Prediction of Water Influx of Edge-Water Drive Reservoirs Using Nonparametric Optimal Transformations
- Jassim Abdulaziz Al-ghanim (Kuwait Gulf Oil Co) | Ibrahim Sami Nashawi (Kuwait University) | Adel Malallah (Kuwait U.)
- Document ID
- Society of Petroleum Engineers
- North Africa Technical Conference and Exhibition, 20-22 February, Cairo, Egypt
- Publication Date
- Document Type
- Conference Paper
- 2012. Society of Petroleum Engineers
- 6.1.5 Human Resources, Competence and Training, 5.5 Reservoir Simulation, 5.6.1 Open hole/cased hole log analysis, 5.2 Reservoir Fluid Dynamics, 5.1 Reservoir Characterisation, 7.6.6 Artificial Intelligence
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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.
Petroleum 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, 1943; 1958; 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 radial diffusivity equation; hence, it yields an accurate estimate of water encroachment for practically all flow regimes, provided that the flow geometry is actually radial. van Everdingen and Hurst solutions are for both the constant-terminal-rate case and the constant-terminal-pressure case of finite and infinite edge-water aquifers.
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