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 x_i denote the mole fraction of species i (i=A,B,C) in the CSTR, which is operated in excess B with x_B/x_A=4. The reaction is first-order in A with the reaction rate (-r_A)=k_xx_A, where k_x=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.