Browsing by Subject "Geostatistics"
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Item Analysis of Spatial Performance of Meteorological Drought Indices(2013-01-14) Patil, Sandeep 1986-Meteorological drought indices are commonly calculated from climatic stations that have long-term historical data and then converted to a regular grid using spatial interpolation methods. The gridded drought indices are mapped to aid decision making by policy makers and the general public. This study analyzes the spatial performance of interpolation methods for meteorological drought indices in the United States based on data from the Co-operative Observer Network (COOP) and United States Historical Climatology Network (USHCN) for different months, climatic regions and years. An error analysis was performed using cross-validation and the results were compared for the 9 climate regions that comprise the United States. Errors are generally higher in regions and months dominated by convective precipitation. Errors are also higher in regions like the western United States that are dominated by mountainous terrain. Higher errors are consistently observed in the southeastern U.S. especially in Florida. Interpolation errors are generally higher in the summer than winter. The accuracy of different drought indices was also compared. The Standardized Precipitation and Evapotranspiration Index (SPEI) tends to have lower errors than Standardized Precipitation Index (SPI) in seasons with significant convective precipitation. This is likely because SPEI uses both precipitation and temperature data in its calculation, whereas SPI is based solely on precipitation. There are also variations in interpolation accuracy based on the network that is used. In general, COOP is more accurate than USHCN because the COOP network has a higher density of stations. USHCN is a subset of the COOP network that is comprised of high quality stations that have a long and complete record. However the difference in accuracy is not as significant as the difference in spatial density between the two networks. For multiscalar SPI, USHCN performs better than COOP because the stations tend to have a longer record. The ordinary kriging method (with optimal function fitting) performed better than Inverse Distance Weighted (IDW) methods (power parameters 2.0 and 2.5) in all cases and therefore it is recommended for interpolating drought indices. However, ordinary kriging only provided a statistically significant improvement in accuracy for the Palmer Drought Severity Index (PDSI) with the COOP network. Therefore it can be concluded that IDW is a reasonable method for interpolating drought indices, but optimal ordinary kriging provides some improvement in accuracy. The most significant factor affecting the spatial accuracy of drought indices is seasonality (precipitation climatology) and this holds true for almost all the regions of U.S. for 1-month SPI and SPEI. The high-quality USHCN network gives better interpolation accuracy with 6-, 9- and 12-month SPI and variation in errors amongst the different SPI time scales is minimal. The difference between networks is also significant for PDSI. Although the absolute magnitude of the differences between interpolation with COOP and USHCN are small, the accuracy of interpolation with COOP is much more spatially variable than with USHCN.Item Characterization and modeling of paleokarst reservoirs using multiple-point statistics on a non-gridded basis(2012-12) Erzeybek Balan, Selin; Srinivasan, Sanjay; Lake, Larry W; Bryant, Steven L; Janson, Xavier; Zahm, Christopher KPaleokarst reservoirs consist of complex cave networks, which are formed by various mechanisms and associated collapsed cave facies. Traditionally, cave structures are defined using variogram-based methods in flow models and this description does not precisely represent the reservoir geology. Algorithms based on multiple-point statistics (MPS) are widely used in modeling complex geologic structures. Statistics required for these algorithms are inferred from gridded training images. However, structures like modern cave networks are represented by point data sets. Thus, it is not practical to apply rigid and gridded templates and training images for the simulation of such features. Therefore, a quantitative algorithm to characterize and model paleokarst reservoirs based on physical and geological attributes is needed. In this study, a unique non-gridded MPS analysis and pattern simulation algorithms are developed to infer statistics from modern cave networks and simulate distribution of cave structures in paleokarst reservoirs. Non-gridded MPS technique is practical by eliminating use of grids and gridding procedure, which is challenging to apply on cave network due to its complex structure. Statistics are calculated using commonly available cave networks, which are only represented by central line coordinates sampled along the accessible cave passages. Once the statistics are calibrated, a cave network is simulated by using a pattern simulation algorithm in which the simulation is conditioned to sparse data in the form of locations with cave facies or coordinates of cave structures. To get an accurate model for the spatial extent of the cave facies, an algorithm is also developed to simulate cave zone thickness while simulating the network. The proposed techniques are first implemented to represent connectivity statistics for synthetic data sets, which are used as point-set training images and are analogous to the data typically available for a cave network. Once the applicability of the algorithms is verified, non-gridded MPS analysis and pattern simulation are conducted for the Wind Cave located in South Dakota. The developed algorithms successfully characterize and model cave networks that can only be described by point sets. Subsequently, a cave network system is simulated for the Yates Field in West Texas which is a paleokarst reservoir. Well locations with cave facies and identified cave zone thickness values are used for conditioning the pattern simulation that utilizes the MP-histograms calibrated for Wind Cave. Then, the simulated cave network is implemented into flow simulation models to understand the effects of cave structures on fluid flow. Calibration of flow model against the primary production data is attempted to demonstrate that the pattern simulation algorithm yields detailed description of spatial distribution of cave facies. Moreover, impact of accurately representing network connectivity on flow responses is explored by a water injection case. Fluid flow responses are compared for models with cave networks that are constructed by non-gridded MPS and a traditional modeling workflow using sequential indicator simulation. Applications on the Yates Field show that the cave network and corresponding cave facies are successfully modeled by using the non-gridded MPS. Detailed description of cave facies in the reservoir yields accurate flow simulation results and better future predictions.Item Copula Based Hierarchical Bayesian Models(2010-10-12) Ghosh, SouparnoThe main objective of our study is to employ copula methodology to develop Bayesian hierarchical models to study the dependencies exhibited by temporal, spatial and spatio-temporal processes. We develop hierarchical models for both discrete and continuous outcomes. In doing so we expect to address the dearth of copula based Bayesian hierarchical models to study hydro-meteorological events and other physical processes yielding discrete responses. First, we present Bayesian methods of analysis for longitudinal binary outcomes using Generalized Linear Mixed models (GLMM). We allow flexible marginal association among the repeated outcomes from different time-points. An unique property of this copula-based GLMM is that if the marginal link function is integrated over the distribution of the random effects, its form remains same as that of the conditional link function. This unique property enables us to retain the physical interpretation of the fixed effects under conditional and marginal model and yield proper posterior distribution. We illustrate the performance of the posited model using real life AIDS data and demonstrate its superiority over the traditional Gaussian random effects model. We develop a semiparametric extension of our GLMM and re-analyze the data from the AIDS study. Next, we propose a general class of models to handle non-Gaussian spatial data. The proposed model can deal with geostatistical data that can accommodate skewness, tail-heaviness, multimodality. We fix the distribution of the marginal processes and induce dependence via copulas. We illustrate the superior predictive performance of our approach in modeling precipitation data as compared to other kriging variants. Thereafter, we employ mixture kernels as the copula function to accommodate non-stationary data. We demonstrate the adequacy of this non-stationary model by analyzing permeability data. In both cases we perform extensive simulation studies to investigate the performances of the posited models under misspecification. Finally, we take up the important problem of modeling multivariate extreme values with copulas. We describe, in detail, how dependences can be induced in the block maxima approach and peak over threshold approach by an extreme value copula. We prove the ability of the posited model to handle both strong and weak extremal dependence and derive the conditions for posterior propriety. We analyze the extreme precipitation events in the continental United States for the past 98 years and come up with a suite of predictive maps.Item Geostatistical data integration in complex reservoirs(2014-12) Elahi Naraghi, Morteza; Srinivasan, SanjayOne of the most challenging issues in reservoir modeling is to integrate information coming from different sources at disparate scales and precision. The primary data are borehole measurements, but in most cases, these are too sparse to construct accurate reservoir models. Therefore, in most cases, the information from borehole measurements has to be supplemented with other secondary data. The secondary data for reservoir modeling could be static data such as seismic data or dynamic data such as production history, well test data or time-lapse seismic data. Several algorithms for integrating different types of data have been developed. A novel method for data integration based on the permanence of ratio hypothesis was proposed by Journel in 2002. The premise of the permanence of ratio hypothesis is to assess the information from each data source separately and then merge the information accounting for the redundancy between the information sources. The redundancy between the information from different sources is accounted for using parameters (tau or nu parameters, Krishnan, 2004). The primary goal of this thesis is to derive a practical expression for the tau parameters and demonstrate the procedure for calibrating these parameters using the available data. This thesis presents two new algorithms for data integration in reservoir modeling. The algorithms proposed in this thesis overcome some of the limitations of the current methods for data integration. We present an extension to the direct sampling based multiple-point statistics method. We present a methodology for integrating secondary soft data in that framwork. The algorithm is based on direct pattern search through an ensemble of realizations. We show that the proposed methodology is sutiable for modeling complex channelized reservoirs and reduces the uncertainty associated with production performance due to integration of secondary data. We subsequently present the permanence of ratio hypothesis for data integration in great detail. We present analytical equations for calculating the redundancy factor for discrete or continuous variable modeling. Then, we show how this factor can be infered using available data for different scenarios. We implement the method to model a carbonate reservoir in the Gulf of Mexico. We show that the method has a better performance than when primary hard and secondary soft data are used within the traditional geostatistical framework.Item Groundwater inflow into rock tunnels(2010-08) Chen, Ran; Tonon, Fulvio; Rathje, Ellen; Eichhubl, Peter; Sharp, John M.; Zornberg, Jorge G.Prediction of groundwater inflow into rock tunnels is one of the essential tasks of tunnel engineering. Currently, most of the methods used in the industry are typically based on continuum models, whether analytical, semi-empirical, or numerical. As a consequence, a regular flow along the tunnel is commonly predicted. There are also some discrete fracture network methods based on a discontinous model, which typically yield regular flow or random flow along the tunnel. However, it was observed that, in hard rock tunnels, flow usually concentrates in some areas, and much of the tunnel is dry. The reason is that, in hard rock, most of the water flows in rock fractures and fractures typically occur in a clustered pattern rather than in a regular or random pattern. A new method is developed in this work, which can model the fracture clustering and reproduce the flow concentration. After elaborate literature review, a new algorithm is developed to simulate fractures with clustering properties by using geostatistics. Then, a discrete fracture network is built and simplified. In order to solve the flow problem in the discrete fracture network, an existing analytical-numercial method is improved. Two case studies illustrate the procedure of fracture simulation. Several ideal tunnel cases and one real tunnel project are used to validate the flow analysis. It is found that fracture clustering can be modeled and flow concentration can be reproduced by using the proposed technique.Item Modeling of point bar geology using a grid transformation scheme and geostatistics(2015-12) Li, Henry; Sepehrnoori, Kamy, 1951-; Srinivasan, SanjayPoint bars, the convex inner banks of meandering rivers, exhibit distinct heterogeneities. Modeling these heterogeneities is essential because of the presence of mud/silt layers in point bars impede the flow of fluids in processes strongly controlled by buoyancy or gravity such as the steam chamber rise during Steam-Assisted Gravity Drainage (SAGD). This thesis details the modeling of point bars using geological trends and well data to supplement geostatistical simulation. The modeling processes in this thesis capture the internal geometry of the accretion layers as well as geological trends. Curvilinear grids are constructed between major erosional surfaces where a grid transformation scheme is used to transform the curvilinear coordinates into orthogonal coordinates for geostatistical simulation. The grid transformation allows flexibility in performing statistical simulation in rectangular coordinate while honoring the curvilinear geometry of the point bar. An entire point bar model contains a series of accreting curviplanar grids. Geological modeling is done independently for each grid. The geology captures key trends that make up the heterogeneities in the model. The point bar model created is based on a modern point bar in the Brazos River. Data from thirty-three wells are used in creating the reservoir model. Several distinct trends are observed. There is an upward decrease in sediment size in the point bar. An overall fining downstream trend is observed in the vertical slices of the point bar. Heterolithic bedding is observed where frequent layers of silt extend from the top to near the base analogous to outcrops. Mud and silt dominate the upward regions of the point bar while conglomerate and cobble are mainly present at the base. The flow simulation model investigated the effect of mud drapes and fining heterogeneities on the development of steam chamber in SAGD recovery. The mud drapes impeded the steam chamber rise. The steam chambers were initially divided into pockets based on the flow barriers present. After 1 years of production, the steam chamber reaches the top of the reservoir but continued to be separated by the mud/silt barriers. Comparing to the homogeneous case, the point bar model exhibited lower oil recovery.Item Seismic and sparse data integration through the use of direct sampling(2013-12) Hampton, Travis Payton; Srinivasan, SanjayThe 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.Item Understanding Spatio-Temporal Variability and Associated Physical Controls of Near-Surface Soil Moisture in Different Hydro-Climates(2013-05-06) Joshi, ChampaNear-surface soil moisture is a key state variable of the hydrologic cycle and plays a significant role in the global water and energy balance by affecting several hydrological, ecological, meteorological, geomorphologic, and other natural processes in the land-atmosphere continuum. Presence of soil moisture in the root zone is vital for the crop and plant life cycle. Soil moisture distribution is highly non-linear across time and space. Various geophysical factors (e.g., soil properties, topography, vegetation, and weather/climate) and their interactions control the spatio-temporal evolution of soil moisture at various scales. Understanding these interactions is crucial for the characterization of soil moisture dynamics occurring in the vadose zone. This dissertation focuses on understanding the spatio-temporal variability of near-surface soil moisture and the associated physical control(s) across varying measurement support (point-scale and passive microwave airborne/satellite remote sensing footprint-scale), spatial extents (field-, watershed-, and regional-scale), and changing hydro-climates. Various analysis techniques (e.g., time stability, geostatistics, Empirical Orthogonal Function, and Singular Value Decomposition) have been employed to characterize near-surface soil moisture variability and the role of contributing physical control(s) across space and time. Findings of this study can be helpful in several hydrological research/applications, such as, validation/calibration and downscaling of remote sensing data products, planning and designing effective soil moisture monitoring networks and field campaigns, improving performance of soil moisture retrieval algorithm, flood/drought prediction, climate forecast modeling, and agricultural management practices.