$title Chemical Equilibrium Problem (WALL,SEQ=76)

$onText
A Sample Nonlinear system to solve Chemical Equilibrium models.

Wall, T W, Greening, D, and Woolsey, R E D, Solving Complex Chemical
Equilibria Using a Geometric-Programming Based Technique. OR 34, 3 (1987).

Keywords: nonlinear programming, chemical equilibrium problem, chemical engineering

Update [2019-07-12]: Johan Loefberg noted that in the original model the
  nonnegativity requirement on the variables (representing concentrations) was
  missing. These have been added.
$offText

* objective variable must be declared free, but will be nonnegative due to r1
Variable ba;
Nonnegative Variables so4, baoh, oh, hso4, h;

Equation r1, r2, r3, r4, b1, b2;

* Scaling in powers of 10: ba -5, so4 -5, baoh -12, oh -7, hso4 -10, h -7
r1..  ba*so4     =e= 1;
r2..  baoh/ba/oh =e= 4.8;
r3..  hso4/so4/h =e= .98;
r4..  h*oh       =e= 1;
b1..  ba + 1e-7*baoh            =e= so4   + 1e-5*hso4;
b2..  2*ba + 1e-7*baoh + 1e-2*h =e= 2*so4 + 1e-5*hso4 + 1e-2*oh;

Model wall / all /;

ba.l = 1; so4.l = 1; baoh.l = 1; oh.l = 1; hso4.l = 1; h.l = 1;

* do not have GAMS modify solution
wall.tolproj = 0;

solve wall using nlp minimizing ba;