Algorithmic Monotone Multiscale Finite Volume Methods for Porous Media Flow

Multiscale finite volume methods are known to produce reduced systems with multipoint stencils which, in turn, could give non-monotone and out-of-bound solutions. We propose a novel solution to the monotonicity issue of multiscale methods. The proposed algorithmic monotone (AM- MsFV/MsRSB) framework is based on an algebraic modification to the original MsFV/MsRSB coarse-scale stencil. The AM-MsFV/MsRSB guarantees monotonic and within bound solutions without compromising accuracy for various coarsening ratios; hence, it effectively addresses the challenge of multiscale methods' sensitivity to coarse grid partitioning choices. Moreover, by preserving the near null space of the original operator, the AM-MsRSB showed promising performance when integrated in iterative formulations using both the control volume and the Galerkin-type restriction operators. We also propose a new approach to enhance the performance of MsRSB for MPFA discretized systems, particularly targeting the construction of the prolongation operator. Results show the potential of our approach in terms of accuracy of the computed basis functions and the overall convergence behavior of the multiscale solver while ensuring a monotone solution at all times.Comment: 29 pages, 20 figure

Comparisons of FV-MHMM with other finite volume multiscale methods.

pscaling and multiscale methods in reservoir engineering remain a complicated task especially when dealing with heterogeneities. In this study, we focus on flow field problem with a Darcy’s equation considered at the fine scale. The main difficulty is then to obtain an accurate description of the flow behavior by using multiscale methods available in petroleum engineering. We cross-compare three of the main finite volume formulations: multiscale finite volume method (MsFv), multiscale restriction smoothed (MsRSB) and a new finite volume method, FV-MHMM. Comparisons are done in terms of accuracy to reproduce the fine scale behavior

Upscaling and Multiscale Reservoir Simulation Using Pressure Transient Concepts

Fluid flow in subsurface petroleum reservoirs occurs on a wide range of length scales and capturing all the relevant scales in reservoir modeling is a cumbersome task. Even with the advent of modern computational resources, reservoir simulation of high resolution fine scale geologic models remain a challenge. Therefore, it is customary to use some kind of upscaling procedure to coarsen the multimillion cell geologic models to a scale feasible for practical reservoir simulation. Existing methods for upscaling of geologic models are based on steady state concepts of flow while the actual flow simulations itself is utilized for the purpose of capturing pressure and saturation transients. However, steady state or pseudo steady state limits may never be achieved for a coarse cell volume during a simulation time step in high contrast low permeability systems introducing a potentially significant bias into an upscaling or downscaling calculation. In this dissertation, a novel formulation is proposed which resolves these dynamic effects using an asymptotic pressure solution. Three principal research contributions are made in this dissertation. First, a novel construction of transmissibility in 1D is derived using pseudo steady state concepts which has the advantage of localization over steady state methods, when applied for upscaling problems. This construction is general for all grid geometries usually utilized in industry standard reservoir simulation codes (block centered, radial, corner point). A new form of pressure averaging is proposed to effectively convert a 3D pseudo steady state upscaling into a 1D calculation. Second, a pressure transient diffuse source upscaling formulation is introduced to identify well-connected sub volume that reaches pseudo steady state especially in high contrast systems. The formulation is based on transients approaching pseudo steady state in the upscaling region which can effectively identify the well-connected sub volume that contributes the flow. Third, the pressure transient diffuse source formulation developed for upscaling is extended to the multiscale framework where the large scale changes in pressure are resolved on the coarse grid while the saturations are resolved on the fine scale using downscaled coarse information. Applications are shown for both incompressible and slightly compressible flow

Upscaling and Multiscale Reservoir Simulation Using Pressure Transient Concepts

Fluid flow in subsurface petroleum reservoirs occurs on a wide range of length scales and capturing all the relevant scales in reservoir modeling is a cumbersome task. Even with the advent of modern computational resources, reservoir simulation of high resolution fine scale geologic models remain a challenge. Therefore, it is customary to use some kind of upscaling procedure to coarsen the multimillion cell geologic models to a scale feasible for practical reservoir simulation. Existing methods for upscaling of geologic models are based on steady state concepts of flow while the actual flow simulations itself is utilized for the purpose of capturing pressure and saturation transients. However, steady state or pseudo steady state limits may never be achieved for a coarse cell volume during a simulation time step in high contrast low permeability systems introducing a potentially significant bias into an upscaling or downscaling calculation. In this dissertation, a novel formulation is proposed which resolves these dynamic effects using an asymptotic pressure solution. Three principal research contributions are made in this dissertation. First, a novel construction of transmissibility in 1D is derived using pseudo steady state concepts which has the advantage of localization over steady state methods, when applied for upscaling problems. This construction is general for all grid geometries usually utilized in industry standard reservoir simulation codes (block centered, radial, corner point). A new form of pressure averaging is proposed to effectively convert a 3D pseudo steady state upscaling into a 1D calculation. Second, a pressure transient diffuse source upscaling formulation is introduced to identify well-connected sub volume that reaches pseudo steady state especially in high contrast systems. The formulation is based on transients approaching pseudo steady state in the upscaling region which can effectively identify the well-connected sub volume that contributes the flow. Third, the pressure transient diffuse source formulation developed for upscaling is extended to the multiscale framework where the large scale changes in pressure are resolved on the coarse grid while the saturations are resolved on the fine scale using downscaled coarse information. Applications are shown for both incompressible and slightly compressible flow