Multiple Reactions - University of Pittsburgh

1 L11L11--11 ChE 400- Reactive Process EngineeringChEChE400400--Reactive Process EngineeringReactive Process EngineeringMultiple Reactions We have largely considered single Reactions so far in this class How many industrially important processes involve a single reaction? The job of a chemical engineer is therefore to designL11L11--22 ChE 400- Reactive Process EngineeringChEChE400400--Reactive Process EngineeringReactive Process EngineeringMultiple Reactions We need to develop tools that will allow us to quantify how well (or how poorly) we are doing at producing a desired product There are three concepts that we need to develop for Multiple Reactions .

2 Conversion (similar to single Reactions ) Xj= Selectivity Sj= Yield Yj= L11L11--33 ChE 400- Reactive Process EngineeringChEChE400400--Reactive Process EngineeringReactive Process EngineeringCC22HH2 2 --> 2 > 2 CC(s(s))+ H+ H2 2 (VII) coke formation (explosion!)(VII) coke formation (explosion!) Multiple ReactionsSo far, we have exclusively looked at simple system with only one reaction occuring. However, many reaction systems of practical relevance involve many Reactions occuring at the same time, either in parallel or in series ( sequentially).Let s look at steam cracking of ethanesteam cracking of ethane(~ 80 bio.)

3 To/a world production!):C2H6 -> C2H4+ H2 (I) ethene (ethylene) formation C2H6 -> C2H2+ 2 H2 (II) acetylene formation CC22HH4 4 --> C> C22HH22+ H+ H2 2 (III) acetylene formation from ethylene (III) acetylene formation from ethylene C2H6 +H2-> 2 CH4(IV) methane formation3 C2H6 -> C6H6+ 6 H2 (V) benzene formationC2H6 -> 2 C(s)+ 3 H2 (VI) coke formationCC(s(s))+ H+ H22OO--> CO + H> CO + H2 2 (VIII) coke gasification(VIII) coke gasificationWe distinguish between parallel reactionsand series 400- Reactive Process EngineeringChEChE400400--Reactive Process EngineeringReactive Process EngineeringConversion, Selectivity, YieldConversion:jX=Simple example:A -> B; A -> CBS=Selectivity:(remark :you mustbe sure that you know all products!

4 Or:BS=preferred form !Yield:YB= , selectivityis the crucial quantity!Typically, selectivityselectivityis the crucial quantity!(caveat : note the formulation with mol numbers, not concentrations! -> Why?!)Production rate:FB = YBFA0(and similar for C)Why?L11L11--55 ChE 400- Reactive Process EngineeringChEChE400400--Reactive Process EngineeringReactive Process EngineeringExampleExample::AndrussovAndr ussovprocess process (HCN synthesis) (1)(2)(3)Conversions of methane and ammonia can be very different. Extent to which reaction proceeds via (2) or (3) rather than (1) will be different. Hence:SSHCN,CHHCN,CH44 SSHCN,NHHCN,NH33 Selectivity: ,0,0 BBABBAANNSNN = Selectivity:Selectivity needs a reference point!

5 Selectivity needs a reference point! Definition ambiguous if product formed from more than one reactant! L11L11--66 ChE 400- Reactive Process EngineeringChEChE400400--Reactive Process EngineeringReactive Process EngineeringSi: even more (Simplified) Example(Simplified) Example::Methane CouplingMethane Coupling2 CH4+ 1/2O2<=>C2H6+ H2O(1)CH4+ 2 O2=> CO2+ 2 H2O(2)Assume equal amounts of methane react along (1) & (2): 1 mol CH4-> mol C2H6+ mol we did not know the reaction equations we might be tempted to calculate: SC== nC=/ (nC=+ nCO2) = / = 1 we reacted equal amounts of CH4along both pathways: shouldn t SC== ?

6 !What if I don t know the reaction equations (hence no i!) ? (Often the case for very complex reactant mixtures, networks of many parallel and series Reactions !) BS=Selectivity: atom selectivity :, jiS=L11L11--77 ChE 400- Reactive Process EngineeringChEChE400400--Reactive Process EngineeringReactive Process EngineeringSelectivity: one last differential selectivity: BS =Also called instantaneous selectivity in batch = ..or local selectivity in (plug) flow reactors: BS =And for once we can also use concentrations!

7 BABABdNSdN = =( Why ?? )( Why ?? )Example reaction:A -> B -> CL11L11--88 ChE 400- Reactive Process EngineeringChEChE400400--Reactive Process EngineeringReactive Process EngineeringSelectivity: Parallel ReactionsADULet s look at a reactant, which can form a desired product D, and an undesired side-product U in parallel (X)Cost ($$$)Total CostSeparations CostReactor CostTwo problems: repair of low S generally not possible undesired side-product usually needs to be separatedL11L11--99 ChE 400- Reactive Process EngineeringChEChE400400--Reactive Process EngineeringReactive Process EngineeringParallel Reactions .

8 Selectivity IIADUrD= kDCAd= k0,Dexp{-ED/RT} CAdrU= kUCAu= k0,Uexp{-EU/RT} CAu(S )-1~ D/ UrU/rD= DUk0U/k0 Dexp{-(EU-ED)/RT} CA(u-d)S ~S ~exp{exp{--(E(EDD--EEUU)/RT} )/RT} CCAA(d(d--uu)) PFR (BR) > CSTR no dilution high pressure(I) d > uS increases with CSTR or PFR w/high recycle dilution low pressure(II) d < uS increases with(III) ED < EUS decreases with(IV) ED > EUS increases withS = S = DDrrDD/ (/ ( DDrrDD+ + UUrrUU))(S )(S )--11= 1 + = 1 + UUrrUU// DDrrDDDifferentialSelectivity:L11L11--10 10 ChE 400- Reactive Process EngineeringChEChE400400--Reactive Process EngineeringReactive Process EngineeringDifferential and Total SParallel Reactions ,different rctn ordersADUk1k2Ar1= k1 CAdr2= k2 CAu(Reactor) Selectivity:SD=LocalLocalselectivity:SD = -0001 AeAFBDDAAAeA AeFFSSdFFFF F == For V = = total S = integral average of local Stotal S = integral average of local Stotal S = integral average of local S DN=Hence we calculate NHence we calculate NDD::(or equivalently with Fj!)

9 L11L11--1111 ChE 400- Reactive Process EngineeringChEChE400400--Reactive Process EngineeringReactive Process EngineeringPFR vs CSTRSD CACA0 CAe1SD CACA0 CAe1If If rctnrctnorder of desired reaction > order of desired reaction > rctnrctnorder of side reaction,order of side reaction,PFR better, otherwise CSTR betterPFR better, otherwise CSTR betterWhy?Why?001 AeACDDAAAeCSSdCCC = SD =d < u d < u d > u d > u L11L11--1212 ChE 400- Reactive Process EngineeringChEChE400400--Reactive Process EngineeringReactive Process EngineeringParallel Reaction NetworksMore interesting case:Network of many parallel Reactions ,some with higher , some with lower than desired reactionOptimum yield for CSTR first,Optimum yield for CSTR first,followed by PFRfollowed by PFR(Exact shape of S -CAcurve, and hence also precise sizing ofreactors is dependent on specific network!)

10 SD CACA0 CAe1L11L11--1313 ChE 400- Reactive Process EngineeringChEChE400400--Reactive Process EngineeringReactive Process EngineeringConversion in Multireaction SystemsLet s again consider the simple parallel reaction system:A -> B, r1= k1 CAA -> C, r2= k2 CAHow can we express the concentrations CA, CB, CCin terms of XA?We can t at least not directly! We have to distinguish between XA,1and XA,2!While we still can define a XA= (NA0 NA)/NA0, we have to distinguish between the different pathways to do our book-keeping ( mass balances) for B and C:CB= CA0XA,1CC= CA0XA,2CA=but also:but also:CA=Everything else remains unchanged we now simply have one more quantity to keeptrack of, the different Xji!