Treatment of Individual Wells and Grids in Reservoir Modeling

Abstract

Reservoir modeling, mathematical modeling, or simulation of a petroleum or natural gas reservoir enables the engineer to examine and evaluate the physical a-nd economic consequences of various physical a-nd economic consequences of various alternative production policies.Approximations are inherent in all workable, economical simulators. This paper describes three workable, useful approximations. (1)a method to compare observed field pressures with those calculated by a numerical simulator, (2) a method to reduce three-dimensional problems to two space dimensions with pseudo-third-dimensional features, and (3) a method to calculate the productivity index (PI) and the water-oil ratio (WOR) in a partially penetrating well partially penetrating wellThese methods, although admittedly approximations, are workable and have been found to be very useful. Their general utility will, however, depend upon the extent to which any underlying assumptions used in their formulation apply to a particular problem. particular problemThe objectives, applications and mathematical background of reservoir modeling have been described in other works.Ideally networks should be as shown in Fig. 1. Here, the grids are smaller near the wellbore than farther away. However, the number of grid points becomes large, even in a two-dimensional grid. Also, the small block sizes force one to use very small time steps, which can increase the computer time to the point of rendering the study economically unfeasible. Fig. 1 shows an example where the wells are located on a regular pattern. If that pattern becomes irregular enough, all cells pattern becomes irregular enough, all cells eventually will have to be small.In order to proceed with a study, modelers are forced to use linger grid sizes, as shown in Fig. 2.We realize that, by using large grid sizes, the fundamental flow equations are not truly represented. The network approaches a set of interconnected material balances with flow terms as a function of pressures and saturations. This paper describes the present method of handling wellbores in models with grid sizes many times the wellbore diameters. A method to compare pressures observed in the field with those calculated in the model is presented.A method also is given to reduce three- dimensional problems to two-dimensional grids.SPEJP. 341