Quantitative log interpretation and uncertainty propagation of petrophysical properties and facies classification from rock-physics modeling and formation evaluation analysis

Abstract

Formation evaluation analysis, rock-physics models, and log-facies classification are powerful tools to link the physical properties measured at wells with petrophysical, elastic, and seismic properties. However, this link can be affected by several sources of uncertainty. We proposed a complete statistical workflow for obtaining petrophysical properties at the well location and the corresponding log-facies classification. This methodology is based on traditional formation evaluation models and cluster analysis techniques, but it introduces a full Monte Carlo approach to account for uncertainty evaluation. The workflow includes rock-physics models in log-facies classification to preserve the link between petrophysical properties, elastic properties, and facies. The use of rock-physics model predictions guarantees obtaining a consistent set of well-log data that can be used both to calibrate the usual physical models used in seismic reservoir characterization and to condition reservoir models. The final output is the set of petrophysical curves with the associated uncertainty, the profile of the facies probabilities, and the entropy, or degree of confusion, related to the most probable facies profile. The full statistical approach allows us to propagate the uncertainty from data measured at the well location to the estimated petrophysical curves and facies profiles. We applied the proposed methodology to two different well-log studies to determine its applicability, the advantages of the new integrated approach, and the value of uncertainty analysis.

Petro-Elastic Log-Facies Classification Using the Expectation–Maximization Algorithm and Hidden Markov Models

“…The number of facies has been chosen to preserve the discrimination of facies from well-log data. This preliminary analysis could require a sensitivity analysis (Grana et al 2012). For example, in the North Sea application the eight facies initially defined from core samples by sedimentologists were grouped in only two log-facies types: sand and shale.…”

“…Similarly, distributary channels and crevasse plays show high quartz content and high effective porosity and could be re-classified as sand. For a specific example, the reader is referred to Grana et al (2012).…”

“…A comparison of four methods, namely Bayesian classification, fuzzy logic, k-nearest neighbor, and artificial neural network, is presented in Dubois et al (2007). A Monte Carlo classification method using well logs combined with rock physics models was proposed in Grana et al (2012) in a probabilistic workflow to represent the posterior uncertainty in the classification. A comparison between neural networks and discriminant analysis has been proposed by Wong et al (1995).…”

Petro-elastic facies classification in the Marcellus Shale by applying expectation maximization to measured well logs

“…The well logs used include gamma ray, spectral gamma ray, neutron-porosity, resistivity, photoelectric factor, and sonic logs. Generally, log-facies classification is performed only in the petrophysical domain (Grana et al, 2012). This proposed classification uses a joint petro-elastic domain combining well logs (Ellis and Singer, 2007) and rock physics (Mavko et al, 2009), allowing the facies classification to be readily used in reservoir characterization (Doyen, 2007).…”

Statistical facies classification from multiple seismic attributes: comparison between Bayesian classification and expectation–maximization method and application in petrophysical inversion

“…DaVeiga and Le Ravalec (2012) proposed a statistical facies classification based on maximum-likelihood criteria. Grana, Pirrone, and Mukerji (2012b) proposed a Monte Carlo classification method using well logs combined with rock physics models to represent the posterior uncertainty in the classification. Wang et al (2014) used support vector machines to identify different shale types in unconventional reservoirs.…”