Coarse-scale data assimilation as a generic alternative to localization

Coarse-scale data assimilation (DA) with large ensemble size is proposed as a robust alternative to standard DA with localization for reservoir history matching problems. With coarse-scale DA, the unknown property function associated with each ensemble member is upscaled to a grid significantly coarser than the original reservoir simulator grid. The grid coarsening is automatic, ensemble-specific and non-uniform. The selection of regions where the grid can be coarsened without introducing too large modelling errors is performed using a second-generation wavelet transform allowing for seamless handling of non-dyadic grids and inactive grid cells. An inexpensive local-local upscaling is performed on each ensemble member. A DA algorithm that restarts from initial time is utilized, which avoids the need for downscaling. Since the DA computational cost roughly equals the number of ensemble members times the cost of a single forward simulation, coarse-scale DA allows for a significant increase in the number of ensemble members at the same computational cost as standard DA with localization. Fixing the computational cost for both approaches, the quality of coarse-scale DA is compared to that of standard DA with localization (using state-of-the-art localization techniques) on examples spanning a large degree of variability. It is found that coarse-scale DA is more robust with respect to variation in example type than each of the localization techniques considered with standard DA. Although the paper is concerned with two spatial dimensions, coarse-scale DA is easily extendible to three spatial dimensions, where it is expected that its advantage with respect to standard DA with localization will increase.