Reservoir Engineering Equipment - Performance of Water Drive Reservoirs, Including Pressure Maintenance, by the Reservoir Analyzer

A study has been made to deter~r~irre how the behavior of a water drivee reservoir changes as a function of the permeability of the formation and as a function of the size of the aquifer. The effect of pressure maintenance programs on the rote of nat11rn1 water influx is also studied, (IS well as the influence on the influx of the position of water injection we1ls with reference to the oil-water contact. The results are determined by the use of an electrical reservoir analyzer and are plotted as families of curves of pressure, natural water influx, and water injection vs time or cumulalive production. Two size aquifers are studided. One is limited with a 36-inile radius, and the, other approximates an infinite reservoir. The field remains the same in all respects for the completed. study except that the permeability is changed to agree with that assumed for the aquifer. 1 N TR ODUCTI ON this study was undertaken in -dcr to determine how the pres- sure decline and water influx of a water drive field would change as a function of the rate of fluid withdrawals, as a function of the permeability of the formation, and as a function of the size of the aquifer. The effect of pressure maintenance programs on the rate of natural water influx was also studied as was the position of water injection wells with reference to the oil-water contact. The information has been determined by the use of an electrical reservoir analyzer1, sometimes referred to as a Carter type analyzer. This instrument is an analog type computer which can be set up to represent a water-drive oil field. It can reproduce the past performance of the field in terms of analogous electrical quantities when the proper circuit analog of resistors and condensers has been determined, also, it can determine the future behavior for any method of production which may be selected, or permit the comparison among several different methods. Although most applications of the reservoir analyzer"" have been to thc study of specific field performance, it is intended to use the analyzer here to help understand how various reservoir characteristics effect the final performance of the field and to sec under what conditions water injection will be of benefit and to what extent. Within the oil industry the performance of water-drive reservoirs was first described analytically by LV. Hurst' and M. Muskat2 for certain types of boundary conditions. The solutions of the equations developed involved products of exponential functions and Bessel functions. Later publications by Hurst4 and van Ever-clingen" and the hooks of Muskat6 gave further information on reservoirs with other boundary conditions. They also presented rather extensive curves and tables to help evaluate the analytical expressions involved. A rccent series of publications by Chatas. bascd on the work of Hurst and van Everdingen, gives quite complete charts and tables of data to evaluate the pressure decline or water influx in infinite or limited radial reservoirs. and in linear reservoirs. The curves in all of these publications are given in dimensionless form