A 2D FDEM-based THM coupling scheme for modeling deformation and fracturing of the rock mass under THM effects

An enriched mixed finite element model for the simulation of microseismic and acoustic emissions in fractured porous media with multi‐phase flow and thermal coupling

“…𝑹 𝑎 is the lumped viscous drag acting on the fluid phase 𝑎 (𝑎 = 𝑤, 𝑔, 𝑛) which is defined by the Darcy seepage law as ẇ𝒂 = 𝒌 𝑎 𝑹 𝑎 (9) where 𝒌 𝑎 is the permeability tensor of the porous medium to the pore fluid 𝑎 defined as…”

“…The second term in Equation ( 28) indicates the effect of the fluid mass transfer (manifested by the fluid flow velocity, ẇ𝑖 in the form of advection) through the boundaries of the control volume in the heat balance equation as a convection term. 40,46 The relative velocities of the fluid phases with respect to the mixture can be eliminated from the thermal energy conservation equations (28) considering the Darcy's seepage law (9), resulting in the following version of the mixture enthalpy balance equation represented in terms of displacement, temperature and fluid pressures variables.…”

“…where 𝛽 𝑠 and 𝐾 𝑠 are the volumetric thermal expansion coefficient and the bulk moduli of the solid phase, respectively. The continuity equations for the flow of the three fluid phases through the deformable solid matrix can be written as follows with substitution of the relative fluid velocity using the Darcy's seepage law (9):…”

“…Simulation of groundwater contamination by industrial chemicals and hydrocarbons in applications like waste injection, modelling of steam and water injection in reservoir stimulation processes for enhanced recovery, and seismic and slope stability analysis in porous formations are only a few to be noted. Several papers have been published recently on the topic of fractured and non‐fractured porous media with single‐ and multi‐phase fluid flow with potential application in geomechanics 4–9 …”

“…Several papers have been published recently on the topic of fractured and non-fractured porous media with single-and multi-phase fluid flow with potential application in geomechanics. [4][5][6][7][8][9] Several numerical models have been proposed over decades for simulation of porous media with multi-phase flow. Depending on the focus of the projects and objectives, the reported works have limitations and restrictions.…”