For many field-scale reservoir simulation models, aquifer regions (both peripheral and bottom) can represent a large percentage of total active grid blocks. The objective of this work is to build an accurate method respecting the fine-scale heterogeneities, but significantly reduce the computational cost of keeping the aquifer grids in the model, where they are deemed necessary to better describe the variable strength of water influx.
The present method can be considered a specialized two-level grid coarsening or upscaling method. Within the aquifer regions, each column of fine cells are 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 cell. The lateral connectivities within the aquifer regions and 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 vertical equilibrium concept. The second method performs a 1D solution for the fine-scale pressure. A spatially variable multi-porosity permeability model can also be accommodated. In parallel implementation, besides the load balancing method, the memory balancing method is also necessary. All these aspects will be explained in the paper.
The method has been applied successfully to several complex full-field simulation models where the transient aquifer water influx has been identified as a key factor. These models include dual porosity, dual permeability models with a complex geologic description. We compare simulation results using the accelerated aquifer calculation method against the original fine-grid simulation model without acceleration and demonstrate the efficacy of the new method. For the models tested, the actual speedup factors achieved are also compared against the theoretically computed improvement factors.
The dual grid method strives to significantly reduce computational cost but retain the fine-scale heterogeneity data to accurately represent the water movement within the water zones of the simulation model. The method differs from the standard upscaling and grid coarsening method where 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. This is analogous to the multiscale method, but we apply this only vertically within the aquifer regions.