Image transforms for determining fit-for-purpose complexity of geostatistical models in flow modeling

Increased diversity of water or energy resources has led to an increased complexity in models aimed at representing accurately dynamic behavior and geological variability in such systems. In terms of variability of properties at least, simple layered models have mostly been replaced with more complex geostatistical models. The newest trend is to replace covariance-based models with geologically more realistic models such as Boolean, multiple-point, surface-, or process-based models. In this paper, we address the following question: given some design purpose or a set of flow-based decision variables, does adding more complexity increase predictability and ultimately improve decisions based on such models? In this paper, we do not attempt to make any generalizing statements or answer this question with yes/no, but provide some initial ideas on practical workflows to discover the needed complexity. We do treat complexity only in the context of decision making under uncertainty. Two workflows are proposed: complexifying versus simplifying. In these workflows, we attempt to extract, using image transforms, relevant features of the variability between geostatistical realizations that are related to uncertainty in flow dynamics. A simple distance-based calibration between the static variability and dynamic variability provides a means to decide on what the relevant complexity of geostatistical models should be for the given purpose.