Pressure transient analysis with exponential and power law boundary flux

•We study a reservoir when it is dominated by the boundary effects or discontinuities.•We analyze the pressure response in the presence of flow at the external border.•We examine two conditions: exponential and power boundary flux.•The solutions could be used for analysis and interpretation of the pressure response.

The widely used conceptual model set to study flow phenomena in an oil reservoir or groundwater system has been for several decades the homogeneous cylindrical model with a fully penetrating well located at its centre. For wells that produce at a constant rate in a bounded reservoir the boundary conditions are usually zero flux at the outer boundary. In this work we analyze the pressure response in the presence of flow at the external border, following an exponential or a power law boundary flux. Our solutions could be used for the analysis and interpretation of the pressure response when it is dominated by the boundary effects or discontinuities.