Three-Dimensional Simulation of Steamflooding

Abstract

Coats, K.H., Member SPE-AIME, Intercomp Resource Development and Engineering, Inc., Houston, Texas George, W.D., Chu, Chieh, Member SPE-AIME, Getty Oil Co., Houston, Tx. Marcum, B.E., Member SPE-AIME, Getty Oil Co., Los Angeles, Calif. Abstract This paper describes a three-dimensional model for numerical simulation of steam injection processes. The model describes three-phase flow processes. The model describes three-phase flow of water, oil, and steam and heat flow in the reservoir and overburden. The method of solution simultaneously solves for the mass and energy balances and eliminates the need for iterating on the mass transfer (condensation) term.Laboratory data are reported for steamfloods of 5,780-cp oil in a 1/4 five-spot sand pack exhibiting three-dimensional flow effects. These experiments provide additional data for checking accuracy and provide additional data for checking accuracy and assumptions in numerical models. Comparisons of model results with several sets of experimental data indicate a need to account for effects of temperature on relative permeability. Calculated areal conformance of a steamflood in a confined five-spot depends strongly upon the alignment of the x-y grid axes relative to the diagonal joining injection and production wells. It has not been determined which, if either, of the two grid types yields the correct areal conformance.Model calculations indicate that steamflood pressure level strongly affects oil recovery. pressure level strongly affects oil recovery. Calculated oil recovery increases with decreasing pressure level. An example application illustrates pressure level. An example application illustrates the ability of the model formulation to efficiently simulate the single-well, cyclic steam stimulation problem. problem Introduction The literature includes many papers treating various aspects of oil recovery by steamflooding, hot waterflooding, and steam stimulation. The papers present laboratory experimental data, field papers present laboratory experimental data, field performance results, models for calculating fluid performance results, models for calculating fluid and heat flow, and experimental data regarding effects of temperature on relative permeability. The ultimate goal of all this work is a reliable engineering analysis to estimate oil recovery for a given mode of operation and to determine alternative operating conditions to maximize oil recovery.Toward that end, our study proposed to develop and validate an efficient, three-dimensional numerical model for simulating steamflooding, hot waterflooding, and steam stimulation. Laboratory steamflood experiments were conducted to provide additional data for validation. Desired model specifications included three-dimensional capability and greater efficiency than reported for previous models. Omitted from the specifications were temperature-dependent relative permeability and steam distillation effects.This paper describes the main features of the three-dimensional, steamflood model developed. Those features include a new method of solution that includes implicit water transmissibilities, that simultaneously solves for mass and energy balances, and that eliminates the need for iteration on the condensation term. Laboratory data are reported for steamfloods in a 1/4 five-spot model exhibiting three-dimensional flow effects. Numerical model applications described include comparisons with experimental data, a representative field-scale steamflood, and a cyclic steam stimulation example. REVIEW OF PREVIOUS WORK Early efforts in mathematical modeling of thermal methods concentrated on simulation of the heat flow and heat loss. Gottfried, in his analysis of in-situ combustion, initiated a series of models that solve fluid mass balances along with the energy balance. Davidson et al. presented an analysis for well performance during cyclic steam injection. Spillette and Nielsen treated hot waterflooding in two dimensions. Shutler described three-phase models for linears and two-dimensional steamflooding, and Abdalla and Coats treated a two-dimensional steamflood model using the IMPES method of solution. SPEJ P. 573

Improved Steamflood Analytical Model

“…3 The five-point difference scheme conventionally used in numerical simulation can introduce significant disparity in results for equivalent parallel and diagonal grids. This disparity was noted by Todd et al 13 for adverse-mobility ratio waterfloods and later by Coats et al 14 for steamfloods. Abou-Kasem and Aziz 15 reported a detailed comparison of the nine-point difference and other numerical schemes as remedies to the grid orientation problem in ¼ of a five-spot steamflood pattern.…”

Documentation of the Thermal Energy Balance Equation used in the USNT Model of the NUFT Flow and Transport Code

“…The balance equation used in NUFT dates back many years, at least to 1974 (Coats et al, 1974), in the thermal modeling of petroleum reservoirs and is still widely used in the petroleum industry. It is also the same equation in the TOUGH2 code (Pruess, 1991, see pp.…”

Numerical modeling of steam injection for the removal of nonaqueous phase liquids from the subsurface: 1. Numerical formulation

“…In general, A. is a complex function of these parameters, and researchers have developed theoretical [Walsh and Decker, 1966;Beck, 1976;Zimmerman, 1989] and empirical [Somerton, 1958;Sugawara and Yoshizawa, 1962;Somerton et al, 1973;1974] methods for predicting A.. One method for estimating the overall thermal conductivity is known as the parallel model [Bejan, 1984]. With this model, the overall thermal conductivity is a combination of the individual conductivities (70) where Ar is usually measured experimentally, Aw is about 0.61 W lm K, and An is calculated by the method of Sato and Riedel [Reid et al, 1987] ( …”

“…Starting with the one-dimensional three-phase model of Shulter [1969], simulation capabilities rapidly improved, and by the mid 1970's, three-dimensional three-phase steamftood simulators had been reported in the petroleum literature [Coats, 1974[Coats, , 1976Vinsome, 1974]. Present commercial steam injection simulators are quite sophisticated, and often include compositional effects (see, for example, Coats, [1980]; Hwang et al, [1982]; Pruess and Bodvarsson, [ 1983]; Rubin and Buchanan, [1985]).…”