This paper identifies numerical problems related to a phenomenon of gas phase appearing or disappearing in IMPES black oil or pseudo miscible simulation, and presents a solution based on the Newton solution method.
The black oil simulator from the U.S. Department of Energy (BOAST) was expanded and enhanced to become a pseudo miscible simulator capable of simulating hydrocarbon miscible displacement process. However, results of a test problem indicated that the expanded BOAST showed high material balance errors and failed to predict correct pressure profile. For a scheme that involved the injection of hydrocarbon solvent followed by chase gas. This led to a thorough evaluation of the formulation if the pressure equation and the treatment of nonlinearities such as solution gas-oil ratio (RSO) and formation volume factor (Bo) of BOAST which uses a conventional IMPES Method. This Method was found to be inadequate for proper handling of gas phase appearing or disappearing since during gas injection, drastic mass transfer is taking place between the gas and the oil, and the usually weak nonlinearities (RSO and Bo) become strong nonlinear terms, i.e. they are functions of not only pressure, but also saturation.
To overcome these problems a formulation if the pressure equation in terms of δP(rather than P as in BOAST) and an iterative IMPES method with a new supplementary gas material balance equation are proposed. In this method, first the pressure equation is solved for δP, then each flow equation is solved for its respective saturation, and finally, a new supplementary gas material balance equation is used to update and adjust Sg,R50 and consequently saturation pressure (SP). The above procedure is repeated until the summation of all saturations is equal to or very close to 1.
This method yields better material balance and correct pressure solutions in black oil or pseudo miscible IMPES simulation.
Numerical simulation of the phenomenon of gas appearance or disappearance has been recognized as one of the major difficulties in fully implicit black oil or thermal simulation1, 2, 3. There are two approaches in circumventing this problem: variable or equation substitution2 and pseudo K values3. A comparison of these two approaches undertaken by Forsyth et al1 concluded that there is little difference in efficiency between them. Naturally, this problem would be more profound in any IMPES type simulation.
The phenomenon of gas appearance or disappearance arises where free gas is released from oil as the reservoir pressure decreases below the bubble point, or the free gas redissolves into the oil when the reservoir is repressurized, or free gas is injected into the undersaturated oil. Gas phase appearance or disappearance is essentially a process in which drastic mass transfer takes place between the oil phase and the gas phase which is reflected numerically by variations of the two related parameters: solution gas ratio (RSO) and oil formation volume factor (Bo).
Usually these two parameters are considered as weak nonlinearities i.e. they are only a function of pressure4.