The diffusivity equation is also solved in dimensionless form lee 1996. Pe281 applied mathematics in reservoir engineering. Several methods have presented to solve the diffusivity equation including numerical and analytical approaches. Dimensionless solution for diffusivity equation for.
Define and use dimensionless variables and dimensionless solutions to illustrate the generic performance of a particular reservoir model. Pdf the governing equation of fluid flow in an oil reservoir is generally nonlinear pde which is simplified as linear for engineering proposes. Gregory king, professor of practice, petroleum and natural gas engineering, the pennsylvania state university. 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. Derivation of the diffusivity equation in radialcylindrical. The governing equation of fluid flow in an oil reservoir is generally nonlinear pde.
Radial diffusivity equation an overview sciencedirect. However, at higher flow velocities, deviations from darcys law are observed as a result of inertial effects or even turbulent. In this nonlinear form, we cannot solve the equation analytically exactly. Thus, the equations are valid for reservoirs containing oil, water, gas or any. 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. Department of chemical engineering, lund university 17,662 views. We say that it is nonlinear because the two density terms in the equation are functions of pressure. This teaching textbook in hydrocarbon reservoir engineering is based on various lecture courses given. Diffusivity equation an overview sciencedirect topics.