Patent ID: 7707018

Claim:
A method for conducting a stress calculation adapted for modeling a set of stresses and displacements in a reservoir, comprising: based at least in part on data indicative of measurements of the reservoir, building, using a processor, a reservoir model over a region of interest by gridding the region of interest, the grid being comprised of one or more cells and having grid nodes, each cell having a cell center, wherein each cell center is used to determine an approximation of displacements; processing, using the processor, the reservoir model to interpolate unknown rock displacements in the region of interest from cell centers to the grid nodes, the interpolation of the unknown rock displacements comprising: defining a linear function in a neighborhood of one of the grid nodes, and using the linear function to interpolate the approximation of displacements for each cell center in the neighborhood of the one of the grid nodes in the neighborhood to determine the unknown rock displacements of the one of the grid nodes, wherein the linear function is Φ=a+b(x−x a )+c(y−y a ), wherein a, b, and c are unknown variables representing the unknown rock displacements, x a and y a represent coordinates, in two dimensions, of the one of the grid nodes, and x and y represent coordinates, in two dimensions, of each cell center in the neighborhood of the one of the grid nodes; integrating, using the processor, a system of linear equations over each cell to form a discrete system of equations, wherein a number of equations in the system of linear equations is determined based on a number of the cell centers; using the discrete system of equations to generate a model, using the processor, of the stresses and displacements in the reservoir; and displaying the model of the stresses and displacements in the reservoir.