An Application of the Isogeometric Analysis Method to Reservoir Simulation

Abstract

The isogeometric analysis method (IGA) has been an emerging technique for exact geometrical discretization and efficient high order approximations in the field of computational engineering. While its potential has been demonstrated in a variety of disciplines, it has yet to be applied extensively to the field of reservoir simulation. This work shows IGA's potential as a useful tool for next generation reservoir simulation, highlighting its ability to exactly capture complex-shaped geometrical features in the reservoir and, consequentially, accurately model the pressure fields. First, an IGA code is validated against the analytic solution for a quarter five-spot pattern as well as a reference solution for a straight line source problem with pressure enforced at the corners of the domain. Next, the numerical efficiency of IGA is compared against a finite element method solution of single phase flow in a 2D representative reservoir containing a centralized ЉS-shapedЉ line source. Results suggest a clear advantage of the IGA method over the classical finite element method, which has lower convergence rates in terms of number of degrees of freedom.