Spectral Simulation and Conditioning to Local Continuity Trends in Geologic Modeling

Spectral simulation has gained application in building geologic models due to the advantage of better honoring the spatial continuity of petrophysical properties, such as reservoir porosity and shale volume. Distinct from sequential simulation methods, spectral simulation is a global algorithm in the sense that a global density spectrum is calculated once and the inverse Fourier transform is performed on the Fourier coefficient also only once to generate a simulation realization. The generated realizations honor the spatial continuity structure globally over the whole field instead of only within a search neighborhood, as with sequential simulation algorithms. However, the disadvantage of global spectral simulation is that it traditionally cannot account for the local information such as the local continuity trends, which are often observed in reservoirs and hence are important to be accounted for in geologic models. This disadvantage has limited wider application of spectral simulation in building geologic models. In this paper, we present ways of conditioning geologic models to the relevant local information. To account for the local continuity trends, we first scale different frequency components of the original model with local-amplitude spectrum ratios that are specific to the local trend. The sum of these scaled frequency components renders a new model that displays the desired local continuity trend. The implementation details of this new method are discussed and examples are provided to illustrate the algorithm.     

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.

---

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.

---

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.

     

Investigating the scale of structural controls on chlorinated hydrocarbon distributions in the fractured-porous unsaturated zone of a sandstone aquifer in the UK

Contaminant migration behaviour in the unsaturated zone of a fractured porous aquifer is discussed in the context of a study site in Cheshire, UK. The site is situated on gently dipping sandstones, adjacent to a linear lagoon historically used to dispose of industrial wastes containing chlorinated solvents. Two cores of more than 100 m length were recovered and measurements of chlorinated hydrocarbons (CHCs), inorganic chemistry, lithology, fracturing and aquifer properties were made. The results show that selecting an appropriate vertical sampling density is crucial both to providing an understanding of contaminant pathways and distinguishing whether CHCs are present in the aqueous or non-aqueous phase. The spacing of such sampling should be on a similar scale to the heterogeneity that controls water and contaminant movement. For some sections of the Permo-Triassic aquifer, significant changes in lithology and permeability occur over vertical distances of less than 1 m and samples need to be collected at this interval, otherwise considerable resolution is lost, potentially leading to erroneous interpretation of data. At this site, although CHC concentrations were high, the consistent ratio of the two main components of the plume (tetrachloroethene and trichloroethene) provided evidence of movement in the aqueous phase rather than in dense non-aqueous phase liquid (DNAPL).     

Validation of a fish farm waste resuspension model by use of a particulate tracer discharged from a point source in a coastal environment

To validate a resuspension model of particulate material (salmonid farm wastes), a UV fluorescent particle tracer was selected with similar settling characteristics. Tracer was introduced to the seabed (water depth ≈30 m) and sediment samples taken on days 0, 3, 10, 17 and 30 to measure the horizontal and vertical distribution of tracer in sediments. A concentric sampling grid was established at radii of 25, 50, 100, 150, 200, 400, 700 and 1, 000 m from the source on transects 30° apart. The bulk of the deployed tracer was initially concentrated in an area 25 m radius from the release point; tracer was observed to steadily decrease to zero over a period of 30 days. In a 200 m region measured from the release point in the direction of the residual current, the redeposition of tracer was low. A Lagrangian particle tracking model was validated using these observed data by varying resuspension model parameters within limits to obtain the best agreement between spatial and temporal distributions. The validated model generally gave good predictions of total mass budgets (±7% of total tracer released), particulary where tracer concentrations were high near the release point. Best fit model parameters (critical erosion shear stress=0.018 N m⁻², erodibility constan=60 g m⁻² d⁻¹) are at the low end of reported parameters for coastal resuspension models. Such a low critical erosion shear stress indicates that the frequency of resuspension and deposition events for freshly deposited material is high.     

Oxygen fugacity and geochemical variations in the martian basalts: implications for martian basalt petrogenesis and the oxidation state of the upper mantle of Mars

The oxygen fugacity of the Dar al Gani 476 martian basalt is determined to be quartz-fayalite-magnetite (QFM) −2.3 ± 0.4 through analysis of olivine, low-Ca pyroxene, and Cr-spinel and is in good agreement with revised results from Fe-Ti oxides that yield QFM −2.5 ± 0.7. This estimate falls within the range of oxygen fugacity for the other martian basalts, QFM −3 to QFM −1. Oxygen fugacity in martian basalts correlates with ⁸⁷Sr/⁸⁶Sr, ¹⁴³Nd/¹⁴⁴Nd, and La/Yb ratios, indicating that the mantle source of the basalts is reduced and that assimilation of crust-like material controls the oxygen fugacity. This allows constraints to be placed on the oxidation state of the martian mantle and on the nature of assimilated crustal material. The assimilated material may be the product of early and extensive hydrothermal alteration of the martian crust, or it may be amphibole- or phlogopite-bearing basaltic rock within the crust. In either case, water may play a significant role in the oxidation of basaltic magmas on Mars, although it may be secondary to assimilation of ferric iron-rich material.