Streamline methods have become an efficient technology for reservoir simulation. The key assumption of the method is that the pressure field can be updated relatively less frequently, and the saturations can be transported along the streamlines defined by the velocity field. The efficiency of the solution method along the streamlines is very important for the overall efficiency of the method.
In this work, the acceleration of the saturation transport using adaptive mesh refinement (AMR) along streamlines is investigated. The refinement strategy is based on the multi-scale wavelet techniques. The one-dimensional solution is decomposed into a set of coarse-grid cell values and a set of solution details, which indicate the smoothness of the solution. This decomposition is recursively applied to the resulting representation until the coarsest mesh level is reached. From this multi-resolution representation of the solution an adaptive grid is constructed by thresholding of negligible details. Then, a second-order finite volume method is used on the obtained adaptive grid.
The performance of the resulting multi-resolution scheme on a synthetic and a real reservoir model is studied, using two-phase incompressible and three-phase black oil compressible data. It is shown that the use of the AMR technique can provide up to a five-fold acceleration compared to the solution of the same numerical method on a uniform grid. The proposed technique is implemented in a commercial reservoir simulator.