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1.
David E. Loper 《地球物理与天体物理流体动力学》2013,107(5):587-602
A benchmark test for flow in karstic aquifers is presented in the form of an exact solution of the harmonic variations of water flux and head within a karst conduit that is imbedded within a three-dimensional porous matrix having a free surface. The variations are driven by a prescribed variation of head applied at one end of the conduit. The benchmark consists of expressions for the spring discharge as a function of time and the conduit head and flux as functions of distance along the conduit and time. These expressions contain three dimensionless parameters, permitting development of a wide range of specific benchmark tests. The expressions are particularly simple in the case of an infinitely deep aquifer. This limiting solution should provide the most severe test for two-dimensional models of karst aquifer flow. Another limiting case of interest is that in which the conduit diameter is equal to the water depth. This limiting solution should provide the easiest test for two-dimensional models. 相似文献
2.
In karst aquifers with significant matrix permeability, water and solutes are exchanged between the conduits and carbonate matrix. Transport through the matrix increases the spread of solutes and increases travel times. This study numerically evaluates advective solute transport in synthetic karst systems that contain 3D branching conduit networks. Particle tracking is performed to analyze the spatial and temporal transport history of solute that arrives at the conduit outlet. Three measures of transport connectivity are used to quantify the solute migration behavior: the skewness of the particle arrival time distribution, the normalized fifth percentile of arrival times, and the fraction of the total travel time that occurs within conduits. All three of these metrics capture the influence of conduit network geometry on solute transport. A more tortuous network leads to enhanced conduit-matrix mixing, which reduces the transport connectivity and yields a broader distribution of solute arrival times. These results demonstrate that the conduit network geometry is an important control on solute transport in karst systems with a permeable matrix. 相似文献
3.
4.
One of the mechanisms of sudden particle release from grain surfaces in natural porous media is a decrease in salt concentration of the permeating fluid to below the critical salt concentration. Particle release can cause a change in hydraulic conductivity of the matrix, either by washing out the fines and thus increasing the pore sizes or by the plugging of pore constrictions. The phenomenon of permeability changes as a result of particle detachment was investigated in a series of column experiments. Coarse and fine sediments from the Hanford Formation in southeast Washington were tested. Columns were subject to a pulse of highly saline solution (NaNO3) followed by a fresh water shock causing particle release. Outflow rates and changes in hydraulic head as well as electric conductivity and pH were monitored over time. No permeability decrease occurred within the coarse matrix alone. However, when a thin layer of fine sediment was embedded within the coarse material (mimicking field conditions at the Hanford site), permeability irreversibly decreased to 10% to 20% of the initial value. Evidence suggests that most of this permeability decrease was a result of particles detached within the fine layer and its subsequent clogging. An additional observation was a sudden increase in pH in the outflow solution, generated in situ during the fresh water shock. Because layered systems are common in natural settings, our results suggest that alteration between sodium solution and fresh water can lead to particle release and subsequently reduce the overall permeability of the matrix. 相似文献
5.
Zdeněk Martinec 《Studia Geophysica et Geodaetica》1990,34(4):313-326
Summary A new method for computing the potential coefficients of the Earth's external gravity field is presented. The gravimetric
boundary-value problem with a free boundary is reduced to the problem with a fixed known telluroid. The main idea of the derivation
consists in a continuation of the quantities from the physical surface to the telluroid by means of Taylor's series expansion
in such a way that the terms whose magnitudes are comparable with the accuracy of today's gravity measurements are retained.
Thus not only linear, but also non-linear terms are taken into account. Explicitly, the terms up to the order of the third
power of the Earth's flattening are retained. The non-linear boundary-value problem on the telluroid is solved by an iteration
procedure with successive approximations. In each iteration step the solution of the non-linear problem is estimated by the
solutions of two linear problems utilizing the fact that the non-linear boundary condition may be split into two parts; the
linear spherical approximation of the gravity anomaly whose magnitude is significantly greater than the others and the non-linear
ellipsoidal corrections. Finally, in order to solve the problem in terms of spherical harmonics, the transform method composed
of the fast Fourier transform and Gauss Legendre quadrature is theoretically outlined. Immediate data processing of gravity
data measured on the physical Earth's surface without any continuation of gravity measurements to a reference level surface
belongs to the main advantage of the presented method. This implies that no preliminary data handling is needed and that the
error data propagation is, consequently, maximally suppressed. 相似文献
6.
A solution conduit has a permeable wall allowing for water exchange and solute transfer between the conduit and its surrounding aquifer matrix. In this paper, we use Laplace Transform to solve a one‐dimensional equation constructed using the Euler approach to describe advective transport of solute in a conduit, a production‐value problem. Both nonuniform cross‐section of the conduit and nonuniform seepage at the conduit wall are considered in the solution. Physical analysis using the Lagrangian approach and a lumping method is performed to verify the solution. Two‐way transfer between conduit water and matrix water is also investigated by using the solution for the production‐value problem as a first‐order approximation. The approximate solution agrees well with the exact solution if dimensionless travel time in the conduit is an order of magnitude smaller than unity. Our analytical solution is based on the assumption that the spatial and/or temporal heterogeneity in the wall solute flux is the dominant factor in the spreading of spring‐breakthrough curves, and conduit dispersion is only a secondary mechanism. Such an approach can lead to the better understanding of water exchange and solute transfer between conduits and aquifer matrix. Highlights:
- 相似文献
7.
The rates of passive degassing from volcanoes are investigated by modelling the convective overturn of dense degassed and
less dense gas-rich magmas in a vertical conduit linking a shallow degassing zone with a deep magma chamber. Laboratory experiments
are used to constrain our theoretical model of the overturn rate and to elaborate on the model of this process presented by
Kazahaya et al. (1994). We also introduce the effects of a CO2–saturated deep chamber and adiabatic cooling of ascending magma. We find that overturn occurs by concentric flow of the magmas
along the conduit, although the details of the flow depend on the magmas' viscosity ratio. Where convective overturn limits
the supply of gas-rich magma, then the gas emission rate is proportional to the flow rate of the overturning magmas (proportional
to the density difference driving convection, the conduit radius to the fourth power, and inversely proportional to the degassed
magma viscosity) and the mass fraction of water that is degassed. Efficient degassing enhances the density difference but
increases the magma viscosity, and this dampens convection. Two degassing volcanoes were modelled. At Stromboli, assuming
a 2 km deep, 30% crystalline basaltic chamber, containing 0.5 wt.% dissolved water, the ∼700 kg s–1 magmatic water flux can be modelled with a 4–10 m radius conduit, degassing 20–100% of the available water and all of the
1 to 4 vol.% CO2 chamber gas. At Mount St. Helens in June 1980, assuming a 7 km deep, 39% crystalline dacitic chamber, containing 4.6 wt.%
dissolved water, the ∼500 kg s–1 magmatic water flux can be modelled with a 22–60 m radius conduit, degassing ∼2–90% of the available water and all of the
0.1 to 3 vol.% CO2 chamber gas. The range of these results is consistent with previous models and observations. Convection driven by degassing
provides a plausible mechanism for transferring volatiles from deep magma chambers to the atmosphere, and it can explain the
gas fluxes measured at many persistently active volcanoes.
Received: 26 September 1997 / Accepted: 11 July 1998 相似文献
8.
1 Introduction Unlike general solids, rocks are porous materialswhich include different scales of pores, such as pores, cracks, fractures, capillary and disfigurement in the crystal, tiny pores and cracks between crystal grains at micro-scale, in which the fluid is water, oil or gas. Thedifferences between rocks and solids can be seen in two aspects, one is stresses bearing states. Solids are only subjected to external stresses, while rocks are subjected to external stresses σ ij (i, j=1,2,3)… 相似文献
9.
A 5-m radius magma-filled conduit will solidify in much less than one year if heat losses to the conduit wall are not offset by some form of forced or free convection of magma from some source body through the conduit. If the forced convection of magma from a source through the conduit is either too weak or is prevented by closure of the conduit at the end nearest the surface, only free convective circulations between the source chamber and conduit are available to balance the wall heat loss. Using an integral approach, the efficiency of free convection is investigated for conduits emplaced in both conductive and hydrothermally convective host rock environments. The results of the model strongly suggest that free circulations within conduits of large aspect ratio provide an efficient mechanism for offsetting heat losses to the conduit wall. The model provides a possible explanation for the occurrence of periodic eruptions from a conduit when the periodicity greatly exceeds the time scale for the cooling of a quiescent conduit by heat loss through the wall. 相似文献
10.
Vahid Mahboub 《Studia Geophysica et Geodaetica》2016,60(2):195-209
A weighted least-squares (WLS) solution to a 3-D non-linear symmetrical similarity transformation within a Gauss-Helmert (GH) model, and/or an errors-in-variables (EIV) model is developed, which does not require linearization. The geodetic weight matrix is the inverse of the observation dispersion matrix (second-order moment). We suppose that the dispersion matrices are non-singular. This is in contrast to Procrustes algorithm within a Gauss-Markov (GM) model, or even its generalized algorithms within the GH and/or EIV models, which cannot accept geodetic weights. It is shown that the errors-invariables in the source system do not affect the estimation of the rotation matrix with arbitrary rotational angles and also the geodetic weights do not participate in the estimation of the rotation matrix. This results in a fundamental correction to the previous algorithm used for this problem since in that algorithm, the rotation matrix is calculated after the multiplication by row-wise weights. An empirical example and a simulation study give insight into the efficiency of the proposed procedure. 相似文献
11.
Flow and transport simulation in karst aquifers remains a significant challenge for the ground water modeling community. Darcy's law–based models cannot simulate the inertial flows characteristic of many karst aquifers. Eddies in these flows can strongly affect solute transport. The simple two-region conduit/matrix paradigm is inadequate for many purposes because it considers only a capacitance rather than a physical domain. Relatively new lattice Boltzmann methods (LBMs) are capable of solving inertial flows and associated solute transport in geometrically complex domains involving karst conduits and heterogeneous matrix rock. LBMs for flow and transport in heterogeneous porous media, which are needed to make the models applicable to large-scale problems, are still under development. Here we explore aspects of these future LBMs, present simple examples illustrating some of the processes that can be simulated, and compare the results with available analytical solutions. Simulations are contrived to mimic simple capacitance-based two-region models involving conduit (mobile) and matrix (immobile) regions and are compared against the analytical solution. There is a high correlation between LBM simulations and the analytical solution for two different mobile region fractions. In more realistic conduit/matrix simulation, the breakthrough curve showed classic features and the two-region model fit slightly better than the advection-dispersion equation (ADE). An LBM-based anisotropic dispersion solver is applied to simulate breakthrough curves from a heterogeneous porous medium, which fit the ADE solution. Finally, breakthrough from a karst-like system consisting of a conduit with inertial regime flow in a heterogeneous aquifer is compared with the advection-dispersion and two-region analytical solutions. 相似文献
12.
The evaluation of the wave-induced pore pressure around a buried pipeline is particularly important for pipeline engineers involved in the design of offshore pipelines. Most previous investigations of the wave-induced dynamic response around an offshore pipeline have limited to two-dimensional cases. In this paper, a three-dimensional model including buried pipeline is established, based on the existing DYNE3WAC models. Based on the proposed numerical model and poro-elastic soil material assumption, the effects of wave and soil characteristics, such as wave period, water depth, shear modulus and permeability, and configuration of pipelines, such as pipeline radius and pipeline buried depth, on the wave-induced excess pore pressure will be examined. Numerical results indicated that the normalized excess pore pressures versus z/h near the pipeline increase as the obliquity angle, wave period and water depth increase, and they decrease as the burial depth and radius of pipeline increase above the pipeline. Soil permeability has obvious influence on the wave-induced normalized excess pore pressure, and different soil material will result in distinct computation results. 相似文献
13.
Li G 《Ground water》2011,49(4):584-592
Often the water flowing in a karst conduit is a combination of contaminated water entering at a sinkhole and cleaner water released from the limestone matrix. Transport processes in the conduit are controlled by advection, mixing (dilution and dispersion), and retention-release. In this article, a karst transport model considering advection, spatially varying dispersion, and dilution (from matrix seepage) is developed. Two approximate Green's functions are obtained using transformation of variables, respectively, for the initial-value problem and for the boundary-value problem. A numerical example illustrates that mixing associated with strong spatially varying conduit dispersion can cause strong skewness and long tailing in spring breakthrough curves. Comparison of the predicted breakthrough curve against that measured from a dye-tracing experiment between Ames Sink and Indian Spring, Northwest Florida, shows that the conduit dispersivity can be as large as 400 m. Such a large number is believed to imply strong solute interaction between the conduit and the matrix and/or multiple flow paths in a conduit network. It is concluded that Taylor dispersion is not dominant in transport in a karst conduit, and the complicated retention-release process between mobile- and immobile waters may be described by strong spatially varying conduit dispersion. 相似文献
14.
Inversion of gravity and/or magnetic data attempts to recover the density and/or magnetic susceptibility distribution in a 3D earth model for subsequent geological interpretation. This is a challenging problem for a number of reasons. First, airborne gravity and magnetic surveys are characterized by very large data volumes. Second, the 3D modelling of data from large‐scale surveys is a computationally challenging problem. Third, gravity and magnetic data are finite and noisy and their inversion is ill posed so regularization must be introduced for the recovery of the most geologically plausible solutions from an infinite number of mathematically equivalent solutions. These difficulties and how they can be addressed in terms of large‐scale 3D potential field inversion are discussed in this paper. Since potential fields are linear, they lend themselves to full parallelization with near‐linear scaling on modern parallel computers. Moreover, we exploit the fact that an instrument’s sensitivity (or footprint) is considerably smaller than the survey area. As multiple footprints superimpose themselves over the same 3D earth model, the sensitivity matrix for the entire earth model is constructed. We use the re‐weighted regularized conjugate gradient method for minimizing the objective functional and incorporate a wide variety of regularization options. We demonstrate our approach with the 3D inversion of 1743 line km of FALCON gravity gradiometry and magnetic data acquired over the Timmins district in Ontario, Canada. Our results are shown to be in good agreement with independent interpretations of the same data. 相似文献
15.
In traditional applications in soil physics it is convention to scale porous media properties, such as hydraulic conductivity, soil water diffusivity, and capillary head, with the gravitational acceleration. In addition, the Richards equation for water flux in partially saturated porous media also contains a gravity term. With the plans to develop plant habitats in space, such as in the International Space Station, it becomes necessary to evaluate these properties and this equation under conditions of microgravitational acceleration. This article develops models for microgravity steady state two-phase flow, as found in irrigation systems, that addresses critical design issues. Conventional dimensionless groups in two-phase mathematical models are scaled with gravity, which must be assigned a value of zero for microgravity modeling. The use of these conventional solutions in microgravity, therefore, is not possible. This article therefore introduces new dimensionless groups for two-phase models. The microgravity models introduced here determined that in addition to porous media properties, important design factors for microgravity systems include applied water potential and the ratio of inner to outer radii for cylindrical and spherical porous media systems. 相似文献
16.
Physics-based distributed models for simulating flow in karst systems are generally based on the discrete–continuum approach in which the flow in the three-dimensional fractured limestone matrix continuum is coupled with the flow in discrete one-dimensional conduits. In this study we present a newly designed discrete–continuum model for simulating flow in karst systems. We use a flexible spatial discretization such that complicated conduit networks can be incorporated. Turbulent conduit flow and turbulent surface flow are described by the diffusion wave equation whereas laminar variably saturated flow in the matrix is described by the Richards equation. Transients between free-surface and pressurized conduit flow are handled by changing the capacity term of the conduit flow equation. This new approach has the advantage that the transients in mixed conduit flow regimes can be handled without the Preissmann slot approach. Conduit–matrix coupling is based on the Peaceman’s well-index such that simulated exchange fluxes across the conduit–matrix interface are less sensitive to the spatial discretization. Coupling with the surface flow domain is based on numerical techniques commonly used in surface–subsurface models and storm water drainage models. Robust algorithms are used to simulate the non-linear flow processes in a coupled fashion. The model is verified and illustrated with simulation examples. 相似文献
17.
《Advances in water resources》1999,23(3):261-269
A study of the effects of grid discretization on the migration of DNAPL within a discrete-fracture network embedded in a porous rock matrix is presented. It is shown that an insufficiently fine discretization of the fracture elements can lead to an overprediction of the volume of DNAPL that continues to migrate vertically at the intersection of a vertical and horizontal fracture. Uniform discretization of elements at the scale of one centimetre (or less) accurately resolved the density and capillary pressure components of the head gradient in the DNAPL. An alternative, non-uniform method of discretization of elements within the discrete-fracture network is presented whereby only fracture elements immediately adjacent to fracture intersections are refined. To further limit the number of elements employed, the porous matrix elements adjacent to the fracture elements are not similarly refined. Results show this alternative method of discretization reduces the numerical error to an acceptable level, while allowing the simulation of field-scale DNAPL contamination problems. The results from two field-scale simulations of a DNAPL-contaminated carbonate bedrock site in Ontario, Canada are presented. These simulations compare different methods of grid discretization, and highlight the importance of grid refinement when simulating DNAPL migration problems in fractured porous media. 相似文献
18.
Locating the zone of saline intrusion in a coastal karst aquifer using springflow data 总被引：2，自引：0，他引：2
Coastal fresh water aquifers are an increasingly desirable resource. In a karstic aquifer, sea water intrusion occurs as a salt water wedge, like in porous media. However, preferential flow conduits may alter the spatial and temporal distribution of the salt water. This is typically the case when the outlet of the aquifer is a brackish spring. This paper shows that salinity and flow rate variations at a spring, where salinity is inversely proportional to discharge, can help to understand the hydrodynamic functioning of the aquifer and to locate the fresh water-sea water mixing zone deep inside the aquifer. The volume of water-filled conduit between the sea water intrusion zone and the spring outlet is calculated by the integral over time of the flow rate during the time lag between the flow rate increase and the salinity decrease as measured at the spring. In the example of the spring at Almyros of Heraklio (Crete, Greece), this time lag is variable, depending on the discharge, but the volume of water-filled conduit appears to be constant, which shows that the processes of salt water intrusion and mixing in the conduit are constant throughout the year. The distance between the spring and the zone where sea water enters the conduit is estimated and provides an indication of the position where only fresh water is present in the conduit. 相似文献
19.
The inversion gravity problem formulated as follows is solved. The excess density in each layer of a fixed horizontal stratified model is a function of horizontal coordinates (σ(ξ, η)) approximated by a specially constructed function. The problem is to reconstruct the function σ = σ(ξ, η) from the external gravity field. If the geological model includes more than one layer, the problem is solved with the use of a set of reference points at which the sought function is given. Variations in a gravity anomaly with respect to the field at a fixed point are used in solving this problem. 相似文献
20.
We present a method to determine equivalent permeability of fractured porous media. Inspired by the previous flow-based upscaling methods, we use a multi-boundary integration approach to compute flow rates within fractures. We apply a recently developed multi-point flux approximation Finite Volume method for discrete fracture model simulation. The method is verified by upscaling an arbitrarily oriented fracture which is crossing a Cartesian grid. We demonstrate the method by applying it to a long fracture, a fracture network and the fracture network with different matrix permeabilities. The equivalent permeability tensors of a long fracture crossing Cartesian grids are symmetric, and have identical values. The application to the fracture network case with increasing matrix permeabilities shows that the matrix permeability influences more the diagonal terms of the equivalent permeability tensor than the off-diagonal terms, but the off-diagonal terms remain important to correctly assess the flow field. 相似文献