[Paper Review] Hysteretic behavior of electrical conductivity in packings of particles

Behzad Ghanbarian, Muhammad Sahimi|arXiv (Cornell University)|Jan 18, 2017

Geophysical and Geoelectrical Methods60 references16 citations

TL;DR

This study proposes a unified theoretical model combining the effective-medium approximation (EMA) and percolation theory to predict hysteretic electrical conductivity in packed spheres during drainage and imbibition. It shows that percolation scaling holds across all saturation levels during drainage, but during imbibition, a crossover to EMA occurs at Swx = 0.5, with minimal influence from pore-size distribution on the σ–Sw relationship.

ABSTRACT

We address the problem of predicting saturation-dependent electrical conductivity σ in packings of spheres during drainage and imbibition. The effective-medium approximation (EMA) and the universal power law of percolation for σ are used, respectively, at higher and low water saturations to predict the conductivity, with the crossover between the two occurring at some intermediate saturation Swx. The main input to the theory is a single parameter that we estimate using the capillary pressure data. The predictions are compared with experimental, as well as numerical data for three distinct types of packings. The results for drainage in all the packings indicate that the universal power law of percolation is valid over the entire range of Sw. For imbibition, however, the universal power law crosses over to the EMA at Swx = 0.5. We also find that the effect of the pore-size distribution on the σ-Sw relation is minimal during both drainage and imbibition.

Motivation & Objective

• To predict saturation-dependent electrical conductivity (σ) in packings of spheres during drainage and imbibition.
• To address the hysteretic behavior of σ in porous media, which is critical for geophysical and hydrological applications.
• To determine the conditions under which percolation theory or effective-medium approximation (EMA) governs σ–Sw relationships.
• To assess the influence of pore-size distribution on the σ–Sw hysteresis loop.
• To validate the model against experimental and numerical data across three distinct packing types.

Proposed method

• Uses the effective-medium approximation (EMA) to model electrical conductivity at intermediate to high water saturations.
• Applies the universal power law of percolation to describe conductivity at low saturations.
• Introduces a crossover saturation Swx where the transition from percolation to EMA behavior occurs.
• Estimates the key model parameter using capillary pressure data, enabling calibration without fitting to σ–Sw data.
• Combines EMA and percolation theory into a single unified framework for both drainage and imbibition paths.
• Validates predictions against experimental and numerical data for three distinct packings of spheres.

Experimental results

Research questions

• RQ1 How does electrical conductivity σ vary with water saturation Sw during drainage and imbibition in packed spheres?
• RQ2 At what saturation Swx does the transition from percolation scaling to EMA behavior occur during imbibition?
• RQ3 To what extent does pore-size distribution affect the σ–Sw hysteresis loop?
• RQ4 Can a single-parameter model calibrated from capillary pressure data accurately predict σ–Sw relations across different packings?
• RQ5 Does the universal power law of percolation hold over the entire saturation range during drainage?

Key findings

• During drainage, the universal power law of percolation accurately describes σ–Sw across the entire saturation range.
• During imbibition, the universal power law crosses over to the effective-medium approximation (EMA) at Swx = 0.5.
• The influence of pore-size distribution on the σ–Sw relationship is minimal during both drainage and imbibition.
• The model’s single calibration parameter, derived from capillary pressure data, enables accurate prediction of σ–Sw without fitting to conductivity data.
• The theoretical framework successfully reproduces experimental and numerical σ–Sw data across three distinct packing types.
• The crossover at Swx = 0.5 during imbibition indicates a shift in the dominant conduction mechanism from percolation to effective-medium behavior.