Abstract
This chapter provides an overview of the fundamental equations for the flow of gases through porous media, along with solutions of interest for various boundary conditions and reservoir geometries. These solutions are required in the design and interpretation of flow and pressure tests. To simplify the solutions and application of the solutions, dimensionless terms are used. The chapter discusses assumptions and approximations necessary for defining the system and solving the differential equations. It illustrates the application of the principle of superposition to solve problems involving interference between wells, variables flow rates, and wells located in noncircular reservoirs. The chapter also explains the use of analytical and numerical solutions of the flow equations. Following this, it explains the formation damage or stimulation, turbulence, and wellbore storage or unloading. For well testing purposes two-phase flow in the reservoir is treated analytically by the use of an equivalent single-phase mobility. The chapter presents the equations of continuity, Darcy's law, and the gas equation of state and combines them to develop a differential equation for flow of gases through porous media. This equation, in generalized coordinate notation, is expressed in rectangular, cylindrical, or spherical coordinates and is solved by suitable techniques. Steady-state, pseudo-steady-state, and unsteady-state flow equations including the gas radial diffusivity equation, basic gas flow equations, solutions, and one-, two-, and three-dimensional coordinate systems, are also described in the chapter.
Published Version
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