Modeling simultaneous oil and water flow with single-phase analytical solutions

Much computer software used to analyze well test and production data and to forecast well performance is based on single-phase analytical liquid or gas solutions. Many attempts have been made to apply the solutions to model multiphase flow. Most work, however, has examined only the simultaneous flow of oil and gas. This dissertation is intended to apply single-phase analytical liquid solutions to model multiphase flow of oil and water. Of primary concern is developing a simple analytical method to forecast the performance of a well producing oil and water simultaneously based on the Perrine-Martin approach. Using this approach, this work critically examines the use of the integral transformation in oil-water flow problems. Additionally, this work develops a new single-phase solution using an outer boundary condition called "the prescribed pressure boundary condition" that might be more appropriate for reservoirs with water influx or waterflooding.;A specific configuration of well, cylindrical reservoir, and cylindrical aquifer is used. The material balance principles are applied to this composite system such that we can relate the water influx to the well production variables and reservoir flow properties. The Fetkovich pseudo-steady state water influx model is used to relate the cumulative water influx and the reservoir-aquifer interface pressure. The average reservoir pressure which is then related to the well performance using single-phase slightly compressible liquid solutions is calculated using a material balance equation. The producing water-oil ratio and the oil and water production rates are obtained from the total rate using relative permeabilities for oil and water and Darcy's law assuming zero capillary pressure gradient. The fluid saturations are computed volumetrically so that the implicit, Muskat-type relation between saturation and pressure is not necessary. This volumetric saturation computation technique does not require knowledge of saturation distribution in the reservoir. Pre- and post-breakthrough criteria are based on the application of the fractional flow principle. Although we consider the constant-rate production case only, it follows that using the results of the constant-rate production case, the method can be readily extended to the constant-pressure production case using the van Everdingen-Hurst identity and an appropriate Duhamel's formula (principle of superposition).