Derivation of the diffusivity equation in radialcylindrical. The diffusivity equation is also solved in dimensionless form lee 1996. Pdf the governing equation of fluid flow in an oil reservoir is generally nonlinear pde which is simplified as linear for engineering proposes. For this equation, the reservoir temperature is supposed to be constant which is a valid assumption in most cases. However, at higher flow velocities, deviations from darcys law are observed as a result of inertial effects or even turbulent. Mohammed abdalla ayoub diffusivity equationlinear petroleum engineering. Parametric analysis of diffusivity equation in oil reservoirs. This teaching textbook in hydrocarbon reservoir engineering is based on various lecture courses given. Define and use dimensionless variables and dimensionless solutions to illustrate the generic performance of a particular reservoir model. Note that this solution of the radial diffusivity equation is mathematically identical to the radial heat conduction equation. The reciprocal of this constant, kc, is defined as the diffusivity constant. Pdf asymptotic solutions of the diffusivity equation and. Tpg4150 reservoir recovery techniques 2017 fluid flow equations norwegian university of science and technology professor jon kleppe department of geoscience and petroleum 3 pv nzrt. The governing equation of fluid flow in an oil reservoir is generally nonlinear pde.
Pe281 applied mathematics in reservoir engineering. Radial diffusivity equation an overview sciencedirect. Thus, the equations are valid for reservoirs containing oil, water, gas or any. Pdf parametric analysis of diffusivity equation in oil. Assume that the formation is homogeneous, isopachous, and isotropic, the reservoir is filled with slightly compressible fluid with a constant compressibility, the flow behavior is isothermal and follows darcys law, and that the gravity and capillary force are negligible. Pdf parametric analysis of diffusivity equation in oil reservoirs. In order to obtain analytical solutions to this equation, we must first linearize it. In particular, the diffusivity equation for a singlephase gas flow is expressed in terms of the. We say that it is nonlinear because the two density terms in the equation are functions of pressure. Dimensionless solution for diffusivity equation for. In this nonlinear form, we cannot solve the equation analytically exactly. Gregory king, professor of practice, petroleum and natural gas engineering, the pennsylvania state university. Student, petroleum engineering department, african university of science and.
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