American Institute of Mining, Metallurgical and Petroleum Engineers Inc.
Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers Office. Such discussions may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.
Generalized heat and fluid flow models are useful in evaluating the effects of heat upon crude oils in a reservoir environment and more particularly that area immediately surrounding a wellbore. The model described allows fluid and heat flow in the two dimensions of a vertical plane. As in other numerical models, each cell is assumed to be homogeneous in pressure, viscosity, temperature, etc. This paper describes how the flow of heat from one cell to another has been superimposed upon the unsteady-state flow of oil, gas, water, and steam between cells. Solutions to problems using this reservoir simulator are shown.
During the last several years the use of numerical models to simulate reservoir conditions have become very commonplace and simulators of several types and configurations have been developed for solution on high speed digital computers. During these same years, thermal recovery techniques have received a great deal of attention, and numerical simulator solutions applied also to this area. The broad term of thermal recovery covers a spectrum from in situ combustion to hot water alteration of fluid saturations around wellbores. Thermal recovery, like many other popular techniques, has a certain amount of "romance" surrounding it. The benefits can be very substantial; however, like any new technique it is subject to misapplication. The purpose of this paper is to describe a numerical simulator that accounts for both fluid and heat flow, and further to relate some of the observations that have evolved from its use.
The concept used in designing this thermal model was to combine fluid and heat flow into one model. The continuity equations written for each mobile phase (oil, gas, and water) were summed employing the method proposed by Fogin et al. The equations were arranged for an implicit solution of the potential distributions using the alternating direction procedure of Peaceman and Rachford. Following the calculation Peaceman and Rachford. Following the calculation of the potential distributions, the saturation distribution and temperature distribution are calculated explicitly. An iterative procedure of the entire calculation sequence permits the use of conductance and expansion coefficients calculated forward in time. This forward approximation is particularly important in the model discussed here because expansion and phase changes are not only functions of pressure but also of temperature. This approach permitted the use of relatively long time increments which are essential for the use of the simulator in the solution of practical engineering problems. problems.