Abstract
Numerical reservoir simulation is subject to uncertainty in physical parameters as a consequence of lack of data. In addition, the numerical solution will never be exact for any choice of numerical method. The resolution of an iterative numerical solver can be increased to arbitrary accuracy by increasing the number of iterations. However, the uncertainty in the physical model renders high precision meaningless if the error from the physical model is dominating the total error. In this situation, a more efficient alternative to reduce the total error for a given computational cost is to balance the error from the model uncertainty to the error from the numerical solver.
In this paper we establish a framework for relating geological model errors to errors from applying an inexact solver for the pressure equation. An essential component of this framework is that both the geological error model and the particular linear solver allow approximations to be interpreted in terms of transmissibilities, thus facilitating a direct comparison between them. We investigate the applicability of the framework to a single phase flow problem. Numerical experiments indicate that there is considerable potential for reducing the solver accuracy without sacrificing the accuracy in the production estimates.