A challenge in petroleum geostatistics is the application of modeling algorithms such as Gaussian simulation to unstructured grids that are being used for flow simulation. Geostatistical modeling is typically applied on a fine scale regular grid and then upscaled to the unstructured grid. This work proposes a fine scale unstructured grid. The grid is designed so that its elements align with the flow simulation grid elements, eliminating the occurrence of intersections between the two grids. Triangular and tetrahedral grids are used for the fine scale grid; however, they introduce a variety of element scales. The approach developed in this work populates the fine scale grid based on the scale of conditioning data. The resulting error due to scale discrepancy is quantified and mitigated though the upscaling process. A methodology to assess the error in upscaled properties is developed and used to control the design of the fine scale grid. Populating the fine scale grid with reservoir properties requires modification of existing geostatistical algorithms. The set of spatial locations for modeling is irregular and three differences that result from this are addressed: random path generation; spatial search; and the covariance lookup table. Results are compiled into an algorithm for sequential indicator and sequential Gaussian simulation on irregular point sets. Checking variogram reproduction on large irregular point sets is a challenge. An algorithm that efficiently computes the experimental variogram for these cases is developed. A flow based upscaling method based on the multipoint flux approximation is developed to upscale permeability models from the fine scale unstructured grid to the flow simulation grid. Triangular grids are assumed for the fine scale. Flow simulation results using the upscaled transmissibilities are very similar to results obtained using traditional flow simulation on high resolution regular grids. / Mining Engineering

Rock physical properties are usually associated with important geologic features within mineral deposits and can be used to define the location, depth and size of the deposit, type of ore, or physical property contrast between the host and country rock. Geophysical surveys are sensitive to physical properties and therefore are widely used in mining exploration, especially in concealed terrains. The surveys can be performed at multiple scales, resulting in corresponding physical property datasets at different scales. Survey scale can vary from core or hand sample, involving few cubic centimeters, to regional-scale surveys providing information about physical property contrasts between distinct regional geological features. The understanding of the relationship between the physical property distributions with the sample volume (e.g. district, deposit, and drill-hole scale) is required where point scale physical property measurements are going to be consistent with measurements at larger volumetric scales during the integration of data for geophysical modeling The approach used to address the problem of understanding the scaling relations of physical properties, was achieved by considering them as second order stationary regionalized variables and then applying the random function formalism, provided by geostatistics theory. Geostatistics provide the required framework to characterize, quantify, model and link the spatial variability of the random variable at the different volumetric scales. The aim of this study is to apply geostatistics to effectively integrate data collected at several scales and bring knowledge to the understanding of the scaling relations of magnetic susceptibility. For this purpose, measurements of magnetic susceptibility available from Flin Flon copper-zinc district in Canada will be used. The data available at point scale were collected with hand portable magnetic susceptibility meter. The larger volumetric scale dataset were acquired using frequency domain electromagnetic instruments capable of measuring larger sample volumes, and then used to obtain magnetic susceptibility models using geophysical inversion algorithms. Once different scale models of magnetic susceptibility were available, quantification of the scaling relation using geostatistics, specifically variogram models and dispersion variance were determined. The understanding provided by the scaling analysis of the Flin-Flon magnetic data is applied to data from the Rio Blanco copper district in central Chile. Magnetic susceptibility measurements collected with a hand magnetic susceptibility meter on drill-core is integrated in larger scale volumes used for geophysical inversion modeling of regional scale airborne magnetic field measurements to recover magnetic susceptibility models. The methodology resulting from this application of geostatistics is used to address the problem of integrating multiple scales of physical property data in an effective way. The resulting physical property models capture the small-scale magnetic susceptibility variability observed and can guide larger-scale variability within geophysical inversion models. Establishing reliable statistical correlations between physical properties and rock units controlling ore within deposits are crucial steps leading predictive mine exploration tools. Any numerical modeling approach to establish these correlations should consider in some way the scaling nature of both physical property and ore content.

Rock physical properties are usually associated with important geologic features within mineral deposits and can be used to define the location, depth and size of the deposit, type of ore, or physical property contrast between the host and country rock. Geophysical surveys are sensitive to physical properties and therefore are widely used in mining exploration, especially in concealed terrains. The surveys can be performed at multiple scales, resulting in corresponding physical property datasets at different scales. Survey scale can vary from core or hand sample, involving few cubic centimeters, to regional-scale surveys providing information about physical property contrasts between distinct regional geological features. The understanding of the relationship between the physical property distributions with the sample volume (e.g. district, deposit, and drill-hole scale) is required where point scale physical property measurements are going to be consistent with measurements at larger volumetric scales during the integration of data for geophysical modeling The approach used to address the problem of understanding the scaling relations of physical properties, was achieved by considering them as second order stationary regionalized variables and then applying the random function formalism, provided by geostatistics theory. Geostatistics provide the required framework to characterize, quantify, model and link the spatial variability of the random variable at the different volumetric scales. The aim of this study is to apply geostatistics to effectively integrate data collected at several scales and bring knowledge to the understanding of the scaling relations of magnetic susceptibility. For this purpose, measurements of magnetic susceptibility available from Flin Flon copper-zinc district in Canada will be used. The data available at point scale were collected with hand portable magnetic susceptibility meter. The larger volumetric scale dataset were acquired using frequency domain electromagnetic instruments capable of measuring larger sample volumes, and then used to obtain magnetic susceptibility models using geophysical inversion algorithms. Once different scale models of magnetic susceptibility were available, quantification of the scaling relation using geostatistics, specifically variogram models and dispersion variance were determined. The understanding provided by the scaling analysis of the Flin-Flon magnetic data is applied to data from the Rio Blanco copper district in central Chile. Magnetic susceptibility measurements collected with a hand magnetic susceptibility meter on drill-core is integrated in larger scale volumes used for geophysical inversion modeling of regional scale airborne magnetic field measurements to recover magnetic susceptibility models. The methodology resulting from this application of geostatistics is used to address the problem of integrating multiple scales of physical property data in an effective way. The resulting physical property models capture the small-scale magnetic susceptibility variability observed and can guide larger-scale variability within geophysical inversion models. Establishing reliable statistical correlations between physical properties and rock units controlling ore within deposits are crucial steps leading predictive mine exploration tools. Any numerical modeling approach to establish these correlations should consider in some way the scaling nature of both physical property and ore content. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

Carbonate strata preserve indicators of local marine environments through time. Such indicators often include microfossils that have relatively unique conditions under which they can survive, including light, nutrients, salinity, and especially water temperature. As such, microfossils are environmental proxies. When these microfossils are preserved in the rock record, they constitute key components of depositional facies. Spence et al. (2004, 2007) has proposed several approaches for determining the facies of a given stratigraphic succession based upon these proxies. Cluster analysis can be used to determine microfossil groups that represent specific environmental conditions. Identifying which microfossil groups exist through time can indicate local environmental change. When new observations (microfossils) are found, classification analysis can be used to predict group membership. Kristen Briggs (2005) identified the microfossils present in sedimentary strata within a specific time interval (Morrowan) of Pennsylvanian-age rocks. In this study we expand analysis to overlying Atokan and Desmoinesian strata. The Bird Spring Formation in Arrow Canyon, Nevada records cycles of environmental change as evidenced by changes in microfossils. Our research investigates cluster and classification analyses as tools for determining the marine facies succession. Light, nutrients, salinity, and water temperature are very dependent on water depth; therefore, our analyses essentially indicate the relative rise and fall of sea-level during Early to Middle Pennsylvanian time.

The integration of seismic attributes and well data is an important step in the development of reservoir models. These models draw upon large data sets including information from well logs, production history, seismic interpretation, and depositional models. Modern integration techniques use the extensive data sets to develop precise models using complex workflows at increased cost of time and computational power. However, a gap exists in which a geostatistically driven procedure could integrate pattern statistics inferred from seismic images and those integrated from analogous geologic systems in order to develop spatially accurate reservoir models. Direct Sampling Seismic Integration Process, DSSIP, was first proposed by Henke and Srinivasan (2010) as an alternative to traditional seismic integration methods. The process provides a probabilistic mapping tool for fast reservoir analysis based on sparse conditioning data in a target reservoir and fully interpreted data from an analog field. DSSIP combines the structural information present in seismic data and facies patterns present in a training reservoir to create a fully realized output map for the target field. In this work, the basic DSSIP algorithm has been further optimized by performing a detailed parameter sensitivity study. The basic DSSIP algorithm has been demonstrated for a real field data set for a deepwater Gulf of Mexico reservoir. The basic DSSIP algorithm has also been analyzed to understand and model the effects of features such as salt canopy that can blur the seismic image. Finally, a modification to the basic algorithm is also presented that uses only a training model and the seismic data for the target reservoir in order to generate reservoir models for the target reservoir. This procedure eliminates the requirement to have a matching pair of training data sets for both the facies distribution and the corresponding seismic response. / text

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A geostatistical inverse method of estimating hydraulic parameters of a heterogeneous porous medium at discrete points in space, called pilot points, is presented. In this inverse method the parameter estimation problem is posed as a nonlinear optimization problem with a likelihood based objective function. The likelihood based objective function is expressed in terms of head residuals at head measurement locations in the flow domain, where head residuals are the differences between measured and model-predicted head values. Model predictions of head at each iteration of the optimization problem are obtained by solving a forward problem that is based on nonlocal conditional ensemble mean flow equations. Nonlocal moment equations make possible optimal deterministic predictions of fluid flow in randomly heterogenous porous media as well as assessment of the associated predictive uncertainty. In this work, the nonlocal moment equations are approximated to second order in the standard deviation of log-transformed hydraulic conductivity, and are solved using the finite element method. To enhance computational efficiency, computations are carried out in the complex Laplace-transform space, after which the results are inverted numerically to the real temporal domain for analysis and presentation. Whereas a forward solution can be conditioned on known values of hydraulic parameters, inversion allows further conditioning of the solution on measurements of system state variables, as well as for the estimation of unknown hydraulic parameters. The Levenberg-Marquardt algorithm is used to solve the optimization problem. The inverse method is illustrated through two numerical examples where parameter estimates and the corresponding predictions of system state are conditioned on measurements of head only, and on measurements of head and log-transformed hydraulic conductivity with prior information. An example in which predictions of system state are conditioned only on measurements of log-conductivity is also included for comparison. A fourth example is included in which the estimation of spatially constant specific storage is demonstrated. In all the examples, a superimposed mean uniform and convergent transient flow field through a bounded square domain is used. The examples show that conditioning on measurements of both head and hydraulic parameters with prior information yields more reliable (low uncertainty and good fit) predictions of system state, than when such information is not incorporated into the estimation process.

One critical consideration in the design of buildings constructed in the western United States is the weight of settled snow on the roof of the structure. Engineers are tasked with selecting a design snow load that ensures that the building is safe and reliable, without making the construction overly expensive. Western states use historical snow records at weather stations scattered throughout the region to estimate appropriate design snow loads. Various mapping techniques are then used to predict design snow loads between the weather stations. Each state uses different mapping techniques to create their snow load requirements, yet these different techniques have never been compared. In addition, none of the current mapping techniques can account for the uncertainty in the design snow load estimates. We address both issues by formally comparing the existing mapping techniques, as well as creating a new mapping technique that allows the estimated design snow loads to be represented as an interval of values, rather than a single value. In the process, we have improved upon existing methods for creating design snow load requirements and have produced a new tool capable of handling uncertain climate data.

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