Multiscale Data Integration Using Markov Random Fields and Markov Chain Monte Carlo: A Field Application in the Middle-East

摘要

Integrating multi-resolution data sources into high-resolutionreservoir models for accurate performance forecasting is anoutstanding challenge in reservoir characterization. Well logs,cores, seismic and production data scan different length scalesof heterogeneity and have different degrees of precision.Current geostatistical techniques for data integration rely on astationarity assumption that is often not borne out by fielddata. Geologic processes can vary abruptly and systematicallyover the domain of interest. In addition, geostatistical methodsrequire modeling and specification of variograms that canoften be difficult to obtain in field situations.In this paper, we present a case study from the Middle Eastto demonstrate the feasibility of a hierarchical approach tospatial modeling based on Markov Random Fields (MRF) andmulti-resolution algorithms in image analysis. The field islocated in Saudi Arabia south of Riyadh and produceshydrocarbons from the Unayzah Formation, a late Permiansiliclastic reservoir. Our proposed approach provides anefficient and powerful framework for data integrationaccounting for the scale and precision of different data types.Unlike their geostatistical counterparts that simultaneouslyspecify distributions across the entire field, the MRF are basedon a collection of full conditional distributions that rely onlocal neighborhood of each element. This critical focus onlocal specification provides several advantages: (a) MRFs arefar more computationally tractable and are ideally suited tosimulation-based computation such as MCMC (Markov ChainMonte Carlo) methods, and (b) model extensions to accountfor non-stationarities, discontinuity and varying spatial properties at various scales of resolution are accessible in theMRF.We construct fine scale porosity distribution from well andseismic data explicitly accounting for the varying scale andprecision of the data types. First, we derive a relationshipbetween the neutron porosity and the seismic amplitudes.Second, we integrate the seismically derived coarse-scaleporosity with fine-scale well data to generate a 3-D field-wideporosity distribution using MRF. The field applicationdemonstrates the feasibility of this emerging technology forpractical reservoir characterization.