A new ELLAM implementation for modeling solute transport in fractured porous media
Authors: Ramasomanana Fanilo Heninkaja , Fahs Marwan , Baalousha Husam , Barth Nicolas , Ahzi Said 
Published: June 2019

The fluid flow and solute transport through fractures in rocks are processes that have importance for many areas of the geosciences, ranging from groundwater hydrology to petroleum engineering. It is well known that fractures play an important role in flow and transport processes through geologic formation and number of environmentally relevant problems require the analysis of mass transport in subsurface systems. As Qatar»s aquifer is Karstic, the development of an appropriate numerical model is necessary to take account the high contrast between the fractures and the porous matrix. Fractures are the set of rock discontinuities that can occur in geological formations at different scales. They intensively affect the transport processes because they represent the preferential flow and mass migration paths. In this study, we introduce an adaptation of the Eulerian Lagrangian Localized Adjoint Method (ELLAM) [1] for the simulation of mass transport in fractured porous media. The fractures are represented explicitly using the discrete fracture model (DFM) which handles explicitly the fractures and matrix. It involves describing each fracture individually and discretizing fractures as well as matrix [2]. Specific physical and geometrical properties are imposed for the fractures and matrix domains. This model can be used in the domains where a relatively small number of fractures exist. DFM is the most accurate model because fractures are considered without any simplification. However, this model requires enormous computational time and memory due to the dense meshes resulting from the explicit discretization of the fractures. As a consequence, its use requires highly efficient numerical methods for solving the flow and mass transport. The flow problem is solved using the Mixed Hybrid Finite Element Method (MHFEM) [3] which is well known to be accurate and efficient for complex geometries. It provides consistent and accurate velocity even in highly heterogeneous domain, which is a relevant property for flow in FPM. The obtained velocity field is then used to solve the mass transport problem with ELLAM. ELLAM combines an Eulerian and Lagrangian treatments without any splitting procedure by considering trial functions that depend on time and space. The results obtained by Celia et al. [1] demonstrated the mass conservation of the ELLAM in its formulation and its high computational efficiency compared to classical numerical method. In this work, a new ELLAM implementation is developed to address numerical artifacts (spurious oscillations and numerical dispersion) arising from the high contrast of velocities between fractures and porous matrix. Moreover, the efficiency of the developed ELLAM implementation was improved, taking advantage of the parallel computing on shared memory architecture for the tasks related to particles tracking and linear system resolving. The performance of ELLAM was tested by comparison against the Eulerian discontinuous Galerkin method based on several benchmarks dealing with different fracture configurations. The results highlight the robustness and accuracy of ELLAM, as it allows the use of large time steps, and overcomes the Courant-Friedrichs-Lewy (CFL) restriction. This work contribute to the Aquifer Storage and Recovery (ASR) project of Qatar which aims at artificially storing water in the aquifer for future use by developing an efficient and accurate model for mass transport in fractured porous media. References [1] Celia, M.A., Russell, T.F., Herrera, I., Ewing, R.E.: An Eulerian-Lagrangian localized adjoint method for the advection-diffusion equation. Advances in Water Resources. 13, 187–206 (1990). doi:10.1016/0309-1708(90)90041-2 [2] Karimi-Fard, M., Durlofsky, L.J., Aziz, K.: An Efficient Discrete-Fracture Model Applicable for General-Purpose Reservoir Simulators. SPE Journal. 9, 227–236 (2004). doi:10.2118/88812-PA [3] Younes, A., Ackerer, P., Delay, F.: Mixed finite elements for solving 2-D diffusion-type equations. Reviews of Geophysics. 48, (2010). doi:10.1029/2008RG000277