Geostatistical Modeling of the Spaces of Local, Spatial, and Response Uncertainty for Continuous Petrophysical Properties
P. Goovaerts, 2006. "Geostatistical Modeling of the Spaces of Local, Spatial, and Response Uncertainty for Continuous Petrophysical Properties", Stochastic Modeling and Geostatistics: Principles, Methods, and Case Studies, Volume II, T. C. Coburn, J. M. Yarus, R. L. Chambers
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In the characterization of petroleum reservoirs, three types of uncertainty typically arise: (1) the uncertainty about the value of a petrophysical attribute at an unsampled location (local uncertainty); (2) the joint uncertainty about attribute values at several locations taken together (spatial uncertainty); and (3) the uncertainty about production forecasts, such as time to recover a given proportion of the oil (response uncertainty). In each case, the probabilistic way to assess the uncertainty consists of determining the distribution or set of possible outcomes (e.g., local permeability value, permeability grid, or production parameters), which is referred to as the space of uncertainty.
This chapter reviews the major geostatistical algorithms available to model both local and spatial uncertainties of continuous attributes. Goodness criteria are introduced for each type of space of uncertainty, and the impacts of the following parameters are discussed: stochastic-simulation algorithm, number of realizations, and ergodic fluctuations. Conclusions are drawn on the relations between the different spaces of uncertainty. The discussion is illustrated using an exhaustive set of 102 × 102 permeability values.
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Since publication of the first volume of Stochastic Modeling and Geostatistics in 1994, there has been an explosion of interest and activity in geostatistical methods and spatial stochastic modeling techniques. Many of the computational algorithms and methodological approaches that were available then have greatly matured, and new, even better ones have come to the forefront. Advances in computing and increased focus on software commercialization have resulted in improved access to, and usability of, the available tools and techniques. Against this backdrop, Stochastic Modeling and Geostatistics Volume II provides a much-needed update on this important technology. As in the case of the first volume, it largely focuses on applications and case studies from the petroleum and related fields, but it also contains an appropriate mix of the theory and methods developed throughout the past decade. Geologists, petroleum engineers, and other individuals working in the earth and environmental sciences will find Stochastic Modeling and Geostatistics Volume II to be an important addition to their technical information resources.