Analysis of nonlinear effects in fluid flows through porous media

Abstract

This article examines the nonlinear effects of fluid flow in a porous medium, governed by a new semi-analytical equation, from three aspects: equation derivation, experimental verification, and macroscale simulation modelling. The rigorous derivation of the new equation is presented with a semi-analytical approach in which the gas slippage effect and inertial forces are described. The latter effect is controlled by Fochheimer number, which is defined as a product of tortuosity and Reynolds number. The new equation successfully predicts the deviations from Darcy’s law in low-permeability media when the gas slippage effect occurs. The Klinkenberg gas slippage factor is obtained as a function of porous media’s structural parameter (porosity and intrinsic permeability) and gas property (mean free path of gas molecules). The equation validations are performed by core flow experiments for a wide range of reservoir properties, which yield good matching relationship between modelled and observed values. In addition, the proposed semi-analytical equation is used to simulate gas flow in the radial model.