Rapid Simulation of Naturally Fractured Unconventional Reservoirs with Unstructured Grids Using the Fast Marching Method
Authors: Yang Changdong , King Michael J. , Datta-Gupta Akhil 
Published: February 2017

Abstract
Hydraulic fracturing treatment in naturally fractured unconventional reservoirs generally induce complex fracture geometries. Thus an unstructured grid, instead of a Cartesian or corner point grid, is preferred to accurately model the geometry of the fractures and the performance of such reservoirs. The drawback of conventional simulation on unstructured grids is the potentially heavy computational cost. A novel approach has recently been introduced to provide rapid simulation of unconventional reservoirs, which first captures the drainage volume during the transient propagation process using the Fast Marching Method (FMM) and then rapidly solves fluid flow equation in an equivalent 1D domain. However, this application is currently limited to calculating the reservoir response with Cartesian or corner-point grids.
In this study, the FMM based simulation method is extended to unstructured grid. A new mesh generation approach is first presented to discretize the complex fracture network, accounting for both hydraulic fractures and natural fractures. Voronoi cells (or perpendicular bisector, i.e. PEBI grids) are constructed with high resolution near the fractures and with larger cells far from fractures. A force-equilibrium algorithm is adopted here to optimize the mesh quality and reduce highly skewed cells. FMM algorithm is computed on the basis of subdivided triangles, which can provide the diffusive time of flight (DToF) at both Voronoi cell vertices and cell centers. Thus, a more accurate calculation of drainage volume in unconventional reservoir with complex fracture networks can be obtained. Finally, fluid flow is calculated in transformed 1D domain, where DToF acts as the 1D spatial coordinate.
Unstructured grids with good mesh quality are constructed to accurately capture the complex fracture network system. The convergence characteristic of FMM on unstructured grids is investigated. Reservoir simulation is efficiently computed based on the drainage volume information from the unstructured grid system using FMM, and the simulation results are validated with finite-difference based and finite-volume based numerical results. There are three key parts of this proposed approach, which are: (i) good mesh generation technique to capture complex fracture networks, (ii) FMM computation on unstructured grids to provide the drainage volume, and (iii) fluid flow calculation in transformed 1D domain.
We extend the reservoir simulation using FMM in unconventional reservoirs from Cartesian and corner point grid systems to unstructured grids. The proposed approach shows orders of magnitude reduction in simulation time for modeling unstructured grids, bringing typical simulation times of hours or days down to minutes, which is quite attractive for high-resolution models. Through the numerical examples, the proposed method is demonstrated to be an accurate and efficient approach to simulate naturally fractured unconventional reservoirs with unstructured grids.