Data integration into high resolution reservoir models using geostatistics and multiscale Markov random fields

Integrating multiresolution data into reservoir models for accurate performance forecasting is a longstanding challenge in reservoir characterization. Important information about the reservoir rocks scan different length scales of heterogeneity and have different degrees of precision. Data from core plugs, well logs, and seismic testing must all be included in the construction of a geological reservoir model. Hence, spatial models that are defined over a hierarchy of scales are required to integrate these data.; This study developed two different techniques to integrate different reservoir data that have different scales and precision. The first technique uses nonparametric transformation and non-Gaussian cosimulation to infer water saturation distribution in the interwell region by using the relationship between seismic velocity and formation resistivity. We have applied our methodology to a synthetic model as well as a field example. The synthetic example validates the approach and involves reproducing a pregenerated primary data set using sparse primary and dense secondary data. The field example uses cross-well seismic velocity and well data from the Buena Vista Hills field, a fractured siliceous shale reservoir in California.; The second data integration technique is a hierarchical approach to spatial modeling based on Markov Random Fields (MRF) and multiresolution algorithms in image analysis. Being locally specific provides several advantages: (a) MRFs are computationally tractable and ideally suited to simulation-based computation such as MCMC (Markov Chain Monte Carlo) methods, and (b) model extensions to account for nonstationary, discontinuity, and varying spatial properties are easily accessible in the MRF framework. Our proposed method is computationally efficient and well-suited to reconstruct fine-scale spatial fields from coarser, multiscale samples (e.g., based on seismic and production data) and sparse fine scale conditioning data (e.g., well data). Moreover, it can easily account for the complex, nonlinear interactions between different scales as well as precision of the data at various scales in a consistent fashion. We illustrate our method using a variety of examples that demonstrate the power and versatility of the proposed approach. A comparison with data integration techniques such as Sequential Gaussian Simulation with Block Kriging (SGSBK) and wavelets indicates similar performance with less restrictive assumptions.