An element-free Galerkin method using vertically integrated multiphase flow model for carbon sequestration

In this paper, the element-free Galerkin (EFG) method is applied to the study of vertically integrated two-phase flow of CO2 and brine in a deep saline aquifer. The methodology comprises of solving two simultaneous partial differential equations (PDEs) involving pressure and saturation terms, which are obtained by combining mass and momentum conservation equations. The obtained pressure and the average CO2 saturation resulting from the model will help to study the spatial and temporal distribution of the aquifer, bottom pressure buildup and the CO2 storage capacity of the aquifer respectively. The temporal analysis is solved using an IMplicit Pressure and Explicit Saturation (IMPES) solution strategy. A local refinement zone is introduced to capture the asymptotic pressure solution near the injection wells. Furthermore, the region surrounding the well is modelled as a non-homogeneous interface using Functionally Graded Materials (FGMs) analogy. Various case studies such as the horizontal aquifer, the sloped aquifer, the non-homogenous aquifer and, the horizontal aquifer with multiple wells have been presented to show the efficiency of the proposed model. The performance of the proposed EFG method is compared with that of FEM and XFEM numerical solutions. It is observed that the EFG method can capture average CO2 saturation (height of CO2) more effectively than the FEM and as effectively as the XFEM at the injection well. Moreover, it is easier to use the EFG method to solve complex aquifer problems, having non-homogeneity and multiple wells by considering a local nodal refinement around the well with ease. The simplicity of the proposed EFG method is demonstrated in this paper.