Economic Operation of a Fixed-Bed Filter
Author's Data: Housam BINOUS
Department of Chemical Engineering
National Institute of Applied Sciences and Technology
Tunis, TUNISIA
Email: binoushousam@yahoo.com

The solution provided in this notebook is in agrrement with the values reported by Edgar et al. (2001). The author has solved this problem using GAMS and obtained the same results: Vf=973.549 and Q=14.151. GAMS file is available from author upon request. 

Reference:
Edgar, Himmelblau and Lasdon in Optimization of Chemical Processes, McGraw-Hill International Edition, 2001

q1=10;
Vb=200;
tb=10;

Vf=700*3*Log[10,(10/0.081*1/3*1/Q)];

objectiv = 116*((10^6*q1/(1440*(Vf-Vb)/(Vf/Q+tb))))^0.86+4.73*10^3*(Vf/(Vf-Vb)-1)*q1 ;

sol=NMinimize[{objectiv,Q≥0},Q]

Vf/.sol[[2]]