A Robust Iterative Method for Flash Calculations Using the Soave-Redlich-Kwong or the Peng-Robinson Equation of State

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Abstract
A robust algorithm for flash calculations using the Soave-Redlich-Kwong or Peng-Robinson equation of state is presented. It first uses a special version of the Successive Substitution 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 bubble-, dew- or critical point and detects also the single-phase region without computing the saturation pressure. INTRODUCTION The calculation of vapor-liquid equilibrium using an equation of state in multicomponent systems yields a system of non-linear equations which must be solved iteratively. The method of Successive Substitution is commonly used but it exhibits poor rate of convergence, or in some cases no convergence, near the dew-, bubble or critical point. To overcome convergence problems, Newton's method has been used by Fussel and Yanosik1 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 dew-, bubble- or critical point it involves more work to arrive at the solution than the method of Successive Substitution. The single-phase region is usually determined by computing the saturation pressure and comparing it with the pressure of the system. This requires additional work and it is sometimes difficult to decide whether dew point or bubble point pressure should be computed (they involve different equations).

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