First-order reactions ation for a system of Nequal-size mixed reactors i For ith vessel :; Co=业CX,-X) Vo 一rAi Fore =0 Col(1-Ci/C)-(1-C/C)] kC C--C or kC C2=1+k虹 The sizes are equal,so all are same. 16
16 • First-order reactions ( ) ( ) ( ) The sizes are equal, so all are same. 1 1 1 For 0 For ith vessel : i 1 1 0 0 1 0 0 1 0 0 0 i i i i i i i i i A i i i i i i k C C or k C C C k C C C i C C C ε r C X X v V F C V = + − = − − − = = − − = = = − − − −
CN =Co(1-XN) definition Therefore Co CL...CxL=+kt,) C N 1-Xy% Ci C2 ae:w-gr If N->oo reduce to the plug flow 1, Ir-knC In- 17
17 ( ) C C k τ C C k N N k C C C C C C C X C P N N i N i N N N N 0 1 0 N reactors 1 2 1 1 0 0 ln 1 If N reduce to the plug flow Rearrangin g 1 1 1 1 Therefore = → − = = = = + − = − CN = C0 (1− X N ) definition
Use L'Hospital's law m ()-a'ha C C0Tp 18
18 ( ) ( ) ( ) p N 0 2 N 0 2 N 1 N 0 x x N 1 N 0 N N 1 N 0 N C C k 1 N 1 k 1 C C N 1 1 C C a a a N 1 k 1 C C 1 C C k N = = − − = = − = − → → ln ln lim lim ln Use L'Hospital' slaw
30 First-order reaction kT= 50 10 N=1 20 10 8 N=2 N=3 N=4 W=6 -N=∞N=10 0.01 0.1 1-XA-CAO CA Figure 6.5 Comparison of performance of a series of N equal-size mixed flow reactors with a plug flow reactor for the first-order reaction 19 A→R,ε=0
19
Second-order reactions With the same per-condition and same procedure,the performance of a second- order bimolecular-type reaction with no excess of either reactant can be found -2+21+2y1214h whereas for plug flow 是-1+C知 20
20 • Second-order reactions • With the same per-condition and same procedure, the performance of a secondorder bimolecular-type reaction with no excess of either reactant can be found P i i N C k N k k C k C 0 0 0 1 C C whereas for plug flow 1 2 1 2 1 4 2 2 4 1 = + − + − + + = − +