In recent years, the use of numerical reservoir simulation to predict reservoir's future performance has shown a steady and strong increase. For meaningful result, however, reservoir simulation requires an extensive amount of data. In addition many months of time is generally required to assemble and collect the data. Therefore, reservoir simulation is often impractical for small fields.
This paper presents the development and results of a comprehensive and rigorous material balance mathematical model which simulate an oil reservoir bounded by a gas-cap and a finite aquifer. The model Incorporates the dynamics of oil/water and gas/oil contacts movements within a hypothetical cone-shaped, radial reservoir geometry. The basic components in the model are the material balance equation, water-influx model, a model for tracking the oil/water contact position, and a model for tracking the gas/oil contact.
The model was used to study the phenomenon of "late-water drive" which is an apparent increase in the activity of water influx in the late part of reservoir's life. The study concluded that the "late-water drive" phenomenon is caused primarily by the expansion of trapped gas behind the advancing oil/water contact. The study showed that even small aquifers (aquifer-to- reservoir radii ratio Ra/Ro < 3) demonstrated strong water influx activity in the late part of reservoir's life. This behavior is often misinterpreted as an influx from a large aquifer.
This paper presents the results of a sensitivity analysis of the effect of aquifer size, gas-cap size, reservoir's permeability, etc on the movements of all fluid contacts in particular and reservoir performance in general. In addition, it was demonstrated that average reservoir pressure must be corrected to the original oil/water contact (commonly not done in conventional reservoir analysis studies) in order to correctly calculate water influx. The procedure of pressure correction is given with many examples of reservoir's performance prediction with and without pressure correction.
Many reservoirs are bounded on a portion or all of their peripheries by an aquifer. Aquifers may be an open system (chargeable) or a closed system (not chargeable). In most of the practical applications the closed finite aquifer system is commonly encountered and is the system considered in this study.
In response to a pressure drop in the reservoir, the aquifer reacts by water influx into the reservoir. Determining the rate of water influx is important in the reservoir engineering analysis and is the subject of considerable work in the last few decades. One of the most widely used techniques of calculating water influx is the Van Everdingen-Hurst (VEH) technique 1. Van Everdingen and Hurst used the Laplace transform to solve the partial differential equation governing single-phase radial flow in porous media.
The aquifer supplies water to the reservoir in response to pressure decline felt at the aquifer inner boundary. Consequently, water invades a portion of the oil zone, trapping both oil and gas behind the front. As a result of water encroachment, the oil-water interface (OWC) advances into the oil zone.