The Gibbs tangent plane criterion has become important in determining
the quality of obtained solutions to the phase and chemical equilibriu
m problem. The ability to determine if a postulated solution is thermo
dynamically stable with respect to perturbations in any or all of the
phases is very useful in the search for the title equilibrium solution
. Previous approaches have focused on finding stationary points of the
tangent plane distance function. Obtaining all stationary points, how
ever cannot be guaranteed due to the complex and nonlinear nature of t
he models used to predict equilibrium. Simpler fomulations for the sta
bility problem are presented for special problems where nonideal liqui
d phases can be adequately modeled using the NRTL and UNIQUAC activity
coefficient equations. It shows how the global minimum of the tangent
plane distance function can be obtained for these problems. A global
optimization approach is advantageous because a nonnegative solution c
an be asserted to be the globally stable equilibrium one, unlike avail
able local algorithms. For the NRTL equation, the GOP algorithm of Flo
udas and Visweswaran (1990, 1993) is used to guarantee obtaining epsil
on-global convergence to the global minimum. For the UNIQUAC equation,
a branch and bound algorithm based on that of Falk and Soland (1969)
is used to guarantee convergence to the global solution. Computational
results demonstrate the efficiency of both global optimization algori
thms in solving various challenging problems.