Simulation of Steamflooding With Distillation and Solution Gas
Authors: Coats K.H. 
Published: December 2007

Abstract
This paper describes a three-dimensional numerical model for simulating steam-injection processes. The model accounts for solution gas and steam distillation of oil. The relative-permeability treatment presented includes a flexible but simple representation of temperature dependence and a history-dependent hysteresis in gas relative permeability. Since computational stability is a major difficulty in steamflood simulation, an implicit treatment of transmissibilities and capillary pressure is presented in detail. Model applications include comparisons with laboratory data, sensitivity experiments, and a field steam-injection test.

Introduction
Shutler and Abdalla and Coats described two-dimensional, three-phase flow numerical models for simulating steam-injection processes. Weinstein et al. described a one-dimensional model that accounted for steam distillation of oil. Coats et al. described a three-dimensional steamflood model that neglected steam distillation of oil, release of solution gas at elevated temperatures, and temperature dependence of relative permeability. This paper describes an extended formulation that includes these three phenomena and uses a more implicit treatment of capillary pressures and transmissibilities in the fluid-saturation calculations. The extended formulation represents a step toward a fully compositional thermal model without incurring the computational expense of the latter.
The relative-permeability treatment described includes a rather flexible but simple representation of temperature dependence and incorporates a hysteresis in gas-phase relative permeability that varies with the historical maximum grid-block gas saturation. The phase-behavior representation is the weakest element of this work. We have found insufficient data relative to PVT behavior of a heavy-oil/steam system to justify sophisticated schemes of the type used in isothermal hydrocarbon systems. The PVT treatment presented is the simplest we could construct subject to the objectives of "directional correctness," reasonable quantitative accuracy, and ability to obtain required parameters from laboratory data either normally parameters from laboratory data either normally available or readily determinable.
Model results presented include a comparison with laboratory data for a steamflood of a distillable oil; sensitivity results indicating effects and relative importance of various types of input data; and a comparison between calculated and observed injection rates for a Cold Lake (Alta.) steam-injection test. The latter is of interest in regard to reservations we have had regarding a model's ability to predict steam-injection rates into virtually immobile oil (100,000 cp). The field-test data showed initial and sustained steam-injection rates of 1,400 STB/D (cold-water equivalent). We discuss several reservoir-fluid parameters that had little effect and one independently measured parameter that had a pronounced effect on the calculated injection rate. pronounced effect on the calculated injection rate. MODEL DESCRIPTION
The model consists and sewn equations expressing conservation of energy, conservation of mass, and constraints on sums of liquid and gas phase mol fractions. The mass-conservation equations apply to water and to each of three hydrocarbon components. In finite-difference form these equations are the following.
SPEJ
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