A Hierarchical Streamline-Assisted History Matching Approach with Global and Local Parameter Updates
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The effective strategies for traditional manual history matching commonly follow a structured approach with a sequence of adjustments from global to regional parameters followed by local changes in model properties, associated with matching for pressure (reservoir energy), flood front progression, and individual well performance. In contrast, many of the automatic history matching methods utilize parameter sensitivities or gradients to directly update the fine-scale reservoir properties, potentially combining elements at all of these scales. In this paper we present a hierarchical streamline-assisted history matching approach that emulates the traditional structured procedures. First, a probabilistic approach is used to understand the uncertainty in the large-scale static and dynamic parameters, and to calibrate these global parameters. In this global calibration, the intent is to develop multiple models that all sensibly match the field performance. This global calibration is followed by a streamline sensitivity-based deterministic model calibration for local permeability changes in which each of the distinct models created in the global match are history matched in additional detail. In the probabilistic global calibration, design of experiments and response surface methodologies with evolutionary algorithms are used to calibrate the global parameters. Typical parameters are regional pore volume multipliers, regional vertical and areal transmissibility multipliers, fault transmissibilities and aquifer strength. Key global parameters are first identified via a sensitivity analysis and an initial ensemble of models that span these parameters is created. The cases studied in this sensitivity analysis are used to construct a proxy model using experimental design and response surface analysis. An improved genetic algorithm with heat-bath sampling is used to generate an updated ensemble of models conditioned to static MDT pressures and total liquid rates at the wells, corresponding to a traditional pressure history match. Next, each ensemble member is updated using water-cut, GOR and flowing BHP via sensitivity-based local permeability calibration. We utilize streamline-derived analytic sensitivities to determine the spatial distribution and magnitude of these local changes. The proposed approach was tested by a 3D synthetic case and a field application. Our hierarchical approach appears to be stable in the sense that the local changes for permeability (inner loop) do not invalidate the pressure history match (outer loop). This is not entirely unexpected since the local permeability changes are regularized by a 'norm' constraint that minimizes deviations from the globally updated model. None the less, this is a very useful property in that it allows us to powerfully combine history matching procedures on global and local scales. Copyright 2010, Society of Petroleum Engineers.
author list (cited authors)
Yin, J., Park, H., Datta-Gupta, A., King, M. J., & Choudhary, M. K.