Figure A.2 (page 640):

Gibbs energy contours for the pentane reactions as a function of the two reaction extents.

Code for Figure A.2

Text of the GNU GPL.

main.m

%% Copyright (C) 2001, James B. Rawlings and John G. Ekerdt
%%
%% This program is free software; you can redistribute it and/or
%% modify it under the terms of the GNU General Public License as
%% published by the Free Software Foundation; either version 2, or (at
%% your option) any later version.
%%
%% This program is distributed in the hope that it will be useful, but
%% WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
%% General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program; see the file COPYING.  If not, write to
%% the Free Software Foundation, 59 Temple Place - Suite 330, Boston,
%% MA 02111-1307, USA.

global K1 K2 P ext0 Gval dels unk zlast

deltag1 = -3.72; % kcal/mol
deltag2 = -4.49; % kcal/mol
T       = 400;   % K
P       = 2.5;   % atm
R       = 1.987; % cal/mol/K
K1 = exp(-deltag1*1000/(R*T));
K2 = exp(-deltag2*1000/(R*T));




% first optimize free energy
% min_z G(z) s.t. x_1,x_2 >0,  x_1 + x_2 < 0.5

Gval = 0;
w0 = [0.2; 0.2];
A = [1, 1];
b = 0.5;
[w, obj, info] = fmincon(@G, w0, A, b, [], [], [0;0], [0.5;0.5]);
w

if (info != 1)
  info, w, obj
end

% next prepare contour plot

Glevels = [0, -1, -2, -2.5, -2.5, -2.53, -2.55 -2.559];
nlev = length(Glevels);
alpha = [0.05, 0.05,   0.075, 0.05, 0.05, 0.05, 0.04, 0.02];
x0vec = [1e-3, 1e-3, 1e-3, .133, .133, .133, .133, .133; ...
          .02,  .15,  .35,   .3,  .3,   .3,    .3,   .3];
delx  = [0.01, 0.01, 0.01, 0.01, -0.01, 0, 0, 0; ...
            0     0,    0,    0,     0, 0, 0, 0];
sfinal = [9, 9, 9, 9, 9, 9, 9, 5];

for i = 1:nlev
  Gval = Glevels(i);
  %%  find a point on the contour corresponding to s=0
  ext0 = x0vec(:,i);
  unk = [2]; 
  x0 = ext0(unk);
  [x, fval, info] = fsolve(@Gcontour, x0);
  fsolve_failed = info <= 0;
  infovec(i) = info;
  fcnvec(:,i) = Gcontour(x);
  ext = ext0;
  ext(unk) = x;
  zlast = ext;
  extinit(:,i) = ext;
  %% continuation in arclength
  dels = alpha(i);
  svec = dels:dels:sfinal(i);
  narc =length(svec);
  z0 = ext + delx(:,i);
  unk = [1 2];
  for j = 1:narc
    s = svec(j);
    [z, fval, info] = fsolve('inflate',z0);
    fsolve_ok = info > 0;
    %% stop when contour completed
    if (z(1) > 0 && z(2) > 0 && 0.5-(z(1)+z(2)) > 0 && fsolve_ok)
      ztable{i}(:,j) = z;
      %% project initial guess along the arc for next point on contour
      z0 = 2*z - zlast;
      zlast = z;
    else
      break
    end
  end
  ztable(i) = {[ext, ztable{i}]};
  zsave = ztable{i}';
  save ('-ascii', sprintf ('contour_pentane-%d.dat', i), 'zsave');
end
feasbound = [0, 0.5; 0.5, 0];  % store boundary of feasible region
save ('-ascii', sprintf ('contour_pentane-%d.dat', nlev+1), 'feasbound');


%%plot results
  hold on;
  plot([0.5,0], [0, 0.5]); % one leg of feasible region
  for i = 1:nlev
    plot(ztable{i}(1,:), ztable{i}(2,:));
  end
title ('Figure A.2')

Gcontour.m

function retval = Gcontour(var)
  global K1 K2 P Gval ext0 unk
  w = ext0;
  w(unk) = var;
  retval = G(w);

G.m

function retval = G(w)
  global K1 K2 P Gval
  x = w(1);
  y = w(2);
  z = 0.5 - x - y;
  p = 0.5 + z;
  if (x == 0)
    xlogx = 0;
  else
    xlogx = abs(x)*log(abs(x/p));
  end
  if (y == 0)
    ylogy = 0;
  else
    ylogy = abs(y)*log(abs(y/p));
  end
  if (z == 0)
    zlogz = 0;
  else
    zlogz = abs(z)*log(abs(z/p));
  end
  retval = -Gval -(x*log(K1) + y*log(K2)) + p*log(P) + ...
     2*zlogz + xlogx + ylogy;

inflate.m

function retval = inflate(z)
  global zlast dels
  retval = [ Gcontour(z) ; norm(z-zlast) - dels^2 ];

Data files

contour_pentane-1.dat

 1.00000000e-03 2.10972632e-02
 2.62955481e-03 1.92013331e-02
 4.33078987e-03 1.73694490e-02
 6.08065761e-03 1.55839623e-02
 7.86942046e-03 1.38374436e-02
 9.69188338e-03 1.21261199e-02
 1.15450888e-02 1.04481361e-02
 1.34274693e-02 8.80294801e-03
 1.53385301e-02 7.19116442e-03
 1.72788310e-02 5.61470235e-03
 1.92502834e-02 4.07737501e-03
 2.12571058e-02 2.58651496e-03
 2.33091662e-02 1.15856247e-03

contour_pentane-2.dat

 1.00000000e-03 1.55949156e-01
 2.35234151e-03 1.53846495e-01
 3.76809463e-03 1.51785999e-01
 5.22656014e-03 1.49755512e-01
 6.71794884e-03 1.47749082e-01
 8.23643848e-03 1.45763084e-01
 9.77813369e-03 1.43795045e-01
 1.13402311e-02 1.41843161e-01
 1.29206096e-02 1.39906049e-01
 1.45176050e-02 1.37982613e-01
 1.61298741e-02 1.36071962e-01
 1.77563093e-02 1.34173354e-01
 1.93959805e-02 1.32286167e-01
 2.10480953e-02 1.30409863e-01
 2.27119705e-02 1.28543980e-01
 2.43870106e-02 1.26688113e-01
 2.60726918e-02 1.24841906e-01
 2.77685503e-02 1.23005044e-01
 2.94741722e-02 1.21177244e-01
 3.11891860e-02 1.19358253e-01
 3.29132567e-02 1.17547844e-01
 3.46460806e-02 1.15745811e-01
 3.63873816e-02 1.13951969e-01
 3.81369071e-02 1.12166147e-01
 3.98944260e-02 1.10388191e-01
 4.16597258e-02 1.08617960e-01
 4.34326107e-02 1.06855326e-01
 4.52129155e-02 1.05100155e-01
 4.70004567e-02 1.03352355e-01
 4.87950792e-02 1.01611829e-01
 5.05966389e-02 9.98784845e-02
 5.24050018e-02 9.81522399e-02
 5.42200433e-02 9.64330196e-02
 5.60416470e-02 9.47207547e-02
 5.78697047e-02 9.30153825e-02
 5.97041151e-02 9.13168462e-02
 6.15447840e-02 8.96250946e-02
 6.33916231e-02 8.79400817e-02
 6.52445503e-02 8.62617662e-02
 6.71034887e-02 8.45901118e-02
 6.89683668e-02 8.29250866e-02
 7.08391180e-02 8.12666632e-02
 7.27156801e-02 7.96148183e-02
 7.45979955e-02 7.79695326e-02
 7.64860106e-02 7.63307910e-02
 7.83796761e-02 7.46985822e-02
 8.02789463e-02 7.30728988e-02
 8.21837793e-02 7.14537370e-02
 8.40941367e-02 6.98410970e-02
 8.60099837e-02 6.82349827e-02
 8.79312887e-02 6.66354017e-02
 8.98580235e-02 6.50423652e-02
 9.17901633e-02 6.34558886e-02
 9.37276862e-02 6.18759907e-02
 9.56705737e-02 6.03026946e-02
 9.76188102e-02 5.87360272e-02
 9.95723835e-02 5.71760195e-02
 1.01531284e-01 5.56227067e-02
 1.03495507e-01 5.40761286e-02
 1.05465048e-01 5.25363292e-02
 1.07439908e-01 5.10033576e-02
 1.09420091e-01 4.94772676e-02
 1.11405604e-01 4.79581183e-02
 1.13396458e-01 4.64459743e-02
 1.15392666e-01 4.49409060e-02
 1.17394248e-01 4.34429900e-02
 1.19401224e-01 4.19523096e-02
 1.21413621e-01 4.04689550e-02
 1.23431470e-01 3.89930243e-02
 1.25454805e-01 3.75246236e-02
 1.27483667e-01 3.60638680e-02
 1.29518102e-01 3.46108826e-02
 1.31558161e-01 3.31658028e-02
 1.33603900e-01 3.17287761e-02
 1.35655386e-01 3.02999628e-02
 1.37712689e-01 2.88795377e-02
 1.39775890e-01 2.74676918e-02
 1.41845079e-01 2.60646340e-02
 1.43920355e-01 2.46705940e-02
 1.46001830e-01 2.32858247e-02
 1.48089629e-01 2.19106057e-02
 1.50183892e-01 2.05452475e-02
 1.52284776e-01 1.91900967e-02
 1.54392433e-01 1.78455597e-02
 1.56507091e-01 1.65120591e-02
 1.58628980e-01 1.51900958e-02
 1.60758367e-01 1.38802440e-02
 1.62895561e-01 1.25831703e-02
 1.65040927e-01 1.12996573e-02
 1.67194897e-01 1.00306377e-02
 1.69357997e-01 8.77724280e-03
 1.71530875e-01 7.54087613e-03
 1.73714353e-01 6.32332848e-03
 1.75909514e-01 5.12697207e-03
 1.78117851e-01 3.95511556e-03
 1.80341581e-01 2.81273808e-03
 1.82584408e-01 1.70832571e-03
 1.84854222e-01 6.60497854e-04

contour_pentane-3.dat

 1.00000000e-03 3.38812970e-01
 3.59612382e-03 3.33822903e-01
 6.41605524e-03 3.28955808e-01
 9.37878927e-03 3.24174299e-01
 1.24503900e-02 3.19461986e-01
 1.56113779e-02 3.14809161e-01
 1.88488916e-02 3.10209256e-01
 2.21537148e-02 3.05657468e-01
 2.55188759e-02 3.01150106e-01
 2.89388940e-02 2.96684224e-01
 3.24093346e-02 2.92257412e-01
 3.59265290e-02 2.87867654e-01
 3.94873871e-02 2.83513241e-01
 4.30892686e-02 2.79192700e-01
 4.67298904e-02 2.74904752e-01
 5.04072579e-02 2.70648276e-01
 5.41196139e-02 2.66422280e-01
 5.78653985e-02 2.62225886e-01
 6.16432187e-02 2.58058309e-01
 6.54518230e-02 2.53918845e-01
 6.92900822e-02 2.49806864e-01
 7.31569723e-02 2.45721795e-01
 7.70515621e-02 2.41663126e-01
 8.09730013e-02 2.37630393e-01
 8.49205115e-02 2.33623176e-01
 8.88933782e-02 2.29641096e-01
 9.28909442e-02 2.25683813e-01
 9.69126038e-02 2.21751018e-01
 1.00957798e-01 2.17842433e-01
 1.05026009e-01 2.13957812e-01
 1.09116758e-01 2.10096932e-01
 1.13229602e-01 2.06259597e-01
 1.17364130e-01 2.02445635e-01
 1.21519960e-01 1.98654897e-01
 1.25696739e-01 1.94887252e-01
 1.29894137e-01 1.91142592e-01
 1.34111850e-01 1.87420829e-01
 1.38349595e-01 1.83721891e-01
 1.42607111e-01 1.80045728e-01
 1.46884156e-01 1.76392303e-01
 1.51180506e-01 1.72761600e-01
 1.55495955e-01 1.69153619e-01
 1.59830312e-01 1.65568375e-01
 1.64183403e-01 1.62005901e-01
 1.68555071e-01 1.58466247e-01
 1.72945169e-01 1.54949478e-01
 1.77353567e-01 1.51455676e-01
 1.81780147e-01 1.47984940e-01
 1.86224804e-01 1.44537383e-01
 1.90687447e-01 1.41113139e-01
 1.95167994e-01 1.37712357e-01
 1.99666377e-01 1.34335202e-01
 2.04182540e-01 1.30981861e-01
 2.08716436e-01 1.27652534e-01
 2.13268031e-01 1.24347446e-01
 2.17837301e-01 1.21066837e-01
 2.22424233e-01 1.17810969e-01
 2.27028827e-01 1.14580127e-01
 2.31651090e-01 1.11374615e-01
 2.36291043e-01 1.08194762e-01
 2.40948715e-01 1.05040921e-01
 2.45624149e-01 1.01913471e-01
 2.50317397e-01 9.88128178e-02
 2.55028522e-01 9.57393949e-02
 2.59757598e-01 9.26936670e-02
 2.64504713e-01 8.96761304e-02
 2.69269964e-01 8.66873159e-02
 2.74053460e-01 8.37277907e-02
 2.78855323e-01 8.07981611e-02
 2.83675689e-01 7.78990752e-02
 2.88514705e-01 7.50312266e-02
 2.93372530e-01 7.21953571e-02
 2.98249340e-01 6.93922612e-02
 3.03145324e-01 6.66227904e-02
 3.08060685e-01 6.38878582e-02
 3.12995641e-01 6.11884453e-02
 3.17950428e-01 5.85256063e-02
 3.22925297e-01 5.59004762e-02
 3.27920515e-01 5.33142792e-02
 3.32936371e-01 5.07683370e-02
 3.37973167e-01 4.82640799e-02
 3.43031230e-01 4.58030582e-02
 3.48110903e-01 4.33869565e-02
 3.53212552e-01 4.10176097e-02
 3.58336563e-01 3.86970214e-02
 3.63483347e-01 3.64273863e-02
 3.68653335e-01 3.42111163e-02
 3.73846982e-01 3.20508716e-02
 3.79064766e-01 2.99495983e-02
 3.84307190e-01 2.79105747e-02
 3.89574777e-01 2.59374675e-02
 3.94868072e-01 2.40344041e-02
 4.00187639e-01 2.22060629e-02
 4.05534056e-01 2.04577926e-02
 4.10907911e-01 1.87957709e-02
 4.16309788e-01 1.72272227e-02
 4.21740260e-01 1.57607291e-02
 4.27199855e-01 1.44066835e-02
 4.32689021e-01 1.31779914e-02
 4.38208034e-01 1.20911981e-02
 4.43756826e-01 1.11684117e-02
 4.49334567e-01 1.04407930e-02
 4.54938586e-01 9.95540647e-03
 4.60561155e-01 9.79005787e-03
 4.66178150e-01 1.00900701e-02
 4.71696865e-01 1.11783768e-02
 4.76596290e-01 1.39417555e-02
 4.78173211e-01 1.93411933e-02

contour_pentane-4.dat

 1.33000000e-01 3.11802250e-01
 1.34812503e-01 3.10080357e-01
 1.36631787e-01 3.08365625e-01
 1.38457823e-01 3.06658086e-01
 1.40290594e-01 3.04957778e-01
 1.42130087e-01 3.03264744e-01
 1.43976291e-01 3.01579031e-01
 1.45829201e-01 2.99900692e-01
 1.47688816e-01 2.98229784e-01
 1.49555140e-01 2.96566372e-01
 1.51428179e-01 2.94910526e-01
 1.53307948e-01 2.93262323e-01
 1.55194463e-01 2.91621846e-01
 1.57087749e-01 2.89989187e-01
 1.58987832e-01 2.88364443e-01
 1.60894748e-01 2.86747724e-01
 1.62808537e-01 2.85139145e-01
 1.64729245e-01 2.83538833e-01
 1.66656924e-01 2.81946925e-01
 1.68591637e-01 2.80363570e-01
 1.70533449e-01 2.78788931e-01
 1.72482439e-01 2.77223182e-01
 1.74438691e-01 2.75666515e-01
 1.76402301e-01 2.74119137e-01
 1.78373373e-01 2.72581274e-01
 1.80352024e-01 2.71053174e-01
 1.82338386e-01 2.69535107e-01
 1.84332600e-01 2.68027367e-01
 1.86334825e-01 2.66530280e-01
 1.88345239e-01 2.65044203e-01
 1.90364035e-01 2.63569529e-01
 1.92391431e-01 2.62106696e-01
 1.94427666e-01 2.60656187e-01
 1.96473009e-01 2.59218543e-01
 1.98527760e-01 2.57794370e-01
 2.00592253e-01 2.56384348e-01
 2.02666815e-01 2.54989287e-01
 2.04751912e-01 2.53610023e-01
 2.06848027e-01 2.52247562e-01
 2.08955708e-01 2.50903062e-01
 2.11075581e-01 2.49577867e-01
 2.13208367e-01 2.48273557e-01
 2.15354904e-01 2.46992004e-01
 2.17516172e-01 2.45735453e-01
 2.19693330e-01 2.44506640e-01
 2.21887762e-01 2.43308946e-01
 2.24101136e-01 2.42146632e-01
 2.26335500e-01 2.41025196e-01
 2.28593394e-01 2.39951924e-01
 2.30878029e-01 2.38936817e-01
 2.33193515e-01 2.37994201e-01
 2.35545159e-01 2.37145806e-01
 2.37939657e-01 2.36427210e-01
 2.40384148e-01 2.35903316e-01
 2.42876884e-01 2.35712808e-01
 2.45325234e-01 2.36218386e-01
 2.46993400e-01 2.38080448e-01
 2.47159740e-01 2.40574896e-01
 2.46585294e-01 2.43008010e-01
 2.45676941e-01 2.45337151e-01
 2.44581759e-01 2.47584502e-01
 2.43365947e-01 2.49768948e-01
 2.42064894e-01 2.51903722e-01
 2.40699804e-01 2.53998127e-01
 2.39284460e-01 2.56058904e-01
 2.37828362e-01 2.58091090e-01
 2.36338360e-01 2.60098549e-01
 2.34819564e-01 2.62084314e-01
 2.33275897e-01 2.64050805e-01
 2.31710428e-01 2.65999987e-01
 2.30125603e-01 2.67933463e-01
 2.28523392e-01 2.69852557e-01
 2.26905388e-01 2.71758354e-01
 2.25272877e-01 2.73651739e-01
 2.23626877e-01 2.75533409e-01
 2.21968153e-01 2.77403873e-01
 2.20297197e-01 2.79263418e-01
 2.18614141e-01 2.81112018e-01
 2.16918455e-01 2.82949039e-01

contour_pentane-5.dat

 1.33000000e-01 3.11802250e-01
 1.31194304e-01 3.13531267e-01
 1.29395433e-01 3.15267400e-01
 1.27603428e-01 3.17010620e-01
 1.25818331e-01 3.18760913e-01
 1.24040182e-01 3.20518264e-01
 1.22269029e-01 3.22282667e-01
 1.20504924e-01 3.24054116e-01
 1.18747921e-01 3.25832611e-01
 1.16998082e-01 3.27618154e-01
 1.15255471e-01 3.29410752e-01
 1.13520156e-01 3.31210415e-01
 1.11792213e-01 3.33017156e-01
 1.10071719e-01 3.34830994e-01
 1.08358759e-01 3.36651948e-01
 1.06653422e-01 3.38480045e-01
 1.04955804e-01 3.40315311e-01
 1.03266004e-01 3.42157779e-01
 1.01584130e-01 3.44007486e-01
 9.99102940e-02 3.45864470e-01
 9.82446165e-02 3.47728777e-01
 9.65872239e-02 3.49600453e-01
 9.49382503e-02 3.51479552e-01
 9.32978377e-02 3.53366130e-01
 9.16661363e-02 3.55260248e-01
 9.00433053e-02 3.57161972e-01
 8.84295132e-02 3.59071374e-01
 8.68249388e-02 3.60988530e-01
 8.52297716e-02 3.62913521e-01
 8.36442127e-02 3.64846436e-01
 8.20684759e-02 3.66787367e-01
 8.05027884e-02 3.68736415e-01
 7.89473922e-02 3.70693688e-01
 7.74025451e-02 3.72659299e-01
 7.58685224e-02 3.74633372e-01
 7.43456184e-02 3.76616037e-01
 7.28341483e-02 3.78607435e-01
 7.13344503e-02 3.80607716e-01
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