Prediction of Water Influx of Edge-Water Drive Reservoirs Using Nonparametric Optimal Transformations

Abstract

The accurate estimation of water influx into a petroleum reservoir is very important in many reservoir engineering applications, such as material balance calculation, design of pressure maintenance programs, and advanced reservoir simulation studies. These applications have heavily relied on the classical work of van Everdingen and Hurst for finite and infinite edge-water drive reservoirs. However, for both types of water drive reservoirs, the calculation of water influx is not a straight forward task. Table lookup and interpolation between time entries are needed, and furthermore for finite aquifers, interpolation between tables may be also required.The paper presents nonparametric optimal transformations models for the prediction of dimensionless water-influx and dimensionless pressure drop for finite and infinite edge-water drive reservoirs using Graphical Alternating Conditional Expectation (GRACE). In order to achieve maximum efficiency, all the terms involved in the models are used in dimensionless form. GRACE transformations are totally data driven and do not assume any a priori functional form. The results of the various cases are in excellent agreement with the original tables of van Everdingen and Hurst. IntroductionPetroleum reservoirs are often surrounded from the edge or the bottom by water aquifers that support the reservoir pressure through water influx. In response to a pressure drop in the petroleum reservoir, the water aquifer reacts to offset, or retard, pressure decline by providing a source of water influx or encroachment. To determine the effect that an aquifer has on the oil and gas production, it is important to estimate the amount of water that has entered into the reservoir from the aquifer. Such calculation is not a simple and risk-free task due to the involvement of many unknown parameters. For instance, aquifer pressure, thickness, permeability, porosity, shape, and areal extent are usually all unknown variables. Furthermore, water aquifer models are classified according to the flow geometry as either edge-water or bottom-water drive (Figures 1 and 2). These models have completely different flow behavior. The type of the water aquifer, its size, properties, and the amount of water that it can deliver into the reservoir for a certain pressure drop during a specific period of time affect the entire production life of the reservoir. A good knowledge of the aquifer properties, specifically the amount of water that it can provide into the reservoir, dictates the production schedule and the development strategies that need to be implemented in order to optimize oil recovery. Many authors have presented different models for estimating the water influx. These models apply to different flow regimes, including steady-state, modified steady-state (Schilthius, 1963), pseudo-steady-state (Hurst, 19431958;Leung, 1986), and unsteady-state (Fetkovitch, 1971;Leung, 1988). van Everdingen and Hurst (1949) presented the most commonly used water-influx model. This model is basically a solution of the radi...

A Global Search Algorithm for Determining Water Influx in Naturally Fractured Reservoirs

“…N = I 1 r eD s f (s) K 1 s f (s) + I 1 s f (s) K 1 r eD s f (s) (15) where s is the Laplace space operator (dimensionless); I 0 (x) are Bessel functions of the first type of zero order (dimensionless); I 1 (x) are Bessel functions of the first type of one order (dimensionless); K 0 (x) are Bessel functions of the second type of zero order (dimensionless); and K 1 (x) are Bessel functions of the second type of one order (dimensionless).…”

“…Some scholars have developed some methods to determine water influx [15][16][17][18]. In 2007, Kryuchkov et al [16] proposed using microscopic computer tomography technology to detect water invasion, which avoids the tedious process of solving mathematical models.…”

“…The method was simple and reliable, but the cost was high. In 2012, Al-Ghanim [15] proposed a nonparametric optimal transformations method to predict the water influx in the edge water drive reservoirs. This method can directly calculate water influx without looking up tables and interpolation.…”

Comparative Study of Oil Recovery Factor Determination for Edge and Bottom Water Drive Mechanism Using Water Influx Models

“…Water influx volume as well as the flow geometrics has a significant role to play in the recovery factor. Estimation of water influx volumes into the reservoir is significant in number of applications such as material balance for estimation of reserves, reservoir simulation studies for model calibration, production scheduling and setting up development strategies to optimize hydrocarbon recovery [4]. An accurate estimation of water influx into the reservoir is required with the aid of an efficiency aquifer model that can capture the real dynamics of petroleum subsurface system.…”

Analyzing and forecasting the performance of water drive gas reservoirs

“…Whenever we make a production forecast, we use a model of the reservoir and production system, in the form of mathematical models to simplify the reality. The aim of the forecaster, in making reliable predictions, is to use a model that is sufficiently representative of the physical processes and constraints, and that adequately allows to reduce the uncertainties [3].…”