Wei-Prater Mechanism 
Author's Data: Housam BINOUS
Department of Chemical Engineering
National Institute of Applied Sciences and Technology
Tunis, TUNISIA
Email: binoushousam@yahoo.com

Reference:G. F. Froment and K. B. Bischoff, Chemical Reactor Analysis and Design, 2rd edition, Wiley, 1990.

Transformation matrix to obtain reaction paths in three-species reaction mixture as an equilateral triangular diagram.

P={{1,0.5},{0,0.866025}};

Solution of the governing equations

Sol[a_,b_,c_]:=DSolve[{D[c1[t],{t,1}]==-k12 c1[t]+k21 c2[t]+k31 c3[t]-k13 c1[t],D[c2[t],{t,1}]==k12 c1[t]-k21 c2[t]+k32 c3[t]-k23 c2[t],D[c3[t],{t,1}]==k13 c1[t]-k31 c3[t]-k32 c3[t]+k23 c2[t],c1[0]==a,c2[0]==b,c3[0]==c},{c1[t],c2[t],c3[t]},t]

Numerical values for the rate constants

k12=0.1;k13=0.1;k23=0.1;k21=1;k31=1;k32=1;

Prametric Plot of the species' concentrations

plot[a_,b_,c_]:=ParametricPlot[Evaluate[First[P.{c2[t],c3[t]}/.Sol[a,b,c]]],{t,0,50},PlotStyle->RGBColor[0,1,0],DisplayFunction->Identity]

Rection paths in the three-species reaction mixture. Compositions are plotted in an equilateral triangular graph as shown in figure 1.7.2-1 page 44 of  G. F. Froment and K. B. Bischoff, Chemical Reactor Analysis and Design, 2rd edition, Wiley, 1990.

\(Show[
      Flatten[Table[{plot[0.1\ i, 0.1\ \((10 - i)\), 0], 
            plot[0, 0.1\ i, 0.1\ \((10 - i)\)], 
            plot[0.1\ i, 0, 0.1\ \((10 - i)\)]}, {i, 0, 10}]], 
      Axes -> False, 
      Epilog -> {RGBColor[1, 0, 0], Line[{{0, 0}, {1, 0}}], 
          Line[{{0, 0}, {0.5, 0.866025}}], Line[{{1, 0}, {0.5, 0.866025}}], 
          PointSize[0.02], RGBColor[0, 0, 1], 
          Point[First[\(P . {c2[t], c3[t]} /. Sol[0, 1, 0]\) /. 
                t -> 50]], 
          Text[\*""\!\(A\_1\)"", {\(-0.1\), \(-0.1\)}], 
          Text[\*""\!\(A\_2\)"", {1.1, \(-0.1\)}], 
          Text[\*""\!\(A\_3\)"", {0.5, 0.96}]}, 
      PlotRange -> {{\(-0.5\), 1.5}, {\(-0.5\), 1.5}}, 
      TextStyle -> \ {FontSize -> 14, 
          FontWeight -> "Bold"}, 
      DisplayFunction -> $DisplayFunction, 
      AspectRatio -> 1]\)