Multiple Reactions. ChE Reactive Process Engineering

Transcription

1 Multiple 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 design L11-1

2 Multiple 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: Conversion (similar to single reactions) X j Selectivity S j Yield Y j L11-2

3 Multiple Reactions So 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 (i.e. sequentially). Let s look at steam cracking of ethane C 2 H 6 -> C 2 H 4 C 2 H 6 -> C 2 H 2 C 2 H -> 2 > 2 C (s) (~ 80 bio. to/a world production!): + H 2 (I) ethene (ethylene) formation + 2 H 2 (II) acetylene formation C 2 H -> 4 > C 2 H 2 + H 2 (III) acetylene formation from ethylene C 2 H 6 +H 2 -> 2 CH 4 (IV) methane formation 3 C 2 H 6 -> C 6 H H 2 (V) benzene formation C 2 H 6 -> 2 C (s) C (s) + 3 H 2 (VI) coke formation + H 2 (VII) coke formation (explosion!) + H 2 O -> > CO + H 2 (VIII) coke gasification We distinguish between parallel reactions and series reactions. L11-3

4 Conversion, Selectivity, Yield L11-4 Simple example: Conversion: Selectivity: Yield: or: X j -> ; -> C S S Y X. S (caveat : note the formulation with mol numbers, not concentrations! -> Why?!) Production rate: F Y F 0 (and similar for C) Typically, selectivity is is the crucial quantity! preferred form! (remark : you must be sure that you know all products!) Why?

5 Selectivity: Complications Selectivity: S N N ν N,0,0 Example: ndrussov process (HCN synthesis) 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: S HCN,CH 4 ν N Definition ambiguous if product formed from more than one reactant! S HCN,NH 3 (1) (2) (3) L11-5 Selectivity needs a reference point!

6 S i : even more problems Selectivity: What if I don t know the reaction equations (hence no ν i!)? (Often the case for very complex reactant mixtures, networks of many parallel and series reactions!) (Simplified) Example: S Methane Coupling 2 CH / 2 O 2 <> C 2 H 6 + H 2 O (1) CH O 2 > CO H 2 O (2) ssume equal amounts of methane react along (1) & (2): 1 mol CH 4 -> 0.25 mol C 2 H mol CO 2. If we did not know the reaction equations we might be tempted to calculate: S C n C / (n C + n CO2 ) 0.25 / / 3. ut we reacted equal amounts of CH 4 along both pathways: shouldn t S C 0.5?! atom selectivity : S ji, L11-6

7 Selectivity: one last slide L11-7 differential selectivity: dn dn lso called instantaneous selectivity in batch reactors S S or local selectivity in (plug) flow reactors: S nd for once we can also use concentrations! ( Why?? ) S dn ν ν ν dn ν Example reaction: -> -> C

8 Selectivity: Parallel Reactions L11-8 Let s look at a reactant, which can form a desired product D, and an undesired side-product U in parallel reactions. Cost ($$$) D U Two problems: repair of low S generally not possible undesired side-product usually needs to be separated Total Cost Reactor Cost Separations Cost Conversion (X)

9 Parallel Reactions: Selectivity II Differential Selectivity: (I) d > u (II) d < u (III) E D < E U D U r D k D C d r U k U C u k 0,D exp{-e D /RT} C d k 0,U exp{-e U /RT} C u S ν D r D / (ν( D r D + ν U r U ) (S ) ν U r U /ν D r D (S ) -1 ~ ν D /ν U r U /r D ν DU k 0U /k 0D exp{-(e U -E D )/RT} C (u-d) S ~ exp{-(e D -E U )/RT} C (d-u) S increases with S increases with S decreases with PFR (R) > CSTR no dilution high pressure CSTR or PFR w/high recycle dilution low pressure L11-9 (IV) E D > E U S increases with

10 Differential and Total S Parallel reactions, different rctn orders (Reactor) Selectivity: S D Local selectivity: S D - For V const. k 1 k 2 D U r 1 k 1 C d r 2 k 2 C u Hence we calculate N D : N (or equivalently with F j!). D e F 1 S S df D D F0 Fe F0 Fe F e 1 S S dc D D C0 Ce C C 0 F 0 L total total S integral integral average average of of local local S

11 PFR vs CSTR S D 1 e 1 S S dc D D C0 Ce C C e d < < u S D C 0 C 0 C If rctn order of desired reaction > rctn order of side reaction, PFR better, otherwise CSTR better S D 1 C e d > > u C 0 C L11-11 Why?

12 Parallel Reaction Networks More interesting case: Network of many parallel reactions, some with higher r.o., some with lower r.o. than desired reaction Optimum yield for CSTR first, followed by PFR S D (Exact shape of S -C curve, and hence also precise sizing of reactors is dependent on specific network!) 1 C e C 0 C L

13 Conversion in Multireaction Systems Let s again consider the simple parallel reaction system: ->, r 1 k 1 C -> C, r 2 k 2 C How can we express the concentrations C, C, C C in terms of X? We can t at least not directly! We have to distinguish between X,1 and X,2! While we still can define a X (N 0 N )/N 0, we have to distinguish between the different pathways to do our book-keeping (i.e. mass balances) for and C: : C: : C C 0 X,1 C C C 0 X,2 C but also: C Everything else remains unchanged we now simply have one more quantity to keep track of, i.e. the different X ji! L

14 Series Reactions: Selectivity (lmost) all oxidation reactions follow a sequence of successively deeper oxidation. Example: Ethane oxidation C 2 H 6 + ½ O 2 -> C 2 H 4 + H 2 O (oxidative dehydrogenation) C 2 H 4 + O 2 -> 2 CO + 2 H 2 (syngas formation) CO + H 2 + O 2 -> CO 2 -> -> C Very common: partial vs total oxidation reactions + H 2 O (combustion) Let s assume a PFR for -> -> C, with 1 st order kinetics: r, r Plugging this into the PFR design equation, we get: C ( ) τ C ( τ ) Check the derivation in the textbook (p. 160ff)! You should be able to derive this yourself. L C ( ) C τ So, what does this look like?

15 Series Reactions: CSTR What about the same series reaction in a CSTR? (Same procedure: rate laws into design equation, substitute C 0 and C C0 by expressions in terms of C 0 ) C C C C kτ C So, what does this look like? How is it different from a PFR? C C 2 k k τ For For series series reactions, there there is is always always an an optimum residence time time to to achieve a maximum yield yield towards the the intermediate product For For positive order order kinetics, the the optimum yield yield in in the the PFR PFR is is always always greater than than that that in in a CSTR CSTR L How can we rationalize this? How about the R?

16 Series Rctns - Maximum Yield Maximum in C -> optimum in residence time! How can I calculate the optimum? Look for dc /dτ 0! Do it for the PFR! PFR: (log mean rate constant) -1 conc. conc. [a.u.] [a.u.] PFR vs CSTR: Series Reaction PFR vs CSTR: Series Reaction time time [a.u.] [a.u.] CSTR: (geometric mean rate constant) -1 - PFR - PFR - PFR - PFR C - PFR C - PFR - CSTR - CSTR - CSTR - CSTR C - CSTR C - CSTR L What if C and not is the desired product?

17 Example: We wish to produce a product from a reactant in a PFR with V 4 l/min (a) (b) and C 0 2 mol/l. However, another reaction is also occurring, forming an undesired product C. (oth reactions are irreversible, 1 st order, with k 0.5 min -1 and k C 0.1 min -1 ). ssuming a series reaction -> -> C, calculate the maximum achievable yield of, as well as the necessary reactor volume. ssuming parallel reactions -> and -> C, calculate the reactor volume necessary to achieve the same conversion of as in (a). What is the yield of in this case? Procedure: (a) Calculate τ opt, from there C (τ opt ) and C (τ opt ). From these you obtain S,max and X,max. (b) Calculate τ(x 0.865), from there: V l. l With τ from the equation for C in a PFR/series reactions L Check it it in in LDS, examples and 4-3, 4 incl. the CSTR case!