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

Abstract

A novel mixed enriched finite element model is developed for coupled non‐linear thermo‐hydro‐mechanical simulation of fractured porous media with three‐phase flow and thermal coupling. Simulation of induced acoustic emission (AE) and microseismic emission (ME) due to tensile fracturing and shear slip instability of pre‐existing fracture interfaces is carried out and the numerical results of the emitted signals are analysed. The mathematical model is based on the generalized Biot's theory for coupled interaction of solid and fluid phases. A computationally robust non‐linear solver is developed to handle the severe non‐linearities arising from fluid saturations, relative permeabilities of fluids, constitutive models of interfaces and convective thermal coupling. To model pre‐existing natural fractures and faults, discrete fracture propagation and nucleation of cracks (micro‐cracking) independently of the original mesh topology, a local Partition‐of‐Unity (PU) finite element method, namely, the Phantom Node Method (PNM) is implemented. The cohesive fracture modelling scheme is implemented to account for the non‐linear behaviour of fracturing and localization, and to rectify the non‐physical stress singularity condition at the fracture tip. Effects of different system parameters on fracturing, shear‐slip instability and the associated induced AEs and MEs are investigated through various numerical results.

A mixed nonlocal finite element model for thermo‐poro‐elasto‐plastic simulation of porous media with multiphase fluid flow

“…Substituting the gradient components represented in (14) into the flow rule (8) the spherical/hydrostatic and the deviatoric contributions of the plastic strain tensor may be derived:…”

“…To further expand the algorithmic tangent modulus we first obtain an expression for 𝜕n 𝝔D 𝜕𝜺 by taking derivative of n 𝝔D with respect to 𝜺 using Equation (14). From Equation ( 86)…”

“…Komijani and his co-workers also extended the use of the developed enriched finite element models to simulation of induced microseismic and acoustic emissions due to fracture reactivation and tensile fracture propagation in single phase and multi-phase flow cases. [12][13][14] Numerical modellings of the coupling between solid deformation, fluid flow, and heat transfer with or without material nonlinearity considerations dates back to the works of Lewis and Schrefler 15 (1-phase and 2-phase flow, isothermal and non-isothermal, elasto-plastic), Lewis et al 16 and Rahman and Lewis 17 (3-phase flow, isothermal, elastic). The topic was later extended and investigated by Ngien et al 18 and Gajo et al 19 (3-phase flow, isothermal, elastic), Ghorbani et al 20 (2-phase flow, isothermal, elasto-plastic), Gong et al 21 (3-phase fluid (passive gas phase), non-isothermal, elasto-plastic).…”