Numerical Modeling of Effective Thermal Conductivity for Polymineralic Rocks using Lattice Element Method

TL;DR

This work addresses the challenge of predicting rock effective thermal conductivity (ETC) under coupled pressure and temperature in polymineralic media. It introduces a thermo-mechanically coupled Lattice Element Method (LEM) that represents microstructure with a random Voronoi lattice, assigns mineral phases via a stochastic overlay, and uses Hertzian-contact heat transfer with anisotropic mineral conductivities to resolve intergranular heating and fracturing. Key contributions include calibrating a spatial distribution of grain-contact quality from ambient measurements, validating the ambient predictions against room-temperature data and mixing-model bounds, and verifying the approach under in situ TP conditions with good agreement to experimental data across the TP grid. The model demonstrates physically grounded, transferable predictions of heat transport in heterogeneous geomaterials and offers a framework for predicting subsurface heat flow without reliance on detailed imaging, expanding capabilities for geothermal and reservoir studies.

Abstract

Accurate prediction of rock thermal conductivity under in-situ conditions is essential for characterizing subsurface heat flow. This study presents a numerical framework based on the Lattice Element Method (LEM) for simulating the effective thermal conductivity of polymineralic rocks under coupled pressure-temperature conditions. The model resolves interactions among heat transfer, grain contacts, and mechanical deformation within a microstructure-representative lattice. The methodology enables consistent treatment of heat conduction, nonlinear contact evolution, and thermally induced intergranular fracturing. Heterogeneity is introduced through a stochastic, volume-fraction-constrained discretization that preserves the measured mineral composition and porosity, while mineral anisotropy and fracture behavior are captured through element-level constitutive laws. The framework is evaluated using experimental data for two dry sandstones under ambient and elevated pressures and temperatures. Effective thermal conductivity is computed over the same pressure-temperature ranges and compared directly with the measurements. The results indicate that the predictions are capable of reproducing the characteristic trends and absolute levels. The close agreement between experimental observations and model predictions confirms that the thermo-mechanical coupled LEM provides a physically grounded and transferable approach for modeling heat transport in heterogeneous, polymineralic media.

Figures (13)

• Figure 1: LEM discretizations generated with increasing geometric randomness $\text{R}_{\text{F}}$: (a) $\text{R}_{\text{F}} \approx 0$, (b) $\text{R}_{\text{F}} = 0.5$, and (c) $\text{R}_{\text{F}}=1$. The blue lines represent the Delaunay edges forming the lattice of intergranular contacts, which transmit mechanical loads and heat.
• Figure 2: A schematic representation of particle i and the thermal fluxes exchanged with its neighboring particles.
• Figure 3: (a) Example of the discretized lattice and selected domain; assigned mineral grains with crystallographic axes defining thermal anisotropy with $\text{k}_{\parallel}$ (b) aligned with the vertical heat-flow direction, and (c) a configuration rotated by $45~^{\circ}$ .
• Figure 4: Stochastic LEM discretizations of (a) S#8, and (b) S#12 based on measured phase fractions. Phases are randomly assigned according to the experimentally determined proportions.
• Figure 5: (a) Three-dimensional schematic representation, and (b) cross-sectional view of the cubic press assembly of comparative steady state configuration. The blue block denotes the zirconia reference (axial thickness 20 mm) and the orange block denotes the rock sample (axial thickness 43 mm). The grey regions represent the top and bottom platens and the lateral guards held at temperatures $\text{T}_1$, $\text{T}_3$, and $\text{T}_{\text{S}}$, respectively. A constant axial gradient is imposed between $\text{T}_1$, and $\text{T}_3$ ($\text{T}_1 > \text{T}_{\text{S}}>\text{T}_3$). $\text{T}_2$ marks the measurement point, centered at the reference material height.