Adaptive hierarchical upscaling of flow in heterogeneous reservoirs based on an a posteriori error estimate

This paper treats the upscaling of the absolute permeability in a heterogeneous reservoir. By replacing the fine scale permeability tensor with an upscaled, or effective permeability tensor, a modelling error is introduced. An a posteriori error estimate on this modelling error is formulated and tested. An implementation of the theory, based on domain decomposition coupled with a hierarchical representation of the absolute permeability field, is given. As hierarchical basis functions we have chosen the Haar system, which leads to a wavelet representation of the permeability. The wavelet representation offers a natural upscaling technique which resembles the highcut filters commonly used in signal analysis. This procedure represents an adaptive upscaling method. The numerical results show that this method conserves both the dissipation and the mean velocity in the problem fairly well. The a posteriori error estimate on the modelling error coupled with domain decomposition methods constitutes a powerful modelling tool.     

半拉格朗日方法在全球原始方程模式中的实现

简单介绍了半拉格朗日平流方案的基本概念,并详细总结了基估全球原始方程模式,特别是在ＩＦＳ的具体实现过程,拉格朗日平流的观点是着流体质点看流体运动,基贩关键是流体轨迹的计算。轨迹中点和起始点水平坐标的示得可以利用球面三角,直接在球极坐标中进行,并采用一些较高的近似。为了充分获得半拉格朗日方案析益处,在起始点的内插能工巧匠春阶数至少应在四阶以上,为避免昂贵的三维三次内插,可以采用三维“准三次”内插 。     

Generation of Magnetic Fields During the Protogalactic Collapse

Large-scale galactic magnetic fields are probably caused by some magnetic field amplification mechanism starting from a seed field. This seed field is still enigmatic. In this contribution it is shown that macroscopic sheared relative velocities of the charged and neutral components of a protogalactic partially ionized plasma generate magnetic fields during the protogalactic collapse. Plasma-neutral gas fluid simulations are performed in order to illustrate this magnetic field-self generation mechanism.     

Kinetic shear resistance,fluid pressures and radiation efficiency during seismic faulting

Summary During earthquake faulting, radiation efficiency and the degree stress relief are critically dependent on the kinetic shear resistance. This is often assumed to stay constant during slip, but geological evidence suggests that for moderate or large shallow earthquakes it may decrease dramatically to near-zero values once slip is initiated, either by melt formation or by transient increases in fluid pressure on the fault plane. The latter, probably more common process may arise partly through an interaction between temperature and water pressure, and partly through dilatancy recovery as shear stress is relieved. If the fault remains undrained, stress relief should be absolute with seismic efficiency reaching high values, so that stress drops give a measure of the level of tectonic shear stress in fault zones. Supporting evidence comes from the observation that apparent stress is generally about half the stress drop.     

Genesis of tin and tantalum mineralization in pegmatites from the Bynoe area,Pine Creek Geosyncline,Northern Territory

The tin‐ and tantalum‐bearing pegmatites of the Bynoe area are located in the western Pine Creek Geosyncline. They are emplaced within psammopelitic rocks in the contact aureole of the Two Sisters Granite. The latter is a Palaeoproterozoic, fractionated, granite with S‐type characteristics and comprises a syn‐ to late‐orogenic, variably foliated, medium‐grained biotite granite and a post‐orogenic, coarse‐grained biotite‐muscovite granite. The pegmatites comprise a border zone of fine grained muscovite + quartz followed inward by a wall zone of coarse grained muscovite + quartz which is in turn followed by an intermediate zone of quartz + feldspar + muscovite. A core zone of massive quartz is present in some occurrences. Feldspars in the intermediate zone are almost completely altered to kaolinite. This zone contains the bulk of cassiterite, tantalite and columbite mineralization. Fluid inclusions in pegmatitic quartz indicate that early Type A (CO₂ + H₂O ± CH₄) inclusions were trapped at the H₂O‐CO₂ solvus at P～100 MPa, T～300°C (range 240–328°C) and salinity ～6 wt% eq NaCl. Pressure‐salinity corrected temperatures on Type B (H₂O + ～20% vapour), C (H₂O + < 15% vapour) and D (H₂O + halite + vapour) inclusions also fall within the range of Type A inclusions. Oxygen and hydrogen isotope data show that kaolin was either formed in isotopic equilibrium with meteoric waters or subsequent to its formation, from hydrothermal fluid, underwent isotopic exchange with meteoric waters. Fluid inclusion waters from core zone quartz show enrichment in deuterium suggesting metamorphic influence. Isotope values on muscovite are consistent with a magmatic origin. It is suggested that the pegmatites were derived from the post‐orogenic phase of the Two Sisters Granite. Precipitation of cassiterite took place at about 300°C from an aqueous fluid largely as a result of increase in pH due to feldspar alteration.     

Understanding of hydraulic properties from configurations of stochastically distributed fracture networks

A systematic investigation of the effect of configurations of stochastically distributed fracture networks on hydraulic behaviour for fractured rock masses could provide either quantitative or qualitative correlation between the structural configuration of the fracture network and its corresponding hydraulic behaviour, and enhance our understanding of appropriate application of groundwater flow and contaminant transport modelling in fractured rock masses. In this study, the effect of block sizes, intersection angles of fracture sets, standard deviations of fracture orientation, and fracture densities on directional block hydraulic conductivity and representative elementary volume is systematically investigated in two dimensions by implementing a numerical discrete fracture fluid flow model and incorporating stochastically distributed fracture configurations. It is shown from this investigation that the configuration of a stochastically distributed fracture network has a significant quantitative or qualitative effect on the hydraulic behaviour of fractured rock masses. Compared with the deterministic fracture configurations that have been extensively dealt with in a previous study, this investigation is expected to be more practical and adequate, since fracture geometry parameters are inherently stochastically distributed in the field. Moreover, the methodology and approach presented in this study may be generally applied to any fracture system in investigating the hydraulic behaviours from configurations of the fracture system while establishing a ‘bridge’ from the discrete fracture network flow modelling to equivalent continuum modelling in fractured rock masses. Copyright © 2007 John Wiley & Sons, Ltd.     

A finite element approach to the simulation of hydraulic fractures with lag

We presented a finite‐element‐based algorithm to simulate plane‐strain, straight hydraulic fractures in an impermeable elastic medium. The algorithm accounts for the nonlinear coupling between the fluid pressure and the crack opening and separately tracks the evolution of the crack tip and the fluid front. It therefore allows the existence of a fluid lag. The fluid front is advanced explicitly in time, but an implicit strategy is needed for the crack tip to guarantee the satisfaction of Griffith's criterion at each time step. We enforced the coupling between the fluid and the rock by simultaneously solving for the pressure field in the fluid and the crack opening at each time step. We provided verification of our algorithm by performing sample simulations and comparing them with two known similarity solutions. Copyright © 2012 John Wiley & Sons, Ltd.     

Numerical simulation of fully saturated porous materials

Fully coupled, porous solid–fluid formulation, implementation and related modeling and simulation issues are presented in this work. To this end, coupled dynamic field equations with u?p?U formulation are used to simulate pore fluid and soil skeleton (elastic–plastic porous solid) responses. Present formulation allows, among other features, for water accelerations to be taken into account. This proves to be useful in modeling dynamic interaction of media of different stiffnesses (as in soil–foundation–structure interaction). Fluid compressibility is also explicitly taken into account, thus allowing excursions into modeling of limited cases of non‐saturated porous media. In addition to these features, present formulation and implementation models in a realistic way the physical damping, which dissipates energy. In particular, the velocity proportional damping is appropriately modeled and simulated by taking into account the interaction of pore fluid and solid skeleton. Similarly, the displacement proportional damping is physically modeled through elastic–plastic processes in soil skeleton. An advanced material model for sand is used in present work and is discussed at some length. Also explored in this paper are the verification and validation issues related to fully coupled modeling and simulations of porous media. Illustrative examples describing the dynamical behavior of porous media (saturated soils) are presented. The verified and validated methods and material models are used to predict the behavior of level and sloping grounds subjected to seismic shaking. Copyright © 2008 John Wiley & Sons, Ltd.     

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The effect of heterogeneous stress and strain on metamorphic fluid flow,Mary Kathleen,Australia, and a model for large-scale fluid circulation *

In the Proterozoic Mary Kathleen Fold Belt, northern Australia, infiltration of large volumes of externally derived fluid occurred synchronously with regional amphibolite-facies metamorphism and deformation. This paper develops a model of structurally controlled fluid migration by comparing the distribution of fossil fluid pathways with the inferred stress and strain patterns during the deformation. Intense fluid flow was localized within strong, relatively brittle meta-intrusive bodies, and in discrete, veined, brecciated and altered zones around their margins. In metasediments folded in a ductile manner outside these areas, fluid infiltration was negligible. The direct correlation between structural styles and the magnitude of veining and metasomatism suggests control of permeability enhancement, and hence fluid flow, by deformation. Finite difference modelling of a strong body in a weaker matrix has been used to evaluate the variation of stresses during the deformation, from which it is clear that stress and strain heterogeneities have systematically influenced the development and maintenance of metamorphic fluid pathways. Particular regions in which mean stress may be significantly lower than the average lithostatic pressures include the ‘strain shadow’zones adjacent to the strong bodies, other dilatant zones around the bodies, and the bodies themselves. This geometry is favourable not only for localized brittle deformation under amphilobite facies conditions, but also for focused fluid flow in the low mean stress regions, as evidenced by the abundance of veins. Fluid access through these metamorphic aquifers occurred during tensile failure episodes, with particularly large dilations and decimetre-scale veining in areas of strain incompatibility. It appears likely that fluid circulated many times through the Fold Belt, with flow concentrated in the metamorphic aquifers. A model is developed that explains both the structurally focused fluid flow and the postulated multi-pass recirculation by dilatancy pumping, the ‘pump engines’comprising the low mean stress zones.