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

Plans to initiate a pilot steam displacement project with injection into zones as deep as project with injection into zones as deep as 2700' prompted concern for the wellbore heat losses that could be expected. To evaluate this aspect of the pilot design, a computer program was developed. The program and predictive technique were tested by comparing with other published methods and with measured casing temperature data. Agreement of predicted casing temperatures with measured temperature data was within three percent. The program was then used to predict wellbore heat losses under a variety of possible completion designs for steam injection wells in the S1-B zone of the Cat Canyon Field located near Santa Maria, California. These results show that under certain completion conditions, heat losses could be as high as 22 percent. Introduction In 1974, Getty Oil Company began design of a pilot steam displacement project in the S1-B sand of the Cat Canyon Field, Santa Barbara County, California. This zone is a thick, unconsolidated sand which produces nine degree API crude oil through use of cyclic steam stimulation. Wells range to 2700' in depth. In addition, the relatively high injection pressures required (1600 - 2000 psig) result in steam temperatures of approximately 620 degrees F. This combination of deep wells and high steam temperatures prompted concern about the wellbore heat losses which would be sustained. A review of published heat loss calculation methods indicated that very high heat losses could occur under some completion conditions. This review also revealed that each calculation technique had limitations which were of concern. A computer program was then developed which incorporates the best features of the various published techniques, but which is capable of handling more complicated well completion techniques. It is capable of handling cases in which steam quality varies as a function of depth, and also performs a complete heat balance of the steam injection system from steam generator discharge to sand-face. Following program verification, a study of various steam injection completion alternatives was conducted. COMPUTER PROGRAM DESCRIPTION The computer program developed (hereafter called HEATLOSS) calculates wellbore heatlosses based upon conservation of radial heat flow. That is, the steady-state heat flow due to thermal energy lost by the injected steam is assumed to be equal to the transient radial heat flow to the formation. An overall heat transfer coefficient, Uti, is calculated based upon equations for the conductive heat flow through various components of the injector completion and conduction-convection and radiation heat transfer coefficients in the annulus. An iterative procedure is used for this purpose (see the appendix for a detailed discussion of the calculation methods). Having calculated the heat transfer rate (from uti), knowing the steam mass flow rate, and by implicitly determining the steam pressure change, the variation in steam quality is calculated. In addition to the wellbore heat losses, surface steam line heat losses are also considered. These surface lines can be as long as one-half mile, in which case the heat losses can be substantial. The surface lines can be simulated as buried, exposed and not insulated, or exposed and insulated.