A robust algorithmic phase equilibria protocol and its application to a multipurpose compositional simulator

Abstract

This study presents a new multipurpose compositional model for petroleum reservoirs. The proposed formulation allows the simulation of the isothermal and non-isothermal secondary or tertiary recovery processes, as well as condensate reservoirs where mass transfer of components between phases is considered to be significant. Although the current study limits the number of phases to four (4), the formulation presented in this study does not impose any limitation to the number of phases to be considered. The present compositional model utilizes either Soave–Redlich–Kwong (1972) or Peng and Robinson [Ind. Eng. Chem. Fundam. 15 (1976) 59; Can. J. Chem. Eng. (1976) 595] equations of state to describe the phase behavior of the system in lieu of predetermined equilibrium constants. The phase equilibrium package is capable of handling co-existing liquid phases and is equipped with a robust critical point determination technique, which is used in identifying the phases obtained under the existing temperature and pressure conditions. A linear programming algorithmic protocol utilized to determine the interaction coefficients and/or C 7+ component(s) critical properties is also presented. The partial differential equations describing the transport phenomena in porous media are approximated using the finite-difference technique and are coupled with the flow equations. The resulting system of equations is solved simultaneously using the generalized Newton–Raphson procedure. The simulator has been tested using published data for several options. Results are found to be in good agreement. Also, various sensitivity checks were conducted by varying different parameters in order to test the performance of the model under different conditions. The fully implicit nature of the proposed model is found to be an advantage so that no stability problems have been encountered when large time-step sizes are utilized.