In this study, we have developed a new method to generate a multi-directional pore network for representing a porous medium. The method is based on a regular cubic lattice network, which has two elements: pore bodies located at the regular lattice points and pore throats connecting the pore bodies. One of the main features of our network is that pore throats can be oriented in 13 different directions, allowing a maximum coordination number of 26 that is possible in a regular lattice in 3D space. The coordination number of pore bodies ranges from 0 to 26, with a pre-specified average value for the whole network. We have applied this method to reconstruct real sandstone and granular sand samples through utilizing information on their coordination number distributions. Good agreement was found between simulation results and observation data on coordination number distribution and other network properties, such as number of pore bodies and pore throats and average coordination number. Our method can be especially useful in studying the effect of structure and coordination number distribution of pore networks on transport and multiphase flow in porous media systems.

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[1] Pore network models of two-phase flow in porous media are widely used to investigate constitutive relationships between saturation and relative permeability as well as capillary pressure. However, results of many studies show a discrepancy between calculated relative permeability and corresponding measured values. Often, calculated values overestimate the measured values. An important feature of almost all pore network models is that the resistance to flow is assumed to come from pore throats only; i.e., the resistance of pore bodies to the flow is considered to be negligible compare to the resistance of pore throats. We contend that this simplification may considerably affect the results for relative permeability curves. In this study, we present a new formulation for pore network modeling of two-phase flow, which allows for the calculation of wetting phase fluxes in the edges of (partially) drained pores. In a quantitative investigation, we have shown the significance of this effect. The pore space is represented by cubic pore bodies and parallelepiped pore throats in a Multi-Directional Pore Network model. This model allows for a distribution of coordination numbers ranging between 1 and 26. This topological property, together with geometrical distributions of pore sizes, is used to mimic the microstructure of real porous media. In the presence of the nonwetting phase, the wetting fluid is considered to fill only spaces along edges of cubic pore bodies. We show that the resistance to the flow of the wetting phase within these filaments of fluids are comparable to the resistance to the wetting phase flow within pore throats. Resulting saturation-relative permeability relationships show very good agreement with measured curves. Explicit representation of wetting phase filaments and calculation of different fluxes within pore bodies may also lead to improved predictions of transport properties such as dispersivities and mass transfer coefficients.Citation: Raoof, A., and S. M. Hassanizadeh (2012), A new formulation for pore-network modeling of two-phase flow, Water Resour.

The main objec ve of this research was to enhance our understanding of and obtain quanta ve rela on between Darcy-scale adsorp on parameters and pore-scale fl ow and adsorp on parameters, using a three-dimensional mul direc onal pore-network model. This helps to scale up from a simplifi ed but reasonable representa on of microscopic physics to the scale of interest in prac cal applica ons. This upscaling is performed in two stages: (i) from local scale to the eff ec ve pore scale and (ii) from eff ec ve pore scale to the scale of a core. The fi rst stage of this upscaling from local scale to eff ec ve pore scale has been reported in an earlier manuscript. There, we found rela onships between localscale parameters (such as equilibrium adsorp on coeffi cient, k d , and Peclet number, Pe) and eff ec ve parameters (such as a achment coeffi cient, k a , and detachment coeffi cient, k det ). Here, we perform upscaling by means of a three-dimensional mul direc onal network model, which is composed of a large number of interconnected pore bodies (represented by spheres) and pore throats (represented by tubes). Upscaled transport parameters are obtained by fi ng the solu on of classical advec on -dispersion equa on with adsorp on to the average concentra on breakthrough curves at the outlet of the pore network. This procedure has resulted in rela onships for upscaled adsorp on parameters in terms of the microscale adsorp on coeffi cient and fl ow velocity.