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Bayesian modeling requires the specification of prior and likelihood models. In reservoir characterization, it is common practice to estimate the prior from a training image. This paper considers a multi-grid approach for the construction of prior models for binary variables. On each grid level we adopt a Markov random field (MRF) conditioned on values in previous levels. Parameter estimation in MRFs is complicated by a computationally intractable normalizing constant. To cope with this problem, we generate a partially ordered Markov model (POMM) approximation to the MRF and use this in the model fitting procedure. Approximate unconditional simulation from the fitted model can easily be done by again adopting the POMM approximation to the fitted MRF. Approximate conditional simulation, for a given and easy to compute likelihood function, can also be performed either by the Metropolis-Hastings algorithm based on an approximation to the fitted MRF or by constructing a new POMM approximation to this approximate conditional distribution. The proposed methods are illustrated using three frequently used binary training images. [ABSTRACT FROM AUTHOR]

Facies bodies in geostatistical models of deep-water depositional environments generally represent channel-levee-overbank-lobe morphologies. Such models adequately capture one set of the erosional and depositional processes resulting from turbidity currents traveling downslope to the ocean basin floor. However, depositional morphologies diverge from the straight forward channel-levee-overbank-lobe paradigm when the topography of the slope or the shape of the basin impacts the timing and magnitude of turbidity current deposition. Subaqueous mass-transport-deposits (MTDs) present the need for an exception to the channel-levee-overbank-lobe archetype. Irregular surface topography of subaqueous MTDs can play a primary role in controlling sand deposition from turbidity currents. MTD topography creates mini-basins in which sand accumulates in irregularly-shaped deposits. These accumulations are difficult to laterally correlate using well-log data due to their variable and unpredictable shape and size. Prediction is further complicated because sandstone bodies typical of this setting are difficult to resolve in seismic-reflection data. An event-based model is presented, called DFTopoSim, which simulates debris flows and turbidity currents. The accommodation space on top of and between debris flow lobes is filled in by sand from turbidity currents. When applied to a subsurface case in the Molasse Basin of Upper Austria, DFTopoSim predicts sand packages consistent with observations from core, well, and seismic data and the interpretation of the sedimentologic processes. DFTopoSim expands the set of available geostatistical deep-water depositional models beyond the standard channel-levee-overbank-lobe model. [ABSTRACT FROM AUTHOR]

We present a methodology based on the ensemble Kalman filter (EnKF) and the level set method for the continuous model updating of geological facies with respect to production data. Geological facies are modeled using an implicit surface representation and conditioned to production data using the ensemble Kalman filter. The methodology is based on Gaussian random fields used to deform the facies boundaries. The Gaussian random fields are used as the model parameter vector to be updated sequentially within the EnKF when new measurements are available. We show the successful application of the methodology to two synthetic reservoir models. [ABSTRACT FROM AUTHOR]

Multiple-point statistics are used to model facies heterogeneities in the vadose zone of the Komadugu-Yobe River valley (southeastern Niger) which is presently submitted to an undergoing intensive agricultural development; therefore, increasing quantitative and qualitative pressures are exerted on groundwater resources. The sand-clay heterogeneities are analyzed by means of a Landsat image acquired during a high flow period over a 160 km stretch in the downstream part of the valley and a set of 50 boreholes drilled near the town of Diffa (4 km×4 km area). The horizontal variograms of heterogeneities are characterized by a noticeably constant length scale of 380 m and clayey objects are shown to be randomly distributed in space according to a Poisson process. A set of two-dimensional vertical images is built based on a Boolean procedure and the Snesim algorithm is used to simulate synthetic three-dimensional media. When the vertical correlation length is fitted, the three-dimensional model satisfactorily reproduces the second order statistics of heterogeneities and the specific facies patterns. [ABSTRACT FROM AUTHOR]

We present an approach for modeling facies bodies in which a highly constrained stochastic object model is used to integrate detailed seismic interpretation of the reservoir's sedimentological architecture directly in a three-dimensional reservoir model. The approach fills the gap between the use of seismic data in a true deterministic sense, in which the facies body top and base are resolved and mapped directly, and stochastic methods in which the relationship between seismic attributes and facies is defined by conditional probabilities. The lateral geometry of the facies bodies is controlled by seismic interpretations on horizon slices or by direct body extraction, whereas facies body thickness and cross-sectional shape are defined by a mixture of seismic data, well data, and user defined object shapes. The stochastic terms in the model are used to incorporate local geometric variability, which is used to increase the geological realism of the facies bodies and allow for correct, flexible well conditioning. The result is a set of three-dimensional facies bodies that are constrained to the seismic interpretations and well data. Each body is defined as a parametric object that includes information such as location of the body axis, depositional direction, axis-to-margin normals, and external body geometry. The parametric information is useful for defining geologically realistic intrabody petrophysical trends and for controlling connectivity between stacked facies bodies. [ABSTRACT FROM AUTHOR]