Presentation Date: Feb 14, 2026
AGSA Abstract
Non-Darcy (Forchheimer) flow is frequently encountered in high-velocity near-wellbore regions, tight formations, and fractured media, where the linear Darcy law no longer provides an accurate description of pressure–flow behavior. The nonlinear nature of Forchheimer’s formulation complicates the derivation of closed-form transient solutions, and many previous studies have relied on numerical or semi-analytical techniques. In this work, a fully analytical approach based on the Laplace transform is applied to the unsteady-state Forchheimer flow problem in an infinite reservoir. The governing partial differential equation is derived by combining the Forchheimer momentum equation with the continuity equation and compressibility relations, and is expressed in dimensionless form. A Laplace transform in time converts the governing equation into a modified Bessel equation, which is solved exactly under constant-rate inner boundary and vanishing outer boundary conditions. Analytical inversion of the Laplace-domain solution yields a closed-form expression for the dimensionless pressure in terms of the exponential integral function. A late-time logarithmic approximation is then obtained, which provides a simple and numerically stable relationship between dimensionless pressure, dimensionless time, radius, and the Forchheimer factor. The resulting expressions reproduce the expected diffusive behavior while explicitly capturing inertial effects, and they offer a rigorous basis for analyzing transient high-velocity flow near wells in porous media.
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