A pore-scale numerical investigation on the impact of heterogeneity in predicting flow properties of carbonate rocks.

Abstract:

Fluid flow through rocks is overly complex due to the diversity of grains and diagenesis. Flow properties such as permeability (the ease of flow through rocks), and tortuosity (the degree of twist in the flow path of rocks) are commonly estimated with porosity as the key parameter. While these estimates might be effective in making accurate predictions in relatively homogeneous porous media, it does not suite prediction in heterogeneous rocks.

This study aims to investigate the effect of heterogeneity on porosity-permeability, and porosity-tortuosity relationships at pore-scale. The results will help gauge the applicability of porosity dependent equations to heterogeneous porous media.

Three sets of synthetic grain size distributions data with grain size ranging from 2 to 20 μm were used to generate three types of porous media, namely: Alpha with a uniformity coefficient (C_U) of 1 and an ordered arrangement of the grains in space, Beta with a C_U of 1 and a stochastic arrangement of the grains in space, and Charlie with a C_U of 7 and an ordered arrangement of the grains in space. Here, uniformity coefficient is defined as the ratio of the effective grain size d₆₀ to the effective grain size d₁₀, where d_X is the diameter for which X percent of the particles are smaller. A C_U closer to 1 indicates well sorted particles while a C_U greater than 5 indicates poor sorting. Water flow through the three types of porous media was simulated with STAR CCM+, a CFD software which solves Navier-Stoke equation using the finite element methodology. Porosity, tortuosity, and permeability were obtained from each simulation and analysed for relationships.

Results from this analysis show permeability and tortuosity is function of the distribution of grain sizes as well as the arrangement of these grains relative to each other. Therefore, we propose the use of grain size distribution data or associated pore size distribution data instead of porosity to make more accurate estimations of permeability and tortuosity for heterogeneous porous media.

The use of porosity-permeability, and porosity-tortuosity relationships to predict permeability and tortuosity is inappropriate for highly heterogenous porous media. There is need to develop workflows that accounts for pore/grain size distribution data, especially for carbonate sedimentary rocks.