Convex hull method for the determination of vapour-liquid equilibria (VLE) phase diagrams for binary and ternary systems

Abstract

Flash calculations are widely used and constitute an integral part of modelling vapour-liquid equilibria in compositional simulators. However, it has been discovered that during compositional simulations, flash calculations take 50-70% of the overall computational time because the procedure currently used is iterative. Hence, several methods such as the reduced variable method, compositional space adaptive tabulation (CSAT) and the tie-line table look-up (TTL) have been developed to improve on the computational speed of most flash calculations during compositional simulations. Unfortunately, most of these methods are still iterative, and pose convergence problems, even though some are developed with efficient Newton-Raphson algorithms. Non-iterative techniques may be the best option to speed up the computational time during simulations. This paper presents a non-iterative procedure for the determination of fluid phase diagrams using the convex hull method and Peng-Robinson equation of state. Convex hull is a mathematical method, and algorithmic implementations of this method are available in many software packages, of which Matlab was used in this work. Unlike the conventional flash calculation method, programs developed with convex hull does not the need an accurate start value to make fluid phase diagrams and determine phase properties for binary and ternary mixtures. The time taken to complete a simulation run using convex hull and the conventional flash calculation method were noted, and the numerical results from both methods was validated against a range of experimental data for different mixtures. The results show good agreement in all the cases investigated. From the analyses, it was shown that the convex hull method is faster than the conventional flash calculation method in achieving convergence and also gave better predictions close to the critical point. The reliability of the results and the additional time benefits are indication that the convex hull method has a promising prospect of becoming an efficient procedure for modelling vapour-liquid phase equilibria calculations for compositional simulations.

Experimental and Computational Determination of Optimal Boron Content in Layered Superconductor Sc$_{20}$C$_{8-x}$B$_x$C$_{20}$

“…Generally, such a plot is referred to as the energy convex hull diagram. 18,19 For example, this technique allows us to discuss the phase stability with respect to differences in the content between each in multi-component systems. [20][21][22] In this paper, we examined the most stable B composition in Sc 20 (C, B) 8 C 20 assuming the B-C replacement in the C layer.…”

Analytically approximate solution to the VLE problem with the SRK equation of state

“…For each system there is only a one-time effort, and therefore, the wastes caused by the repetitive efforts can be avoided. By the way, we also show that for exact solutions, the VLE problem with any cubic EoS can be reduced to solving a transcendental equation with one unknown, which can significantly simplify the methods currently employed [2,7].…”

“…Vapor-liquid equilibrium (VLE) calculation plays a central role in thermodynamics and process simulations [1,7]. With an equation of state (EoS), the chemical potential equilibrium condition, or the Maxwell constructions [4], generates a transcendental function with logarithm terms.…”

“…The costs of computing resources are significant as well. As reported [7], the phase equilibrium computation is the most expensive step in chemical process simulations. Some efforts have been made for developing analytical solutions, but mostly in the neighbourhood of the critical point [8,9].…”

Análise estatística da influência cio parâmetro de interação binária Kjj nas equações de Soave-Redlich-Kwong e Peng Robison aplicadas a mistura de CO2 e C$H\2

“…As equações de estados cúbicas, apesar de sua simplicidade, têm se mostrado como simulação de modelos termodinâmicos muito versáteis. Elas são capazes de representar a continuidade entre as fases fluidas e, consequentemente, podem ser usadas para representar equilíbrio líquido-vapor (ELV ) de misturas, sendo que estes cálculos podem ser usados para determinar limites de fase por meio de cálculos de ponto de orvalho e ponto de bolha [3]. No componente puro, as moléculas estão sempre rodeadas por espécies semelhantes; em uma mistura, elas estão cercadas por espécies semelhantes e diferentes.…”