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• A load-balanced domain decomposition algorithm for 3D embedded unstructured grids. • Implementation of parallel simulations for embedded discrete fracture model. • Discussion on inter-processor communication patterns of embedded discrete fracture model. • Satisfactory scalability and parallel efficiency for a two-phase flow model with up 36 million grids on 1024 CPU cores. Recently, embedded discrete fracture model (EDFM) using non-conforming staggered 3D unstructured grids was presented for the numerical simulation of fluid-flows in large-scale complex fractured porous media. In this paper, we implement load-balanced parallel simulations for this approach on distributed memory systems. A load-balanced domain decomposition algorithm is presented to partition matrix grids and embedded fracture grids uniformly. We classify all grid connections on the boundary of subdomains to five types and illustrate corresponding inter-processor connections. A packaged inter-processor communication approach is implemented based on message passing interface (MPI) to improve communication efficiency for this simulation method. A two-phase parallel simulator is developed, and block coupled method is adopted to assemble the equations discretized in matrix and grid domains using two-point flux approximation (TPFA) finite volume method. The load-balanced algorithm is tested by nonuniformly distributed fracture networks. The performance and scalability are also tested on 1024 CPU cores by two complex fracture network models with up to 25 million matrix grids and 11 million embedded fracture grids. The results show satisfactory parallel efficiency and scalability. [ABSTRACT FROM AUTHOR]

• An improved embedded discrete fracture model for 3D unstructured grids. • Efficient and robust domain connectivity algorithms for 3D unstructured grids. • Block coupled solving method for overlapping matrix and fracture domains. • Tested for solving two-phase flow in a field-scale highly complex fracture network. Numerical simulation in 3D complex fractured media is challenging as the geometric discretization of porous media and fracture domains is on multiple scales. In this paper, we present an improved embedded discrete fracture model (EDFM) for 3D unstructured non-matching grids, and correspondingly efficient and robust domain connectivity algorithms are developed. Unlike traditional EDFM, improved EDFM is capable to simulate flows on 3D staggered overlapping unstructured matrix and fracture grids. We illustrate flux exchange patterns and formulas of improved EDFM. Two types of domain connectivity are built to assemble hybrid dimensional overlapping grids of matrix and fracture domains to a coupled linear system using finite volume method. Building domain connectivity is an important challenge for 3D hybrid-dimensional unstructured non-matching grids. We classify all points of domain connectivity into three types. A face indexed octree is employed for spatial binary search. Two types of grid adjacency information are used to accelerate the calculation of grid intersection points. Fracture-matrix intersection information is adopted to accelerate fracture-fracture connectivity generation. The performance of the algorithms is tested by 8 cases in different scales and compared with traversal method. Improved EDFM is validated against discrete fracture model and traditional EDFM using a two-phase flow solver. A case with highly complex fracture network is simulated to demonstrate the capacity of improved EDFM in real complex physical problems. The effects of grid type and resolution are also analyzed in this work. [ABSTRACT FROM AUTHOR]

Abstract: Numerical simulation in naturally fractured media is challenging because of the coexistence of porous media and fractures on multiple scales that need to be coupled. We present a new approach to reservoir simulation that gives accurate resolution of both large-scale and fine-scale flow patterns. Multiscale methods are suitable for this type of modeling, because it enables capturing the large scale behavior of the solution without solving all the small features. Dual-porosity models in view of their strength and simplicity can be mainly used for sugar-cube representation of fractured media. In such a representation, the transfer function between the fracture and the matrix block can be readily calculated for water-wet media. For a mixed-wet system, the evaluation of the transfer function becomes complicated due to the effect of gravity. In this work, we use a multiscale finite element method (MsFEM) for two-phase flow in fractured media using the discrete-fracture model. By combining MsFEM with the discrete-fracture model, we aim towards a numerical scheme that facilitates fractured reservoir simulation without upscaling. MsFEM uses a standard Darcy model to approximate the pressure and saturation on a coarse grid, whereas fine scale effects are captured through basis functions constructed by solving local flow problems using the discrete-fracture model. The accuracy and the robustness of MsFEM are shown through several examples. In the first example, we consider several small fractures in a matrix and then compare the results solved by the finite element method. Then, we use the MsFEM in more complex models. The results indicate that the MsFEM is a promising path toward direct simulation of highly resolution geomodels. [Copyright &y& Elsevier]

Abstract: In this paper we propose a locally conservative Galerkin (LCG) finite element method for two-phase flow simulations in heterogeneous porous media. The main idea of the method is to use the property of local conservation at steady state conditions in order to define a numerical flux at element boundaries. It provides a way to apply standard Galerkin finite element method in two-phase flow simulations in porous media. The LCG method has all the advantages of the standard finite element method while explicitly conserving fluxes over each element. All the examples presented show that the formulation employed is accurate and robust, while using less CPU time than finite volume method. [Copyright &y& Elsevier]