Chapter 6 Design for Single Reaction In this chapter we deal with single reaction.These are reactions whose progress can be described and followed adequately by using one and only one rate expression coupled with the necessary stoichiometric and equilibrium expressions. For such reactions product distribution is fixed; hence,the important factor in comparing design is the reactor size
1 Chapter 6 Design for Single Reaction In this chapter we deal with single reaction. These are reactions whose progress can be described and followed adequately by using one and only one rate expression coupled with the necessary stoichiometric and equilibrium expressions. For such reactions product distribution is fixed; hence, the important factor in comparing design is the reactor size
6.1 Size Comparison of Single Reactors ·Batch reactor Batch reactor has the advantage of small instrumentation cost and flexibility of operation.It has the disadvantage of high labor and handling cost,often considerable shutdown time to empty,clean out,and refill,and poorer quality control of the product. 2
2 6.1 Size Comparison of Single Reactors • Batch reactor • Batch reactor has the advantage of small instrumentation cost and flexibility of operation. It has the disadvantage of high labor and handling cost, often considerable shutdown time to empty, clean out, and refill, and poorer quality control of the product
Regarding reactor size,for a given duty and a constant volume system,an element of fluid reacts for the same length of time in the batch and in the plug flow reactor.Thus, the same volume of these reactors is needed to do a given job. On a long-term production basis we must correct the size requirement estimate to account for the shutdown time between batches. 3
3 • Regarding reactor size, for a given duty and a constant volume system, an element of fluid reacts for the same length of time in the batch and in the plug flow reactor. Thus, the same volume of these reactors is needed to do a given job. • On a long-term production basis we must correct the size requirement estimate to account for the shutdown time between batches
Mixed versus plug flow reactor,first-and second-order reaction Make a comparison for large class of reactions approximated by the simple nth- order rate law: w-张-c where n varies anywhere from zero to three.For mixed flow Eq.5.11 gives Tm CAOY CAoXA=1 XA(1+EAXA) FA0m-TA kCAo(1-XA)” whereas for plug flow Eq.5.17 gives 4
4 • Mixed versus plug flow reactor, first- and second-order reaction • Make a comparison for large class of reactions approximated by the simple nthorder rate law:
Dividing we find that (TCAO)m .[x+l (1) (TCAO)p 。ix With constant density,or s =0,this expression integrates to XA (TCAO)m n卡1 (rCX)p 可 or (2) n=1 (TCAO )p -In(1-XA)p 5
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100 。 Third order(n=3) Second order (n=2) =2 EA =1 0 1 223 10 First order and() (n=1) 1 0 2 n 0.5 n=0.25 1 0.01 0.1 1.0 6 1-XA
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For n=2 (1-X4” m XA --x广- 、n-1 XA X 1-X4)-1-X1-X1-1-X》1-x 7
7 ( ) ( ) ( ) ( ) ( ) (( ) ) ( ) ( ) ( )( ( )) A A A A A A A A A A p n A m n A A p n A m n A X X X X X X X X X X n X X X C C n − = − − − = − − − = − − − = − − − − = = − − − − 1 1 1 1 1 1 1 1 1 1 1 1 1 1 For 2 2 1 1 2 1 0 1 0
Above figure shows 1.For any particular duty and for all positive reaction orders the mixed reactor is always larger than the plug flow reactor.The ratio of volumes increases with reaction order. 2.When conversion is small,the reactor performance is only slightly affected by flow type.The performance ratio increases very rapidly at high conver- sion;consequently,a proper representation of the flow becomes very impor- tant in this range of conversion. 3.Density variation during reaction affects design;however,it is normally of secondary importance compared to the difference in flow type. Remember that the essential factor for reactor size is reaction rate, which is controlled only by concentration of reactant A,besides temperature. The order of reaction,conversion,expansion factor are all related to concentration. 8
8 Above figure shows Remember that the essential factor for reactor size is reaction rate, which is controlled only by concentration of reactant A, besides temperature. The order of reaction, conversion, expansion factor are all related to concentration
Variation of reactant ratio for second-order reaction A+B->products,M=CBo/CAo (3.13) 一rA=-rB=KCACB behave as second-order reactions of one component when the reactant ratio is unity.Thus -rA=kCACB=kC when M=1 (3) On the other hand,when a large excess of reactant B is used then its concentration does not change appreciably(Ca=CBo)and the reaction approaches first-order behavior with respect to the limiting component A,or -rA kCACB =(kCBO)CA =k'CA when M>1 (4) Thus in Fig.6.1,and in terms of the limiting component A,the size ratio of mixed to plug flow reactors is represented by the region between the first-order and the second-order curves
9 • Variation of reactant ratio for second-order reaction
·General graphical comparison ·For a nth-order Any rate curve reaction(n>0),it can be seen that Area Tm/CAO mixed flow Area Tp/CAO always needs a larger volume than does plug XA flow for any Figure 6.2 Comparison of performance of mixed flow and plug flow reactors for any reac- given duty. tion kinetics. 10
10 • General graphical comparison • For a nth -order reaction(n>0), it can be seen that mixed flow always needs a larger volume than does plug flow for any given duty
