Geomechanical model for fracture deformation under hydraulic, mechanical and thermal loads

Hydraulic flow and transport (heat and solute) within crystalline rocks is dominated by the fracture systems found within them. In situ stress conditions have a significant impact on the hydraulic, mechanical and thermal coupled processes, and quantification of these processes provides a key to understanding the often transient time-dependent behaviour of crystalline rocks. In this paper, a geomechanical model is presented which describes fracture closure as a function of effective stress and the changes in parameters such as storage, permeability, porosity and aperture. Allowing the fracture closure to be defined by the change in normal effective stress provides a link to the numerical consideration of parametrical changes due to rock stress alterations caused for example by changes in fracture fluid pressure, stress release, tectonic stress, thermal stress, orientation of the natural fracture in the pervasive stress system and local changes in a rock mass due to stress alteration. The model uses geometrical considerations based on a fractal distribution of apertures on the fracture surface, and applies well-established analytical elastic deformation solutions to calculate the deformation response to changes in effective stress. Analysis of the fractal generation method allows a standard normal distribution of fracture apertures to be predicted for all common fractal dimensions relating to a 2D surface. Changes in the fracture aperture are related to hydraulic functions such as permeability, storage and porosity of the fracture. The geomechanical model is experimentally validated against laboratory scale experimental data gained from the closure of a fractured sample recovered at a depth of 3,800 m from the KTB pilot borehole. Parameters for matching the experimental data were established externally, the only fitting parameters applied were the minimum and maximum contact area between the surfaces and the number of allowable contacts. The model provides an insight into the key processes determining the closure of a fracture, and can act as a material input function for numerical models linking the effects of changes in the stress field, hydraulic or thermal conditions, to the flow and transport parameters of a fractured system.

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Résumé L’écoulement et le transport (chaleur et soluté) dans les roches cristallines sont dominés par les systèmes de fracture. Les conditions de stress in-situ ont un impact significatif sur l’hydraulique, les processus couplés de mécanique et thermique et la quantification de ces processus apportent une clé pour comprendre le comportement transitoire des roches cristallines. Dans cet article un modèle géomécanique est présenté, modèle qui décrit la fermeture des fractures comme une fonction de la contrainte effective et des changements de paramètres tels le coefficient d’emmagasinement, la perméabilité, la porosité et l’ouverture. En s’accordant que la fermeture des fractures est définit par les changements de la contrainte effective normale, on apporte le lien avec la considération numérique des changements paramétriques dus aux altérations de la contrainte des roches, causés par exemple par des variations de la pression des fluides dans les fractures, du dégagement de la contrainte, des contraintes tectoniques et thermiques, des orientations des fractures naturelles dans le système de contraintes pénétrantes, et des changements locaux dans un massif de roches dus à l’altération des contraintes. Le modèle utilise des considérations géométriques basées sur une distribution fractale des ouvertures à la surface des fractures, et permet d’établir des solutions analytiques de la déformation élastique pour calculer la réponse de la déformation à la contrainte effective. L’analyse de la méthode par génération fractale permet de prédire une distribution normale standard de l’ouverture des fractures, pour toutes les dimensions fractales en relation avec les surfaces 2D. Les changements dans l’ouverture des fractures sont mis en relation avec les fonctions hydrauliques tels la perméabilité, l’emmagasinement et la porosité de la fracture. Le modèle géoméchanique est expérimentalement validé à l’échelle du laboratoire sur un échantillon fracturé récupéré à une profondeur de 3,800 mètres sur le puits du site pilote KTB. Les paramètres du calibrage des données expérimentales ont été établies extérieurement, les seuls paramètres utilisés étant les surfaces de contact minimum et maximum, et le nombre de contacts permis. Le modèle apporte une connaissance perspicace sur le processus clé déterminant la fermeture des fractures, et peut servir de fonction input dans les modèles numériques reliant les effets des variations de la contrainte du terrain, les conditions hydrauliques ou thermales, les paramètres de l’écoulement et du transport et les systèmes de fracture.

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Resumen El flujo hidráulico y transporte (de calor y solutos) dentro de rocas cristalinas está dominado por los sistemas de fracturas que se encuentran en ellas. Las condiciones de esfuerzos in-situ tienen un impacto significativo en los procesos aparejados termales, mecánicos e hidráulicos y la cuantificación de estos procesos aporta una clave para entender el frecuente comportamiento transitorio dependiente de las rocas cristalinas. En este artículo se presenta un modelo geomecánico que describe el cierre de fracturas en función del esfuerzo efectivo y los cambios en parámetros tal como almacenamiento, permeabilidad, porosidad y apertura. El definir el cierre de fractura mediante el cambio en esfuerzo normal efectivo aporta un vínculo con la consideración numérica de cambios paramétricos ocasionados por alteraciones de esfuerzos en la roca causadas, por ejemplo, por cambios en presión de fluidos en fractura, liberación de esfuerzo, esfuerzo tectónico, esfuerzo termal, orientación de fracturas naturales en el sistema de esfuerzos penetrante, y cambios locales en una masa rocosa ocasionados por alteración de esfuerzos. El modelo utiliza consideraciones geométricas basadas en la distribución fractal de aperturas en la superficie de fractura y aplica soluciones analíticas bien establecidas de deformación elástica para calcular la respuesta de deformación a cambios en el esfuerzo efectivo. Los análisis del método de generación fractal permiten predecir una distribución normal standard para la distribución de aperturas de fracturas para todas las dimensiones fractales comunes que se relacionan con una superficie 2D. Los cambios en la apertura de fractura se relacionan con funciones hidráulicas tal como permeabilidad, almacenamiento y porosidad de la fractura. El modelo geomecánico se ha validado experimentalmente en contra de datos experimentales a escala de laboratorio obtenidos a partir del cierre de una muestra fracturada recuperada a una profundidad de 3,800 m en el pozo piloto KTB. Se establecieron externamente parámetros que se ajustan a los datos experimentales, con los parámetros de ajuste aplicados que fueron el área máxima y mínima de contacto entre las superficies y el número de contactos permisibles. El modelo arroja luz sobre los procesos clave que determinan el cierre de una fractura y puede actuar como un material de función de entrada para modelos numéricos que vinculan los efectos de cambios en el campo de esfuerzos, condiciones termales o hidráulicas, con los parámetros de flujo y transporte de un sistema fracturado.

     

Metal binding to dissolved organic matter and adsorption to ferrihydrite in shallow peat groundwaters: Application to diamond exploration in the James Bay Lowlands,Canada

The speciation and solubility of kimberlite pathfinder metals (Ni, Nd, Ba and K) in shallow peat groundwaters is investigated over the Yankee, Zulu and Golf kimberlites in the Attawapiskat region, James Bay Lowlands, Canada. The purpose of this study is to examine the relationship between dissolved organic matter (DOM) complexation with kimberlite pathfinder metals and determine the spatial distribution of those metals in shallow peat groundwaters along sampling transects over subcropping kimberlites. Nickel, Nd, Ba and K complexation with DOM and the adsorption of these metals onto ferrihydrite were calculated using Visual MINTEQ 3.0 and the NICA-Donnan database. Calculations predict almost 100% of soluble Nd, Ni and Ba form complexes with DOM at sampling sites with little to no contribution from upwelling groundwater (i.e., dissolved organic C (DOC) concentrations = 40–132 mg/L, pH = 3.9–5.5, and log ionic strength ??3). In only the most ombrotrophic peat groundwater conditions does a majority fraction of K bind to DOM. By contrast, under conditions with large contributions from upwelling groundwaters (i.e., DOC concentrations ?40 mg/L, pH = 5.5–6.5, and log ionic strength = ?3 to ?2), as little as 10% of Nd and Ni, and 0% K and Ba are predicted to complex with DOM. The modeling calculations suggest the dominant control on metal–DOM complexation, particularly with respect to Ni and Nd, is competitive effects for DOM binding sites due to elevated ionic strength where there is evidence of strong groundwater upwelling. Visual MINTEQ modeling of metal adsorption on ferrihydrite surfaces predicts that under strong upwelling conditions, Ni and Nd are scavenged from solution due to increased ferrihydrite precipitation and decreased fractions of metals complexed with DOM. Analytical geochemical data are consistent with model predictions of metal adsorption on ferrihydrite. Total dissolved Ni and Nd concentrations at sites of strong upwelling are up to five times lower than waters with little to no upwelling and log ferrihydrite saturation indices (logSI_ferr) indicate precipitation (values up to 5) at sites of strong groundwater upwelling. Where the majority of Ni and Nd complex with DOM and ferrihydrite is highly under saturated (logSI_ferr = ?18 to ?5), the concentrations of total Ni and Nd are elevated compared to other sites along sampling transects. Metal complexation with DOM effectively inhibits metal scavenging from solution via adsorption and/or from forming secondary mineral precipitates. Also, because alkaline earth metals do not compete strongly with Ni and Nd for adsorption sites on ferrihydrite surfaces, but do compete strongly for insoluble organic sites, Ni and Nd are more likely to adsorb onto ferrihydrite.     

Multi-angle backscatter classification and sub-bottom profiling for improved seafloor characterization

This study applies three classification methods exploiting the angular dependence of acoustic seafloor backscatter along with high resolution sub-bottom profiling for seafloor sediment characterization in the Eckernförde Bay, Baltic Sea Germany. This area is well suited for acoustic backscatter studies due to its shallowness, its smooth bathymetry and the presence of a wide range of sediment types. Backscatter data were acquired using a Seabeam1180 (180 kHz) multibeam echosounder and sub-bottom profiler data were recorded using a SES-2000 parametric sonar transmitting 6 and 12 kHz. The high density of seafloor soundings allowed extracting backscatter layers for five beam angles over a large part of the surveyed area. A Bayesian probability method was employed for sediment classification based on the backscatter variability at a single incidence angle, whereas Maximum Likelihood Classification (MLC) and Principal Components Analysis (PCA) were applied to the multi-angle layers. The Bayesian approach was used for identifying the optimum number of acoustic classes because cluster validation is carried out prior to class assignment and class outputs are ordinal categorical values. The method is based on the principle that backscatter values from a single incidence angle express a normal distribution for a particular sediment type. The resulting Bayesian classes were well correlated to median grain sizes and the percentage of coarse material. The MLC method uses angular response information from five layers of training areas extracted from the Bayesian classification map. The subsequent PCA analysis is based on the transformation of these five layers into two principal components that comprise most of the data variability. These principal components were clustered in five classes after running an external cluster validation test. In general both methods MLC and PCA, separated the various sediment types effectively, showing good agreement (kappa >0.7) with the Bayesian approach which also correlates well with ground truth data (r²?>?0.7). In addition, sub-bottom data were used in conjunction with the Bayesian classification results to characterize acoustic classes with respect to their geological and stratigraphic interpretation. The joined interpretation of seafloor and sub-seafloor data sets proved to be an efficient approach for a better understanding of seafloor backscatter patchiness and to discriminate acoustically similar classes in different geological/bathymetric settings.     

Coupling hydrogeological with surface runoff model in a Poltva case study in Western Ukraine

This paper presents the hydrological coupling of the software framework OpenGeoSys (OGS) with the EPA Storm Water Management Model (SWMM). Conceptual models include the Saint Venant equation for river flow, the 2D Darcy equations for confined and unconfined groundwater flow, a two-way hydrological coupling flux in a compartment coupling approach (conductance concept), and Lagrangian particles for solute transport in the river course. A SWMM river–OGS aquifer inter-compartment coupling flux is examined for discharging groundwater in a systematic parameter sensitivity analysis. The parameter study involves a small perturbation (first-order) sensitivity analysis and is performed for a synthetic test example base-by-base through a comprehensive range of aquifer parametrizations. Through parametrization, the test cases enables to determine the leakance parameter for simulating streambed clogging and non-ocillatory river-aquifer water exchange rates with the sequential (partitioned) coupling scheme. The implementation is further tested with a hypothetical but realistic 1D river–2D aquifer model of the Poltva catchment, where discharging groundwater in the upland area affects the river–aquifer coupling fluxes downstream in the river course (propagating feedbacks). Groundwater contribution in the moving river water is numerically determined with Lagrangian particles. A numerical experiment demonstrates that the integrated river–aquifer model is a serviceable and realistic constituent in a complete compartment model of the Poltva catchment.     

Chemical and structural relations of epitaxial xenotime and zircon substratum in sedimentary and hydrothermal environments: a TEM study

Xenotime overgrowths on detrital zircon in siliciclastic sediments have been reported in numerous studies. However, in natural samples, solid solution of zircon and xenotime is limited to near-end-member compositions. In order to characterize the interface region between both minerals and to draw inferences on the growth mechanisms of authigenic xenotime, we studied xenotime overgrowths on detrital zircon grains from two Phanerozoic sandstone samples with contrasting post-depositional histories. In one sample, the small (≤10 μm), pyramidal xenotime overgrowths are of diagenetic origin and grew without major discontinuity on the detrital zircon grain. The second sample shows up to >50-μm-wide, porous and inclusion-rich, hydrothermal xenotime overgrowths on detrital zircon, whereas the transition zone between both minerals is accompanied by large pore volume. Chemical compositions of the xenotime precipitates from the two samples differ particularly in Y, REE, Th and Sc concentrations, whereas high MREE availability in the diagenetic sample and the presence of Sc in the hydrothermal sample, respectively, appear to have promoted xenotime growth. Transmission electron microscopy on electron-transparent foils cut from the interface region shows that both the diagenetic xenotime and the hydrothermal xenotime are crystalline and grew in optical and crystallographic continuity to their detrital zircon substrata. Only a narrow transition zone (≤90 nm—diagenetic sample, 200–300 nm—hydrothermal sample) between zircon and xenotime is in part made up of nanometre-scale crystalline domains that are slightly distorted and may have formed from dissolution–re-precipitation processes at the zircon rim along with precipitation from the respective fluid.     

A data exploration framework for validation and setup of hydrological models

Over the course of hydrological research projects often a large number of heterogeneous data sets are acquired from sources as diverse as boreholes, gauging stations or satellite imagery. This data then need to be integrated into models for the simulation of hydrological processes. We propose a framework for exploration of geoscientific data and visually guided preparation of such models. Data sets from a large number of sources can be imported, combined and validated to avoid potential problems due to artefacts or inconsistencies between data sets in a subsequent simulation. Boundary conditions and domain discretisations for surface and subsurface models can be created and tested regarding criteria indicating possible numerical instabilities. All data sets including simulation results can be integrated into a user-controlled 3D scene and aspects of the data can be enhanced using a number of established visualisation techniques including thresholding and user-defined transfer functions. We present the application of this framework for the preparation of a model for simulation of groundwater flow in a river catchment in southwest Germany investigated in the scope of the WESS project.     

Impact of climate and CO2 on a millennium-long tree-ring carbon isotope record

We present one millennium-long (1171-year), and three 100 year long annually resolved δ¹³C tree-ring chronologies from ecologically varying Juniperus stands in the Karakorum Mountains (northern Pakistan), and evaluate their response to climatic and atmospheric CO₂ changes. All δ¹³C records show a gradual decrease since the beginning of the 19th century, which is commonly associated with a depletion of atmospheric δ¹³C due to fossil fuel burning. Climate calibration of high-frequency δ¹³C variations indicates a pronounced summer temperature signal for all sites. The low-frequency component of the same records, however, deviates from long-term temperature trends, even after correction for changes in anthropogenic CO₂. We hypothesize that these high-elevation trees show a response to both climate and elevated atmospheric CO₂ concentration and the latter might explain the offset with target temperature data. We applied several corrections to tree-ring δ¹³C records, considering a range of potential CO₂ discrimination changes over the past 150 years and calculated the goodness of fit with the target via calibration/verification tests (R², residual trend, and Durbin-Watson statistics). These tests revealed that at our sites, carbon isotope fixation on longer timescales is affected by increasing atmospheric CO₂ concentrations at a discrimination rate of about 0.012‰/ppmv. Although this statistically derived value may be site related, our findings have implications for the interpretation of any long-term trends in climate reconstructions using tree-ring δ¹³C, as we demonstrate with our millennium-long δ¹³C Karakorum record. While we find indications for warmth during the Medieval Warm Period (higher than today’s mean summer temperature), we also show that the low-frequency temperature pattern critically depends on the correction applied. Patterns of long-term climate variation, including the Medieval Warm Period, the Little Ice Age, and 20th century warmth are most similar to existing evidence when a strong influence of increased atmospheric CO₂ on plant physiology is assumed.     

Accuracy of numerical simulations of contaminant transport in heterogeneous aquifers: A comparative study

This work deals with a comparison of different numerical schemes for the simulation of contaminant transport in heterogeneous porous media. The numerical methods under consideration are Galerkin finite element (GFE), finite volume (FV), and mixed hybrid finite element (MHFE). Concerning the GFE we use linear and quadratic finite elements with and without upwind stabilization. Besides the classical MHFE a new and an upwind scheme are tested. We consider higher order finite volume schemes as well as two time discretization methods: backward Euler (BE) and the second order backward differentiation formula BDF (2). It is well known that numerical (or artificial) diffusion may cause large errors. Moreover, when the Péclet number is large, a numerical code without some stabilising techniques produces oscillating solutions. Upwind schemes increase the stability but show more numerical diffusion. In this paper we quantify the numerical diffusion for the different discretization schemes and its dependency on the Péclet number. We consider an academic example and a realistic simulation of solute transport in heterogeneous aquifer. In the latter case, the stochastic estimates used as reference were obtained with global random walk (GRW) simulations, free of numerical diffusion. The results presented can be used by researchers to test their numerical schemes and stabilization techniques for simulation of contaminant transport in groundwater.