Numerical analysis of anisotropic stiffness and strength for geomaterials

In numerical modelling,selection of the constitutive model is a critical factor in predicting the actual response of a geomaterial.The use of oversimplified or inadequate models may not be sufficient to reproduce the actual geomaterial behaviour.That selection is especially relevant in the case of aniso-tropic rocks,and particularly for shales and slates,whose behaviour may be affected,e.g.well stability in geothermal or oil and gas production operations.In this paper,an alternative anisotropic constitutive model has been implemented in the finite element method software CODE_BRIGHT,which is able to account for the anisotropy of shales and slates in terms of both deformability and strength.For this purpose,a transversely isotropic version of the generalised Hooke’s law is adopted to represent the stiffness anisotropy,while a nonuniform scaling of the stress tensor is introduced in the plastic model to represent the strength anisotropy.Furthermore,a detailed approach has been proposed to determine the model parameters based on the stressestrain results of laboratory tests.Moreover,numerical analyses are performed to model uniaxial and triaxial tests on Vaca Muerta shale,Bossier shale and slate from the northwest of Spain(NW Spain slate).The experimental data have been recovered from the literature in the case of the shale and,in the case of the slate,performed by the authors in terms of stress-strain curves and strengths.A good agreement can be generally observed between numerical and experi-mental results,hence showing the potential applicability of the approach to actual case studies.Therefore,the presented constitutive model may be a promising approach for analysing the anisotropic behaviour of rocks and its impact on well stability or other relevant geomechanical problems in aniso-tropic rocks.

Comparison of numerical codes for coupled thermo-hydro-mechanical simulations of fractured media

Geo-energy and geo-engineering applications,such as improved oil recovery(IOR),geologic carbon storage,and enhanced geothermal systems(EGSs),involve coupled thermo-hydro-mechanical(THM)processes that result from fluid injection and production.In some cases,reservoirs are highly fractured and the geomechanical response is controlled by fractures.Therefore,fractures should explicitly be included into numerical models to realistically simulate the THM responses of the subsurface.In this study,we perform coupled THM numerical simulations of water injection into naturally fractured reservoirs(NFRs)using CODE_BRIGHT and TOUGH-UDEC codes.CODE_BRIGHT is a finite element method(FEM)code that performs fully coupled THM analysis in geological media and TOUGH-UDEC sequentially solves coupled THM processes by combining a finite volume method(FVM)code that solves nonisothermal multiphase flow(TOUGH2)with a distinct element method(DEM)code that solves the mechanical problem(UDEC).First,we validate the two codes against a semi-analytical solution for water injection into a single deformable fracture considering variable permeability based on the cubic law.Then,we compare simulation results of the two codes in an idealized conceptual model that includes one horizontal fracture and in a more realistic model with multiple fractures.Each code models fractures differently.UDEC calculates fracture deformation from the fracture normal and shear stiffnesses,while CODE_BRIGHT treats fractures as equivalent porous media and uses the equivalent Young’s modulus and Poisson’s ratio of the fracture.Finally,we obtain comparable results of pressure,temperature,stress and displacement distributions and evolutions for the single horizontal fracture model.Despite some similarities,the two codes provide increasingly different results as model complexity increases.These differences highlight the challenging task of accurately modeling coupled THM processes in fractured media given their high nonlinearity.