Advances in geostatistics during the past ten years have led to fine-gridded reservoir models containing several millions of grid blocks. With steady increases in computer power, researchers have been able to reduce the effect of the upscaling phase on the erasement of heterogeneity in flow models.
However, cells in fine gridded reservoir models still represent thousands of cubic meters in which heterogeneity is usually ignored at that scale. This is called the Missing Scale.
Usually, scaling-up petrophysical properties from the scale of the plug to that of fine-gridded models is conducted either using simplistic methods between all scales, or by applying more sophisticated methods between plug and the laminae scale only.
The implicit assumption that rocks can be modeled as if they were homogeneous at the Missing Scale (between the lamina and the sedimentary body) leads to the neglect of significant effects on recovery due to capillary trapping or accentuation of bypass. This paper illustrates and quantifies problems induced by building overly simplistic models.
In an extensive study conducted on channel-type reservoirs, small-scale heterogeneity is input in models by way of anisotropic horizontal permeability. Waterflooding and primary depletion flow simulations are run using such models. Productions (recovery and production times) are compared with results from models run with isotropic permeability values. Various case studies are conducted to investigate the sensitivity of results to geology, relative permeabilities, mobility ratios, etc… They reveal the importance of taking into account the missing scale, with respect to a problem.
The Missing Scale can only be taken into account if the facies and sedimentary structures that are responsible for heterogeneity within sedimentary bodies are properly described.
A comprehensive study of the structures was conducted on a fluviatile environment. It yielded a classification of the structures with respect to the effects they should have on flow.
Finally, after evaluating the consequences of current modeling practices on flows, the different stochastic simulation techniques which could be potentially used in modeling small-scale heterogeneity are appraised. A pseudo-genetic modeling method is proposed for meandering channels.