Chapter 6: Mathematical Preliminaries and Boundary and Initial Conditions for Pressure Diffusion in Formation Testing
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Published:2021
"Mathematical Preliminaries and Boundary and Initial Conditions for Pressure Diffusion in Formation Testing", Wireline Formation Testing: Hardware, Pressure Transient Testing, Interpretation and Sampling, Fikri J. Kuchuk, T. S. Ramakrishnan, Mustafa Onur
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In this chapter, we present the governing partial-differential equations of pressure diffusion, and the boundary and initial conditions for different flow geometries of formation testing tools. Wellbore pressure, with skin and wellbore storage effects, is also covered in this chapter. In Chapter 3, we defined homogeneous, inhomogeneous, and heterogeneous porous media, as well as anisotropic homogeneous media. We assume that formation and fluid parameters are time-invariant and the permeability tensor is independent of fluid properties.
For flow of a slightly compressible fluid with constant compressibility (ct) and viscosity (μ), the pressure diffusion equation in an anisotropic homogeneous porous medium in a Cartesian coordinate system can be written as
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