A continuous projection-based embedded fracture model for the numerical simulation of groundwater contaminant transport using 2D unstructured meshes

Resumo

Groundwater is one of the most important sources of fresh water worldwide. It is used extensively for industrial processes, agriculture and domestic applications, and is indispensable in regions with limited surface water availability. The pollution of groundwater stored in aquifers can pose serious risks to human health and also harm the ecological environment. In many geological settings, aquifers are located within naturally fractured reservoirs (NFRs)—rock formations that contain fractures rock formations which can function either as a high permeable conduit or as a barrier. These fractures arise from geological processes and exhibit diverse properties, increasing the complexity of constructing accurate simulation tools. The development of robust and accurate computational models is of utmost importance to understand the processes of contaminant transport in aquifers. In this work, we propose a new algorithm based on the Continuous Projection-based Embedded Discrete Fracture Model (CpEDFM) to model fractures in 2D domains. The method maps the nodes of the cells that contain embedded fractures onto a graph, where, in 2D, the edges between graph nodes correspond to control surfaces. A pathfinding algorithm is then applied to determine the shortest path between the nodes representing the fracture endpoints. This path is subsequently projected back onto the reservoir grid, selecting the cell faces that will receive the fracture projections while ensuring projection continuity. In our formulation, the pressure equation is solved using the Finite Volume Method (FVM) by means of a Multipoint Flux Approximation with Diamond stencil (MPFA-D), while the concentration equation is solved using the classical First-Order Upwind Method (FOUM). The system of equations in solved by the segregated Implicit Pressure, Explicit Concentration (IMPEC) scheme. To assess the robustness and accuracy of the proposed formulation, we solve some benchmark problems commonly found in the literature.