A modified Archie’s law for two conducting phases

Many types of mixing model are used widely within the earth sciences to determine the electrical properties of porous media consisting of solid and fluid phases of known conductivities, volume fractions and distributions (i.e. phase connectivities). Most models are valid for two or more conducting phases. However, of the simple models only Archie’s law includes a variable term, the Archie cementation exponent m, that describes the connectivity of the phases. Unfortunately, Archie’s law is only valid for one conducting phase distributed within a non-conducting phase, which makes it inapplicable in instances where the rock matrix has a significant conductivity such as for clay-rich rocks and in calculations involving partial melting. More complex models exist which account for multiple conducting phases and control over phase conductivity. We have adapted the conventional Archie’s law to produce a simple modified Archie’s law that can be used with two conducting phases of any conductivity and any volume fraction, while retaining the ability to model variable connectivities within those phases that result from variations in their distribution. The modified model has two exponents (m and p) that describe the connectivity of each of the two phases. The exponents are related through an equation that depends also on the volume fractions of the two phases. The modified and the conventional versions of Archie’s law have been tested on a granular analogue porous medium with a conducting matrix and a pore space saturated with a range of saline fluids with different salinities and conductivities. The new model describes the experimentally determined electrical behaviour of the system extremely well, improving greatly on the conventional Archie’s law.     

Phase variations of ULF magnetic field in the region of fault tectonics

The experiment on phase measurements of three components of a ULF magnetic field generated by a high-power controlled source in the region dominated by fault tectonics is described. The measurements were carried out along two orthogonal directions. It is established that the phase sharply varies by about 180° between some measurement points. The phase jumps are found to be confined to the conductive geological faults, which opens the possibility of locating the faults using the phases of ELF magnetic fields.     

双相各向异性介质中弹性波方程的有限元解法及波场模拟

基于双相各向异性介质模型,首先推导了双相各向异性介质中弹性波传播的动力学方程及其Galerkin变分方程和有限元运动方程,然后给出了孔隙弹性波方程的有限元数值解法以及二维双相PTL介质中波场模拟的人为吸收边界条件. 最后,利用本文给出的有限元方法对双相PTL介质和双相各向同性介质中的弹性波传播进行了数值模拟. 结果表明:有限元方法和吸收边界条件有效、可行,在理想相界条件下,不论是从固体位移,还是从流体位移的波场快照都能看到明显的慢速拟P波;在黏滞相界情况下,能否观察到慢速拟P波,与含流体地层介质的耗散性质有关.对实际含流体介质,从流体位移分量的波场快照比从固体位移波场快照更容易观察到慢速拟P波.     

The effect of refreezing on the isotopic composition of melting snowpack

The isotopic composition of solid and liquid portions of natural melting snowpack is investigated in detail by the separating of liquid water from snow grains at different depths of the snowpack. The slope of the δD–δ¹⁸O line for the liquid phase is found to be lower than for the solid phase. This is proved to be due to the isotopic fractionation occurring in the melt–freeze mass exchange within the snowpack. Melting of the snowpack has no clear impact on the δD–δ¹⁸O line for the solid phase, but the slope of the δD–δ¹⁸O line for the liquid shows an overall slight decrease in the melting period. When the snowpack is refrozen, the refreezing process would inevitably cause the slope of the solid phase to decrease because of the discrepancy between the slopes of the two phases. Thus the slope of the solid would become lower and lower as the diurnal melt–freeze episodes cycle throughout the melting season. This effect is then demonstrated by looking into the isotopic composition changes of glacier firn. The extent of the effect depends on the snowpack properties and environmental conditions. The slope changes also result in a decreasing trend in deuterium excess. Copyright © 2007 John Wiley & Sons, Ltd.     

Magnetic components contributing to the NRM of Middle Siwalik red beds

The components of the NRM in Middle Siwalik red beds are carried by two phases of hematite, a red pigment phase and a specular hematite phase. We present evidence in the form of a conglomerate test that the specularite phase carries a remanence acquired during or shortly after deposition. The red pigment, however, post-dates deposition, in many cases by at least one reversal boundary. This secondary component has a higher coercivity but a lower blocking temperature in these rocks and can therefore be selectively removed by thermal demagnetization to reveal a primary magnetization useful for magnetostratigraphic studies.     

A lattice Boltzmann study on the impact of the geometrical properties of porous media on the steady state relative permeabilities on two-phase immiscible flows

In the current paper, the effect of the geometrical characteristics of 2-D porous media on the relative permeability in immiscible two-phase flows is studied. The generation of the different artificial porous media is performed using a Boolean model based on a random distribution of overlapping circles/ellipses, the size and shape of which are chosen to satisfy the specific Minkowski functionals (i.e. volume fraction, solid line contour length, connectivity). The study aims to identify how each different Minkowski functional affects the relative permeability of each phase at various saturations of the non-wetting phase. A 2-D multi-relaxation time (MRT) lattice Boltzmann model (LBM) that can handle high density ratios is employed in the simulation. The relationship between the driving forces G and the relative permeabilities of the two phases for every artificial structure is quantified. It is found that for high non-wetting phase saturations (fully connected flow), a non-linear relationship exists between the non-wetting phase flow rate and the driving force, whilst this relationship becomes linear at higher magnitudes of the latter. The force magnitude required to approach the linear region is highly influenced by the pore size distribution and the connectivity of the solid phase. For lower non-wetting phase saturation values, its relative permeability in the linear regime decreases as the fraction of small pores in the structure increases and the non-wetting phase flow becomes disconnected. A strong influence of the solid phase connectivity is also observed.     

频率域声-弹耦合地震波波动方程有限差分方法

本文针对声-弹耦合介质,为尽可能的减少频率域正演模拟的计算内存,提高计算效率,在一阶非均质位移-应力波动方程的基础上,借助等效交错网格思想并充分考虑密度参数空间变化对地震波传播的影响,推导了声-弹耦合地震波波动方程.在流相介质和固相介质中分别采用非均质情况频率域二阶声压标量波、二阶纯位移控制方程,为保证流、固相介质间地震波能量的稳定传输和有效交换,提出了声-弹耦合界面转换过渡层方法,并详细阐述了过渡层与上下介质空间差分具体耦合方法.在与非均质纯位移波动方程正演结果对比分析的基础上,首先采用各向同性单层流相介质模型进行正演模拟验证了声-弹耦合方程数值模拟中过渡层策略的有效性和准确性,随后又数值模拟了地震波在声-弹耦合介质简单模型和复杂Marmousi2模型中的传播,验证了本文方法稳定性和准确性,同时该方法可以简单的推广到三维情况.     

The system enstatite-wollastonite at high pressures and temperatures,with emphasis on diopside

High-pressure phase transformations for three intermediate compositions (including diopside) in the system enstatite (MgSiO₃)-wollastonite (CaSiO₃) were investigated in the pressure range 100–300 kbar at about 1000°C in a diamond-anvil press coupled with laser heating. The phase behaviour of the two end components (enstatite and wollastonite) at high pressure has been reported earlier. The results of this study reveal that there is very limited solid solution of diopside (CaMgSi₂O₆) in the various high-pressure phase assemblages of enstatite. At pressures greater than about 200 kbar, diopside and a composition between diopside and wollastonite were found to transform into non-quenchable phases, as does wollastonite. It is thought probable that diopside and wollastonite form solid solutions with the perovskite structure at high pressure, but that on release of pressure it is not possible to preserve the high-pressure modification.     

On the applicability of the Biot solution to the problems of elastic propagation in saturated porous media

In this paper, the solution of the system of homogeneous Biot equations, which was derived by Biot for the displacement vectors of plane monochrome elastic waves propagating in a homogeneous infinite two-phase medium, is expanded to the case where the propagation area of the elastic waves is limited and the wavefront is a piecewise smooth curved surface. It is shown that the arbitrary system of homogeneous Biot equations for the displacement vectors of the solid and liquid phases can be reduced to three different equations pertaining to the class of Helmholtz equations. From this, irrespective of the geometry of the seismic wavefront and the boundaries of the studied two-phase medium, there is the following. (1) Each displacement vector (of the solid and liquid phase) splits into three independent vectors satisfying three different Helmholtz equations. Two of these vectors correspond to the two types of compressional waves, namely, fast waves (waves of the first kind) and slow waves (waves of the second kind). The third vector describes shear waves. (2) The similar (related to the same wave type) components of the displacement vector in the solid and liquid phases satisfy the same Helmholtz equation and are linked with each other through a corresponding scalar factor that is expressed in terms of the coefficients of the Biot equations. Taking into account the established properties of the displacement vectors in the solid and liquid phases seems to be helpful in the problems dealing with calculation of elastic fields of arbitrary sources in piecewise-homogeneous two-phase media.     

Mathematical modeling of colloid and virus cotransport in porous media: Application to experimental data

A conceptual mathematical model was developed to describe the simultaneous transport (cotransport) of viruses and colloids in three-dimensional, water saturated, homogeneous porous media with uniform flow. The model accounts for the migration of individual virus and colloid particles as well as viruses attached onto colloids. Viruses can be suspended in the aqueous phase, attached onto suspended colloids and the solid matrix, and attached onto colloids previously attached on the solid matrix. Colloids can be suspended in the aqueous phase or attached on the solid matrix. Viruses in all four phases (suspended in the aqueous phase, attached onto suspended colloid particles, attached on the solid matrix, and attached onto colloids previously attached on the solid matrix) may undergo inactivation with different inactivation coefficients. The governing coupled partial differential equations were solved numerically using finite difference methods, which were implemented explicitly or implicitly so that both stability and speed factors were satisfied. Furthermore, the experimental data collected by Syngouna and Chrysikopoulos [1] were satisfactorily fitted by the newly developed cotransport model.     

Pluie ou neige? Dispositif de mesures pluviographiques dans les Andes de Bolivie et interprétation des enregistrements/Rainfall or snowfall? Device for measuring the precipitation phase in the Bolivian Andes and analysis of the records

Abstract

Abstract The knowledge of the precipitation phase, solid or liquid, is important in high mountains, in order to use models of water and energy balances. During an experiment led in the Bolivian Andes, a complete weather station was installed at an altitude close to 4800 m, including two raingauge recorders, the first one with added antifreeze and oil, based on weight measurement, and the other one with tipping buckets. This device allowed a realistic partition of the liquid and solid phases in this region of tropical mountains, where the observed snow pack at the ground level is strongly influenced by the extremely high solar radiation and where the snow cover is ephemeral. The automation of the ?raingauges? method, compared with several other classical methods, shows satisfactory results.     

Thermodynamics and constitutive theory for multiphase porous-media flow considering internal geometric constraints

This paper provides the thermodynamic approach and constitutive theory for closure of the conservation equations for multiphase flow in porous media. The starting point for the analysis is the balance equations of mass, momentum, and energy for two fluid phases, a solid phase, the interfaces between the phases and the common lines where interfaces meet. These equations have been derived at the macroscale, a scale on the order of tens of pore diameters. Additionally, the entropy inequality for the multiphase system at this scale is utilized. The internal energy at the macroscale is postulated to depend thermodynamically on the extensive properties of the system. This energy is then decomposed to provide energy forms for each of the system components. To obtain constitutive information from the entropy inequality, information about the mechanical behavior of the internal geometric structure of the phase distributions must be known. This information is obtained from averaging theorems, thermodynamic analysis, and from linearization of the entropy inequality at near equilibrium conditions. The final forms of the equations developed show that capillary pressure is a function of interphase area per unit volume as well as saturation. The standard equations used to model multiphase flow are found to be very restricted forms of the general equations, and the assumptions that are needed for these equations to hold are identified.     

Analytical representation of Green’s functions of the Biot equations for elastic waves in a homogeneous two-phase medium

The system of Biot vector equations in the frequency space includes two elliptic-type vector partial differential equations with unknown displacement vectors in the solid and liquid phases. Considering the Biot equations, alongside with Pride’s equations, the key approaches to the theoretical study of the elastic waves in the two-phase fluid-saturated media, the author suggests an analytical solution for the inhomogeneous Biot equations in the frequency space, which is reduced to finding its fundamental solution (Green’s function). The solution of this problem consists of solutions for two systems of Biot equations. In the first system, only the first equation is inhomogeneous, while in the second system, only the second equation is inhomogeneous and, as it is shown, its right-hand side is exclusively a potential function. The fundamental solution of the full system of inhomogeneous Biot equations (in which both equations are inhomogeneous) is represented in the form of Green’s matrix-tensor, for the scalar elements of which the analytical relations are presented. The obtained formulas describing the elastic displacements of both the solid and liquid phases reflect three wave types, namely, compressional waves of the first and the second kind (the fast and the slow waves, respectively) and shear waves. Similar terms (those describing the same type of the elastic waves in the solid and liquid phases) in the expressions for Green’s functions are linked with each other through the coefficient that links the components of the displacement vectors of the solid and liquid phases corresponding to the given wave type.

     

Analytical representation of Green’s functions of the Biot equations for elastic waves in a homogeneous two-phase medium

The system of Biot vector equations in the frequency space includes two elliptic-type vector partial differential equations with unknown displacement vectors in the solid and liquid phases. Considering the Biot equations, alongside with Pride??s equations, the key approaches to the theoretical study of the elastic waves in the two-phase fluid-saturated media, the author suggests an analytical solution for the inhomogeneous Biot equations in the frequency space, which is reduced to finding its fundamental solution (Green??s function). The solution of this problem consists of solutions for two systems of Biot equations. In the first system, only the first equation is inhomogeneous, while in the second system, only the second equation is inhomogeneous and, as it is shown, its right-hand side is exclusively a potential function. The fundamental solution of the full system of inhomogeneous Biot equations (in which both equations are inhomogeneous) is represented in the form of Green??s matrix-tensor, for the scalar elements of which the analytical relations are presented. The obtained formulas describing the elastic displacements of both the solid and liquid phases reflect three wave types, namely, compressional waves of the first and the second kind (the fast and the slow waves, respectively) and shear waves. Similar terms (those describing the same type of the elastic waves in the solid and liquid phases) in the expressions for Green??s functions are linked with each other through the coefficient that links the components of the displacement vectors of the solid and liquid phases corresponding to the given wave type.     

Dune Mining and the Nhlabane Estuary, South Africa: the Effect of a Dredger Crossing on the Zoobenthic Community

The Nhlabane Estuary, located on the north-east coast of South Africa, is situated in a titanium dune mining lease area. During 1993, a mining dredger and concentrator crossed the middle reaches of the estuary. For this purpose, two berm walls were constructed across the estuary. Two impacts stemmed from the crossing. A series of fine sediment intrusions into the estuary from the berm wall area occurred during late 1993 and early 1994 and caused a rapid decline in benthic densities and number of taxa. Recovery of the affected area was slow and characterized by initial proliferation of opportunistic colonizers. The berm walls, which divided the estuary in half, were kept in place for nearly three years and caused changes in water quality and the benthic community of the upper and lower halves of the estuary. Artificial breaching of the estuary in August 1995 and removal of the berm walls in May 1996 initiated recovery of the estuary. The success of a second dredger crossing, scheduled for January 1999, depends on addressing the mistakes made during the first crossing and on the speed with which the carefully planned crossing operation, berm wall removal and estuary rehabilitation proceed.     

A new regime of volcanic eruption due to the relative motion between liquid and gas

In explosive magma eruptions, magma ascends through a conduit as a Poiseuille flow at depth, and gas exsolves gradually and expands as the pressure decreases (bubbly flow regime). When the volume fraction of gas becomes sufficiently large, liquid or solid parts of magma fragment into droplets or ashes, and the flow dynamics becomes governed by the gas phase (gas–ash flow regime). We propose a new flow regime, which we call fractured-turbulent flow regime, between the bubbly flow regime and the gas–ash flow regime. In the new regime, both liquid magma and gas are continuous phases. The high connectivity of the two phases allows the relative velocity between them to increase significantly. We present one sample calculation, which displays basically explosive characteristics, but has three features distinct from previous models. The explosive characteristics are manifested as the fragmentation of the magma and the high speed jet that issues from the vent. The first distinct feature is a nearly lithostatic pressure distribution, which results from the increase of the height of the fragmentation surface. The second one is the atmospheric pressure at the vent; the flow is not choked. The third one is that the relative velocity between the gas and the ash is large at the vent despite the large interaction force between the two phases. The large relative velocity is established in the fractured-turbulent regime, and is maintained in the subsequent gas–ash flow regime.     

Propagation of seismic waves in patchy-saturated porous media: double-porosity representation

Propagation of harmonic plane waves is studied in a patchy-saturated porous medium. Patchy distribution of the two immiscible fluids is considered in a porous frame with uniform skeletal properties. A composition of two types of patches, connected through continuous paths, constitutes a double-porosity medium. Different compressibilities of pore-fluids in two porous phases facilitate the wave-induced fluid-flow in this composite material. Constitutive relations are considered with frequency-dependent complex elastic coefficients, which define the dissipative behaviour of porous aggregate due to the flow of viscous fluid in connected patches. Relevant equations of motion are solved to explain the propagation of three compressional waves and one shear wave in patchy-saturated porous solids. A numerical example is solved to illustrate dispersion in phase velocity and quality factor of attenuated waves in patchy-saturated porous materials. Role of fluid–solid inertial coupling in Darcy's law is emphasized to keep a check on the dispersion of wave velocities in the porous composite. Effects of patchy saturation on phase velocities and quality factors of attenuation are analysed using the double-porosity formulation as well as the reduced single-porosity equivalents.     

A unifying framework for watershed thermodynamics: balance equations for mass,momentum, energy and entropy,and the second law of thermodynamics

The basic aim of this paper is to formulate rigorous conservation equations for mass, momentum, energy and entropy for a watershed organized around the channel network. The approach adopted is based on the subdivision of the whole watershed into smaller discrete units, called representative elementary watersheds (REW), and the formulation of conservation equations for these REWs. The REW as a spatial domain is divided into five different subregions: (1) unsaturated zone; (2) saturated zone; (3) concentrated overland flow; (4) saturated overland flow; and (5) channel reach. These subregions all occupy separate volumina. Within the REW, the subregions interact with each other, with the atmosphere on top and with the groundwater or impermeable strata at the bottom, and are characterized by typical flow time scales.The balance equations are derived for water, solid and air phases in the unsaturated zone, water and solid phases in the saturated zone and only the water phase in the two overland flow zones and the channel. In this way REW-scale balance equations, and respective exchange terms for mass, momentum, energy and entropy between neighbouring subregions and phases, are obtained. Averaging of the balance equations over time allows to keep the theory general such that the hydrologic system can be studied over a range of time scales. Finally, the entropy inequality for the entire watershed as an ensemble of subregions is derived as constraint-type relationship for the development of constitutive relationships, which are necessary for the closure of the problem. The exploitation of the second law and the derivation of constitutive equations for specific types of watersheds will be the subject of a subsequent paper.     

The February–July 2007 eruption of the summit crater of Klyuchevskoi volcano, Kamchatka

Observations of the summit eruption of Klyuchevskoi volcano in the period from February 15, 2007 to July 9, 2007 are considered. This typical (for this volcano) summit eruption was explosive-effusive in character. The ejectamenta volume is estimated at 0.025 km³. Calculation of active phases of the volcano was carried out in accordance with V.A. Shirokov’s technique. The identified active phases agree well with the eruptive periods. The 2007 summit eruption corresponds to an active phase (May 2006 to May 2009) favorable for the volcano’s eruption. Geodetic observations carried out since 1979 along a radial profile have revealed uplifts and subsidences of the northeastern slope of the volcano. The maximum displacement of 23 cm was recorded in 2007 on the site closest to the volcano crater at a distance of 11 km from the summit crater center. In the course of two previous summit eruptions (2003–2004 and 2005) insignificant uplifts and subsidences of the slope were also noted, although the general ascent of the slope remained. This indicated possible repeated eruptions in the nearest future. Changes in the seismicity before, during and after the eruption are also discussed.     

On the 650-km seismic discontinuity

The pressure-temperature conditions and the variations of both density and bulk sound velocity in the vicinity of the 650-km discontinuity have been compared with those calculated for the phase transitions in both the olivine and the pyroxene-garnet components of the mantle material. These studies suggest that the mantle below about 650 km is composed primarily of perovskite phase, as distinct from the olivine-rich upper mantle. Thus, the “650-km” discontinuity is not likely to be associated with any of the equilibrium phase boundaries observed in olivine, pyroxene, and garnet, and is proposed instead to be a chemical change. It is suggested that the following factors may be responsible for chemical separation: the pyroxene-garnet component transforms to much denser phases possessing the ilmenite and perovskite structures before the breakdown of the spinel phase into a mixture of perovskite plus rocksalt phases. The perovskite phase is also much denser than the rocksalt phase and the two phases may not form a gravitationally stable mixture. Thus, the denser phases may tend to sink to or stay at the deep part of the mantle, causing chemical separation. Possible separation processes are discussed and the supporting observations are presented.