Multiscale Mimetic Solvers for Efficient Streamline Simulation of Fractured Reservoirs

Abstract

Advances in reservoir characterization and modeling have given the industry improved ability to build detailed geological models of petroleum reservoirs. These models are characterized by complex shapes and structures with discontinuous material properties that span many orders of magnitude. Models that represent fractures explicitly as volumetric objects pose a particular challenge to standard simulation technology with regard to accuracy and computational efficiency. We present a new simulation approach based on streamlines in combination with a new multiscale mimetic pressure solver with improved capabilities for complex fractured reservoirs. The multiscale solver approximates the flux as a linear combination of numerically computed basis functions defined over a coarsened simulation grid consisting of collections of cells from the geological model. Here, we use a mimetic multipoint flux approximation to compute the multiscale basis functions. This method has limited sensitivity to grid distortions. The multiscale technology is very robust with respect to fine-scale models containing geological objects such as fractures and fracture corridors. The methodology is very flexible in the choice of the coarse grids introduced to reduce the computational cost of each pressure solve. This can have a large impact on iterative modeling workflows.

Application of Flow Diagnostics and Multiscale Methods for Reservoir Management

“…By far, the most well-developed method in terms of geomodel complexity is the multiscale mixed finite-element method, which is posed in terms of degrees-of-freedom associated with the fluxes between neighboring coarse blocks. The method only requires a primal coarse partition and can hence easily be formulated on structured, stratigraphic grids as well as fullyunstructured, polyhedral grids (Aarnes et al 2006(Aarnes et al , 2008Krogstad et al 2009;Natvig et al 2011;Alpak et al 2012;Lie et al 2014). An extended approach based on proper orthogonal decompositions (POD) was suggested by Krogstad (2011) for problems in which one wants to investigate new cases that represent minor changes to scenarios that have already been simulated by a multiphase simulation.…”

“…This makes multiscale simulation a better tool for characterizing volumetric sweep and locating bypassed and immobile oil compared with traditional upscaling, which always implies a loss of information when homogenizing fine-scale structures. Previous research has shown that multiscale and streamline methods constitute a powerful and computationally efficient combination (Aarnes et al 2005;Stenerud et al 2008;Natvig et al 2011).…”

The multiscale restriction smoothed basis method for fractured porous media (F-MsRSB)

“…Physical properties inside fractures and their length scales can be very di↵erent from those of the surrounding rock, adding significantly to the computational challenges, specially once realistic length scales and complex fracture network maps are considered. As a result, a variety of modelling approaches and numerical methods for di↵erent types of fractured reservoirs have been proposed [32][33][34][35][36][37][38][39][40][41][42][43][43][44][45][46][47]. Among them, the embedded fracture modelling approach [1, 37-39, 48, 49] benefits from independent grids for fracture and matrix, a promising approach for naturally fractured reservoirs and also for cases with dynamic fracture creations and closure of, e.g., geothermal systems.…”

“…Therefore, it is highly important to develop e cient multiscale methods for fractured formations. Early attempts at developing multiscale methods for fractured media were based on a mixed finite-element formulation in which high-conductive fractures were either represented explicitly as volumetric objects [40] or the fracture-matrix interaction was modelled by the Stokes-Brinkmann equations [41,50]. Within the MSFV framework, Hajibeygi et al [1] developed the first multiscale method for fractured porous media, in which additional fracture basis functions were introduced to map each fracture network into one coarse-scale degree of freedom (DOF).…”

Flow-based Grid Coarsening for Transport Simulations

“…If the transport is to be computed on the same coarse grid as used in the multiscale flow solver, the best choice is to use a standard implicit finitevolume method with the coarse-scale fluxes computed by the multiscale solver. To solve the transport without upscaling-using the fine-scale, approximate fluxes-the best choice is probably a streamline method, e.g., as described in [1,20], or one can use similar operatorsplitting techniques to develop highly-efficient finite-volume solvers [18,19] that use flow information to obtain an optimal ordering of the nonlinear discrete transport equations so that these can be solved in a cell-by-cell or block-by-block fashion. This gives local control over the (computationally expensive) nonlinear iterations and can significantly reduce the computational cost compared with standard (implicit) finite-volume methods.…”