Method and system for reservoir modeling

摘要

A method is presented for modeling reservoir properties. The method includes constructing a coarse computational mesh for the reservoir. The coarse computational mesh comprises a plurality of cells. The method further includes determining a plurality of flows for each of the plurality of cells based on Dirichlet boundary conditions. Additionally, the method includes determining a solution to a coarse pressure equation for the reservoir based on the plurality of flows.

主权项

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; andselecting additional pressure points away from the first pressure point, wherein a spacing, h, of the additional pressure points, comprises:h=min⁢{b1+c⁡(km-a)2,d1+c⁢⁢δ⁢⁢km2} where km 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; andcomputing 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.