Water Influx Into a Reservoir and Its Application to the Equation of Volumetric Balance

Abstract

Abstract This is a presentation of the diffusivity theory for the calculation of thewater drive on an oil reservoir in which the history of reservoir pressure withtime are the essential parameters for the determination of the rate andcumulative water encroachment into a field. The main body of the paper isessentially the application of the principles underlined here to actual fielddata. It consists of the work plots of the radial-flow case, and includes adiscussion of an illustrated problem for which the water-drive calculations aretreated in conjunction with the volumetric-balance equation. The appendix is amathematical treatment of the linear, radial, and spherical cases of waterinflux into a reservoir. Introduction The evaluation of oil reserves and the prediction of pressure behavior withdifferent rates of production are related to the volumetric balance of thefluids entering and leaving the space occupied by the oil and gas originallypresent in the formation; that is to say, important information can be gleanedfrom a volumetric study of the oil, gas, and water produced from a formation asit affects the extent of change in volume of oil zone, the gas cap, and theamount of water influx from the adjoining water sands. It is not the purpose of this paper to enter into a discussion of theequation of volumetric balance, in which such pertinent information assubsurface sampling and the measurement of reservoir pressures play apredominant part, as this has been discussed in detail by others. However, there is an inherent difficulty that has limited the general application ofthis equation to a study of oil reservoirs; that is, the insufficient knowledgeof the analytics for expressing the water drive on a field as a function ofreservoir pressure. This to a large degree has been overcome and it is thepurpose of this paper to present this theory in such form as to be applicablefor reservoir calculations. T.P. 1473