Multiscale Data Integration With Markov Random Fields and Markov Chain Monte Carlo: A Field Application in the Middle East
- Adel Malallah (Kuwait U.) | Hector Perez (Ecopetrol) | Akhil Datta-Gupta (Texas A&M U.) | Waleed Alamoudi (Saudi Aramco)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- December 2004
- Document Type
- Journal Paper
- 416 - 426
- 2004. Society of Petroleum Engineers
- 5.1.7 Seismic Processing and Interpretation, 1.6.9 Coring, Fishing, 7.6.2 Data Integration, 5.1 Reservoir Characterisation, 5.1.5 Geologic Modeling, 1.10.1 Drill string components and drilling tools (tubulars, jars, subs, stabilisers, reamers, etc), 5.8.7 Carbonate Reservoir, 1.2.3 Rock properties, 5.5.2 Core Analysis, 5.5 Reservoir Simulation, 5.6.1 Open hole/cased hole log analysis, 4.3.4 Scale
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Integrating 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.
The principal goal of reservoir characterization is to provide a reservoir model for accurate reservoir performance prediction. Integrating various data sources is an essential task in reservoir characterization. In general, we have hard data such as well logs and cores and soft data such as seismic traces, production history, a conceptual depositional model, and regional geological analysis. Seismic data in particular can play a major role in enhancing the geological model. It can be a block constraint when generating property distributions at a finer scale. However, integrating such information into the reservoir model is nontrivial. This is because different data sources scan different length scales of heterogeneity and can have different degrees of precision.1 It is essential that reservoir models preserve small-scale property variations observed in well logs and core measurements and capture the large-scale structure and continuity observed in global measurements such as seismic and production data.
The large coverage area of seismic data has established that such data sources can play a major role in characterizing the reservoir. Most applications of seismic data for reservoir characterization have focused on the relationship between seismic attributes such as amplitudes or impedance and porosity.2,3 Two basic approaches have been adopted for integrating seismic data into reservoir models. For high-resolution seismic data, several geostatistical techniques such as cokriging and collocated cokriging have been proposed to estimate areal distribution of porosity.4-6 On the lower-resolution spectrum, there are methods to combine multiscale data where seismic data impose a block constraint for the finer scale.3,4,6-11 These include techniques such as sequential Gaussian simulation with block kriging3 and Bayesian updating of point kriging.10,11 Most kriging-based methods are restricted to multi-Gaussian and stationary random fields. They therefore require data transformation and variogram construction.3,4,6-11 In practice, variogram modeling with a limited data set can be difficult and strongly user dependent. Improper variograms can lead to errors and inaccuracies in the estimation. Thus, one might also need to consider the uncertainty in variogram models during estimation.12 However, conventional geostatistical methods do not provide an effective framework to take into account the uncertainty of the variogram. Furthermore, most of the multiscale integration algorithms assume a linear relationship between the scales.
An alternative approach to traditional geostatistical methods is based on multiscale MRFs that can effectively integrate diverse data sources into high-resolution reservoir models. MRF methods have been applied widely in imaging processing13-15 and spatial modeling. In the oil industry, this technique is relatively new. There are limited applications in determining the reservoir facies16,17 distribution and spatial modeling of reservoir properties with synthetic examples.18 However, field-scale application of MRF has remained a challenging goal.
In this paper, we further investigate our previously proposed method18 with the main objective of gaining insight on the practical implementation of this technique by a field application in the Middle East. The particular field studied here, the CNR field in Saudi Arabia, is located south of Riyadh and produces hydrocarbons from the Unayzah formation, a late Permian siliclastic reservoir. Our goal is to generate a 3D high-resolution porosity model by integrating seismic and well-log data through an MRF method.
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