Dynamic Ranking of Multiple Realizations by Use of the Fast-Marching Method

Abstract

Summary One of the great challenges in reservoir modeling is to understand and quantify the dynamic uncertainties in geocellular models. Uncertainties in static parameters are easy to identify in geocellular models. Unfortunately, those models contain at least one to two orders of magnitude more gridblocks than typical simulation models. This means that, without significant upscaling, the dynamic uncertainties in these models cannot easily be assessed. Further, if we would like to select only a few geological models that can be carried forward for future performance predictions, we do not have an objective method of selecting the models that can properly capture the dynamic-uncertainty range. One possible solution is to use a faster simulation technique, such as streamline simulation. However, even streamline simulation requires solving a pressure equation at least once. For highly heterogeneous reservoir models with multimillion cells and in the presence of capillary effects or an expansion-dominated process, this can pose a challenge. If we use static permeability thresholds to determine the connected volume, it would not account for how tortuous the connection is between the connected gridblock and the well location. In this paper, we use the fast-marching method (FMM) as a computationally efficient method for calculating the pressure/front propagation time on the basis of reservoir properties. This method is based on solving the Eikonal equation by use of upwind finite-difference approximation. In this method, pressure/front location (radius of investigation) can be calculated as a function of time without running any flow simulation. We demonstrate that dynamically connected volume based on pressure-propagation time is a very good proxy for ultimate recovery from a well in the primary-depletion process. With a predetermined threshold propagation time, a large number of geocellular models can be ranked. FMM can be scaled almost linearly with the number of gridblocks in the model. Two main advantages of this ranking method compared with other methods are that this method determines dynamic connectivity in the reservoir and that it is computationally much more efficient. We demonstrate the validity of the method by comparing ranking of multiple geocellular realizations (on Cartesian grid with heterogeneous and anisotropic permeability) by use of FMM with ranking from flow simulation. This method will allow us to select the geological models that can truly capture the range of dynamic uncertainty very efficiently.