Effective representation of reservoir heterogeneities and the subsequent modeling of fluid flow remain the greatest challenge in reservoir engineering. A good reservoir model is one that integrates the relevant aspects of geological, geophysical and production data. Any single type of data is not enough to constrain reservoir uncertainty to a level conducive to reasonably accurate prediction. Uncertainty is a hard fact better dealt with upfront, focusing on the most consequential model decisions, e.g. geological scenarios or flow types, rather than wingflaps of multiple geostatistical realizations.
This tutorial will review current reservoir characterization and modeling approaches and present some new perspectives. Different algorithms have been developed to stochastically simulate reservoir properties using sparse measured data. In these methods, the spatial variability represented by the underlying joint distribution is in the form of the spatial covariance. The major drawback of these traditional variogram-based modeling is that they are not able to reproduce complex spatial patterns. Multiple-point statistical algorithms, however, can reconstruct such curvilinear features. In this presentation, we will explore the link between the multiple point spatial pattern connectivity and the Fourier spectrum. This will allow us to infer statistical functions describing reservoir connectivity more efficiently. Subsequently, we will present a simulation algorithm in Fourier domain in which the amplitude of Fourier transform is calculated directly from power spectrum (Fourier transform of covariance function). The phase identification can be achieved by either solving an optimization problem to match the available conditioning data or from higher order spectra such as bispectrum or trispectrum. We demonstrate the application of the the algorithm for the simulation of complex reservoir features conditioned to sparse data.
The presentation concludes with some perspectives on production history matching of complex reservoir systems. An ensemble-based model selection framework is presented that facilitates integration of diverse data and assessment of residual uncertainty.
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