Abstract
Among the classic models used in the evaluation of aquifer properties, the most used are Van Everdingen & Hurst, (1949), Fetkovich approximate (1971), Carter & Tracy (1960), Allard & Chen (1984), and Leung (1986). Due to the inherent uncertainties in the aquifer characteristics, all the models require historical reservoir performance data to evaluate aquifer property parameters. The fact that the reservoir-aquifer boundary pressure is not constant with time gives rise to computational challenges. Most authors seek to eliminate this disadvantage by bringing up approximate models. Fetkovich assumes a constant boundary pressure while deriving his model and required a superposition to get a proper result. This led to the introduction of some forms of pressure approximation and iterations; any error introduced is constituted by this. Higher computational ability is mostly required especially in the evaluation of the Everdingen & Hurst model due to the application of Duhamel superposition principle. More uncertainty however is also seen in the geometry and areal continuity of the aquifer itself.
In this paper, a fast and simple approach was used to develop a new aquifer influx model for a finite aquifer system that admits a pseudo-steady-state flow regime. The partial differential equation that characterizes the flow of aquifer in the reservoir was considered. It was simplified through some basic assumption and in turn resulted to ordinary differential equation, with an appropriate boundary condition, a solution was gotten that enables a direct calculation of cumulative water influx at a given time without the use of superposition or pressure approximations or iterative means. In other to derive a solution under varying reservoir-aquifer boundary pressure the dependency of the boundary pressure with time was described as an exponential trend, which is mostly the case.
In other to validate the developed model, comparison was made with Carter & Tracy, Fetkovich and Van Everdingen Models. Van Everdingen and Hurst Model was used as the standard for comparison since it represents the exact solution of radial diffusivity equation. Two case examples were considered. The results show a close match between the developed model and the existing models, also from the error analysis made, it was noticed that the predictions of the newly developed model were better than that of the Carter & Tracy.