CONSERVATIVE MODELS FOR GEORESERVOIRS: PARAMETRIC ENTROPY AND TEMPORAL ENTROPY IN OUTCOMES

The stratal architecture in aquifer systems affects the behavior of fluid flow and the dispersion of mass. The spatial distribution and connectivity of higher permeability strata plays an important role. The Shannon entropy is a useful metric for quantifying model uncertainty. Models that represent geologic structure have reduced entropy in the spatial distribution of permeability, as compared to models without structure. Importantly, though structure reduces spatial entropy in the parameter field, it can lead to maximum entropy in the model outcomes. Geologic structure will have a large impact on increasing the entropy in the distribution of mass residence times when it manifests as preferential flow pathways through the system via connected high-permeability sediments. As per the percolation theory, at certain volume fractions the full connectivity of the high-permeability sediments will not be represented unless the model is three-dimensional. At these volume fractions, two-dimensional models can profoundly under-represent the entropy in the real, three-dimensional, aquifer system. Thus to be conservative, stochastic models must be three-dimensional and include geologic structure.