Effects of medium thermoelasticity on high Rayleigh number steady-state heat transfer and mineralization in deformable fluid-saturated porous media heated from below

In this paper, a solution method is presented to deal with fully coupled problems between medium deformation, pore-fluid flow and heat transfer in fluid-saturated porous media having supercritical Rayleigh numbers. To validate the present solution method, analytical solutions to a benchmark problem are derived for some special cases. After the solution method is validated, a numerical study is carried out to investigate the effects of medium thermoelasticity on high Rayleigh number steady-state heat transfer and mineralization in fluid-saturated media when they are heated from below. The related numerical results have demonstrated that: (1) medium thermoelasticity has a little influence on the overall pattern of convective pore-fluid flow, but it has a considerable effect on the localization of medium deformation, pore-fluid flow, heat transfer and mineralization in a porous medium, especially when the porous medium is comprised of soft rock masses; (2) convective pore-fluid flow plays a very important role in the localization of medium deformation, heat transfer and mineralization in a porous medium. (C) 1999 Elsevier Science S.A. All rights reserved.

A numerical study of pore-fluid, thermal and mass flow iu fluid-saturated porous rock basins

We present a numerical methodology for the study of convective pore-fluid, thermal and mass flow in fluid-saturated porous rock basins. lit particular, we investigate the occurrence and distribution pattern of temperature gradient driven convective pore-fluid flow and hydrocarbon transport in the Australian North West Shelf basin. The related numerical results have demonstrated that: (1) The finite element method combined with the progressive asymptotic approach procedure is a useful tool for dealing with temperature gradient driven pore-fluid flow and mass transport in fluid-saturated hydrothermal basins; (2) Convective pore-fluid flow generally becomes focused in more permeable layers, especially when the layers are thick enough to accommodate the appropriate convective cells; (3) Large dislocation of strata has a significant influence off the distribution patterns of convective pore;fluid flow, thermal flow and hydrocarbon transport in the North West Shelf basin; (4) As a direct consequence of the formation of convective pore-fluid cells, the hydrocarbon concentration is highly localized in the range bounded by two major faults in the basin.

Phase diagram of a Heisenberg spin-Peierls model with quantum phonons

Using a new version of the density-matrix renormalization group we determine the phase diagram of a model of an antiferromagnetic Heisenberg spin chain where the spins interact with quantum phonons. A quantum phase transition from a gapless spin-fluid state to a gapped dimerized phase occurs at a nonzero value of the spin-phonon coupling. The transition is in the same universality class as that of a frustrated spin chain, to which the model maps in the diabatic limit. We argue that realistic modeling of known spin-Peierls materials should include the effects of quantum phonons.

Finite element analysis of flow patterns near geological lenses in hydrodynamic and hydrothermal systems

We use theoretical and numerical methods to investigate the general pore-fluid flow patterns near geological lenses in hydrodynamic and hydrothermal systems respectively. Analytical solutions have been rigorously derived for the pore-fluid velocity, stream function and excess pore-fluid pressure near a circular lens in a hydrodynamic system. These analytical solutions provide not only a better understanding of the physics behind the problem, but also a valuable benchmark solution for validating any numerical method. Since a geological lens is surrounded by a medium of large extent in nature and the finite element method is efficient at modelling only media of finite size, the determination of the size of the computational domain of a finite element model, which is often overlooked by numerical analysts, is very important in order to ensure both the efficiency of the method and the accuracy of the numerical solution obtained. To highlight this issue, we use the derived analytical solutions to deduce a rigorous mathematical formula for designing the computational domain size of a finite element model. The proposed mathematical formula has indicated that, no matter how fine the mesh or how high the order of elements, the desired accuracy of a finite element solution for pore-fluid flow near a geological lens cannot be achieved unless the size of the finite element model is determined appropriately. Once the finite element computational model has been appropriately designed and validated in a hydrodynamic system, it is used to examine general pore-fluid flow patterns near geological lenses in hydrothermal systems. Some interesting conclusions on the behaviour of geological lenses in hydrodynamic and hydrothermal systems have been reached through the analytical and numerical analyses carried out in this paper.

Finite element modelling of reactive mass transport problems in fluid-saturated porous media

We use the finite element method to solve reactive mass transport problems in fluid-saturated porous media. In particular, we discuss the mathematical expression of the chemical reaction terms involved in the mass transport equations for an isothermal, non-equilibrium chemical reaction. It has turned out that the Arrhenius law in chemistry is a good mathematical expression for such non-equilibrium chemical reactions especially from the computational point of view. Using the finite element method and the Arrhenius law, we investigate the distributions of PH (i.e. the concentration of H+) and the relevant reactive species in a groundwater system. Although the main focus of this study is on the contaminant transport problems in groundwater systems, the related numerical techniques and principles are equally applicable to the orebody formation problems in the geosciences. Copyright (C) 1999 John Wiley & Sons, Ltd.

Sensitivity of multiple frequency bioelectrical impedance analysis to changes in ion status

Bioelectrical impedance analysis has found extensive application as a simple noninvasive method for the assessment of body fluid volumes, The measured impedance is, however, not only related to the volume of fluid but also to its inherent resistivity. The primary determinant of the resistivities of body fluids is the concentration of ions. The aim of this study was to investigate the sensitivity of bioelectrical impedance analysis to bodily ion status. Whole body impedance over a range of frequencies (4-1012 kHz) of rats was measured during infusion of various concentrations of saline into rats concomitant with measurement of total body and intracellular water by tracer dilution techniques. Extracellular resistance (R-o), intracellular resistance (R-i) and impedance at the characteristic frequency (Z(c)) were calculated. R-o and Z(c) were used to predict extracellular and total body water respectively using previously published formulae. The results showed that whilst R-o and Z(c) decreased proportionately to the amount of NaCl infused, R-i increased only slightly. Impedances at the end of infusion predicted increases iu TBW and ECW of approximately 4-6% despite a volume increase of less than 0.5% in TBW due to the volume of fluid infused. These data are discussed in relation to the assumption of constant resistivity in the prediction of fluid volumes from impedance data.

Finite element modelling of dissipative structures for nonequilibrium chemical reactions in fluid-saturated porous media

We use the finite element method to model and predict the dissipative structures of chemical species for a nonequilibrium chemical reaction system in a fluid-saturated porous medium. In particular, we explore the conditions under which dissipative structures of the species may exist in the Brusselator type of nonequilibrium chemical reaction. Since this is the first time the finite element method and related strategies have been used to study the chemical instability problems in a fluid-saturated porous medium, it is essential to validate the method and strategies before they are put into application. For this purpose, we have rigorously derived the analytical solutions for dissipative structures of chemical species in a benchmark problem, which geometrically is a square. Comparison of the numerical solutions with the analytical ones demonstrates that the proposed numerical method and strategy are robust enough to solve chemical instability problems in a fluid-saturated porous medium. Finally, the related numerical results from two application examples indicate that both the regime and the magnitude of pore-fluid flow have significant effects on the nature of the dissipative structures that developed for a nonequilibrium chemical reaction system in a fluid-saturated porous medium. The motivation for this study is that self-organization under conditions of pore-fluid flow in a porous medium is a potential mechanism of the orebody formation and mineralization in the upper crust of the Earth. (C) 2000 Elsevier Science S.A. All rights reserved.

Strain-dependent fluid flow defined through rock mass classification schemes

Strain-dependent hydraulic conductivities are uniquely defined by an environmental factor, representing applied normal and shear strains, combined with intrinsic material parameters representing mass and component deformation moduli, initial conductivities, and mass structure. The components representing mass moduli and structure are defined in terms of RQD (rock quality designation) and RMR (rock mass rating) to represent the response of a whole spectrum of rock masses, varying from highly fractured (crushed) rock to intact rock. These two empirical parameters determine the hydraulic response of a fractured medium to the induced-deformations The constitutive relations are verified against available published data and applied to study one-dimensional, strain-dependent fluid flow. Analytical results indicate that both normal and shear strains exert a significant influence on the processes of fluid flow and that the magnitude of this influence is regulated by the values of RQD and RMR.

Numerical modelling of double diffusion driven reactive flow transport in deformable fluid-saturated porous media with particular consideration of temperature-dependent chemical reaction rates

Numerical methods ave used to solve double diffusion driven reactive flow transport problems in deformable fluid-saturated porous media. in particular, thp temperature dependent reaction rate in the non-equilibrium chemical reactions is considered. A general numerical solution method, which is a combination of the finite difference method in FLAG and the finite element method in FIDAP, to solve the fully coupled problem involving material deformation, pore-fluid flow, heat transfer and species transport/chemical reactions in deformable fluid-saturated porous media has been developed The coupled problem is divided into two subproblems which are solved interactively until the convergence requirement is met. Owing to the approximate nature of the numerical method, if is essential to justify the numerical solutions through some kind of theoretical analysis. This has been highlighted in this paper The related numerical results, which are justified by the theoretical analysis, have demonstrated that the proposed solution method is useful for and applicable to a wide range of fully coupled problems in the field of science and engineering.

Petrographic and isotope constraints on the origin of authigenic carbonate minerals and the associated fluid evolution in Late Permian coal measures, Bowen Basin (Queensland), Australia

Authigenic carbonate minerals are ubiquitous throughout the Late Permian coal measures of the Bowen Basin, Queensland, Australia. In the northern Bowen Basin, carbonates include the following assemblages: siderite I (delta O-18(SMOW) = +11.4 to + 17%, delta C-13(PDB) = - 5.3 to + 120), Fe-Mg calcite-ankerite-siderite II mineral association (delta O-18(SMOW) = +7.2 to + 10.20, delta C-13(PDB) = 10.9 to - 1.80 for ankerite) and a later calcite (delta O-18(SMOW) = +5.9 to + 14.60, delta C-13(PDB) = -11.4 to + 4.40). In the southern Bowen Basin, the carbonate phase consists only of calcite (delta O-18(SMOW) = +12.5 to + 14.80, delta C-13(PDB) = -19.4 to + 0.80), where it occurs extensively throughout all stratigraphic levels. Siderite I occurs in mudrocks and sandstones and predates all other carbonate minerals. This carbonate phase is interpreted to have formed as an early diagenetic mineral from meteoric waters under cold climate and reducing conditions. Fe-Mg calcite-ankerite-siderite Il occur in sandstones as replacement of volcanic rock fragments. Clay minerals (illite-smectite, chlorite and kaolinite) postdate Ca-Fe-Mg carbonates, and precipitation of the later calcite is associated with clay mineral formation. The Ca-Fe-Mg carbonates and later calcite of the northern Bowen Basin are regarded as having formed as a result of hydrothermal activity during the latest Triassic extensional tectonic event which affected this part of the basin, rather than deep burial diagenesis during the Middle to Late Triassic as previously reported. This hypothesis is based on the timing relationships of the authigenic mineral phases and the low delta O-18 values of ankerite and calcite, together with radiometric dating of illitic clays and recently published regional geological evidence. Following the precipitation of the Ca-Fe-Mg carbonates from strongly O-18-depleted meteoric-hydrothermal fluids, continuing fluid circulation and water-rock interaction resulted in dissolution of these carbonate phases as well as labile fragments of volcaniclastic rocks. Subsequently, the later calcite and day minerals precipitated from relatively evolved (O-18-enriched) fluids. The nearly uniform delta O-18 values of the southern Bowen Basin calcite have been attributed to very low water/rock ratio in the system, where the fluid isotropic composition was buffered by the delta O-18 values of rocks. (C) 2000 Elsevier Science B.V. All rights reserved.

Hybrid modelling of coupled pore fluid-solid deformation problems

A hybrid formulation for coupled pore fluid-solid deformation problems is proposed. The scheme is a hybrid in the sense that we use a vertex centered finite volume formulation for the analysis of the pore fluid and a particle method for the solid in our model. The pore fluid formally occupies the same space as the solid particles. The size of the particles is not necessarily equal to the physical size of materials. A finite volume mesh for the pore fluid flow is generated by Delaunay triangulation. Each triangle possesses an initial porosity. Changes of the porosity are specified by the translations of the mass centers of particles. Net pore pressure gradients are applied to the particle centers and are considered in the particle momentum balance. The potential of our model is illustrated by means of a simulation of coupled fracture and fluid flow developed in porous rock under biaxial compression condition.

Finite element modelling of three-dimensional convection problems in fluid-saturated porous media heated from below

We use the finite element method to model three-dimensional convective pore-fluid flow in fluid-saturated porous media when they are heated from below. In particular, we employ the particle-tracking technique to mimic the trajectories of particles in three-dimensional fluid flow problems. The related numerical results demonstrated that: (1) The progressive asymptotic approach procedure, which was previously developed for the finite element modelling of two-dimensional convective pore-fluid flow problems, is equally applicable to the finite element modelling of three-dimensional convective pore-fluid flow in fluid-saturated porous media heated from below. (2) The perturbation of gravity at different planes has a significant effect on the pattern of three-dimensional convective pore-fluid flow and therefore, may influence the pattern of orebody formation and mineralization in three-dimensional hydrothermal systems. Copyright (C) 2001 John Wiley & Sons, Ltd.

Finite element modeling of fluid-rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins

In order to use the finite element method for solving fluid-rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins effectively and efficiently, we have presented, in this paper, the new concept and numerical algorithms to deal with the fundamental issues associated with the fluid-rock interaction problems. These fundamental issues are often overlooked by some purely numerical modelers. (1) Since the fluid-rock interaction problem involves heterogeneous chemical reactions between reactive aqueous chemical species in the pore-fluid and solid minerals in the rock masses, it is necessary to develop the new concept of the generalized concentration of a solid mineral, so that two types of reactive mass transport equations, namely, the conventional mass transport equation for the aqueous chemical species in the pore-fluid and the degenerated mass transport equation for the solid minerals in the rock mass, can be solved simultaneously in computation. (2) Since the reaction area between the pore-fluid and mineral surfaces is basically a function of the generalized concentration of the solid mineral, there is a definite need to appropriately consider the dependence of the dissolution rate of a dissolving mineral on its generalized concentration in the numerical analysis. (3) Considering the direct consequence of the porosity evolution with time in the transient analysis of fluid-rock interaction problems; we have proposed the term splitting algorithm and the concept of the equivalent source/sink terms in mass transport equations so that the problem of variable mesh Peclet number and Courant number has been successfully converted into the problem of constant mesh Peclet and Courant numbers. The numerical results from an application example have demonstrated the usefulness of the proposed concepts and the robustness of the proposed numerical algorithms in dealing with fluid-rock interaction problems in pore-fluid saturated hydrothermal/sedimentary basins. (C) 2001 Elsevier Science B.V. All rights reserved.

Finite element modelling of reactive fluids mixing and mineralization in pore-fluid saturated hydrothermal/sedimentary basins

We present the finite element simulations of reactive mineral carrying fluids mixing and mineralization in pore-fluid saturated hydrothermal/sedimentary basins. In particular we explore the mixing of reactive sulfide and sulfate fluids and the relevant patterns of mineralization for Load, zinc and iron minerals in the regime of temperature-gradient-driven convective flow. Since the mineralization and ore body formation may last quite a long period of time in a hydrothermal basin, it is commonly assumed that, in the geochemistry, the solutions of minerals are in an equilibrium state or near an equilibrium state. Therefore, the mineralization rate of a particular kind of mineral can be expressed as the product of the pore-fluid velocity and the equilibrium concentration of this particular kind of mineral Using the present mineralization rate of a mineral, the potential of the modern mineralization theory is illustrated by means of finite element studies related to reactive mineral-carrying fluids mixing problems in materially homogeneous and inhomogeneous porous rock basins.

General properties of cosmological models with an isotropic singularity

Much of the published work regarding the Isotropic Singularity is performed under the assumption that the matter source for the cosmological model is a barotropic perfect fluid, or even a perfect fluid with a gamma-law equation of state. There are, however, some general properties of cosmological models which admit an Isotropic Singularity, irrespective of the matter source. In particular, we show that the Isotropic Singularity is a point-like singularity and that vacuum space-times cannot admit an Isotropic Singularity. The relationships between the Isotropic Singularity, and the energy conditions, and the Hubble parameter is explored. A review of work by the authors, regarding the Isotropic Singularity, is presented.