An analysis of upscaling techniques for reservoir simulation

In the past two decades, a great many upscaling procedures have been proposed. The major methods are power-law average, renormalization technique, pressure-solver method, tenser method, and pseudofunction technique. The common problem of conventional upscaling methods is that they tend to smear out the spatially continuous extremes, such as shale barriers and open fractures. However, experience and previous simulation works in heterogeneous reservoirs have shown that oil recovery (especially water breakthrough oil recovery) mainly depends on the spatial connectivity of the extreme permeability values. The main idea of upscaling is to replace a number of heterogeneous fine grid blocks with one equivalent coarse homogeneous grid block. So, the essence of upscaling is averaging. Therefore, we think that all upscaling approaches could be sorted as two types. One is explicit averaging model: including power law averaging, renormalization technique, and global upscaling. The other is implicit averaging model: pressure-solver methods and pseudofunctions. If regarding their theoretical strategies, we may classify them as another two types, one is grid-upgridding-oriented approaches, such as global upscaling, sedimentological approach of upscaling; and the other is property-upscaling-oriented approaches, which include most of the traditional upscaling methods. It goes without saying that some information loss in upscaling is inevitable. The key issue is how to optimize the upscaling technique and minimize the information loss. Lasseter et al. (1986) proposed that scaleup of properties should be done from the scale of a representative elementary volume (REV), a volume for which the measured property does not change with an increase in scale over a given limit of scale. The notion of REV is physical-model oriented and proposed a criterion for upscaling technique. However, the decisive factor in upscaling is the grid system rather than individual physical point. This paper concludes that how to obtain REV for real system, how to evaluate the upscaling results quantitatively, how to treat extremes of permeability as well as how to perform upscaling for naturally fractured reservoirs and carbonate reservoirs are the remaining major challeng problems in this area. It is concluded that a great effort should be made on how to obtain the REV grid, which could best describe the heterogeneity of given reservoir at given scale. Second, how to perform the upscaling of all properties based on REV grid is also a critical aspect and should be considered according to different extent and pattern of heterogeneity of original geological model, respectively.