Patent Document ID: 9058445
Application ID: 13805651
Patent Flag: 1

Claim One:
1. A method for modeling properties of a reservoir, comprising: constructing a coarse computational mesh for the reservoir in a computer system, wherein the coarse computational mesh comprises a plurality of cells; determining a plurality of flows for each of the plurality of cells based on Dirichlet boundary conditions, wherein determining the plurality of flows for each of the plurality of cells comprises: selecting a plurality of pressure points along a plurality of boundaries of the cell, wherein selecting the plurality of pressure points at the boundary comprises: selecting a mid-point of a boundary of the cell if a scalar permeability or all entries of a permeability tensor at the boundary is less than a first pre-determined threshold; selecting two points close to two ends of the boundary if a maximum permeability or a maximum entry of the permeability tensor at the boundary is greater than the first pre-determined threshold; selecting a first pressure point if the maximum of the scalar permeability or entries of the permeability tensor is greater than the first pre-determined threshold; selecting the first pressure point where the scalar permeability or an entry of the permeability tensor reaches the maximum; and selecting additional pressure points away from the first pressure point, wherein a spacing, h, of the additional pressure points, comprises: h = min ⁢ { b 1 + c ⁡ ( k m - a ) 2 , d 1 + c ⁢ ⁢ δ ⁢ ⁢ k m 2 } where k m is equal to the maximum entry of the permeability tensor, and a, b, c, and d are constant parameters; associating the plurality of pressure points with a corresponding plurality of segments; determining a plurality of solutions to a steady-state pressure equation for the cell based on the plurality of pressure points at the boundary and a first Dirichlet boundary condition; computing a first flow rate across each of the plurality of segments based on a steady-state pressure equation solution; determining a solution to an inhomogenous pressure equation for the cell based on a second Dirichlet boundary condition; and computing a second flow rate across each of the plurality of segments based on the solution to the inhomogenous pressure equation, wherein the plurality of flows comprise the second flow rate; and determining a solution to a coarse pressure equation for the reservoir based on the plurality of flows.