Pressure Transient Analysis of Two-Phase Flow Problems

Abstract

Summary This paper considers the analysis of pressure drawdown and buildup data for two-phase flow problems. Of primary concern is the analysis of data influenced by saturation gradients that exist within the reservoir. Wellbore storage effects are assumed to be negligible. The pressure data considered are obtained from a two-dimensional (2D) numerical coning model for an oil/water system. We consider constant-rate production followed by a buildup period and assume that the top, bottom and outer boundaries of the reservoir are sealed. First, we consider the case where the producing interval is equal to the total formation thickness. Second, we discuss the effect of partial penetration. In both cases, we show that average pressure can be estimated by the Matthews-Brons-Hazebroek method and consider the computation of the skin facture. We also show that a reservoir limit test can estimate reservoir PV only if the total mobility adjacent to the wellbore does not vary with time. Introduction This work investigates methods that determine reservoir parameters from pressure drawdown and buildup data in a reservoir in which oil and water flow simultaneously. We examine the pressure response at a well located at the center of a cylindrical reservoir. We also consider the pressure response at fully penetrating and partially penetrating wells. For complete penetration problems, we show that if horizontal saturation gradients are negligible, then the skin factor, the total mobility, and individual phase mobilities can be calculated from either the drawdown or buildup data. These individual phase mobilities represent thickness-averaged values. If oil and water are mobile only over a portion of the reservoir, then the average oil mobility in the zone where oil is mobile and the average water mobility in the zone where water is mobile can also be obtained. For partial penetration problems, we show that if the wellbore pressure is unaffected by the outer boundary, then a semilog plot of either buildup or drawdown data may exhibit two straight lines. The first semilog straight line, however, occurs at very early times and will seldom be identifiable in practice. Thus, we restrict our attention to the estimates of reservoir parameters that can be obtained from the slope of the second semilog straight line. We show that the slope of the second semilog straight line yields a reliable estimate of the thickness-averaged total mobility in the region of the reservoir away from the wellbore where horizontal saturation gradients are negligible. We delineate conditions under which individual phase mobilities can be calculated from the second straight line. To the best of our knowledge, studies of partially penetrating wells, for the most part, have been restricted to single-phase flow problems. The primary concern of this study is to examine the applicability of classical methods for the determination of phase mobilities, skin factor, average reservoir pressure, and reservoir PV. The analysis of two-phase flow data dominated by wellbore storage is discussed in Ref.1. All our results were obtained from a numerical simulator discussed in Appendix A. Most works on pressure transient data affected by multiphase flow examine only the simultaneous flow of oil and gas. Currently, methods for analyzing multiphase flow data are based on the modifications to the single-phase flow problem, suggested by Perrine and later justified by Martin. Perrine and Martin suggest that total and individual phase mobilities can be determined if the appropriate flow rates are known. The relevant equations for computing the mobilities are given elsewhere. Unfortunately the theoretical justification for the results given in Ref. 4 and 5 assumes that saturation gradients are negligible. We show that if saturation gradients exist, individual phase mobilities can be computed only for a restrictive set of conditions. The basic contributions of this work areto specify the conditions for which the Perrine and Martin approach is valid (when saturation gradients are important),to specify the correct procedures to be used to analyze pressure data when two fluids are produced simultaneously, andto interpret results (in physical terms) from an analysis on the basis of the Perfine and Martin approach. Although our primary intent was to investigate pressure transient behavior, questions involving the simulation of the system arose. In particular, from the viewpoint of well-test analysis, we required the wellbore pressure to be independent of depth (except for the differences in fluid head) and also required that the flow rate (oil and water, or oil) be constant. SPEFE P. 151^