The Rachford-Rice equation needs to be solved during phase split calculations required in several petroleum engineering applications such as reservoir simulation, determination of minimum miscible pressure, pipeline flow, etc. This calculation often has to be repeated for every discretization block and for every time step, thus claiming a significant fraction of the total computation time (CPU). Existing techniques exhibit a fairly poor performance when a bubble of a very light composition or a droplet of a very heavy one is present in the mixture. As the computation time in parallel computing implementations is determined by the slowest grid block calculation, this latency bears a huge impact on the total required CPU time.
In this work, a transformation of the conventional Rachford-Rice function is proposed with which the original equation is rewritten as a function of a single hyperbolic term instead of the vapor fraction. The transformed function is monotonic and strictly concave and can be fitted by low order rational model functions. A novel algorithm, which is able to fit such rational model functions and does not require the calculation of a derivative, is proposed instead of the Newton-Raphson straight line. The root of these functions is obtained directly by performing simple computations and is utilized as the next estimation.
The proposed method converges rapidly, as it requires only a single function evaluation at each iteration even in the case of negative flash or near-critical calculations. Every single estimate lies within the valid vapor fraction range thus ensuring robustness without the need for utilizing bracketing. Several test cases demonstrate an excellent performance compared to the existing methods hence leading to a robust solution and substantial CPU time savings.