摘要
According to the assumption of slightly compressible fluid, the quadraticgradient term in the nonlinear partial differential equations for the traditional well-test model isusually neglected. The linear partial differential equation is thus established. It is known thatneglecting the quadratic gradient term results in errors for long-time well tests. A nonlinear flowmodel for fractal medium is constructed and the quadratic gradient term is considered. The exactsolutions of the fractal reservoir models are obtained by Laplace transform and Weber transform in aconstant-rate and constant-pressure production for an infinitely large system. This paper addressesthe variation of pressure with fluid compressibility coefficient and fractal reservoir parameters.The plots of the typical pressure curves are constructed, and the results can be applied towell-test analysis.
According to the assumption of slightly compressible fluid, the quadraticgradient term in the nonlinear partial differential equations for the traditional well-test model isusually neglected. The linear partial differential equation is thus established. It is known thatneglecting the quadratic gradient term results in errors for long-time well tests. A nonlinear flowmodel for fractal medium is constructed and the quadratic gradient term is considered. The exactsolutions of the fractal reservoir models are obtained by Laplace transform and Weber transform in aconstant-rate and constant-pressure production for an infinitely large system. This paper addressesthe variation of pressure with fluid compressibility coefficient and fractal reservoir parameters.The plots of the typical pressure curves are constructed, and the results can be applied towell-test analysis.
