Energy geotechnics involves the use of geotechnical principles to understand and engineer the coupled thermo-hydro-chemo-mechanical processes encountered in collecting, exchanging, storing, and protecting energy resources in the subsurface. In addition to research on these fundamental coupled processes and characterization of relevant material properties, applied research is being performed to develop analytical tools for the design and analysis of different geo-energy applications. The aims of this paper are to discuss the fundamental physics and constitutive models that are common to these different applications, and to summarize recent advances in the development of relevant analytical tools.

This paper presents the development, implementation and verification of a coupled convective–conductive heat flow and transport model in the discrete element method (DEM). Thermal conduction is already available in DEM codes such as the particle flow code (PFC). However, current DEM codes rarely account for convective heat transport. There are many important phenomena in different applications that involve convective heat transport due to flow of fluid through permeable solid material, where the fluid and the permeable solids have different initial temperatures. Heat transfer from convection is dependent on the fluid flow velocity through existing and new instantaneously forming flow paths in solid and is typically much faster than conduction. The complete formulation of the heat convection model, its implementation and coupling with fluid flow and heat conduction in PFC^2D, and its validation are described in detail. While DEM has been widely used for studying fundamental mechanisms in geomaterials, little effort has been devoted toward extending DEM for studying coupling between conductive heat flow and convective heat transport problems. The developments presented in this paper will enable application of DEM to study coupled hydro-thermo-mechanical processes in geomaterials such as in geothermal systems, hydrocarbon production, environmental engineering and nuclear waste storage.

The micromechanics of proppant settling in quiescent fluid in a rough and relatively narrow rock fracture is investigated. The study focuses on particle–particle and particle–wall interactions in a dense-phase particle settling. The study used a coupled discrete element method and computational fluid dynamics (DEM–CFD) code because DEM–CFD is the most suitable computational method for modeling the frequent interactions of dense assembly of rigid particles and enables modeling of two-way solid–fluid interactions. Due to frequent particle–particle interactions of grains submerged in fluids, the particle interaction model in DEM is improved by the incorporation of the effects of lubrication due to a layer of fluid surrounding particles. Results of the numerical study are compared to previous experimental and theoretical relationships. The findings of the study highlight conditions that lead to proppant aggregation due to the fluid viscosity and fracture width in relation to particle diameter ratio. In the light of the DEM–CFD results, it was found that published relationships are inadequate in describing the settling rates for proppant in a rough and narrow hydraulic fracture and high fluid viscosity. Micromechanical particle interactions during settling and erratic upward and fluid counter-flow may cause proppant trajectories that are not always in the direction of gravity in a rough fracture resulting in clogging of the fracture or forming faster settling particle agglomerates. The maximum packing density 0.3–0.4 (3.9–5.9 lbs/gal) of proppant in a narrow and rough hydraulic fracture was obtained in this study, which is lower than the usually assumed one of 0.5 (9.8 lbs/gal) for any given fracture roughness.

The study presented in this paper investigates the effects of fluid lubrication on solid particles flow and transport in slurries at high solids concentrations. Particle–particle and particle–wall collisions influence the behavior of slurries constrained between two parallel walls thereby affecting solids transport and the fluid flow field. As the concentration of the particles increases, collisions become more frequent compared to the dilute flow, and their effect on the flow field cannot be neglected. Particularly, lubrication from a thin fluid layer formed between approaching particles acts as non-linear damper affecting particle kinetic energy and post-collision behaviors. The Discrete Element Method coupled with Computational Fluid Dynamics (DEM–CFD), with a new user-defined contact model that accounts for particle lubrication and as implemented in the commercially available two-dimensional Particle Flow Code (PFC^2D), was used to improve the understanding of the micro-mechanical behavior that contributes to particle clogging in a channel. It was found that the balance of fluid drag, related to the pressure drop in the channel and slurry properties such as fluid viscosity, particles volumetric concentration, particles size and channel size substantially contribute to the particle agglomeration even without considering gravity.

Coupling of the Discrete Element Method with Computational Fluid Dynamics (DEM–CFD) is a widely used approach for modeling particle–fluid interactions.Although DEM–CFD focuses on particle–fluid interaction, the particle–particle contact behavior is usually modeled using a simple Kelvin–Voigt contact model which may not represent realistic interactions of particles in high viscosity fluids. This paper presents an implementation of a new user-defined contact model that accounts for the effects of lubrication of fluid between two approaching particles while maintaining all other DEM–CFD particle–fluid interaction phenomena. Theoretical model that yields a non-linear restitution coefficient for submerged particle collisions, which was developed by Davis et al. (J Fluid Mech 163:479–497, 1986), is implemented in a DEM–CFD code. In this model, the behavior of particles at a contact depends on fluid properties, particle velocities and distance between particle surfaces. When two particles approach each other in a fluid, their kinetic energy decreases gradually because of a lubrication effect associated with the thin fluid layer between the particles. Particle post-collision behavior is governed by a simplified elastic contact law. With lubrication, it is possible that particles are not able to rebound if the approaching velocity is completely damped by lubrication, and in this case the particles agglomerate in the fluid. Tangential surface friction-slip forces are activated as in the case of dry particle contact. The lubrication model represents an advanced submerged particle collision approach that permits improved accuracy when modeling problems with high particle concentrations in a fluid. An application of the new model is shown in a simple sediment transport problem.