Simulation of dynamic pressure response of finite gas reservoirs experiencing time varying flux in the external boundary

• Governing equation of gas flow in porous media is solved by orthogonal collocation.
• Performance of the orthogonal collocation is validated by exact analytical solution.
• Orthogonal collocation calculates the dynamic pressure of reservoir with AARD = 0.36%.
• General solution is proposed for evaluation the effect of time varying boundary flux.
• Effect of exponential boundary flux on the dynamic pressure response is studied.

Pressure transient response (PTR) of a hydrocarbon reservoir to the alteration of production or injection rate can be computed through solution of its associated diffusivity equation. The PTR is likely the most important data for characterizing a hydrocarbon reservoir, forecasting its future productive performance, designing the appropriate stimulation scenario, and optimizing its management activity.The aim of this study is to simulate the effect of a time varying boundary flux on the PTR of a bounded gas reservoir using a simple and straightforward approximate scheme. The physical model can be viewed as a finite homogeneous reservoir experiencing a constant production rate at its inner boundary and an exponential flux in its outer boundary. Since direct handling of the time varying boundary condition is often hard, it makes a traditional solution applying Laplace transform or/and its inverse very tedious and time consuming. Therefore in this study the orthogonal collocation (OC) method which is elegant in its simplicity and efficient in its application is employed for simulating the PTR of the considered model.Reliability of the OC methodology is verified by comparing its result with an exact analytical solution for the closed reservoir. The proposed OC method has predicted the exact analytical solution with the absolute average relative deviation (AARD %) of 0.36%. Thereafter a general approximate solution is proposed to describe the PTR of gas reservoir with the time varying flux in the external boundary. The effect of boundary type, boundary flux, and boundary radius on the characteristic shape of the derivative graph has been investigated. The numerical results indicate that the PTR of a gas reservoir that experiencing time varying flux in its outer border can be successfully simulated using this approximate approach.