At present, uniform upscaling division methods are routinely used to upscale geologic model grids, resulting in overly fine grids in some areas of the model. To improve computational efficiency, we have examined the effect of model upscaling with different upscaling parameters with the goal of producing a nonuniform grid with uniform accuracy. We based our nonuniform upscaling grid method on geologic characteristics including reservoir thickness, physical properties, reservoir spacing, and water flooding. Most of the logging curves of thin reservoirs are finger-like, allowing us to define the grid size according to the reservoir thickness. We use two different strategies to discretize uniform and composite reservoirs and represent reservoir thickness that exhibit bell- and funnel-shaped logging curves. Although one grid point accurately represents a uniform reservoir, we find that composite reservoirs require four or five points to accurately represent the physical properties of a composite reservoir. For the thick reservoirs (>5 m) with box- or composite-type logging curves, the physical properties inside the reservoir do not change much; therefore, we use a grid point to represent the reservoir thickness information. Using these metrics, we constructed alternative “moderate” and “efficient” vertical grid upscaling strategies. Taking the 15 sedimentary units with a total thickness of 72 m as an example, the statistical results show that the computational efficiency using our data-adaptive grid can be increased more than five times compared to the traditional uniform fine-grid method while retaining the same accuracy.
Nonuniform Finite Difference Scheme for the Three-Dimensional Time-Fractional Black–Scholes Equation
