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2.
An important task in modern geostatistics is the assessment and quantification of resource and reserve uncertainty. This uncertainty
is valuable support information for many management decisions. Uncertainty at specific locations and uncertainty in the global
resource is of interest. There are many different methods to build models of uncertainty, including Kriging, Cokriging, and
Inverse Distance. Each method leads to different results. A method is proposed to combine local uncertainties predicted by
different models to obtain a combined measure of uncertainty that combines good features of each alternative. The new estimator
is the overlap of alternate conditional distributions. 相似文献
3.
Jason A. McLennan Weishan Ren Oy Leuangthong C. V. Deutsch 《Natural Resources Research》2006,15(2):119-127
The application of steam-assisted gravity drainage (SAGD) to recover heavy oil sands is becoming increasingly important in
the northern Alberta McMurray Formation because of the vast resources/reserves accessible with this mechanism. Selecting the
stratigraphic elevations of SAGD well pairs is a vital decision for reservoir evaluation and planning. The inherent uncertainty
in the distribution of geological variables significantly influences this decision. Geostatistical simulation is used to capture
geological uncertainty, which is used can be transformed into a distribution of the best possible well pair elevations.
A simple exhaustive calculation scheme is used to determine the optimum stratigraphic location of a SAGD well pair where the
recovery R is maximized. There are three basic steps to the methodology: (1) model the uncertainty in the top continuous bitumen (TCB)
and bottom continuous bitumen (BCB) surfaces, (2) calculate the recovery at all possible elevation increments within the TCB
and BCB interval, and (3) identify the elevation that maximizes R. This is repeated for multiple TCB/BCB pairs of surfaces
to assess uncertainty. The methodology is described and implemented on a subset of data from the Athabasca Oilsands in Fort
McMurray, Alberta. 相似文献
4.
Reservoir models have large uncertainty because of spatial variability and limited sample data. The ultimate aim is to use simultaneously all available data sources to reduce uncertainty and provide reliable reservoir models for resource assessment and flow simulation. Seismic impedance or some other attribute provides a key source of data for reservoir modeling. These seismic data are at a coarser scale than the hard well data and it not an exact measurement of facies proportions or porosity. A requirement for data integration is the cross-covariance between the well and seismic data.The size-scaling behavior of the cross correlation for different measurement scales was nvestigated. The size-scaling relationship is derived theoretically and validated by numerical studies (including an example with real data). The limit properties of the cross-correlation coefficient when the averaging volume becomes large is shown. After some averaging volume, the volume-dependent cross-correlation coefficient reaches a limit value. This plateau value is controlled mainly by the large-scale behavior of the cross and direct variograms.The cross correlation can increase or decrease with volume support depending on the relative importance of long- and short-scale covariance structures. If the direct and cross variograms are proportional, there is no change in the cross correlation as the averaging volume changes. Our study shows that the volume-dependent cross-correlation coefficient is sensitive to the shape of the cross variogram and differences between the direct variograms of the well data and seismic data. 相似文献
5.
Most geostatistical studies consider multiple-related variables. These relationships often show complex features such as nonlinearity, heteroscedasticity, and mineralogical or other constraints. These features are not handled by the well-established Gaussian simulation techniques. Earth science variables are rarely Gaussian. Transformation or anamorphosis techniques make each variable univariate Gaussian, but do not enforce bivariate or higher order Gaussianity. The stepwise conditional transformation technique is proposed to transform multiple variables to be univariate Gaussian and multivariate Gaussian with no cross correlation. This makes it remarkably easy to simulate multiple variables with arbitrarily complex relationships: (1) transform the multiple variables, (2) perform independent Gaussian simulation on the transformed variables, and (3) back transform to the original variables. The back transformation enforces reproduction of the original complex features. The methodology and underlying assumptions are explained. Several petroleum and mining examples are used to show features of the transformation and implementation details. 相似文献
6.
Indicator Simulation Accounting for Multiple-Point Statistics 总被引:7,自引:0,他引:7
Geostatistical simulation aims at reproducing the variability of the real underlying phenomena. When nonlinear features or large-range connectivity is present, the traditional variogram-based simulation approaches do not provide good reproduction of those features. Connectivity of high and low values is often critical for grades in a mineral deposit. Multiple-point statistics can help to characterize these features. The use of multiple-point statistics in geostatistical simulation was proposed more than 10 years ago, on the basis of the use of training images to extract the statistics. This paper proposes the use of multiple-point statistics extracted from actual data. A method is developed to simulate continuous variables. The indicator kriging probabilities used in sequential indicator simulation are modified by probabilities extracted from multiple-point configurations. The correction is done under the assumption of conditional independence. The practical implementation of the method is illustrated with data from a porphyry copper mine. 相似文献
7.
Transformation of Residuals to Avoid Artifacts in Geostatistical Modelling with a Trend 总被引:1,自引:0,他引:1
Trend modelling is an important part of natural resource characterization. A common approach to account for a variable with a trend is to decompose it into a relatively smoothly varying trend and a more variable residual component. Then, the residuals are stochastically modelled independent of the trend. This decomposition can result in values outside the plausible range of variability, such as grades below zero or ratios that exceed 1.0. We transform the residuals conditional to the trend component to explicitly remove these complex features prior to geostatistical modelling. Back transformation of the modelled residual values allows the complex relations to be reproduced. A petroleum-related application shows the robustness of the proposed transformation. Furthermore, a mining application shows that when this conditional transformation is applied to the original variable, instead of the residual, simulated values are assured to be nonnegative. 相似文献
8.
9.
There is a need to bridge theory and practice for incorporating parameter uncertainty in geostatistical simulation modeling workflows. Simulation workflows are a standard practice in natural resource and recovery modeling, but the incorporation of multivariate parameter uncertainty into those workflows is challenging. However, the objectives can be met without considerable extra effort and programming. The sampling distributions of statistics comprise the core theoretical notion with the addition of the spatial degrees of freedom to account for the redundancy in the spatially correlated data. Prior parameter uncertainty is estimated from multivariate spatial resampling. Simulation-based transfer of prior parameter uncertainty results in posterior distributions which are updated by data conditioning and the model domain extents and configuration. The results are theoretically tractable and practical to achieve, providing realistic assessments of uncertainty by accounting for large-scale parameter uncertainty, which is often the most important component impacting a project. A simulation-based multivariate workflow demonstrates joint modeling of intrinsic shale properties and uncertainty in estimated ultimate recovery in a shale gas project. The multivariate workflow accounts for joint prior parameter uncertainty given the current well locations and results in posterior estimates on global distributions of all modeled properties. This is achieved by transferring the joint prior parameter uncertainty through conditional simulations. 相似文献
10.
Jared L. Deutsch Kevin Palmer Clayton V. Deutsch Jozef Szymanski Thomas H. Etsell 《Natural Resources Research》2016,25(2):161-181
High-resolution spatial numerical models of metallurgical properties constrained by geological controls and more extensively by measured grade and geomechanical properties constitute an important part of geometallurgy. Geostatistical and other numerical techniques are adapted and developed to construct these high-resolution models accounting for all available data. Important issues that must be addressed include unequal sampling of the metallurgical properties versus grade assays, measurements at different scale, and complex nonlinear averaging of many metallurgical parameters. This paper establishes techniques to address each of these issues with the required implementation details and also demonstrates geometallurgical mineral deposit characterization for a copper–molybdenum deposit in South America. High-resolution models of grades and comminution indices are constructed, checked, and are rigorously validated. The workflow demonstrated in this case study is applicable to many other deposit types. 相似文献