Investigating Apparent Deviations from Darcy’s Law in Heterogeneous Rocks: Insights from Neutron Imaging

Abstract

Darcy’s law provides a fundamental framework for understanding fluid flow through porous media. However, deviations from its linear superficial velocity-hydraulic gradient (v-i) relationship have been widely reported, at high and low flow rates. While previous studies have attributed the low flow rate deviations to factors such as fluid properties, boundary effects, and experimental artifacts, the role of material heterogeneity has received less attention. This study employs neutron imaging to investigate how rock heterogeneity influences macroscopically observed flow behavior. Volume-controlled percolation tests were conducted on Idaho Gray sandstone cores under near-single-phase conditions using heavy water (D₂O) and normal water (H₂O) across a wide range of flow rates. Bulk measurements (pore pressure at the sample boundaries and the controlled injection flow rate) revealed a decline in hydraulic conductivity at lower injection rates. Through a novel method for interpreting the breakthrough curves (BTC) derived from the neutron imaging data, we are able to quantify the volume of pores active in the flow during each test. The neutron radiography imaging acquired during the flow tests revealed that flow paths were strongly influenced by the rock’s heterogeneous pore structure, with higher flow rates promoting more uniform front propagation. This suggests greater pore space access at higher injection rates and implies the presence of threshold pressure gradients needed to access different parts of the pore network. The BTC analysis from neutron image shows a decrease in the volume of pores active in the flow (effective porosity) with decreasing injection rates, aligning with the observed reduction in hydraulic conductivity. By linking nonlinearity in vi-curves to variations in effective porosity, this study highlights the critical role of heterogeneity in controlling the fluid flow behavior. These findings underscore the importance of understanding the role of spatial variability in porous media when interpreting macroscopic (bulk) permeability measurements, especially when interpreting apparent deviations from Darcy’s law.