Direct simulation of fluid‐solid mechanics in porous media using the discrete element and lattice‐Boltzmann methods

Abstract

A detailed understanding of the coupling between fluid and solid mechanics is important for understanding many processes in Earth sciences. Numerical models are a popular means for exploring these processes, but most models do not adequately handle all aspects of this coupling. This paper presents the application of a micromechanically based fluid‐solid coupling scheme, lattice‐Boltzmann discrete element method (LBDEM), for porous media simulation. The LBDEM approach couples the lattice‐Boltzmann method for fluid mechanics and a discrete element method for solid mechanics. At the heart of this coupling is a previously developed boundary condition that has never been applied to coupled fluid‐solid mechanics in porous media. Quantitative comparisons of model results to a one‐dimensional analytical solution for fluid flow in a slightly deformable medium indicate a good match to the predicted continuum‐scale fluid diffusion‐like profile. Coupling of the numerical formulation is demonstrated through simulation of porous medium consolidation with the model capturing poroelastic behavior, such as the coupling between applied stress and fluid pressure rise. Finally, the LBDEM model is used to simulate the genesis and propagation of natural hydraulic fractures. The model provides insight into the relationship between fluid flow and propagation of fractures in strongly coupled systems. The LBDEM model captures the dominant dynamics of fluid‐solid micromechanics of hydraulic fracturing and classes of problems that involve strongly coupled fluid‐solid behavior.