Numerical, Three-Phase Simulation of the Linear Steamflood Process

Abstract

This paper describes a numerical mathematical model of the steamflood process that depends on fewer rest rictiye assumptions than models previously reported. The solution, however, is obtained economically. Example calculations are presented that, on comparison with experimental results, tend to validate the model. Results that expose certain process mechanics are discussed. The model describes the simultaneous /low of three phases-oil, water and gas-in one dimension. lt includes the effects of three-phase relative permeabilities, capillary pressure, and temperature-~ and pressure-dependent fluid properties. Interphase mass transfer 0/ water-steam is allowed, but the oil is assumed nonvolatile and the hydrocarbon gas insoluble in the liquid phases. The model allows beat convection in one dimension and two-dimensional heat conduction in a verticaI cross-sect ion spanning the oil sand and adjacent strata. The hydrocarbon-steam gas composition is tracked, but the effect of gas composition on u,ater-steam phase behavior is neglected. The model is solved numerically in three separate stages. Tbe three-phase mass balances are solved simultaneously using Newtonian iteration on, nonlinearities occurring in the accumulation terms. The energy balance is solved separately by noniterative application of the alternating-direction implicit procedure. Separate solution Of tbe composition balance is accomplished by straightforward solution of the finite difference equations. Tbe method of effecting nonsimultaneous, stnble solution of the mass and energy balances is the key to the success of the model.