Pore Network Modeling: Alternative Methods to Account for Trapping and Spatial Correlation

Abstract

Pore network models have served as a predictive tool for soil and rock properties with a broad range of applications, particularly in oil recovery, geothermal energy from underground reservoirs, and pollutant transport in soils and aquifers [39]. They rely on the representation of the void space within porous materials as a network of interconnected pores with idealised geometries. Typically, a two-phase flow simulation of a drainage (or imbibition) process is employed, and by averaging the physical properties at the pore scale, macroscopic parameters such as capillary pressure and relative permeability can be estimated. One of the most demanding tasks in these models is to include the possibility of fluids to remain trapped inside the pore space. In this work I proposed a trapping rule which uses the information of neighboring pores instead of a search algorithm. This approximation reduces the simulation time significantly and does not perturb the accuracy of results. Additionally, I included spatial correlation to generate the pore sizes using a matrix decomposition method. Results show higher relative permeabilities and smaller values for irreducible saturation, which emphasizes the effects of ignoring the intrinsic correlation seen in pore sizes from actual porous media. Finally, I implemented the algorithm from Raoof et al. (2010) [38] to generate the topology of a Fontainebleau sandstone by solving an optimization problem using the steepest descent algorithm with a stochastic approximation for the gradient. A drainage simulation is performed on this representative network and relative permeability is compared with published results. The limitations of this algorithm are discussed and other methods are suggested to create a more faithful representation of the pore space.