Aquifer Acceleration in Parallel Implicit Field-Scale Reservoir Simulation
Authors: Du Shouhong , Fung Larry S. , Dogru Ali H. 
Published: February 2018

Summary
Grid coarsening outside of the areas of interest is a common method to reduce computational cost in reservoir simulation. Aquifer regions are candidates for grid coarsening. In this situation, upscaling is applied to the fine grid to generate coarse-grid flow properties. The efficacy of the approach can be judged easily by comparing the simulation results between the coarse-grid model and the fine-grid model. For many reservoirs in the Middle East bordered by active aquifers, transient water influx is an important recovery mechanism that needs to be modeled correctly. Our experience has shown that the standard grid coarsening and upscaling method do not produce correct results in this situation. Therefore, the objective of this work is to build a method that retains the fine-scale heterogeneities to accurately represent the water movement, but to significantly reduce the computational cost of the aquifer grids in the model.
The new method can be viewed as a modified two-level multigrid (MTL-MG) or a specialized adaptation of the multiscale method. It makes use of the vertical-equilibrium (VE) concept in the fine-scale pressure reconstruction in which it is applicable. The method differs from the standard grid coarsening and upscaling method in which the coarse-grid properties are computed a priori. Instead, the fine-scale information is restricted to the coarse grid during Newton's iteration to represent the fine-scale flow behavior. Within the aquifer regions, each column of fine cells is coarsened vertically based on fine-scale z-transmissibility. A coarsened column may consist of a single amalgamated aquifer cell or multiple vertically disconnected aquifer cells separated by flow barriers. The pore volume (PV), compressibility, and lateral flow terms of the coarse cell are restricted from the fine-grid cells. The lateral connectivity within the aquifer regions and the one between the aquifer and the reservoir are honored, inclusive of the fine-scale description of faults, pinchouts, and null cells. Reservoir regions are not coarsened. Two alternatives exist for the fine-scale pressure reconstruction from the coarse-grid solution. The first method uses the VE concept. When VE applies, pressure variation can be analytically computed in the solution update step. Otherwise, the second method is to apply a 1D z-line solve for the fine-scale aquifer pressure from the coarse-grid solution.
Simulation results for several examples are included to demonstrate the efficacy and efficiency of the method. We have applied the method to several Saudi Arabian complex full-field simulation models in which the transient aquifer water influx has been identified as a key factor. These models include dual-porosity/dual-permeability (DPDP) models, as well as models with faults and pinchouts in corner-point-geometry grids, for both history match and prediction period. The method is flexible and allows for the optional selection of aquifer regions to be coarsened, either only peripheral aquifers or both the peripheral and bottom aquifers. The new method gives nearly identical results compared with the original runs without coarsening, but with significant reduction in computer time or hardware cost. These results will be detailed in the paper.