History matching by simultaneous calibration of flow functions
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Reliable predictions of reservoir flow response corresponding to various recovery schemes require a realistic geological model of heterogeneity and an understanding of its relationship with the flow properties. This dissertation presents results on the implementation of a novel approach for the integration of dynamic data into reservoir models that combines stochastic techniques for simultaneous calibration of geological models and multiphase flow functions associated with porelevel spatial representations of porous media. In this probabilistic approach, a stochastic simulator is used to model the spatial distribution of a discrete number of rock types identified by rock/connectivity indexes (CIs). Each CI corresponds to a particular pore network structure with a characteristic connectivity. Primary drainage and imbibition displacement processes are modeled on the 3-D pore networks to generate multiphase flow functions corresponding to networks with different CIs. During history matching, the stochastic simulator perturbs the spatial distribution of the CIs to match the simulated pressures and flow rates to historic data, while preserving the geological model of heterogeneity. This goal is accomplished by applying a probabilistic approach for gradual deformation of spatial distribution of rock types characterized by different CIs. Perturbation of the CIs in turn results in the update of all the flow functions including the effective permeability, porosity of the rock, the relative permeabilities and capillary pressure. The convergence rate of the proposed method is comparable to other current techniques with the distinction of enabling consistent updates to all the flow functions. The resultant models are geologically consistent in terms of all the flow functions, and consequently, predictions obtained using these models are likely to be more accurate. To compare and contrast this comprehensive approach to reservoir modeling against other approaches that rely on modeling and perturbing only the permeability field, a realistic case study is presented with implementation of both approaches. Comparison is made with the history-matched model obtained only by perturbing permeability. It is argued that reliable predictions of future production can only be made when the entire suite of flow functions is consistent with the real reservoir.