Modeling of non-Darcy flow through anisotropic porous media: Role of pore space profiles

• The effect of curvature of throats on intrinsic properties of the porous media is investigated.
• Conical, parabolic, hyperbolic and sinusoidal throat profiles are used and compared.
• Analytical solution of 1D Navier–Stokes equations for converging/diverging pores is applied.
• The non-Darcy coefficient mostly depends on throat curvatures while permeability is not.
• Non-Darcy behavior is mostly affected by throat radius than pore radius and throat length.
• Pore morphology and anisotropy of the network are taken into account.

Excess pressure drop induced by inertial effects limits the applicability of Darcy's law for modeling of fluid flow through porous media at high velocities. It is expected such additional pressure drop is influenced by pore/morphology of porous media. This work concerns with fundamental understanding of how throat curvature affects intrinsic properties of porous media at non-Darcy flow conditions using network modeling. Conical, parabolic, hyperbolic, and sinusoidal capillary ducts with three types of imposed anisotropy are used to construct the network in a more realistic manner. Solutions of one dimensional Navier–Stokes equation for incompressible fluid flow through converging/diverging pore geometries have been utilized to acquire the pressure drop versus volumetric flow rate to investigate the role of various pore space profiles on the properties of porous media, which make the results of this work different from previous studies in the literature. Macroscopic inherent parameters of porous media such as tortuosity, porosity, permeability as well as non-Darcy coefficient are evaluated as outputs of the model. It has been revealed that the non-Darcy coefficient mainly depends on throat curvatures while permeability is not. While average throat radius is constant, both permeability and non-Darcy coefficient are increasing with average body radius. Among induced anisotropies, alteration of throat radius is the most effective parameter on non-Darcy coefficient. Regarding the throat morphology, some new general correlations for predicting the non-Darcy coefficient as a function of porosity, tortuosity, permeability, and the ratio of diverging/converging tubes in the network have been proposed. Results of this study could help better understanding of how the morphology of pores/throats affects the non-Darcy coefficient.