! APMonitor Modeling Language ! http://www.apmonitor.com ! Binary Distillation Column from ! ! Hahn, J. and T.F. Edgar, An improved method for nonlinear model reduction using balancing of ! empirical gramians, Computers and Chemical Engineering, 26, pp. 1379-1397, (2002) ! ! Liquid mole fraction of component A ! at reflux ratio = 2 ! ! Condenser 0.93541941614016 ! Tray 1 0.90052553715795 ! Tray 2 0.86229645132283 ! . 0.82169940277993 ! . 0.77999079584355 ! . 0.73857168629759 ! . 0.69880490932694 ! . 0.66184253445732 ! . 0.62850777645505 ! . 0.59925269993058 ! . 0.57418567956453 ! . 0.55314422743545 ! . 0.53578454439850 ! . 0.52166550959767 ! . 0.51031495114413 ! . 0.50127509227528 ! . 0.49412891686784 ! . 0.48544992019184 ! . 0.47420248108803 ! . 0.45980349896163 ! . 0.44164297270225 ! . 0.41919109776836 ! . 0.39205549194059 ! . 0.36024592617390 ! . 0.32407993023343 ! . 0.28467681591738 ! . 0.24320921343484 ! . 0.20181568276528 ! . 0.16177269003094 ! Tray 29 0.12514970961746 ! Tray 30 0.09245832612765 ! Reboiler 0.06458317697321 Model binary Parameters ! reflux ratio rr = 0.7 ! Feed Flowrate (mol/min) Feed = 2.0 ! 24.0/60.0 ! Mole Fraction of Feed x_Feed = 0.5 ! Relative Volatility = (yA/xA)/(yB/xB) = KA/KB = alpha(A,B) vol=1.6 ! Total Molar Holdup in the Condenser atray=0.25 ! Total Molar Holdup on each Tray acond=0.5 ! Total Molar Holdup in the Reboiler areb=0.1 End Parameters Variables ! mole fraction of component A x[1:32] = 0.3 End Variables Intermediates ! Distillate Flowrate (mol/min) D=0.5*Feed ! Flowrate of the Liquid in the Rectification Section (mol/min) L=rr*D ! Vapor Flowrate in the Column (mol/min) V=L+D ! Flowrate of the Liquid in the Stripping Section (mol/min) FL=Feed+L ! Vapor Mole Fractions of Component A ! From the equilibrium assumption and mole balances ! 1) vol = (yA/xA) / (yB/xB) ! 2) xA + xB = 1 ! 3) yA + yB = 1 y[1:32] = x[1:32]*vol/(1+(vol-1)*x[1:32]) End Intermediates Equations ! condenser acond * $x[1] = V*(y[2]-x[1]) ! 15 column stages atray * $x[2:16] = L*(x[1:15]-x[2:16]) - V*(y[2:16]-y[3:17]) ! feed tray atray * $x[17] = Feed*x_Feed + L*x[16] - FL*x[17] - V*(y[17]-y[18]) ! 14 column stages atray * $x[18:31] = FL*(x[17:30]-x[18:31]) - V*(y[18:31]-y[19:32]) ! reboiler areb * $x[32] = FL*x[31] - (Feed-D)*x[32] - V*y[32] End Equations End Model