Multiscale Data Integration With Markov Random Fields and Markov Chain Monte Carlo: A Field Application in the Middle East
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SummaryIntegrating multiresolution data sources into high-resolution reservoir models for accurate performance forecasting is an outstanding challenge in reservoir characterization. Well logs, cores, and seismic and production data scan different length scales of heterogeneity and have different degrees of precision. Current geostatistical techniques for data integration rely on a stationarity assumption that often is not borne out by field data. Geologic processes can vary abruptly and systematically over the domain of interest. In addition, geostatistical methods require modeling and specification of variograms that can often be difficult to obtain in field situations.In this paper, we present a case study from the Middle East to demonstrate the feasibility of a hierarchical approach to spatial modeling based on Markov random fields (MRFs) and multiresolution algorithms in image analysis. The field is located in Saudi Arabia, south of Riyadh, and produces hydrocarbons from the Unayzah formation, a late Permian siliclastic reservoir. Our proposed approach provides a powerful framework for data integration accounting for the scale and precision of different data types. Unlike their geostatistical counterparts, which simultaneously specify distributions across the entire field, the MRFs are based on a collection of full conditional distributions that rely on the local neighborhood of each element. This critical focus on local specification provides several advantages: (a) MRFs are far more computationally tractable and are ideally suited to simulation-based computation such as Markov Chain Monte Carlo (MCMC) methods, and (b) model extensions to account for nonstationarities, discontinuity, and varying spatial properties at various scales of resolution are accessible in the MRFs.We construct fine-scale porosity distribution from well and seismic data, explicitly accounting for the varying scale and precision of the data types. First, we derive a relationship between the neutron porosity and the seismic amplitudes. Second, we integrate the seismically derived coarse-scale porosity with fine-scale well data to generate a 3D fieldwide porosity distribution using MRF. The field application demonstrates the feasibility of this emerging technology for practical reservoir characterization.
