In order to get desired accuracy in reservoir simulation, one must refine the grid in certain regions, for example, the regions around wells. When this is done in conventional simulators, unnecessary refinement occurs in some regions. This problem is avoided by the use of "Local Grid Refinement" (LGR) techniques, but the resulting matrix is large and of irregular sparsity. In this paper we address several practical aspects of some methods of LGR, including practical aspects of some methods of LGR, including the use of hybrid grid, and then present three highly efficient methods of solving resulting problems with some Domain Decomposition (DD) techniques. In the first method, a relaxation in the unknowns is performed. In the second one, we use overlapping performed. In the second one, we use overlapping boundaries between the subdomains. In the last one, a coarse grid solution is obtained first and it provides the boundary conditions for the fine grid solution. The LGR and DD methods developed in this work were implemented and tested in a three-dimensional, three-phase, black-oil model. The results are presented in this paper for three examples. It is also presented in this paper for three examples. It is also shown that the DD technique with overlapping boundaries is extremely efficient for solving problems containing one or more LGR regions. The method problems containing one or more LGR regions. The method proposed in this paper can easily take advantage of proposed in this paper can easily take advantage of parallel processors. Also, it is easy to implement the parallel processors. Also, it is easy to implement the proposed techniques in existing simulators. proposed techniques in existing simulators. The LGR and DD techniques discussed in this paper improve the accuracy of reservoir simulation paper improve the accuracy of reservoir simulation around wells and in other regions of high activity. Using these techniques, one not only obtains the correct well pressure, but also the correct saturation near the well. A consequence of this is that WOR and GOR are predicted accurately without well pseudofunctions. pseudofunctions
Reservoir performance forecasting is accomplished by reservoir simulators that solve coupled non-linear partial differential equations describing multicomponent, multiphase flow in the reservoir.
In most cases the flow equations are reduced to a system of non-linear algebraic equations by finite-difference techniques and then linearized by the Newton-Raphson method. The resulting linear system has a sparse matrix that can be solved by direct methods for small problems and by iterative methods for larger problems. In the practical application of this tool the number of equations can be more than 100,000 and can even approach 1,000,000. Special gridding and solution techniques are required to take advantage of the physical characteristics of the problem.
Recently, there has been a lot of interest in the application of LGR2-10 in reservoir simulation. This technique gives high resolution in regions where the flow rates are high, such as near the wells, without introducing small blocks in regions of low activity.
The structure of the Jacobian resulting from LGR can be exploited by the use of DD techniques.