Adaptive Newton's method for reservoir simulation

摘要

A method of performing a simulation of a subsurface hydrocarbon reservoir. The reservoir is approximated by a reservoir model having a plurality of cells. Each cell has an equation set representing a reservoir property. An initial guess is provided to a solution for a system of equations formed using the equation set for each of the cells. An iterative root-finding method and the initial guess are used to solve for a solution to the system of equations. When the number of non-converged cells is greater than a predetermined amount, neighboring converged cells are added to the non-converged cells. Parts of the method are repeated, substituting the solved solution for the initial guess and the equation sets corresponding to the non-converged cells for the first system of equations, until substantially all equation sets satisfy the convergence criterion. The solved solution is outputted as a simulation of the subsurface reservoir.

主权项

1. A method of performing a simulation of a subsurface hydrocarbon reservoir, the reservoir being approximated by a reservoir model having a plurality of cells, each cell having associated therewith an equation set representing a reservoir property, the method comprising:
(a) providing an initial guess to a solution for a system of equations formed using the equation set for each cell in the plurality of cells, wherein providing the initial guess comprises using a Jacobian matrix; (b) using an iterative root-finding method and the initial guess to solve for a solution to the system of equations in a computer; (c) establishing a list of unconverged cells, the unconverged cells having equation sets that have not satisfied a convergence criterion; (d) when the number of unconverged cells is greater than a predetermined amount, adding, to the list of unconverged cells, neighbor cells of the unconverged cells, each of said neighbor cells having an equation set that satisfies the convergence criterion; (e) repeating parts (b), (c), and (d), substituting the solved solution for the initial guess or the most recent solved solution and substituting the equation sets corresponding to the cells in the list of unconverged cells for the system of equations or equation sets from the most recent iteration, until substantially all equation sets satisfy the convergence criterion, and wherein the size of the Jacobian matrix varies with each iteration; (f) when substantially all equation sets satisfy the convergence criterion, employing a post-Newton material balance corrector and outputting the solved solution as a simulation of the subsurface reservoir; and (g) managing hydrocarbons based on the simulation.