A Pore Network Model for the Calculation of Non-Darcy Flow Coefficients in Fluid Flow Through Porous Media

Determination of Forchheimer equation coefficients a and b

“…A dependence of the coefficients a and b on the Reynolds number will eventually be important for consolidated porous media. For the laminar flow regime, the simulation approach by Lao et al (2004) is adequate, but one has to consider our remarks. If turbulence occurs, one should use the approach of Ahmed and Sunada (1969), where additional losses due to direction changes, contractions of the conduits, etc., should also be taken into account.…”

“…A potential guideline for the adequate estimation of the non-linear energy losses in fractured or karst aquifers might be the simulation approach by Lao et al (2004). They used the pore diameter distribution proposed by Yanuka et al (1986) to create artificial porous media, composed of straight pipes of cylindrical cross-section and random orientation in space.…”

“…The computation of the flow field of the above-mentioned network demonstrated that, on a macroscopic scale, the flow is described by the Forchheimer equation, where the coefficient a is related to energy losses in the straight pipe sections and the Poiseuille law, and where the inertial coefficient b depends on minor losses that are induced at pipe junctions. A serious drawback of the approach by Lao et al (2004) is that the use of the relations by Bird et al (1960), which are valid for fully developed turbulence and large Reynolds numbers, is not compatible with the use of the Poiseuille law, which is valid for creeping flow; Lao et al (2004) could not reproduce the experimental data by Jones (1987).…”

Agglomeration and filtration of colloidal suspensions with DVLO interactions in simulation and experiment

“…Some simulations are based on Darcy's law and phenomenological equations for the local porosity and local permeability of the filter cake [1][2][3][4]. Kim et al consider the aggregates as solid cores with porous shells and determine the filter cake's permeability with Stokes' equation and Brinkman's extension of Darcy's law [1,2].…”

“…Kim et al consider the aggregates as solid cores with porous shells and determine the filter cake's permeability with Stokes' equation and Brinkman's extension of Darcy's law [1,2]. Lao et al replace the pore system with a network of pipes and junctions and then calculate the flow in the tubes with the Poiseuille equation [3]. Eisfeld et al propose a pseudo-continuous model for statistically described domain geometries, where the solid/liquid interaction is represented by a coupling term in the Navier-Stokes equation [4].…”