Unstable drainage dynamics during multiphase flow across capillary heterogeneities

TL;DR

This study addresses how capillary heterogeneity in porous media drives unstable, non-unique drainage by linking pore-scale connectivity to macro-scale flow using fast 4D X-ray imaging of gas–brine drainage in a layered sandstone. The centimeter-scale capillary barrier, formed by a low-porosity layer oblique to flow, temporarily halts and redirects invasion, with breakthrough times varying by up to a factor of four due to small perturbations in upstream invasion. The results show that pore-scale structure amplifies variability at larger scales, challenging deterministic continuum models and underscoring the need for probabilistic frameworks in subsurface multiphase flow. The imaging approach provides a powerful, multiscale view of dynamic flow processes with broad implications for CO2 storage, groundwater management, and other porous-media applications, while highlighting future challenges in data handling and imaging across scales.

Abstract

We use novel, fast 4D Synchrotron X-ray imaging with large field-of-view to reveal pore- and macro-scale drainage dynamics during gas-brine flow through a layered sandstone rock sample. We show that a single centimetre-scale layer, similar in pore size distribution to the surrounding rock but with reduced connectivity, temporarily inhibits and redirects gas flow, acting as a capillary barrier. Subtle variations in gas invasion upstream of the barrier lead to different downstream migration pathways over repeated experiments, resulting in unstable and unpredictable drainage behaviour, with breakthrough times varying by up to a factor of four. The results show that heterogeneity in pore-scale connectivity can amplify variability in macroscopic flow, challenging deterministic assumptions in existing continuum models. By linking structural heterogeneity to flow instability, this work underscores the need for probabilistic modelling approaches in multiphase flow and highlights broader implications for managing fluid transport in natural and engineered porous systems.

Figures (4)

• Figure 1: Slice average N2 saturation along unit core length for high flow rate (10-1 ml/min) (a) R1, (b) R2, and low flow rate (10-2 ml/min) (c) R1, (d) R2 (with $\sim$ 0.5 and 0.05 pore volumes between scans at high and low flow rate respectively). Each slice has an averaged length of 1mm, chosen to give well-defined REV flow properties.(e) Slice average N2 saturation along unit core length for repeat experiments after $\sim$ 1.4 pore volumes of N2 injected. (f) 3D porosity displayed as upscaled $\sim$ 1 mm3 voxels. Relative flow direction indicated.
• Figure 2: N2 saturation distribution within the heterogeneity region at the end of drainage for high flow rate (a) R1, (b) R2, and low flow rate (c) R1, (d) R2. The N2 saturation distribution is displayed as a 3D volume rendering, with the brine and rock phases excluded. Relative flow direction indicated.
• Figure 3: (a) Difference images between scans during low flow rate experiments (R1, top, and R2, bottom). Increases in N2 are shown in purple, decreases (limited) in blue, with a dashed line marking the heterogeneity. Difference images are calculated at the displayed pore volumes of injected N2 injected displayed, with timestamps for R2 at 3x longer intervals. (b) Differential pressure response across the core (R1, top, and R2, bottom), averaged over 20 second intervals to reduce noise. Grey shading marks the period during which N2 breaks through the heterogeneity. Key events are highlighted, with the interval between N2 reaching the heterogeneity and the core outlet corresponding to the time window shown in the difference images.
• Figure 4: (a) Upper and lower boundary regions on a 3D volume rending of low flow rate R1 N2 saturation (end of drainage) and an image of the core. (b) top - Pore size distribution (bodies and throats) within the upper and lower boundary region defined for the R1 experiment, overlaid by N2 occupied pores at the end of low flow rate drainage in each region. The probability is relative to the total number of pores and throats within the lower region. Bottom - Coordination number distribution of the upper and lower region pores.