Pseudo-Aquifer Index: A New Concept for Estimating Transient Water Influx using Kumar-Ramey Average Pressure Equation

Abstract

This paper presents a new concept of Pseudo-Aquifer Index and a major departure from classical methods to estimate transient water influx using Kumar-Ramey equation employing reservoir average pressure obtained from transient tests for a central well in a constant pressure reservoir. The new method overcomes the two limitations of the conventional methods of van Everdingen-Hurst (1949), Carter-Tracy (1960), Fetkovich (1971), and similar other studies. These methods require apriori knowledge of (1) pressure history at the reservoir-aquifer boundary (oil-water contact or OWC) with time, and (2) aquifer characterization in terms of rock and fluid properties, depth, and geometric configuration. Such data for aquifer and OWC pressure history carry a high degree of uncertainty at the beginning of a newly discovered complex offshore or onshore reservoir development. Kumar-Ramey (1974) presented dimensionless water-influx (WeD) as a function of dimensionless average pressure and producing time which yields cumulative water-influx volumes as a fraction of cumulative reservoir withdrawal. Kumar (1977) also provided the dimensionless pressure at the reservoir aquifer boundary with time. Plots of dimensionless average pressure, dimensionless boundary pressures at the OWC, and cumulative water influx function (WeD) are presented as a function of producing times for the three cases of pseudo-aquifer-index of 0.25, 0.50, and 1.0. Some of this data is obtained from Kumar (1977) and is transformed into polynomial equations. Two examples show the applications, and compare transient water-influx results with those obtained from van Everdingen-Hurst method. A log-log type curve of dimensionless average pressure and time is included for determination of reservoir properties when average pressure is known A considerable advantage of the new method is its simplicity, generality, ease in use, and implementation in reservoir engineering software and simulation when compared to conventional methods. This study is also the first to provide a systemic characterization of transient boundary (OWC) pressures in closed and partial water drive reservoirs.