Capturing the two‐way hydromechanical coupling effect on fluid‐driven fracture in a dual‐graph lattice beam model

Fluid‐driven fractures of brittle rock is simulated via a dual‐graph lattice model. The new discrete hydromechanical model incorporates a two‐way coupling mechanism between the discrete element model and the flow network. By adopting an operator‐split algorithm, the coupling model is able to replicate the transient poroelasticity coupling mechanism and the resultant Mandel‐Cryer hydromechanical coupling effect in a discrete mechanics framework. As crack propagation, coalescence and branching are all path‐dependent and irreversible processes, capturing this transient coupling effect is important for capturing the essence of the fluid‐driven fracture in simulations. Injection simulations indicate that the onset and propagation of fractures is highly sensitive to the ratio between the injection rate and the effective permeability. Furthermore, we show that in a permeable rock, the borehole breakdown pressure, the pressure at which fractures start to grow from the borehole, depends on both the given ratio between injection rate and permeability and the Biot coefficient.     

A continuum‐discrete model using Darcy's law: formulation and verification

This paper presents a numerical scheme for fluid‐particle coupled discrete element method (DEM), which is based on poro‐elasticity. The motion of the particles is resolved by means of DEM. While within the proposition of Darcian regime, the fluid is assumed as a continuum phase on a Eulerian mesh, and the continuity equation on the fluid mesh for a compressible fluid is solved using the FEM. Analytical solutions of traditional soil mechanics examples, such as the isotropic compression and one‐dimensional upward seepage flow, were used to validate the proposed algorithm quantitatively. The numerical results showed very good agreement with the analytical solutions, which show the correctness of this algorithm. Sensitivity studies on the effect of some influential factors of the coupling scheme such as pore fluid bulk modulus, volumetric strain calculation, and fluid mesh size were performed to display the accuracy, efficiency, and robustness of the numerical algorithm. It is revealed that the pore fluid bulk modulus is a critical parameter that can affect the accuracy of the results. Because of the iterative coupling scheme of these algorithms, high value of fluid bulk modulus can result in instability and consequently reduction in the maximum possible time‐step. Furthermore, the increase of the fluid mesh size reduces the accuracy of the calculated pore pressure. This study enhances our current understanding of the capacity of fluid‐particle coupled DEM to simulate the mechanical behavior of saturated granular materials. Copyright © 2014 John Wiley & Sons, Ltd.     

A new computational strategy for solving two‐phase flow in strongly heterogeneous poroelastic media of evolving scales

We develop a new computational methodology for solving two‐phase flow in highly heterogeneous porous media incorporating geomechanical coupling subject to uncertainty in the poromechanical parameters. Within the framework of a staggered‐in‐time coupling algorithm, the numerical method proposed herein relies on a Petrov–Galerkin postprocessing approach projected on the Raviart–Thomas space to compute the Darcy velocity of the mixture in conjunction with a locally conservative higher order finite volume discretization of the nonlinear transport equation for the saturation and an operator splitting procedure based on the difference in the time‐scales of transport and geomechanics to compute the effects of transient porosity upon saturation. Notable features of the numerical modeling proposed herein are the local conservation properties inherited by the discrete fluxes that are crucial to correctly capture the fingering patterns arising from the interaction between heterogeneity and nonlinear viscous coupling. Water flooding in a poroelastic formation subject to an overburden is simulated with the geology characterized by multiscale self‐similar permeability and Young modulus random fields with power‐law covariance structure. Statistical moments of the poromechanical unknowns are computed within the framework of a high‐resolution Monte Carlo method. Numerical results illustrate the necessity of adopting locally conservative schemes to obtain reliable predictions of secondary recovery and finger growth in strongly heterogeneous deformable reservoirs. Copyright © 2011 John Wiley & Sons, Ltd.     

Coupled formulation and algorithms for the simulation of non‐planar three‐dimensional hydraulic fractures using the generalized finite element method

This paper presents a coupled hydro‐mechanical formulation for the simulation of non‐planar three‐dimensional hydraulic fractures. Deformation in the rock is modeled using linear elasticity, and the lubrication theory is adopted for the fluid flow in the fracture. The governing equations of the fluid flow and elasticity and the subsequent discretization are fully coupled. A Generalized/eXtended Finite Element Method (G/XFEM) is adopted for the discretization of the coupled system of equations. A Newton–Raphson method is used to solve the resulting system of nonlinear equations. A discretization strategy for the fluid flow problem on non‐planar three‐dimensional surfaces and a computationally efficient strategy for handling time integration combined with mesh adaptivity are also presented. Several three‐dimensional numerical verification examples are solved. The examples illustrate the generality and accuracy of the proposed coupled formulation and discretization strategies. Copyright © 2015 John Wiley & Sons, Ltd.     

A coupled two‐phase fluid flow and elastoplastic deformation model for unsaturated soils: theory,implementation, and application

Although numerous numerical models have been proposed for simulating the coupled hydromechanical behaviors in unsaturated soils, few studies satisfactorily reproduced the soil–water–air three‐phase coupling processes. Particularly, the impacts of deformation dependence of water retention curve, bonding stress, and gas flow on the coupled processes were less examined within a coupled soil–water–air model. Based on our newly developed constitutive models (Hu et al., 2013, 2014, 2015) in which the soil–water–air couplings have been appropriately captured, this study develops a computer code named F²Mus3D to investigate the coupled processes with a focus on the above impacts. In the numerical implementation, the generalized‐α time integration scheme was adopted to solve the equations, and a return‐mapping implicit stress integration scheme was used to update the state variables. The numerical model was verified by two well‐designed laboratory tests and was applied for modeling the coupled elastoplastic deformation and two‐phase fluid flow processes in a homogenous soil slope induced by rainfall infiltration. The simulation results demonstrated that the numerical model well reproduces the initiation of a sheared zone at the toe of the slope and its propagation toward the crest as the rain infiltration proceeds, which manifests a typical mechanism for rainfall‐induced shallow landslides. The simulated plastic strain and deformation would be remarkably underestimated when the bonding stress and/or the deformation‐dependent nature of hydraulic properties are ignored in the coupled model. But on the contrary, the negligence of gas flow in the slope soil results in an overestimation of the rainfall‐induced deformation. Copyright © 2015 John Wiley & Sons, Ltd.     

A numerical study of particle motion and two‐phase interaction in aeolian sand transport using a coupled large eddy simulation – discrete element method

Wind‐blown sand movement, considered as a particle‐laden two‐phase flow, was simulated by a new numerical code developed in the present study. The discrete element method was employed to model the contact force between sand particles. Large eddy simulation was used to solve the turbulent atmospheric boundary layer. Motions of sand particles were traced in the Lagrangian frame. Within the near‐surface region of the atmospheric boundary layer, interparticle collisions will significantly alter the velocity of sand. The sand phase is quite dense in this region, and its feedback force on fluid motion cannot be ignored. By considering the interparticle collision and two‐phase interaction, four‐way coupling was achieved in the numerical code. Profiles of sand velocity from the simulations were in good agreement with experimental measurements. The mass flux shows an exponential decay and is comparable to reported experimental and field measurements. The turbulence intensities and shear stress of sand particles were estimated from particle root‐mean‐square velocities. Distributions of slip velocity and feedback force were analysed to reveal the interactions between sand particles and the continuous fluid phase.     

Three‐dimensional simulations of tensile cracks in geomaterials by coupling meshless and finite element method

Failure in geotechnical engineering is often related to tension‐induced cracking in geomaterials. In this paper, a coupled meshless method and FEM is developed to analyze the problem of three‐dimensional cracking. The radial point interpolation method (RPIM) is used to model cracks in the smeared crack framework with an isotropic damage model. The identification of the meshless region is based on the stress state computed by FEM, and the adaptive coupling of RPIM and FEM is achieved by a direct algorithm. Mesh‐bias dependency, which poses difficulties in FEM‐based cracking simulations, is circumvented by a crack tracking algorithm. The performance of our scheme is demonstrated by two numerical examples, that is, the four‐point bending test on concrete beam and the surface cracks caused by tunnel excavation. Copyright © 2014 John Wiley & Sons, Ltd.     

Multi‐species diffusion analysis in porous media under various dry density and temperature conditions: molecular dynamics simulation,homogenization analysis,and finite element method

In porous media, chemical species that dissolve in pore water can be transported via diffusion mechanisms or advective fluxes, close to or far away from where precipitation occurs. In the case of a high‐level radioactive waste disposal system, compacted bentonite is used in a buffer material in an engineering barrier system to minimize the amount of specific nuclides that breach into the surrounding host rock. To minimize breaching, it is very important to understand the transport mechanism of multiple chemical species in porous media. In the following research, we introduced FEM analysis methods using the results of the molecular dynamics simulation and homogenization analysis (MD/HA) method. First, the diffusion coefficients of ions (Cl^?, I^?, and Na⁺) in different water layers of Na‐beidellite were calculated using the MD/HA procedure under various dry density (1.2, 1.6, and 2.0 Mg/m³) and temperature (293, 323, and 363 K) conditions. Next, using FEM analysis that used the MD/HA results as input parameters, the diffusion behaviors of ions in porous media were calculated. The results indicate that the diffusion coefficients of the interlayer water in Na‐beidellite are different from the diffusion coefficients under dry density conditions. Further, the concentration profiles (C_t/C₀) of iodine and chloride are proportional to temperature but inversely proportional to dry density. Copyright © 2014 John Wiley & Sons, Ltd.     

Calculating the internodal transmissibilities using finite analytic method and its application for multi‐phase flow in heterogeneous porous media

In the traditional numerical reservoir simulations, the internodal transmissibility is usually defined as the harmonic mean of the permeabilities of the adjacent grids. This definition underestimates the phase flux and the speed of the saturation front, especially for the strong heterogeneous case. In this article, the internodal transmissibility is recalculated according to the nodal analytic solution. The redefined internodal transmissibility can be used directly to calculate the multiphase flow in the numerical reservoir simulations. Numerical examples show that, compared to the traditional numerical methods, the proposed scheme makes the convergences much faster as the refinement parameter increases, and the accuracy is independent of the heterogeneity. Copyright © 2016 John Wiley & Sons, Ltd.