Phase stability analysis of liquid-liquid equilibrium with stochastic methods

Abstract

-Minimization of Gibbs free energy using activity coefficient models and nonlinear equation solution techniques is commonly applied to phase stability problems. However, when conventional techniques, such as the Newton-Raphson method, are employed, serious convergence problems may arise. Due to the existence of multiple solutions, several problems can be found in modeling liquid-liquid equilibrium of multicomponent systems, which are highly dependent on the initial guess. In this work phase stability analysis of liquid-liquid equilibrium is investigated using the NRTL model. For this purpose, two distinct stochastic numerical algorithms are employed to minimize the tangent plane distance of Gibbs free energy: a subdivision algorithm that can find all roots of nonlinear equations for liquid-liquid stability analysis and the Simulated Annealing method. Results obtained in this work for the two stochastic algorithms are compared with those of the Interval Newton method from the literature. Several different binary and multicomponent systems from the literature were successfully investigated.

Multilocal Programming and Applications

“…Confirming the results from [37], at the first two compositions only one stationary point was found, giving the indication that only one liquid phase will be formed. On the contrary, the other two compositions present a negative value of the T PDF at the global minimum, suggesting phase instability.…”

“…The performance of the SSA can be assessed by verifying that all the 30 runs converge to the function value ( f * ) at the stationary point (x * ). It also must be stressed that the average time is much uniform when comparing with the results in [37] and [17].…”

“…Consider the binary system water (1) + butyl glycol (2) at 5 o C. It might seem a simple example, but this is a canonical example, where multiple stationary points and local solutions can be found. Additionally, for some compositions, in [37] it was concluded that the stationary points found in [17], using the interval Newton method, are not true roots as shown by the simulated annealing method.…”

GE Models and Algorithms for Condensed Phase Equilibrium Data Regression in Ternary Systems: Limitations and Proposals

“…For example, McDonald and Floudas (1995) [42] work on global optimization strategies with Mixed Integer Non linear Programming methods (MINLP), Dominguez and col. (2002) [43] develop Interval Arithmetic methods and Nagatani and col. (2008) [44] work in Stochastic methods. These are only some examples that evidence the necessity of dedicating more effort in the development of robust algorithms that allow avoiding the typical problems that still arise.…”

A reliable procedure to predict salt precipitation in pure phases

“…9). Stochastic optimization methods can also be used (e.g., , , M. J. E. M. Cardoso and M. Castier Nagatani et al, 2008), but they do not provide a mathematical guarantee of locating the global minimum of the phase stability function. In fact, if the phase stability test is carried out properly and always finds the global minimum of the function G Ω , a local optimization algorithm can be used to minimize the Gibbs free energy during the phase split calculation.…”