Solute movement through intact columns of cryoturbated Upper Chalk

Cryoturbated Upper Chalk is a dichotomous porous medium wherein the intra‐fragment porosity provides water storage and the inter‐fragment porosity provides potential pathways for relatively rapid flow near saturation. Chloride tracer movement through 43 cm long and 45 cm diameter undisturbed chalk columns was studied at water application rates of 0·3, 1·0, and 1·5 cm h^?1. Microscale heterogeneity in effluent was recorded using a grid collection system consisting of 98 funnel‐shaped cells each 3·5 cm in diameter. The total porosity of the columns was 0·47 ± 0·02 m³ m^?3, approximately 13% of pores were ≥ 15 µm diameter, and the saturated hydraulic conductivity was 12·66 ± 1·31 m day^?1. Although the column remained unsaturated during the leaching even at all application rates, proportionate flow through macropores increased as the application rate decreased. The number of dry cells (with 0 ml of effluent) increased as application rate decreased. Half of the leachate was collected from 15, 19 and 22 cells at 0·3, 1·0, 1·5 cm h^?1 application rates respectively. Similar breakthrough curves (BTCs) were obtained at all three application rates when plotted as a function of cumulative drainage, but they were distinctly different when plotted as a function of time. The BTCs indicate that the columns have similar drainage requirement irrespective of application rates, as the rise to the maxima (C/C_o) is almost similar. However, the time required to achieve that leaching requirement varies with application rates, and residence time was less in the case of a higher application rate. A two‐region convection–dispersion model was used to describe the BTCs and fitted well (r² = 0·97–0·99). There was a linear relationship between dispersion coefficient and pore water velocity (correlation coefficient r = 0·95). The results demonstrate the microscale heterogeneity of hydrodynamic properties in the Upper Chalk. Copyright © 2007 John Wiley & Sons, Ltd.     

Experimental evidence of the double-porosity effects in geomaterials

Double-porosity is an important characteristic of microstructure in a large range of geomaterials. It designs porous media with connected fissures/fractures or aggregated soils. The origin of double-porosity can be natural or/and it can result from mechanical, chemical or biological damage. The presence of double-porosity can significantly affect the behaviour of geomaterials. In this paper we provide an experimental evidence of the double-porosity effects by performing laboratory experiments. Series of tracer dispersion experiments (in saturated and unsaturated steady-state water flow conditions) in a physical model of double-porosity geomaterial were carried out. For the comparative purposes, experiments of the same type were also performed in a singleporosity model medium. The results clearly showed that the double-porosity microstructure leads to the non-Fickian behaviour of the tracer (early breakthrough and long tail) in both saturated and unsaturated cases.     

Hydraulic Properties of Stony Vadose Zonesa

Hydraulic properties of saturated and unsaturated stony soils were studied on a 3.35 m long column, 1.24 m in diameter, filled with alternating sand and boulder layers. The boulders averaged 6.2 × 15 × 20 cm in size and were laid down on their flat side. Tensiometers and a neutron probe access tube were placed in the column for measuring pressure heads and water contents, respectively. Saturated conditions were obtained by ponding the column. The resulting hydraulic conductivity K was 5.1 m/day. This value could also be calculated from the measured K for the sand alone on separate samples, using a simple equation that takes into account the void ratio of the sand alone and that of the boulder-sand mixture. Unsaturated K was determined by applying water at less than ponded infiltration rates. Resulting relations between the unsaturated K and water content or negative pressure head could also be estimated from the relation between unsaturated K and pressure head for the sand alone and the calculated saturated K of the boulder-sand mixture. The method of Millington and Quirk for calculating the relation between unsaturated K and water content also gave reasonable results. The dispersivity of the boulder-sand column was 18 times that of the sand alone. Pore velocity was accurately estimated as the Darcy velocity divided by the volumetric water content. Hydraulic properties of stony vadose zones are difficult to determine. This work shows that they can be estimated from K relations measured in the laboratory on samples of the soil between the rocks. Knowledge of hydraulic properties of vadose zones is important in predicting movement of water and pollutants to the underlying ground water.     

Changes in water table level influence solute transport in uniform porous media

Changes in the water table level result in variable water saturation and variable hydrological fluxes at the interface between the unsaturated and saturated zone. This may influence the transport and fate of contaminants in the subsurface. The objective of this study was to examine the impact of a decreasing and an increasing water table on solute transport. We conducted tracer experiments at downward flow conditions in laboratory columns filled with two different uniform porous media under static and transient flow conditions either increasing or decreasing the water table. Tracer breakthrough curves were simulated using a mobile–immobile transport model. The resulting transport parameters were compared to identify dominant transport processes. Changes in the water table level affected dispersivities and mobile water fractions depending on the direction of water table movement and the grain size of the porous media. In fine glass beads, the water flow velocity was similar to the decline rate of the water table, and the mobile water fraction was decreased compared with steady‐state saturated conditions. However, immobile water was negligible. In coarse glass beads, water flow was faster because of fingered flow in the unsaturated part, and the mobile water fraction was smaller than in the fine material. Here, a rising water table led to an even smaller mobile water fraction and increased solute spreading because of diffusive interaction with immobile water. We conclude that changes of the water table need to be considered to correctly simulate transport in the subsurface at the transition of the unsaturated–saturated zone. Copyright © 2014 John Wiley & Sons, Ltd.     

Finite-element analysis of the transport of water and solutes in title-drained soils

The finite-element method based on a Galerkin technique was used to formulate the problem of simulating the two-dimensional (cross-sectional) transient movement of water and solute in saturated or partially saturated nonuniform porous media. The numerical model utilizes linear triangular elements. Nonreactive, as well as reactive solutes whose behaviour can be described by a distribution coefficient or first-order reaction term were considered. The flow portion of the model was tested by comparison of the model results with experimental and finite-difference results for transient flow in an unsaturated sand column and the solute transport portion of the model was tested by comparison with analytical solution results. The model was applied to a hypothetical case involving movement of water and solutes in tile-drained soils. The simulation results showed the development of distinct solute leaching patterns in the soil as drainage proceeded. Although applied to a tile drainage problem in this study, the model should be equally useful in the study of a wide range of two-dimensional water and solute migration problems.     

Analysis of solute transport in a divergent flow tracer test with scale‐dependent dispersion

It has been known for many years that dispersivities increase with solute displacement distance in a subsurface. The increase of dispersivities with solute travel distance results from significant variation in hydraulic properties of porous media and was identified in the literature as scale‐dependent dispersion. In this study, Laplace‐transformed analytical solutions to advection‐dispersion equations in cylindrical coordinates are derived for interpreting a divergent flow tracer test with a constant dispersivity and with a linear scale‐dependent dispersivity. Breakthrough curves obtained using the scale‐dependent dispersivity model are compared to breakthrough curves obtained from the constant dispersivity model to illustrate the salient features of scale‐dependent dispersion in a divergent flow tracer test. The analytical results reveal that the breakthrough curves at the specific location for the constant dispersivity model can produce the same shape as those from the scale‐dependent dispersivity model. This correspondence in curve shape between these two models occurs when the local dispersivity at an observation well in the scale‐dependent dispersivity model is 1·3 times greater than the constant dispersivity in the constant dispersivity model. To confirm this finding, a set of previously reported data is interpreted using both the scale‐dependent dispersivity model and the constant dispersivity model to distinguish the differences in scale dependence of estimated dispersivity from these two models. The analytical result reveals that previously reported dispersivity/distance ratios from the constant dispersivity model should be revised by multiplying these values by a factor of 1·3 for the scale‐dependent dispersion model if the dispersion process is more accurately characterized by scale‐dependent dispersion. Copyright © 2007 John Wiley & Sons, Ltd.     

Transport and fate of nonaqueous phase liquid (NAPL) in variably saturated porous media with evolving scales of heterogeneity

 A stochastic simulation is performed to study multiphase flow and contaminant transport in fractal porous media with evolving scales of heterogeneity. Numerical simulations of residual NAPL mass transfer and subsequent transport of dissolved and/or volatilized NAPL mass in variably saturated media are carried out in conjunction with Monte Carlo techniques. The impact of fractal dimension, plume scale and anisotropy (stratification) of fractal media on relative dispersivities is investigated and discussed. The results indicate the significance of evolving scale of porous media heterogeneity to the NAPL transport in the subsurface. In general, the fractal porous media enhance the dispersivities of NAPL mass plume transport in both the water phase and the gas phase while the influence on the water phase is more significant. The porous media with larger fractal dimension have larger relative dispersivities. The aqueous horizontal dispersivity exhibits a most significant increase against the plume scale.     

Stochastic analysis of unsaturated transport in soils with fractal log-conductivity distribution

Within the framework of stochastic theory and the spectral perturbation techniques, three-dimensional dispersion in partially saturated soils with fractal log hydraulic conductivity distribution is analyzed. Our analysis is focused on the impact of fractal dimension of log hydraulic conductivity distribution, local dispersivity, and unsaturated flow parameters, such as the soil poresize distribution parameter and the moisture distribution parameter, on the spreading behavior of solute plume and the concentration variance. Approximate analytical solutions to the stochastic partial differential equations are derived for the variance of asymptotic solute concentration and asymptotic macrodispersivities.     

Flow in unsaturated random porous media,nonlinear numerical analysis and comparison to analytical stochastic models

This work presents a rigorous numerical validation of analytical stochastic models of steady state unsaturated flow in heterogeneous porous media. It also provides a crucial link between stochastic theory based on simplifying assumptions and empirical field and simulation evidence of variably saturated flow in actual or realistic hypothetical heterogeneous porous media. Statistical properties of unsaturated hydraulic conductivity, soil water tension, and soil water flux in heterogeneous soils are investigated through high resolution Monte Carlo simulations of a wide range of steady state flow problems in a quasi-unbounded domain. In agreement with assumptions in analytical stochastic models of unsaturated flow, hydraulic conductivity and soil water tension are found to be lognormally and normally distributed, respectively. In contrast, simulations indicate that in moderate to strong variable conductivity fields, longitudinal flux is highly skewed. Transverse flux distributions are leptokurtic. the moments of the probability distributions obtained from Monte Carlo simulations are compared to modified first-order analytical models. Under moderate to strong heterogeneous soil flux conditions (σ²_y≥1), analytical solutions overestimate variability in soil water tension by up to 40% as soil heterogeneity increases, and underestimate variability of both flux components by up to a factor 5. Theoretically predicted model (cross-)covariance agree well with the numerical sample (cross-)covarianaces. Statistical moments are shown to be consistent with observed physical characteristics of unsaturated flow in heterogeneous soils.©1998 Elsevier Science Limited. All rights reserved     

非饱和土中剪切S波的传播特性分析

基于对非饱和多孔介质的研究成果,考虑孔隙中的液相和气相的相互影响,研究非饱和土地基中剪切S波的传播特性。通过非饱和土中固相、液相和气相的质量平衡方程、动量平衡方程和非饱和土有效应力原理,建立问题的弹性波动方程,经过理论推导给出非饱和土中剪切S波的弥散特征方程。通过数值算例分析剪切S波的波速和衰减系数随饱和度、频率和固有渗透系数等因素的变化规律。结果表明,剪切S波的波速几乎不受饱和度的影响,但其随着频率的增大而减小,随着固有渗透系数的增大先不变后增大;剪切S波的衰减系数随着饱和度和频率的增加均增大,而随着固有渗透系数的增大先不变后增大最后减小。     

The stability of density-driven flows in saturated heterogeneous porous media

This work concludes the investigations into the stability of haline flows in saturated porous media. In the first part [33] a stability criterion for density-driven flow in a saturated homogeneous medium was derived excluding dispersion. In the second part [34], the effects of dispersion were included. The latter criterion made reasonable predictions of the stability regimes (indicated by the number of fingers present) as a function of density and dispersivity variations. We found out that destabilising variables caused an increase in the number of fingers and vice versa. The investigation is extended here for the effects of the medium heterogeneity. The cell problem derived via homogenization theory [20] is solved and its solution used to evaluate the elements of the macrodispersion tensor as functions of time for flow aligned parallel to gravity. The longitudinal coefficient exhibits asymptotic behaviour for favourable and moderately unfavourable density contrasts while it grows indefinitely for higher density contrasts. The range of densities stabilised by medium heterogeneities can thus be estimated from the behaviour of the coefficient. The d³f software program is used for the numerical simulations. The code uses the cell-centred finite volume and the implicit Euler techniques for the spatial and temporal discretisations respectively.     

Macroscopic equations for vapor transport in a multi-layered unsaturated zone

Using the method of homogenization, we present a systematic derivation of the macroscopic equations for air flow and chemical vapor transport in an unsaturated zone with a periodic structure of heterogeneity. The effective specific discharge and hydrodynamic dispersion coefficient are expressible in terms of some cell functions, whose analytical solutions are sought for the simple case of alternate stacking of two strictly plane layers of different properties. For this kind of bi-layered composite, the effects of convection velocity and layer property contrasts on the longitudinal and transverse components of the hydrodynamic dispersion coefficient are investigated.     

Inverse upscaling of hydraulic parameters during constant flux infiltration using borehole radar

Modeling unsaturated flow in porous media requires constitutive relations that describe the soil water retention and soil hydraulic conductivity as a function of either potential or water content. Often, the hydraulic parameters that describe these relations are directly measured on small soil cores, and many cores are needed to upscale to the entire heterogeneous flow field. An alternative to the forward upscaling method using small samples are inverse upscaling methods that incorporate soft data from geophysical measurements observed directly on the larger flow field. In this paper, we demonstrate that the hydraulic parameters can be obtained from cross borehole ground penetrating radar by measuring the first arrival travel time of electromagnetic waves (represented by raypaths) from stationary antennae during a constant flux infiltration experiment. The formulation and coupling of the hydrological and geophysical models rely on a constant velocity wetting front that causes critical refraction at the edge of the front as it passes by the antennae. During this critical refraction period, the slope of the first arrival data can be used to calculate (1) the wetting velocity and (2) the hydraulic conductivity of the wet (or saturated) soil. If the soil is undersaturated during infiltration, then an estimate of the saturated water content is needed before calculating the saturated hydraulic conductivity. The hydraulic conductivity value is then used in a nonlinear global optimization scheme to estimate the remaining two parameters of a Broadbridge and White soil.     

A new saturated/unsaturated model for stormwater infiltration systems

Infiltration systems are widely used as an effective urban stormwater control measure. Most design methods and models roughly approximate the complex physical flow processes in these systems using empirical equations and fixed infiltration rates to calculate emptying times from full. Sophisticated variably saturated flow models are available, but rarely applied owing to their complexity. This paper describes the development and testing of an integrated one‐dimensional model of flow through the porous storage of a typical infiltration system and surrounding soils. The model accounts for the depth in the storage, surrounding soil moisture conditions and the interaction between the storage and surrounding soil. It is a front‐tracking model that innovatively combines a soil‐moisture‐based solution of Richard's equation for unsaturated flow with piston flow through a saturated zone as well as a reservoir equation for flow through a porous storage. This allows the use of a simple non‐iterative numerical solution that can handle ponded infiltration into dry soils. The model is more rigorous than approximate stormwater infiltration system models and could therefore be valuable in everyday practice. A range of test cases commonly used to test soil water flow models for infiltration in unsaturated conditions, drainage from saturation and infiltration under ponded conditions were used to test the model along with an experiment with variable depth in a porous storage over saturated conditions. Results show that the model produces a good fit to the observed data, analytical solutions and Hydrus. Copyright © 2008 John Wiley & Sons, Ltd.     

周期性层状含孔隙、裂隙介质模型纵波衰减特征

地震波在含孔隙、裂隙斑块饱和介质传播过程中会诱发多个尺度孔隙流体流动而产生衰减和速度频散.在含有宏观尺度“Biot流”和介观尺度“局域流”衰减诱导机制的周期性层状孔隙介质模型基础上,引入了微观尺度硬币型和尖灭型裂隙“喷射流”的影响,构建了周期性层状含孔隙、裂隙介质模型.利用双解耦弹性波动方程的方法数值计算了该模型地震频带的纵波衰减和速度频散并与周期性层状孔隙介质模型做了对比研究.分析了该模型在不同裂隙参数（裂隙密度、裂隙纵横比）及裂隙体积含量下的纵波衰减和频散特征,裂隙密度越高对于纵波衰减和频散的影响越大,裂隙纵横比越小,由裂隙引起的纵波衰减部分向高频段移动,裂隙体积含量越少,纵波衰减先降低后小幅增加再降低,频散速度增加,并逐渐接近于周期性层状孔隙介质模型的纵波衰减和频散速度曲线.最后研究了周期性层状含孔隙、裂隙介质模型有效平面波模量的高低频极限以及流固相对位移在该模型中的分布特征.     

Numerical studies of two-dimensional saturated/ unsaturated drainage models

The partial differential equation which governs the seepage of water in unsaturated and saturated porous media is solved numerically by a generalized Newton iteration technique for two models, one ditch drainage model and one earth dam model. For each model, which is two-dimensional, a few hypothetical soils with different moisture retention curves are considered. In both models only drainage from an initially saturated soil occurs; thus, the problem of hysteresis is avoided. The results of the computations are compared with those of corresponding saturated (pure groundwater) models; solutions obtained earlier by this author and others.

Computational instability phenomena appear when the slope of the retention curves is made steep, i.e., for poorly-graded soils.     

Analysis of solute transport with a hyperbolic scale-dependent dispersion model

An empirical hyperbolic scale-dependent dispersion model, which predicts a linear growth of dispersivity close to the origin and the attainment of an asymptotic dispersivity at large distances, is presented for deterministic modelling of field-scale solute transport and the analysis of solute transport experiments. A simple relationship is derived between local dispersivity, which is used in numerical simulations of solute transport, and effective dispersivity, which is estimated from the analysis of tracer breakthrough curves. The scale-dependent dispersion model is used to interpret a field tracer experiment by nonlinear least-squares inversion of a numerical solution for unsaturated transport. Simultaneous inversion of concentration-time data from several sampling locations indicates a linear growth of the dispersion process over the scale of the experiment. These findings are consistent with the results of an earlier analysis based on the use of a constant dispersion coefficient model at each of the sampling depths.     

Acoustic reverberation in a logging tool-borehole-saturated porous medium system

The influence of the elastic and hydrodynamic properties of a rock on the time attenuation coefficient of an acoustic wave, which is reflected from the borehole wall, is considered using the methods of the mechanics of saturated porous media. The calculations were performed for a system consisting of an acoustic logging tool of a finite with a finite diameter, a fluid-filled borehole, and a porous permeable rock. The performed simulation showed that in rocks with a low hydrodynamic permeability, the acoustic-reverberation time is determined by the acoustic impedance of the borehole wall (product of the rock density and the longitudinal-wave velocity in it). In the case of rocks with a permeability of about several hundred millidarcy, the time signal’s attenuation coefficient substantially depends on the rock’s permeability.     

Transect study on solute transport in a macroporous soil

Solute transport experiments using a non-reactive tracer were conducted on short, undisturbed, saturated columns of a sandy loam soil. All columns, 20 cm in diameter and 20 cm long, were collected along a transect of 35 m. Most of the soil columns had pre-existing macropores. The columns were leached at a steady flow-rate under ponding conditions. The resulting breakthrough curves (BTCs) showed a large heterogeneity. Several of the BTCs displayed early breakthrough and long tailing. All the data were interpreted in terms of dimensional time moments, the classical convection-dispersion equation (CDE) and the mobile-immobile transport model (MIM). Experimental time moments were found to vary significantly among the different BTCs. Analysis of the time moments also revealed that the variance of the field-scale BTC was several times larger than the average of the local-scale variance. The pore water velocity v and dispersion coefficient D were obtained by fitting the CDE to the local-scale BTCs, resulting in an average dispersivity of 7·4 cm. Frequency distributions for the CDE parameters v and D were equally well described by a normal or log-normal probability density function (pdf). When a log-normal pdf for D is considered, the variance of the log_e transformed D values (σ_{ln D}²) was found to be 2·1. For the MIM model, two additional parameters were fitted: the fraction of mobile water, θ_m/θ, and the first-order mass transfer coefficient, α. The MIM was more successful in describing the data than the CDE transport model. For the MIM model, the average dispersivity was about 2 cm. The MIM parameters v, D and θ_m/θ were best described by a log-normal pdf rather than a normal pdf. Only the parameter α was better described by a normal pdf. Mobile water fractions, θ_m/θ ranged from 0·01 to 0·98, with a mean of 0·43 (based on a log-normal pdf). When the CDE and MIM were applied to the data, the fitted pore water velocities, v, compared favourably with the effective pore water velocities, v_eff, obtained from moment analysis.     

Lateral water flux in the unsaturated zone: A mechanism for the formation of spatial soil heterogeneity in a headwater catchment

Measurements of soil water potential and water table fluctuations suggest that morphologically distinct soils in a headwater catchment at the Hubbard Brook Experimental Forest in New Hampshire formed as a result of variations in saturated and unsaturated hydrologic fluxes in the mineral soil. Previous work showed that each group of these soils had distinct water table fluctuations in response to precipitation; however, observed variations in soil morphology also occurred above the maximum height of observed saturation. Variations in unsaturated fluxes have been hypothesized to explain differences in soil horizon thickness and presence/absence of specific horizons but have not been explicitly investigated. We examined tensiometer and shallow groundwater well records to identify differences in unsaturated water fluxes among podzols that show distinct morphological and chemical differences. The lack of vertical hydraulic gradients at the study sites suggests that lateral unsaturated flow occurs in several of the soil units. We propose that the variations in soil horizon thickness and presence/absence observed at the site are due in part to slope‐parallel water flux in the unsaturated portion of the solum. In addition, unsaturated flow may be involved in the translocation of spodic material that primes those areas to contribute water with distinct chemistry to the stream network and represents a potential source/sink of organometallic compounds in the landscape.