Abstract
The sets of linear equations which arise in large scale reservoir simulation can present problems for traditional linear solution algorithms. These scale poorly as the number of cells increases, and convergence is limited by the use of permeability distributions from geological modelling, with correlated high permeability channels, and the modelling of long horizontal wells. In addition, there is a requirement that the solver runs well on computers with many parallel processors.
The use of multi-level methods offers the possibility of good scaling with problem size. A common approach has been to use an algebraic multigrid (AMG) method. The integration of such a technique into a parallel reservoir simulation code is described, and the performance of different coarsening and interpolation algorithms compared.
AMG methods generally perform well when solving for a scalar solution to a system of elliptic equations and are not as straightforward to generalize to vector solution variables as traditional grid-based solvers. However, in fully implicit reservoir simulation a solution change in terms of both pressures and saturations or molar densities is generally required. This has lead to the use of solvers which combine an AMG step with a secondary solver step. There can be advantages in selecting nonlinear variables and equation sets to suit this technique, rather than treating the linear solver as a self-contained black box. Such methods are described and compared with traditional methods for black oil and compositional simulation.
