A Derivative-less Approach for Generating Phase Envelopes

Phase envelopes can be generated, in principle by performing a series of saturation pressure calculations at specified temperatures. But this method is not recommended as it is time consuming and is susceptible to convergence problems at higher pressure and temperature conditions. 

Michelsen proposed a procedure for phase envelope generation by first starting the calculation at moderate pressure/temperature conditions and then using the K-values, and fugacities of previous saturation points to estimate the next saturation point. This procedure ensures a reasonable initial estimate and creates no problems when the data passes through the critical point. However, Michelsen uses the Newton-Raphson technique for solving the non-linear equation to calculate successive saturation points. His method is robust and allows a rapid construction of the phase envelope.  Read more>>>>>>>>>>>>>>>>>>>