Comparing the value of the reaction rate group for N=1 and N=2,we find (kCTN=2=TN2=(V/uN2=27.5 (kCoT)N-1 TN-1 (V/U)N-1 90 Since VN-2 2VN=1 the ratio of flow rates becomes N2=90 uv127.5(2)=6.6 Thus,the treatment rate can be raised to 6.6 times the original. Note.If the second reactor had been operated in parallel with the original unit then the treatment rate could only be doubled.Thus,there is a definite advantage in operating these two units in series.This advantage becomes more pronounced at higher conversions. 26
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Mixed flow reactors of different sizes in series Two types of questions may be asked: How to find the outlet conversion from a given reactor system? How to find the best setup to achieve a given conversion? CL,F1=Fo Co C2 C2.F2-Fo Co C0,0,F0 C3,v,F3=f0 C3 27 Figure 6.7 Notation for a series of unequal-size mixed flow reactors
27 • Mixed flow reactors of different sizes in series • Two types of questions may be asked: • How to find the outlet conversion from a given reactor system? • How to find the best setup to achieve a given conversion?
.Finding the conversion in a given system =Co-C or -n t1 C-Co For ith reactor:- 1 -n TC-CH Note for a given system,t;is known Rate versus concentration 对 curve (-r)1=_1 (from Eq.9) Slope =C1 -Co T1 P (-r2 2=-1((from Eq.10) Slope C2-C1 72 L C3 C2 C1 Co Reactant concentration Figure 6.8 Graphical procedure for finding compositions in a series 28 of mixed flow reactors
28 1 1 0 1 1 1 0 1 1 1 For ith reactor : 1 − − − − = − − − = − − = i i i i C C r C C r or r C C Note for a given system, τi is known •Finding the conversion in a given system
Determining the best system for a given conversion X-0 82 X=0 X2 o Co Fo 1 2 Arbitrary curve 2- Area measures Co Fo size of first unit Of second unit X2 0 X1 X2 1 Co Fo Figure 6.9 Graphical representation of the variables for two mixed flow reactors in series
29 • Determining the best system for a given conversion
For a given job,F,Co,X,have known. Also the rate equation knows too. The problem is how to determine X,to make the optimal V+V2. min(V+V2)is as same as min(+). - GGC 6-c G 30
30 ( ) ( ) ( ) ( )2 2 1 0 1 1 0 2 2 1 0 1 1 0 r X X C r X C r X X C r X C − − + − + = − − = − = + + + 1 2 1 2 1 2 1 2 1 2 1 0 0 2 min(V V ) is assame as min( ). the optimal V V . The problem is how to determine X , to make Also the rate equation knows too. For a given job, F , C , X have known.