Abstract
A robust algorithm for flash calculations that uses an equation of state(EOS) is presented. It first uses a special version of the successive substitution(SS) method and switches to Powell's method if poor convergence is observed. Criteria are established for an efficient switch from one method to the other. Experience shows that this method converges near the critical point and also detects the single-phase region without computing the saturation pressure. The Soave-Redlich-Kwong (SRK) and the Peng-Robinson (PR) EOS's are used in this work, but the method is general and applies to any EOS.
Introduction
The calculation of vapor/liquid equilibrium using an EOS in multicomponent systems yields a system of nonlinear equations that must be solved iteratively. The SS method is commonly used, but it exhibits poor rate of convergence near the critical point. To overcome convergence problems, Newton's method has been used by Fussell and Yanosik to solve the equations. The drawback of Newton's method is the necessity of computing a complicated Jacobian matrix and its inverse at every iteration. Hence, for systems removed from their critical point it involves more work to arrive at the solution than the SS method. Furthermore, the radius of convergence of Newton's method is relatively small when compared to that of the SS method; hence, a good initial guess is required before convergence can be achieved. The single-phase region usually is determined by computing the saturation pressure and comparing it with the pressure of the system. This requires additional work, pressure of the system. This requires additional work, and it is sometimes difficult to decide whether a dewpoint or bubblepoint pressure, which involve different equations, should be computed.
This paper presents a robust iterative method for flash calculations using either the SRK or the PR EOS, both of which have received much interest in recent years. The proposed method combines SS with Powell's iteration, proposed method combines SS with Powell's iteration, which is a hybrid algorithm consisting of a quasi-Newton method and a steepest-descent method. The SS method is used initially and is replaced by Powell's method if it demonstrates poor convergence, thus taking advantage of the simplicity of the former method and the robustness of the latter. The SS method has been modified so that the single-phase region can be detected without having to compute the saturation pressure.
The nonlinear equations to be solved by an iteration scheme could behave differently, depending on their form and the variables for which they are solved. In this paper three different approaches are considered with paper three different approaches are considered with Powell's method. One of the three approaches is based Powell's method. One of the three approaches is based on the minimization of the Gibbs free energy. The convergence properties of the proposed schemes are demonstrated by three example problems.
SPEJ
P. 521
Converging Newton’s Method With An Inflection Point of A Function
