摘要:
A multi-scale finite-volume (MSFV) method is provided to solve elliptic problems with a plurality of spatial scales arising from single or multi-phase flows in porous media. An orthogonal 2D grid (20) of coarse grid cells (22) is used. An underlying fine grid (24) of fine grid cells (26) contains fine-scale permeability information. The method captures the effects of small scales on a coarse grid, is conservative, and treats tensor permeabilities correctly. The underlying idea is to construct transmissibilities that capture the local properties of a differential operator, which leads to a multi-point discretization scheme for a finite-volume solution algorithm.
摘要:
A method, system, a program storage device and apparatus are disclosed for conducting a reservoir simulation, using a reservoir model of a region of interest, wherein the region of interest has been gridded into cells. Each cell has one or more unknown variable. Each cell has a node. A graph of the nodes is represented by a sparse matrix. The graph is an initially decomposed into a pre-specified number of domains, such that each cell exists in at least one domain. The cells and domains are numbered. Each cell has a key, the key of each cell is the set of domain numbers to which the cell belongs. Each cell has a class, the class of each cell being the number of elements in the cell. The cells are grouped into connectors, each connector being the set of cells that share the same key. Each connector having a connector class, the connector class being the number of elements in the key of the connector. Each connector having only one higher-order neighbor connector is merged with such higher-order neighbor connector. The class of all locally maximum class connectors is reset to the maximum class of held by any connector. The maximum class connector is forced to contain only one cell. The connectors are ordered in increasing order of class. Interpolation operator and restriction operator are constructed from the ordered connectors. The interpolation operator and restriction operator are used to construct a coarse grid. The coarse grid may be used to determine the unknown variables of the cells.
摘要:
A method, system and apparatus are disclosed for conducting a reservoir simulation, using a reservoir model of a gridded region of interest. The grid of the region of interest includes one or more types of cells, the type of cell being distinguished by the number of unknown variables representing properties of the cells. The cells share a common variable as an unknown variable. The method includes the steps of identifying different cell types for the grid; constructing an overall matrix for the reservoir model based on the different cell types; at least partially decoupling the common variable from the other unknown variables in the matrix by using a reduction process to yield a reduced matrix; mathematically breaking up the variables in the reduced matrix into k subsets by cell types; applying an overlapping multiplicative Schwartz procedure to the reduced matrix to obtain a preconditioner and using the preconditioner to solve for the unknown variables.
摘要:
A multi-scale method to efficiently determine the fine-scale saturation arising from multi-phase flow in a subsurface reservoir is disclosed. The method includes providing a simulation model that includes a fine-scale grid defining a plurality of fine-scale cells, and a coarse-scale grid defining a plurality of coarse-scale cells that are aggregates of the fine-scale cells. The coarse-scale cells are partitioned into saturation regions responsive to velocity and/or saturation changes from the saturation front. A fine-scale saturation is determined for each region and the saturation regions are assembled to obtain a fine-scale saturation distribution. A visual display can be output responsive to the fine-scale saturation distribution.
摘要:
Computer-implemented systems and methods are provided for an upscaling approach based on dynamic simulation of a given model. A system and method can be configured such that the accuracy of the upscaled model is continuously monitored via indirect error measures. If the indirect error measures are bigger than a specified tolerance, the upscaled model is dynamically updated with approximate fine-scale information that is reconstructed by a multi-scale finite volume method. Upscaling of multi-phase flow can include flow information in the underlying fine-scale. Adaptive prolongation and restriction operators are applied for flow and transport equations in constructing an approximate fine-scale solution.