ABSTRACT
Here, our objective is to extend the solutions discussed in Chapters III and IV to a wide class of problems. First, we begin with a discussion of variable-rate solutions using Duhamel’s [1] integral formula. Second, we discuss production of fluids via a wellbore at a constant rate at the surface as opposed to a constant rate at depth. This problem is known as the “wellbore-storage problem” and was first discussed by van Everdingen and Hurst [2]. We also briefly explore the influence of a region of altered permeability around the wellbore that results from the drilling of the well. Third, we consider extending the applicability of our solutions to naturally-fractured or fissured porous media. Specifically, we examine the model considered by Barenblatt, Zheltov, and Kochina [3]. We then extend these results to more complicated visualizations of fissured porous media. Fourth, we consider flow in layered porous media wherein there is communication between the strata only via the wellbore (commingled production). Fifth, we examine methods to couple wellbore hydraulics (pipe flow) with flow in the porous medium, permitting us to explore the interaction between the porous medium and the wellbore through which the subterranean fluid must first flow to be produced at the surface.
