Massively Parallel Sector Scale Discrete Fracture and Matrix Simulations

Abstract

We have been able to solve a reservoir simulation problem which was previously thought of as intractable: We simulated multiphase displacement, including viscous, capillary, and gravitational forces, for highly resolved and geologically realistic models of naturally fractured reservoirs (NFR) at the sector, i.e., kilometre, scale with very reasonable runtime. This has been possible because we used massive parallelisation and hierarchical solvers in conjunction with a new discrete fracture and matrix modelling (DFM) technique that is based on mixed-dimensional unstructured hybrid-element discretisations. High-resolution DFM simulations are important to resolve the non-linear coupling of small scale capillary - viscous and large scale gravitational - viscous processes adequately for sector scale NFR. Cross-scale process coupling in NFR controls oil recovery and NFR often exhibit power-law fracture length distributions, i.e. they do not possess an REV, and highly permeable fractures can extend over the full hydrocarbon column height. As a consequence, emergent displacement patterns have been observed which are difficult to quantify using traditional means of upscaling. However, such patterns could now be used as benchmarks to reach a better concensus on the correctness of promising new upscaling techniques. The parallel DFM technologies presented here allow us to obtain these results much more efficiently and hence explore the parameter space in greater detail. We observed a linear scaling behaviour for up to 64 processes and a significant decrease in runtime when applying our parallel DFM approach to three highly refined NFR simulations. These contain thousands of fractures, up to 5 million elements, and have local grid-refinements below 1 m for model dimensions between 1 and 10 kilometres. We achieved this excellent speedup because we reduced inter-processor communication by minimising the overlap between individual domains and decreased idle time of individual processors by distributing the number of unknowns equally among the processors. Introduction Production from naturally fractured reservoirs (NFR), which contain a major part of the world's remaining oil reserves, is challenging. NFR often suffer from a low final recovery that leaves between 80 to 95% of the oil underground which is retained in the low-permeability rock matrix (Kazemi and Gilman, 1993). Traditionally, production from NFR is simulated with dual-porosity models (Warren and Root, 1963). They represent the reservoir by a flowing domain of high permeability, the network of connected fractures, which is coupled to a stagnant domain, the low-permeability rock matrix. Exchange of oil, gas and water between the two domains is modelled by transfer functions. The rate of fluid transfer between fracture and matrix depends on the pressure gradient between the two domains and a shape factor, which represents the geometry of the rock matrix. The advantage of dual-porosity models is that they can be readily used in standard industry finite-difference or streamline reservoir simulators (Huang et al., 2004).

Preconditioning for Efficiently Applying Algebraic Multigrid in Fully Implicit Reservoir Simulations

“…Unless particular difficulties are present in the original Jacobian system, AMG is an established, highly efficient strategy for solving IMPES-like total-pressure equations (Batycky et al 2009;Geiger et al 2009); thus, AMG should be an efficient choice for the quasi-IMPES pressure equation as well. In fact, because the Jacobian's "elliptic parts" are concentrated inà pp (Masson et al 2004), this resulting pressure equation can be expected to have comparable properties.…”

A Method To Implement Permeability Anisotropy Associated With Fault Damage Zones in Reservoir Simulation

“…These effects can be represented in reservoir simulation by adding them either in the fine-scale geological model or in a coarse-scale reservoir-simulation model. DZs may contain many secondary fractures, so including each one as a discrete feature in the simulation model is limited by the computational power and time of the reservoir simulator (Durlofsky 2003;Geiger et al 2009;Lim et al 2009). However, there has been considerable progress made in upscaling the flow effects of small-scale geological heterogeneities (Corbett et al 1992;Ringrose et al 1993;Pickup et al 2000aPickup et al , 2000bFlodin et al 2001;Jourde et al 2002;Durlofsky 2003;Ahmadov et al 2007;Gong et al 2008).…”

Finite Element Voupled Deformation and Fluid Flow in Fractured Porous Media

“…Fracture network connectivity is not a prerequisite when using the dual permeability method. The discrete fracture model (DFM) approach, an alternative to the dual continuum approach, has received considerable interest over the last few years in the field of reservoir simulation and hydrology (Lee et al, 1999;Kim and Deo, 2000;Karimi-Fard et al, 2004;Matthäi et al, 2007;Tran and Ravoof, 2007;Geiger-Boschung et al, 2009). Fractures are explicitly discretized along with the matrix domain.…”