Abstract: Improved reservoir simulation methods and systems are provided that employ a new velocity model in conjunction with a sequential implicit (SI) formulation or Sequential Fully Implicit (SF) formulation for solving the discrete form of the system of nonlinear partial differential equations. In embodiments, the new velocity model employs a fluid transport equation part based on calculation of phase velocity for a number of fluid phases that involves capillary pressure and a modification coefficient. In embodiments, the modification coefficient can be based on a derivative of capillary pressure with respect to saturation. In another aspect, the new velocity model can employ an estimate of the phase velocity of the water phase vw_est that is based on one or more derivatives of capillary pressure of the water phase as a function of water saturation.

Abstract: A subsurface representation may define subsurface configuration of a subsurface region. A grid connectivity graph for the subsurface representation may include (1) nodes that represent cells within the subsurface representation, and (2) edges between the nodes that represent connectivity between the cells within the subsurface representation. The grid connectivity graph may be filtered to remove edges that do not satisfy a connectivity criterion. The filtered grid connectivity graph may be used to compute a linear solver preconditioner that improves the performance of the subsurface simulation.

Abstract: Systems, computer-readable media, and methods for performing a reservoir simulation by obtaining reservoir data; translating the reservoir data into grid properties to create a grid; dividing the grid into domains; generating coarse grids corresponding to each domain; processing the domains, where processing a domain includes: calculating pressure for the domain using a coarse grid corresponding to the domain, calculating flux for the domain using a coarse grid corresponding to the domain, and calculating transport of fluids for the domain using a coarse grid corresponding to the domain; and generating a reservoir simulation corresponding to the grid based on processing each domain. The domains can be processed in parallel on different computer systems, different processors, or different cores.

Abstract: Improved reservoir simulation methods and systems are provided that employ a new velocity model in conjunction with a sequential implicit (SI) formulation or Sequential Fully Implicit (SF) formulation for solving the discrete form of the system of nonlinear partial differential equations. In embodiments, the new velocity model employs a fluid transport equation part based on calculation of phase velocity for a number of fluid phases that involves capillary pressure and a modification coefficient. In embodiments, the modification coefficient can be based on a derivative of capillary pressure with respect to saturation. In another aspect, the new velocity model can employ an estimate of the phase velocity of the water phase ?w_est that is based on one or more derivatives of capillary pressure of the water phase as a function of water saturation.

Abstract: Methods, computing systems, and computer-readable media for multi-scale modeling. The method includes determining a first matrix for a plurality of fine cells of a model based at least in part on a physical property value represented by respective fine cells, identifying one or more overlapped cells of the plurality of fine cells that are part of at least two of the plurality of subdomains, and determining a second matrix. Determining the second matrix includes determining an intermediate product by multiplying the first matrix by a prolongation matrix, which includes predicting a row of zeros in the intermediate product for the plurality of fine cells that are not the one or more overlapped cells and are not part of the at least two of the plurality of subdomains that include the one or more overlapped cells. Determining the second matrix also includes multiplying the intermediate product by a restriction matrix.

Abstract: Systems, computer-readable media, and methods for performing a reservoir simulation by obtaining reservoir data; translating the reservoir data into grid properties to create a grid; dividing the grid into domains; generating coarse grids corresponding to each domain; processing the domains, where processing a domain includes: calculating pressure for the domain using a coarse grid corresponding to the domain, calculating flux for the domain using a coarse grid corresponding to the domain, and calculating transport of fluids for the domain using a coarse grid corresponding to the domain; and generating a reservoir simulation corresponding to the grid based on processing each domain. The domains can be processed in parallel on different computer systems, different processors, or different cores.

Abstract: Computer-implemented systems and methods for modeling behavior of at least one fluid in a reservoir are disclosed. The techniques can include obtaining measurements of physical parameters, including pressure, at locations within the reservoir, and discretizing, based on a three-dimensional fine grid, a system of partial differential mass balance equations that model, based on the measurements, at least the physical parameters at the locations within the reservoir, such that a system of nonlinear equations is produced. The techniques can include iterating from a current time step to a next time step, such that a solution to the system of nonlinear equations for a time interval that includes the current time step and the next time step is produced. The iterating can include an adaptive multi-fidelity multiscale technique that employs multiple restriction operators, prolongation operators, and coarse grids, to model various computationally challenging reservoir features, behaviors, or both.

Abstract: Computer-implemented systems and methods for modeling behavior of at least one fluid in a reservoir are disclosed. The techniques can include obtaining measurements of physical parameters, including pressure, at locations within the reservoir, and discretizing, based on a three-dimensional fine grid, a system of partial differential mass balance equations that model, based on the measurements, at least the physical parameters at the locations within the reservoir, such that a system of nonlinear equations is produced. The techniques can include iterating from a current time step to a next time step, such that a solution to the system of nonlinear equations for a time interval that includes the current time step and the next time step is produced. The iterating can include an adaptive multi-fidelity multiscale technique that employs multiple restriction operators, prolongation operators, and coarse grids, to model various computationally challenging reservoir features, behaviors, or both.

Abstract: Computing systems, methods, and computer-readable media for modeling behavior of at least one fluid in a reservoir are disclosed. More particularly, the techniques provide consistent and robust numerical formulations for solutions to linear system of equations arising from the linearization of coupled nonlinear hyperbolic/parabolic (elliptic) partial differential equations (PDEs) of fluid flow in heterogeneous anisotropic porous media.

Abstract: Methods, computing systems, and computer-readable media for multi-scale modeling. The method includes determining a first matrix for a plurality of fine cells of a model based at least in part on a physical property value represented by respective fine cells, identifying one or more overlapped cells of the plurality of fine cells that are part of at least two of the plurality of subdomains, and determining a second matrix. Determining the second matrix includes determining an intermediate product by multiplying the first matrix by a prolongation matrix, which includes predicting a row of zeros in the intermediate product for the plurality of fine cells that are not the one or more overlapped cells and are not part of the at least two of the plurality of subdomains that include the one or more overlapped cells. Determining the second matrix also includes multiplying the intermediate product by a restriction matrix.