Pore-network modelling of non-Darcy flow through heterogeneous porous media

A pore-network model (PNM) was developed to simulate non-Darcy flow through porous media. This paper investigates the impact of micro-scale heterogeneity of porous media on the inertial flow using pore-network modelling based on micro X-ray Computed Tomography (XCT) data. Laboratory experiments were carried out on a packed glass spheres sample at flow rates from 0.001 to 0.1 l/s. A pore-network was extracted from the 3D XCT scanned volume of the 50 mm diameter sample to verify the reliability of the model. The validated model was used to evaluate the role of micro-heterogeneity in natural rocks samples. The model was also used to investigate the effect of pore heterogeneity on the onset of the non-Darcy flow regime, and to estimate values of the Darcy permeability, Forchheimer coefficient and apparent permeability of the porous media. The numerical results show that the Reynold's number at which nonlinear flow occurs, is up to several orders of magnitude smaller for the heterogeneous porous domain in comparison with that for the homogeneous porous media. For the Estaillades carbonate rock sample, which has a high degree of heterogeneity, the resulting pressure distribution showed that the sample is composed of different zones, poorly connected to each other. The pressure values within each zone are nearly equal and this creates a number of stagnant zones within the sample and reduces the effective area for fluid flow. Consequently, the velocity distribution within the sample ranges from low, in stagnant zones, to high, at the connection between zones, where the inertial effects can be observed at a low pressure gradient.