Simulation of a reactive tracer experiment using stochastic hydraulic conductivity fields

Reactive tracer tests are performed to derive flow, transport and in situ biodegradation parameters. This paper describes the 3D simulation of a reactive tracer test using the transition probability geostatistical approach. Fifty different equally probable aquifer realizations were generated based on the geological information of 107 boreholes in an area of 62,500 m². One realization was chosen for the reactive transport simulation based on the results of groundwater flow modeling and on particle tracking calculations for the site. Field velocities at the site vary between 0.4 and 3 m/d. The transport of the reactive tracers deuterium ring labeled toluene-d₅ and fully deuterated toluene-d₈ was simulated and first-order biodegradation rates of 0.017 d⁻¹ for toluene-d₅ and 0.012 d⁻¹ for toluene-d₈ were determined.     

Robust estimation of the variogram: I

It is a matter of common experience that ore values often do not follow the normal (or lognormal) distributions assumed for them, but, instead, follow some other heavier-tailed distribution. In this paper we discuss the robust estimation of the variogram when the distribution is normal-like in the central region but heavier than normal in the tails. It is shown that the use of a fourth-root transformation with or without the use of M-estimation yields stable robust estimates of the variogram.Visiting Scientist, NRIMS, during the period in which this work was carried out.     

Geostatistical method to delineate anomalies of multi-scale spatial variation in hydrogeological changes due to the ChiChi earthquake in the ChouShui River alluvial fan in Taiwan

This study uses Ordinary Kriging (OK), Sequential Gaussian Simulation (SGS) and Simulated Annealing Simulation (SAS) to relocate the completely heterotopic dataset from the locations of the Standardized Satellite Oriented Control Point System (SSOCPS) stations to the Groundwater Monitoring Networks (GMNS) stations and factorial kriging to analyze and map relationships among seven variables, including the hydraulic conductivities of three aquifers, the vertical displacements of the ground and groundwater level changes in the wells of three aquifers, and also to delineate the anomalies of multi-scale spatial variation of hydrogeological properties associated with the ChiChi earthquake, measuring 7.3 on the Richter scale, in the ChouShui River alluvial fan in Taiwan. In this study, the anomalies of spatial variation of hydrogeological properties associated with the earthquake are illustrated at micro, local and regional scales of 9, 12 and 36 km, respectively. In the study area, regionalization components associated with variation at local and regional scales are obtained and mapped by factorial kriging. Factorial Kriging Analysis (FKA) also demonstrated that the main effects of the ChiChi earthquake on the spatial variations of groundwater hydrological changes include porous media compression at micro scale, hydrogeological heterogeneousness of the sediments within the aquifer at local scale and the cyclic loading of deviatoric stress at regional scale. Finally, maps of spatial variations of regional components fully depicted all of the anomalies of spatial variation of hydrogeological changes due to the ChiChi earthquake and can be used to identify, confirm and monitor the hydrogeological properties in this study area.     

Application of geostatistics and GIS technique to characterize spatial variabilities of bioavailable micronutrients in paddy soils

To understand the spatial dependency of bioavailable micronutrients in paddy soils, 134 soil samples were taken from Pinghu County, Zhejiang Province, south-east China to characterize the spatial variabilities of bioavailable Cu, Zn, Fe, and Mn. The geostatistics and geographic information system (GIS) techniques were applied. Bioavailable Zn and Mn were fitted to an exponential model with a range of 4.4 km and 2.97 km, respectively. Bioavailable Fe was fitted to the linear model with the longest range of 23.48 km. Bioavailable Cu did not show any spatial correlation with the fitted pure nugget effect model. Bioavailable Zn and Mn had strong spatial dependence due to the effects of intrinsic factors such as parent material, relief and soil types. Bioavailable Fe had moderate spatial dependence over a long distance. The spatial distribution of the four bioavailable micronutrients were significantly correlated to the soil formation factors. Human activity, such as application of fertilizer and pesticide, emission of waste gas and industrial pollution also had significant effects on the spatial distributions of the bioavailable micronutrients.     

Explorative data analysis of heavy metal contaminated soil using multidimensional spatial regression

To obtain data on heavy metal contaminated soil requires laborious and time-consuming data sampling and analysis. Not only has the contamination to be measured, but also additional data characterizing the soil and the boundary conditions of the site, such as pH, land use, and soil fertility. For an integrative approach, combining the analysis of spatial distribution, and of factors influencing the contamination, and its treatment, the Mollifier interpolation was used, which is a non-parametric kernel density regression. The Mollifier was capable of including additional independent variables (beyond the spatial dimensions x and y) in the spatial interpolation and hence explored the combined influence of spatial and other variables, such as land use, on the heavy metal distribution. The Mollifier could also represent the interdependence between different heavy metal concentrations and additional site characteristics. Although the uncertainty measure supplied by the Mollifier at first seems somewhat unusual, it is a valuable feature and supplements the geostatistical uncertainty assessment.     

A method for the interpolation of nonnegative functions with an application to contaminant load estimation

The objective of this work is to extend kriging, a geostatistical interpolation method, to honor parameter nonnegativity. The new method uses a prior probability distribution based on reflected Brownian motion that enforces this constraint. The work presented in this paper focuses on interpolation problems where the unknown is a function of a single variable (e.g. time), and is developed both for the case with and without measurement error in the available data. The algorithms presented for conditional simulations are computationally efficient, particularly in the case with no measurement error. We present an application to the interpolation of dissolved arsenic concentration data from the North Fork of the Humboldt River, Nevada.     

Stochastic analysis of the effect of heterogeneity and fractures on radionuclide transport in a low-permeability clay layer

Deep low-permeability clay layers are considered as safe environments for disposal of high-level radioactive waste. In Belgium, the Boom Clay is a candidate host rock for deep geological disposal. In this study, we analyze the effects of fractures and spatially variable hydraulic conductivity on radionuclide migration through the clay. Fracture geometry and properties are simulated with Monte Carlo simulation. The heterogeneity of hydraulic conductivity is simulated by direct sequential co-simulation using measurements of hydraulic conductivity and four types of secondary variables. The hydraulic conductivity and fracture simulations are used as input for a transport model. Radionuclide fluxes computed with this heterogeneous model are compared with fluxes obtained with a homogeneous model. The output fluxes of the heterogeneous model differ at most 8% from the homogeneous model. The main safety function of the Boom Clay is thus not affected by the fractures and the spatial variability of hydraulic conductivity.     

From well-test data to input to stochastic continuum models: effect of the variable support scale of the hydraulic data

The question of how well the true underlying hydraulic conductivity statistics of heterogeneous media are captured by well tests is addressed. The hydraulic conductivity value and the corresponding support volume associated with a theoretical well are correlated, causing a bias in the statistics derived from well-test analyses. Statistics derived from numerically simulated well tests are compared with the known underlying conductivity statistics and the results indicate an under-prediction by simulations at higher hydraulic conductivities. The deviation starts at about mean conductivity and can be as large as an order of magnitude, with the conductivity in the vicinity of the well defining the upper boundary. In other words, the conductivity value interpreted from the well test cannot be larger than the value that the well test first encounters. Consequently, for data in this simulation exercise, the standard deviation, if only determined for the upper range of the conductivity values, would be underestimated by a factor of 1.6–2. While this specific range is likely to depend on the scale and degree of the underlying heterogeneity as well as the duration of the test, the results should be indicative of a more general behaviour and are likely to occur in other heterogeneous data as well.

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Resumen Se plantea la pregunta de qué tan bien son representadas en las pruebas de pozo, las estadísticas reales de conductividad hidráulica subyacente de medios heterogéneos. Son correlacionados el valor de conductividad hidráulica y el volumen de apoyo correspondiente asociado con un pozo teórico, causando una distorsión en las estadísticas derivadas del análisis de la prueba de pozo. Las estadísticas derivadas de las pruebas de pozo simuladas numéricamente son comparadas con las estadísticas de conductividad subyacente conocidas, y los resultados indican una sub-predicción por las simulaciones hechas con conductividades hidráulicas más altas. La desviación empieza casi con la conductividad media y puede ser tan grande como un orden de magnitud, con la conductividad en la vecindad del pozo definiendo el límite superior. En otras palabras, el valor de conductividad interpretado a partir de la prueba del pozo no puede ser más grande que el valor que la prueba de pozo encuentre primero. Por consiguiente, para los datos en este ejercicio de simulación, la desviación estándar, si solamente fue determinada para el rango superior de los valores de conductividad, se subestimaría en un factor de 1.6–2. Mientras es probable que este rango específico dependa de la escala y del grado de la heterogeneidad subyacente, así como de la duración de la prueba, los resultados deben ser indicativos de un comportamiento más general y son probables también de ocurrir en otros datos heterogéneos.

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Résumé Nous posons ici la question de savoir dans quelle mesure les statistiques de la conductivité hydraulique des milieux hétérogènes pourrait être révélée par des essais de puits. La valeur de la conductivité hydraulique et le volume capté correspondant sont corrélés, créant un biais dans l’analyse des statistiques dérivées des essais de puits. Les statistiques en provenance de simulations numériques d’essais de puits sont comparées avec les statistiques de conductivités connues et les résultats indiquent une sous-évaluation par les simulations, pour les conductivités hydrauliques les plus élevées: la déviation commence à partir de la valeur moyenne de la conductivité et peut atteindre la magnitude d’un ordre de grandeur en considérant la conductivité mesurée au voisinage du puits. Autrement dit, la valeur de la conductivité interprétée via l’essais de pompage ne peut être plus importante que les premières valeurs rencontrées. Par conséquence, pour les données de cet exercice de simulation, la déviation standard sera sous-estimée d’un facteur compris entre 1.6–2 pour les valeurs les plus élevées. Tandis que l’échelle spécifique de valeurs est dépendante de l’échelle et du degré de l’hétérogénéité souterraine, de même que de la durée du test, les résultats pourraient être indicatifs d’un comportement plus général et seraient sans doute observables dans d’autres cas de données hétérogènes.

     

Stochastic analysis of the effect of spatial variability of diffusion parameters on radionuclide transport in a low permeability clay layer

Most studies that incorporate subsurface heterogeneity in groundwater flow and transport models only analyze and simulate the spatial variability of hydraulic conductivity. Heterogeneity of the other flow and transport parameters are usually neglected. This approach is often justified, but there are, however, cases in which disregarding the heterogeneity of the other flow and transport parameters can be questionable. In low permeability media, for instance, diffusion is often the dominant transport mechanism. It therefore seems logical to incorporate the spatial variability of the diffusion parameters in the transport model. This study therefore analyses and simulates the spatial variability of the effective diffusion coefficient and the diffusion accessible porosity with geostatistical techniques and incorporates their heterogeneity in the transport model of a low permeability formation. The formation studied was Boom clay (Belgium), a candidate host rock for the deep geological disposal of high-level radioactive waste. The calculated output radionuclide fluxes of this model are compared with the fluxes calculated with a homogeneous model and a model with a heterogeneous hydraulic conductivity distribution. This analysis shows that the heterogeneity of the diffusion parameters has a much larger effect on the calculated output radionuclide fluxes than the heterogeneity of hydraulic conductivity in the low permeability medium under study.