Chemical Engineering > GATE 2025 > Reactor Optimization
Consider the flowsheet in the figure for manufacturing C via the reaction A+B→C in an isothermal CSTR.
The split in the separator is perfect so that the recycle stream is free of C and the product stream is pure C. Let xi denote the mole fraction of species i (i=A,B,C) in the CSTR, which is operated in excess B with xB/xA=4. The reaction is first-order in A with the reaction rate (-rA)=kxxA, where kx=5.0 kmol/(m3h).
The reactor volume V in m3 is to be optimized to minimize the cost objective J=V+0.25R, where R is the recycle rate in kmol/h. For a product rate P=100 kmol/h, the optimum value of V is ______ m3 (rounded off to the nearest integer).
GIVEN: d/dz (z/(1-z)) = 1/(1-z)2.
The split in the separator is perfect so that the recycle stream is free of C and the product stream is pure C. Let xi denote the mole fraction of species i (i=A,B,C) in the CSTR, which is operated in excess B with xB/xA=4. The reaction is first-order in A with the reaction rate (-rA)=kxxA, where kx=5.0 kmol/(m3h).
GIVEN: d/dz (z/(1-z)) = 1/(1-z)2.
Correct : 12
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