible reaction: Unimolecular: involving one atom (or molecule) Bimolecular: two atoms (or molecules) Termolecular: Three atoms *Elements of Chemical Reaction Engineering Fourth Edition by H. Scott Fogler, Prentice Hall, 2006

Chapter 3 3.1.1 Relative rates of reaction A+(b/a)B->(c/a)C+(d/a)D For every mole of A consumed, c/a moles of C appear. Rate of formation of C = (c/a) rate of disappearance of A: r C = (c/a) (-r A ) = -(c/a) r A Also: r C = (c/d) (r D ) In general: (-r A /a) = (-r B /b) = (r C /c) = (r D /d) 3.2 Reaction order and rate law r = k T f C, C,... ( ) ( ) A A A B This is called a kinetic expression or a rate law

Chapter 3 3.2.1 Power law model and elementary rate laws r k C α C β A A A B = The order of a reaction: the power to which the concentrations are raised in the rate law. The reaction is α order with respect to reactant A The reaction is β order with respect to reactant B N = α+β is the overall order of the reaction Units: -r A (concentration/time) k A (vary with the reaction order) 3 Ex: ra = kaca k A (dm 3 /mol) 2.s -1

Chapter 3 Elementary reaction involves a single step. The stoichiometric coefficients are identical to the power in the rate law. 2NO + O 2NO 2 2 2 r = kc C NO NO O2 3.2.2 Non elementary rate laws A large number of both homogeneous and heterogeneous reactions do not follow single reaction lawsphosgene: carbonyl dichloride 3/2 - Homogeneous: CO + Cl 2 -> COCl 2 rco kccoccl 2 - Heterogeneous: C 6 H 5 CH 3 + H 2 -> C 6 H 6 + CH 4 Methane: M Solid cat Toluene: T Benzene: B = gas phase 2 r = K and K are absorption rate constants + + B T T 1 kp P H K P T K P B B T T

Chapter 3 3.2.3 Reversible reactions aa + bb cc + dd K C C = Thermodynamic equilibrium (e) relationship c d Ce De c a b CAeCBe k Unit of K c : (mol/dm 3 ) d+c-b-a B 2CH 6 6 C12H10 + H k 2 B benzene diphenyl How do we derive rate laws? kb 2B D+ H k 2 B Forward: 2 2 rb, f kbcb; rb, f kbcb Reverse: r rb, r = k BCBC B =r B,net =r B,f +r B,r H2 Concentration equilibrium constant 2 k CC B 2 D H k 2 rb = kb CB CDCH ; r ; 2 B = kb CB Kc = k K k = = B c B B

Chapter 3 Kc as T for exothermic reaction Kc as T for endothermic reaction Keep in mind that (-r A /a) = (-r B /b) = (r C /c) = (r D /d) r r k CC 2 D H k 2 D B B B = = CB ; kd = 1 2 2 Kc 2 This is why we need to define a rate constant in term of particular species CDeC At equilibrium: 2 Kc = 2 C Be H e ΔH RX 1 1 Kc( T) = Kc( T1 ) exp R T1 T ΔH RX : heat of reaction

Chapter 3 3.3 The reaction rate constant k T = Ae A ( ) E/( RT) A: pre-exponential factor or frequency factor E: activation energy in J/mol, cal/mol R: gas constant = 8.314 J/mol.K = 1.987 cal/mol.k T: absolute temperature in K Arrhenius equation E: energy to break bonds and overcome repulsion forces between reactants reaction coordinate helps to visualize the process. E 1 ln ka = ln A R T R T0 ( ) = ( ) k T k T e 1 1 T Energy distribution of reactant molecules: compare fraction of collisions at two different temperatures. As the temperature increases, more molecules have sufficient energy to react. 0 E