Optimization of an Alkylation Process
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 similar results: 

            VARIABLE     x1                    =     1698.095
            VARIABLE     x2                    =    15818.615
            VARIABLE     x3                    =       54.103
            VARIABLE     x4                    =     3031.225
            VARIABLE     x5                    =     2000.000
            VARIABLE     x6                    =       90.115
            VARIABLE     x7                    =       95.000
            VARIABLE     x8                    =       10.493
            VARIABLE     x9                    =        1.562
            VARIABLE     x10                   =      153.535
            VARIABLE     z                     =     1768.807

GAMS file is available from author upon request. 

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

cost = 0.063*x4*x7-5.04*x1-0.035*x2-10*x3-3.36*x5 ;

equ1 =  x5-1.22*x4+x1 == 0 ;
equ2 =  x6 == 98000*x3/(x4*x9+1000*x3) ;
equ3 =  x8 == (x2+x5)/x1 ;

ineq1 =  (x1*(1.12+0.13167*x8-0.00667*(x8^2)))-99/100*x4 ≥ 0 ;
ineq2 =  -(x1*(1.12+0.13167*x8-0.00667*(x8^2)))+100/99*x4 ≥ 0 ;

ineq3 = (86.35+1.098*x8-0.038*(x8^2)+0.325*(x6-89))-99/100*x7 ≥ 0 ;
ineq4 = -(86.35+1.098*x8-0.038*(x8^2)+0.325*(x6-89))+100/99*x7 ≥ 0 ;

ineq5 = (35.82-0.222*x10)-9/10*x9 ≥ 0 ;
ineq6 = -(35.82-0.222*x10)+10/9*x9 ≥ 0 ;

ineq7 = (-133+3*x7)-99/100*x10 ≥ 0 ;
ineq8 = -(-133+3*x7)+100/99*x10 ≥ 0 ;

bound1= 10^-3≤x1≤2000;
bound2= 10^-3≤x2≤16000;
bound3= 10^-3≤x3≤120;
bound4= 10^-3≤x4≤5000;
bound5= 10^-3≤x5≤2000;
bound6= 85≤x6≤93;
bound7= 90≤x7≤95;
bound8= 3≤x8≤12;
bound9= 10^-1≤x9≤4;
bound10= 145≤x10≤162;

sol=NMaximize[{cost,equ1,equ2,equ3,ineq1,ineq2,ineq3,ineq4,ineq5,ineq6,ineq7,ineq8,bound1,bound2,bound3,bound4,bound5,bound6,bound7,bound8,bound9,bound10},{x1,x2,x3,x4,x5,x6,x7,x8,x9,x10}]