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A general framework of model functions for rapid and robust solution of Rachford–Rice type of equations

Gaganis Vasileios, Marinakis Dimitrios, Varotsis Nikolaos

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Summary

For most phase equilibrium calculations, a non-linear function in one unknown, known as the Rachford–Rice equation for vapor–liquid equilibrium problems, needs to be solved for determining the molar fractions of the co-existing phases required for achieving the desired feed separation. Two issues appear when solving this type of equations. Firstly, the existence of as many asymptotes as the number of components present in the mixture splits these equations to a set of n − 1 branches, each one containing a different solution. Therefore, care should be taken to ensure that the obtained solution lies within the branch of interest. Secondly, conventional solution methods often exhibit slow convergence rates which is an issue when repeated solutions are required as in the case of compositional reservoir simulation and pipeline flow.In this work, a general framework for developing new, rapid and robust solution methods is presented utilizing function classes, the members of which exhibit behavior similar to that of the equation to be solved. Fitting such functions, instead of a simple straight line at each iteration of the solution process, as is the case of the Newton–Raphson approach, leads to better subsequent estimates and thus to faster convergence. Moreover, a new initial value estimation method is presented for cases in which the Rachford–Rice function exhibits a very abrupt shape and it is shown that, for such cases, the number of iterations required by the conventional methods can be reduced to only one or two.

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