Application of effective medium theory to estimate gas permeability in tight-gas sandstones

TL;DR

This paper adapts the effective-medium approximation model to upscale gas permeability in tight-gas sandstones, providing more accurate estimates from pore-scale measurements and pore-throat distributions.

Contribution

It introduces a novel application of EMA for permeability upscaling in tight sandstones, comparing cylindrical and slit-shaped pore assumptions, and evaluates its accuracy against CPA.

Findings

EMA estimates are more accurate with cylindrical pores.

EMA predicts permeability within a factor of two of measurements.

EMA outperforms CPA in heterogeneous media.

Abstract

Upscaling Klinkenberg-corrected gas permeability, k, in unconventional tight sandstones has numerous practical applications, particularly in gas exploration and production. In this study, we adapt the effective-medium approximation (EMA) model of Doyen - proposed first to estimate bulk electrical conductivity, {\sigma}_b, and permeability in sandstones from rock images - to scale up {\sigma}_b and k in tight-gas sandstones from pore to core. For this purpose, we calculate two characteristic pore sizes: an effective hydraulic and an effective electrical pore size from pore-throat size distributions - determined from mercury intrusion capillary pressure (MICP) curves - and pore-throat connectivity. The latter is estimated from critical volume fraction (or percolation threshold) for macroscopic flow. Electrical conductivity and permeability are then scaled up from the two characteristic pore sizes, tortuosity, and porosity by assuming two different pore geometries: cylindrical and slit-shaped. Comparison of results obtained for eighteen tight-gas sandstones indicates that the EMA estimates {\sigma}_b and k more accurately when pores are assumed to be cylindrical. We also estimate k from the pore-throat size distributions and the measured electrical conductivity using the EMA and critical path analysis (CPA), another upscaling technique borrowed from statistical physics. Theoretically, the former is valid in relatively heterogeneous porous media with narrow pore-throat size distribution, while the latter is valid in heterogeneous media with broad pore-throat size distribution. Results show that the EMA estimates k more accurately than CPA and arrives within a factor of two of the measurements on average.