Patent ID: 8190405

Claim:
A computer-implemented method of estimating the physical state of a fluid reservoir with known physical characteristics and subject to specified boundary conditions, comprising a processor carrying out the steps of: representing the fluid reservoir as a plurality of nodes arranged in N-dimensional space, where N is an integer greater than 1, each node representing a discrete finite volume of the fluid reservoir and being associated with a set of physical properties, the physical properties associated with the nodes together forming a vector x when arranged in order, with the vector x representing the physical state of the fluid reservoir, and where the discrete finite volumes together represent the entire fluid reservoir; receiving physical data relating to the boundary conditions and the physical characteristics of the fluid reservoir, and determining from the received data the relations which must be satisfied by the component elements of the vector x, the number of relations being sufficient to determine the value of all elements of x; receiving an initial estimate x 0 of the physical properties which will satisfy the relations; and for each of a plurality of iterations, estimating the change dx in the vector x that results in all of the relations being simultaneously satisfied, and at the end of each iteration updating the current value of x according to x=x+dx; wherein estimating dx comprises: determining an error vector r, each element of r representing the extent to which one of the required relations is not satisfied for the current value of the vector x; determining a matrix A, each element of A representing an estimate of the rate of variation of an element of r with respect to changes to an element of x; and at least approximately solving the matrix equation A.dx=r to obtain dx for each iteration; wherein the method used to solve the matrix equation A.dx=r is iterative, and uses a preconditioning matrix B as an approximation to A; wherein the order of nodes to form the vector x provides the matrix A with a substantially nested block tridiagonal structure, with at least some inner blocks having non-zero elements which connect an element of r to elements of x from more than three different nodes; wherein B is a recursively defined incomplete block L.U factorization of A, with the blocking and recursion substantially mirroring the nested block tridiagonal structure of A; and wherein the set of physical properties comprises a measure of at least one of pressure, oil content, water content, gas content, displacement, stress, velocity, and temperature, or combinations involving or derived therefrom.