Scale-dependent petrophysical properties in porous media: a pore-network study

Abstract

Understanding fluid flow and transport in porous media properties has been an active subject of research in the past several decades in hydrology, geosciences and petroleum engineering. However, their scale-dependent characteristics are not yet fully understood. The scale dependence of flow in porous media is attributed to small- and large-scale heterogeneities, such as pore size distribution, pore connectivity, long-range correlations, fractures and faults orientations, and spatial and temporal variations. The main objective of this study is to investigate how permeability (k) and formation factor (F) vary with sample dimension at small scales by means of a combination of pore-network modeling and percolation theory. For this purpose, the permeability and formation factor were simulated in twelve three-dimensional pore networks with different levels of pore-scale heterogeneities. Simulations were carried out at five different network sizes, i.e., 1130, 2250, 3380, 4510 and 6770 µm. Four theoretical models were also developed based on percolation theory to estimate the scale dependence of permeability and formation factor from the pore-throat radius distribution. In addition, two other theoretical scale-dependent permeability models were proposed to estimate the permeability at different scales from the formation factor and/or pore-throat radius distribution. Comparing theoretical estimations with numerical simulations showed that the proposed models estimate the scale dependence of permeability and formation factor accurately. The calculated relative error ranges between -3.7 and 3.8% for the permeability and between 0.21 and 4.04% for the formation factor in the studied pore-networks.