Elastic and elastoplastic finite element simulations of injection into porous reservoirs

Abstract

Underground gas injection has attracted remarkable attention for natural gas storage and carbon dioxide (CO2) geologic sequestration applications. Injection of natural gas into depleted hydrocarbon reservoirs is the most popular storage method. CO2 geologic sequestration plays a vital role in alleviating global warming and climate change issues related to the significant release of CO2 as one of the major greenhouse gases produced from the combustion of fossil fuels.The injection of gas into underground geologic formations builds up the fluid pore pressure, which changes the effective stress, i.e. the stress applied to the rock skeleton. The deformation due to change of stresses could result in various geomechanics related issues across the reservoir interval and over/under burden rocks such as fault or fracture reactivation, collapse of casings, wellbore instabilities and ground uplift. To simulate injection of gas into porous formations and investigate subsequent stress induced events finite element (FE) modelling has been used in the past. This numerical method is suitable for continuum media, similar to porous formations considered for injections.In this study a three-dimensional (3D) finite element program was developed for simulations of gas injection into a porous medium. Both isotropic linear elastic and elasto-plastic behaviours (including von Mises, Mohr-Coulomb and Drucker-Prager yield criteria) were assumed for geomaterials. The program applies isoparametric formulation using 3D 8-noded hexahedron elements and supports different types of loading including those due to body (gravity) force and tractions on outer boundary. The effective stress concept and Biot's theory were integrated in the fundamental formulations in order to account for the gas injection modelling.The developed code was applied to model some typical elastic examples for which analytical solutions exist: this allowed validation of the program. Thereafter several simulations of porous formations carried out to study the injection induced stress and displacements within the injection zone and surrounding formations with horizontal and curved structures. The results indicated the change in the state of stress regime due to injection and its variation at different locations in a non-horizontal structure.The results of elasto-plastic models were also validated against some simple cases with known responses. The model then applied to simulate the development of plastic zone around a porous formation due to gas injection. The results of sensitivity analysis showed how the plastic zone expands when the formation exhibits less strength properties, i.e. cohesion.The 3D FE program was finally applied to study a real case in which injection into a sandstone formation was studied. The stress and displacements before and after injection were estimated considering both isotropic linear elastic and elastoplastic behaviours for the formation. This allowed estimation of ground uplift and the development of the plastic zone around the injection area.