Abstract: A method for solving a matrix equation AX=B, wherein A represents a block sparse matrix, B represents a right hand side block vector and X represents a solution block vector. In one embodiment, the method includes receiving the block sparse matrix and the right hand side block vector, constructing a reduced transformed block sparse matrix from the block sparse matrix, constructing a reduced transformed residual block vector from the block sparse matrix and the right hand side block vector, and solving for the solution block vector using the reduced transformed block sparse matrix and the reduced transformed residual block vector.

Abstract: The invention relates to an object-oriented method for simulating a property of at least one fluid in a fluid-containing physical system in which the physical system is represented by a multiplicity of volumetric cells and a multiplicity of connections between cells. The method uses cell-group objects and connection-group objects in the simulation. The invention can optionally comprise additional objects such as an object containing the entire model of the simulation and another object containing a portion of the entire model.

Abstract: A method is provided for simulating at least one characteristic of a physical system. The physical system is discretized into a plurality of volumetric cells having boundaries therebetween. An initial estimate of state variables is assigned for each cell. For each cell, linear equations are constructed relating its state variables to the state variables of cells adjacent to it. A transportability value is associated with each boundary and the boundaries are ranked corresponding to descending transportability values. The boundary rankings are used to construct topologically one-dimensional strings of cells. A matrix equation for each string is constructed by assembling the linear equations associated with the cells of each string. Improved estimates of the state variables of the cells are determined by solving the matrix equations. These state variables are then used to simulate at least one characteristic of the physical system.

Abstract: Disclosed is a method for estimating properties of a multi-component fluid using pseudocomponents. The fluid is characterized using a set of base components and a set of fluid compositions is defined that corresponds to fluid compositions expected to occur in computations of interest. Pseudocomponents are defined to represent the multi-component fluid by (i) defining an ordered set of vectors corresponding to a characteristic of the base components, each vector containing one entry for each base component, the first vector being most representative of the set of compositions according to a predetermined criterion and each vector thereafter in the set being less representative of the set of compositions than the vector before it, and (ii) selecting a subset of the ordered set that comprises the first vector and a predetermined number of vectors immediately thereafter, the subset of vectors corresponding to a pseudocomponent characterization of the multi-component fluid.

Abstract: A method is disclosed of predicting a characteristic of a fluid-containing physical system such as a reservoir. The physical system is discretized to a plurality of gridcells. For each gridcell, nonlinear governing equations are constructed that are representative of fluid properties for each fluid. The nonlinear terms are linearized to derive linear equations at a current timestep. The linear equations are then solved to determine estimates of the solution. The estimated solution is then improved by a gridcell-by-gridcell computation wherein flows into and out of a particular gridcell are determined using linearized values of nonlinear terms in gridcells adjacent that particular gridcell. The improved solution is used to predict a property of a fluid in the physical system at end of the timestep. These calculation steps are repeated for a plurality of timesteps and the results are used to predict a property of the physical system and the fluids it contains as a function of time.