Spatial variability of the poroelastic response of the heterogeneous medium

In this work, a stochastic methodology is applied to analyze the variability of the poroelastic response of the heterogeneous medium at the field scale. To solve the problem analytically, we restrict our attention to the one-dimensional models, where fluid flow as well as deformation occurs in one direction only under a constant applied stress. Assuming statistic homogeneity, the closed-form solutions that describe the variability of fluid pressure head, and a solid's strain and displacement are developed using a spectral approach based on Fourier–Stieltjes representations for the perturbed quantities. The influence of the correlation length of the log hydraulic conductivity on these results is investigated. It is found that the variances of the solid's strain and displacement increase with the correlation length of the log hydraulic conductivity, while the correlation length of the log hydraulic conductivity plays the role in reducing the variability of the specific discharge.     

Estimating groundwater discharge to surface waters using heat as a tracer in low flux environments: the role of thermal conductivity

Analytical modelling of heat transport was used to address effects of uncertainty in thermal conductivity on groundwater–surface water exchange. In situ thermal conductivities and temperature profiles were measured in a coastal lagoon bed where groundwater is known to discharge. The field site could be divided into three sediment zones where significant spatial changes in thermal conductivity on metre to centimetre scale show that spatial variability connected to the sediment properties must be considered. The application of a literature‐based bulk thermal conductivity of 1.84 Wm^?1 °C^?1, instead of field data that ranged from 0.62 to 2.19 W m^?1 °C^?1, produced a mean overestimation of 2.33 cm d^?1 that, considering the low fluxes of the study area, represents an 89% increase and up to a factor of 3 in the most extreme cases. Incorporating the uncertainty due to sediment heterogeneities leads to an irregular trend of the flux distribution from the shore towards the lagoon. The natural variability of the thermal conductivity associated with changes in the sediment composition resulted in a mean variation of ±0.66 cm d^?1 in fluxes corresponding to a change of ±25.4%. The presence of organic matter in the sediments, a common situation in the near‐shore areas of surface water bodies, is responsible for the decrease of thermal conductivity. The results show that the natural variability of sediment thermal conductivity is a parameter to be considered for low flux environments, and it contributes to a better understanding of groundwater–surface water interactions in natural environments. Copyright © 2015 John Wiley & Sons, Ltd.     

Local‐ and field‐scale infiltration into vertically non‐uniform soils with spatially‐variable surface hydraulic conductivities

We studied the problem of local‐ and field‐scale infiltration over a particular class of heterogeneous soils. At the local scale, the soils are described as being vertically non‐uniform, with the saturated hydraulic conductivity continuously decreasing with depth according to a power law function. Analogous to the Green–Ampt model, analytical expressions are first developed for local‐scale infiltration using a sharp front approximation, and model results are compared with numerical solutions of the Richards equation. These results show that saturation does not occur from below in soils with such vertical non‐uniformity, thereby allowing for the use of a sharp front approximation. Because of vertical non‐uniformity, ponding conditions are achieved locally even for rainfall rates less than the surface saturated hydraulic conductivity. Furthermore, infiltration rates asymptotically approach zero at long times. To determine field‐scale infiltration properties, the spatial variability in the surface saturated hydraulic conductivity is represented by a log‐normal random field. Using cumulative infiltration as the independent variable, expressions are developed for the ensemble mean of field‐scale infiltration and the expected time for a given depth of water to infiltrate over the field. Surface horizontal heterogeneity is found to control field‐scale infiltration at small times, whereas local vertical non‐uniformity exerts a strong control at long times. Copyright © 2011 John Wiley & Sons, Ltd.     

Transport upscaling using multi-rate mass transfer in three-dimensional highly heterogeneous porous media

A methodology for transport upscaling of three-dimensional highly heterogeneous formations is developed and demonstrated. The overall approach requires a prior hydraulic conductivity upscaling using an interblock-centered full-tensor Laplacian-with-skin method followed by transport upscaling. The coarse scale transport equation includes a multi-rate mass transfer term to compensate for the loss of heterogeneity inherent to all upscaling processes. The upscaling procedures for flow and transport are described in detail and then applied to a three-dimensional highly heterogeneous synthetic example. The proposed approach not only reproduces flow and transport at the coarse scale, but it also reproduces the uncertainty associated with the predictions as measured by the ensemble variability of the breakthrough curves.     

The effect of non divergence-free velocity fields on field scale ground water solute transport

Solute plume subjected to field scale hydraulic conductivity heterogeneity shows a large dispersion/macrodispersion, which is the manifestation of existing fields scale heterogeneity on the solute plume. On the other hand, due to the scarcity of hydraulic conductivity measurements at field scale, hydraulic conductivity heterogeneity can only be defined statistically, which makes the hydraulic conductivity a random variable/function. Random hydraulic conductivity as a parameter in flow equation makes the pore flow velocity also random and the ground water solute transport equation is a stochastic differential equation now. In this study, the ensemble average of stochastic ground water solute transport equation is taken by the cumulant expansion method in order to upscale the laboratory scale transport equation to field scale by assuming pore flow velocity is a non stationary, non divergence-free and unsteady random function of space and time. Besides the stochastic explanation of macrodispersion and the velocity correction term obtained by Kavvas and Karakas (J Hydrol 179:321–351, 1996) before a new velocity correction term, which is a function of mean pore flow velocity divergence, is obtained in this study due to strict second order cumulant expansion (without omitting any term after the expansion) performed. The significance of the new velocity correction term is investigated on a one dimensional transport problem driven by a density dependent flow field.     

1DTempPro: Analyzing Temperature Profiles for Groundwater/Surface‐water Exchange

A new computer program, 1DTempPro, is presented for the analysis of vertical one‐dimensional (1D) temperature profiles under saturated flow conditions. 1DTempPro is a graphical user interface to the U.S. Geological Survey code Variably Saturated 2‐Dimensional Heat Transport (VS2DH), which numerically solves the flow and heat‐transport equations. Pre‐ and postprocessor features allow the user to calibrate VS2DH models to estimate vertical groundwater/surface‐water exchange and also hydraulic conductivity for cases where hydraulic head is known.     

Scale‐dependent Poiseuille flow alternatively explains enhanced dispersion in geothermal environments

Fluid flow exerts a critical impact on the convection of thermal energy in geological media, whereas heat transport in turn affects fluid properties, including fluid dynamic viscosity and density. The interplay of flow and heat transport also affects solute transport. To unravel these complex coupled flow, heat, and solute transport processes, here, we present a theory for the idealized scale‐dependent Poiseuille flow model considering a constant temperature gradient (?T) along a single fracture, where fluid dynamic viscosity connects with temperature via an exponential function. The idealized scale‐dependent model is validated based on the solutions from direct numerical simulations. We find that the hydraulic conductivity (K) of the Poiseuille flow either increases or decreases with scales depending on ?T > 0°C/m or ?T < 0°C/m, respectively. Indeed, the degree of changes in K depends on the magnitude of ?T and fracture length. The scale‐dependent model provides an alternative explanation for the well‐known scale‐dependent transport problem, for example, the dispersion coefficient increases with travel distance when ?T > 0°C/m according to the Taylor dispersion theory, because K (or equivalently flux through fractures) scales with fracture length. The proposed theory unravels intertwined interactions between flow and transport processes, which might shed light on understanding many practical geophysical problems, for example, geothermal energy exploration.     

Electrokinetic Migration of Nitrate Through Heterogeneous Granular Porous Media

This study investigates and quantifies the influence of physical heterogeneity in granular porous media, represented by materials with different hydraulic conductivity, on the migration of nitrate, used as an amendment to enhance bioremediation, under an electric field. Laboratory experiments were conducted in a bench‐scale test cell under a low applied direct current using glass bead and clay mixes and synthetic groundwater to represent ideal conditions. The experiments included bromide tracer tests in homogeneous settings to deduce controls on electrokinetic transport of inorganic solutes in the different materials, and comparison of nitrate migration under homogeneous and heterogeneous scenarios. The results indicate that physical heterogeneity of subsurface materials, represented by a contrast between a higher‐hydraulic conductivity and lower‐hydraulic conductivity material normal to the direction of the applied electric field exerts the following controls on nitrate migration: (1) a spatial change in nitrate migration rate due to changes in effective ionic mobility and subsequent accumulation of nitrate at the interface between these materials; and (2) a spatial change in the voltage gradient distribution across the hydraulic conductivity contrast, due to the inverse relationship with effective ionic mobility. These factors will contribute to higher mass transport of nitrate through low hydraulic conductivity zones in heterogeneous porous media, relative to homogeneous host materials. Overall electrokinetic migration of amendments such as nitrate can be increased in heterogeneous granular porous media to enhance the in situ bioremediation of organic contaminants present in low hydraulic conductivity zones.     

Uncertainty estimation of pathlines in ground water models

A method is proposed to estimate the uncertainty of the location of pathlines in two-dimensional, steady-state confined or unconfined flow in aquifers due to the uncertainty of the spatially variable unconditional hydraulic conductivity or transmissivity field. The method is based on concepts of the semianalytical first-order theory given in Stauffer et al. (2002, 2004), which allows estimates of the lateral second moment (variance) of the location of a moving particle. However, this method is reformulated in order to account for nonuniform recharge and nonuniform aquifer thickness. One prominent application is the uncertainty estimation of the catchment of a pumping well by considering the boundary pathlines starting at a stagnation point. In this method, the advective transport of particles is considered, based on the velocity field. In the case of a well catchment, backtracking is applied by using the reversed velocity field. Spatial variability of hydraulic conductivity or transmissivity is considered by taking into account an isotropic exponential covariance function of log-transformed values with parameters describing the variance and correlation length. The method allows postprocessing of results from ground water models with respect to uncertainty estimation. The code PPPath, which was developed for this purpose, provides a postprocessing of pathline computations under PMWIN, which is based on MODFLOW. In order to test the methodology, it was applied to results from Monte Carlo simulations for catchments of pumping wells. The results correspond well. Practical applications illustrate the use of the method in aquifers.     

Combining 3D Hydraulic Tomography with Tracer Tests for Improved Transport Characterization

Hydraulic tomography (HT) is a method for resolving the spatial distribution of hydraulic parameters to some extent, but many details important for solute transport usually remain unresolved. We present a methodology to improve solute transport predictions by combining data from HT with the breakthrough curve (BTC) of a single forced‐gradient tracer test. We estimated the three dimensional (3D) hydraulic‐conductivity field in an alluvial aquifer by inverting tomographic pumping tests performed at the Hydrogeological Research Site Lauswiesen close to Tübingen, Germany, using a regularized pilot‐point method. We compared the estimated parameter field to available profiles of hydraulic‐conductivity variations from direct‐push injection logging (DPIL), and validated the hydraulic‐conductivity field with hydraulic‐head measurements of tests not used in the inversion. After validation, spatially uniform parameters for dual‐domain transport were estimated by fitting tracer data collected during a forced‐gradient tracer test. The dual‐domain assumption was used to parameterize effects of the unresolved heterogeneity of the aquifer and deemed necessary to fit the shape of the BTC using reasonable parameter values. The estimated hydraulic‐conductivity field and transport parameters were subsequently used to successfully predict a second independent tracer test. Our work provides an efficient and practical approach to predict solute transport in heterogeneous aquifers without performing elaborate field tracer tests with a tomographic layout.     

Sensitivity analysis of hydraulic conductivity and Manning's n parameters lead to new method to scale effective hydraulic conductivity across model resolutions

Hydrological modelling is an important tool for research, policy, and management, but uncertainty remains about parameters transferability from field observations made at small scale to models at the catchment scale and larger. This uncertainty compels the need to develop parameter relationships that are translatable across scale. In this study, we compare the changes to modelled processes as resolution is coarsened from 100‐m to 1‐km in a topographically complex, 255‐km² Colorado River headwater catchment. We conducted a sensitivity analysis for hydraulic conductivity (K) and Manning's n parameters across four orders of magnitude. Results showed that K acts as a moderator between surface and subsurface contributions to streamflow, whereas n moderates the duration of high intensity, infiltration‐excess flow. The parametric sensitivity analysis informed development of a new method to scale effective hydraulic conductivity across modelling resolutions in order to compensate for the loss of topographic gradients as resolution is coarsened. A similar mathematical relationship between n and lateral resolution changes was not found, possibly because n is also sensitive to time discretization. This research provides an approach to translate hydraulic conductivity parameters from a calibrated coarse model to higher resolutions where the number of simulations are limited by computational demand.     

Groundwater–surface water interaction in Lake Nasser,Southern Egypt

A cross‐sectional model, based on the two dimensional groundwater flow equation of Edelman, was applied at seven transects distributed over four geological cross sections to estimate groundwater heads and recharge from/or groundwater discharge to Lake Nasser. The lake with a length of 500 km and an average width of 12 km was created over the period 1964–1970, the time for constructing the Aswan High Dam (AHD). The model, constrained by regional‐scale groundwater flow and groundwater head data in the vicinity of the lake, was successfully calibrated to timeseries of piezometeric heads collected at the cross sections in the period 1965–2004. Inverse modeling yielded high values for the horizontal hydraulic conductivity in the range of 6.0 to 31.1 m day^?1 and storage coefficient between 0.01 and 0.40. The results showed the existence of a strong vertical anisotropy of the aquifer. The calibrated horizontal permeability is systematically higher than the vertical permeability (≈1000:1). The calibrated model was used to explore the recharge from/or groundwater discharge to Lake Nasser at the seven transects for a 40‐year period, i.e. from 1965 to 2004. The analysis for the last 20‐year period, 1985–2004, revealed that recharge from Lake Nasser reduced by 37% compared to the estimates for the first 20‐year period, 1965–1984. In the period 1965–2004, seepage of Lake Nasser to the surrounding was estimated at 1.15 × 10⁹ m³ year^?1. This led to a significant rise of the groundwater table. Variance‐based sensitivity and uncertainty analysis on the Edelman results were conducted applying quasi‐Monte Carlo sequences (Latin Hypercube sampling). The maximum standard deviation of the total uncertainty on the groundwater table was 0.88 m at Toshka (west of the lake). The distance from the lake, followed by the storage coefficient and hydraulic conductivity, were identified as the most sensitive parameters. Copyright © 2012 John Wiley & Sons, Ltd.     

Effects of experimental uncertainty on the calculation of hillslope flow paths

Measurement uncertainty is a key hindrance to the quantification of water fluxes at all scales of investigation. Predictions of soil‐water flux rely on accurate or representative measurements of hydraulic gradients and field‐state hydraulic conductivity. We quantified the potential magnitude of errors associated with the parameters and variables used directly and indirectly within the Darcy – Buckingham soil‐water‐flux equation. These potential errors were applied to a field hydrometric data set collected from a forested hillslope in central Singapore, and their effect on flow pathway predictions was assessed. Potential errors in the hydraulic gradient calculations were small, approximately one order of magnitude less than the absolute magnitude of the hydraulic gradients. However, errors associated with field‐state hydraulic conductivity derivation were very large. Borehole (Guelph permeameter) and core‐based (Talsma ring permeameter) techniques were used to measure field‐saturated hydraulic conductivity. Measurements using these two approaches differed by up to 3\9 orders of magnitude, with the difference becoming increasingly marked within the B horizon. The sensitivity of the shape of the predicted unsaturated hydraulic conductivity curve to ±5% moisture content error on the moisture release curve was also assessed. Applied moisture release curve error resulted in hydraulic conductivity predictions of less than ±0\2 orders of magnitude deviation from the apparent conductivity. The flow pathways derived from the borehole saturated hydraulic conductivity approach suggested a dominant near‐surface flow pathway, whereas pathways calculated from the core‐based measurements indicated vertical percolation to depth. Direct tracer evidence supported the latter flow pathway, although tracer velocities were approximately two orders of magnitude smaller than the Darcy predictions. We conclude that saturated hydraulic conductivity is the critical hillslope hydrological parameter, and there is an urgent need to address the issues regarding its measurement further. Copyright © 2000 John Wiley & Sons, Ltd.     

Unsaturated flows in soils with self-similar hydraulic conductivity distribution

In this article, we are concerned with the statistics of steady unsaturated flow in soils with a fractal hydraulic conductivity distribution. It is assumed that the spatial distribution of log hydraulic conductivity can be described as an isotropic stochastic fractal process. The impact of the fractal dimension of this process, the soil pore-size distribution parameter, and the characteristic length scale on the variances of tension head and the effective conductivity is investigated. Results are obtained for one-dimensional and three-dimensional flows. Our results indicate that the tension head variance is scale-dependent for fractal distribution of hydraulic conductivity. Both tension head variance and effective hydraulic conductivity depend strongly on the fractal dimension. The soil pore-size distribution parameter is important in reducing the variability of the unsaturated hydraulic conductivity and of the fluxes.     

Scale effect and calibration of contaminant transport models

The influence on solute transport of the small-scale spatial variation of aquifer hydraulic conductivity (K) was analyzed by comparing results from fine-grid (2 m by 2 m) simulations of a synthetic heterogeneous aquifer to those from coarse-grid (8 m by 4 m) simulations of an equivalent homogeneous aquifer. Realizations of the K field of the heterogeneous aquifer were generated, using the Monte Carlo approach, from a lognormal distribution with mean log K of 2 (K in m/d) and three levels of log K variance of 0.1, 0.5, and 1.0. Numerical simulation results show that the average standard deviation of point concentrations increased from 1.21 to 5.78 when the value of log K variance was increased from 0.1 to 1.0. The average discrepancy between modeled concentrations (obtained from a coarse-grid deterministic numerical simulation) and the actual mean point concentrations (obtained from fine-grid Monte Carlo numerical simulations) increased from 0.91 to 4.23 with the increase in log K variance. The results from this study illustrate the uncertainty in predictions from contaminant transport models due to their inability to simulate the effects of heterogeneities at scales smaller than the model grid.     

Uncertainty in applying the linear poroelasticity model to field situations as a result of periodic loading in heterogeneous aquifers

The solid Earth's surface frequently experience changes in total stresses as a result of periodic loading. When the fluid‐saturated porous media deform in response to changes in stress, the induced variations in pore volume affect the pore water pressure. The fluid flow therefore occurs in response to the gradient in the induced excess pore water pressure. This work aims at quantifying the spatial variability in excess pressure head produced by the periodic loading accounting for the variation of log hydraulic conductivity (lnK). It is important for the rational management of groundwater resources. A closed‐form expression is developed by the nonstationary spectral approach to analyse the influence of the statistical properties of lnK process, the hydraulic parameters, and the spatial position. The general stochastic framework outlined in this work provides a basis for assessing the impact of statistical properties of input aquifer parameters on the output variability (or uncertainty). Copyright © 2014 John Wiley & Sons, Ltd.     

Correlation between bacterial attachment rate coefficients and hydraulic conductivity and its effect on field-scale bacterial transport

It has been widely observed in field experiments that the apparent rate of bacterial attachment, particularly as parameterized by the collision efficiency in filtration-based models, decreases with transport distance (i.e., exhibits scale-dependency). This effect has previously been attributed to microbial heterogeneity; that is, variability in cell–surface properties within a single monoclonal population. We demonstrate that this effect could also be interpreted as a field-scale manifestation of local-scale correlation between physical heterogeneity (hydraulic conductivity variability) and reaction heterogeneity (attachment rate coefficient variability). A field-scale model of bacterial transport developed for the South Oyster field research site located near Oyster, Virginia, and observations from field experiments performed at that site, are used as the basis for this study. Three-dimensional Monte Carlo simulations of bacterial transport were performed under four alternative scenarios: (1) homogeneous hydraulic conductivity (K) and attachment rate coefficient (K_f); (2) heterogeneous K, homogeneous K_f; (3) heterogeneous K and K_f with local correlation based on empirical and theoretical relationships; and (4) heterogeneous K and K_f without local correlation. The results of the 3D simulations were analyzed using 1D model approximations following conventional methods of field data analysis. An apparent decrease with transport distance of effective collision efficiency was observed only in the case where the local properties were both heterogeneous and correlated. This effect was observed despite the fact that the local collision efficiency was specified as a constant in the 3D model, and can therefore be interpreted as a scale effect associated with the local correlated heterogeneity as manifested at the field scale.     

Variability of volume strain in bounded heterogeneous media

The deformation of the solid matrix affects the fluid pore pressure and flow by altering the pore volume. Such interaction in turn affects the storage of groundwater in the void space. Obviously, this subject is of interest in groundwater hydrology. This paper describes an investigation of the effect of aquifer heterogeneity on the variability of the fluid pressure head and solid's volume strain, where the assumption of a constant vertical total stress leads to a relatively simple relationship between changes in solid's volume strain and fluid pressure head. To solve the problem analytically, focus is placed on the one‐dimensional models. It is found from our closed‐form solutions that the variance and correlation length of the log hydraulic conductivity are important in increasing the variability of pressure head and solid's volume strain. It is hoped that our findings will provide a basic framework for understanding and quantifying field‐scale volume strain processes and be useful in stimulating further research in this area. Copyright © 2011 John Wiley & Sons, Ltd.     

Hydraulic conductivity in upland blanket peat: measurement and variability

A key parameter used in wetland hydrological and landform development models is hydraulic conductivity. Head recovery tests are often used to measure hydraulic conductivity, but the calculation techniques are usually confined to rigid soil theory. This is despite reports demonstrating the misapplication of rigid soil theory to non‐rigid soils such as peats. Although values of hydraulic conductivity calculated using compressible techniques have been presented for fenland peats, these data have never, to the authors' knowledge, been compared with such calculations in other peat types. Head recovery tests (slug withdrawal) were performed on piezometers at depths ranging from 10 to 80 cm from the surface on north Pennines blanket peats. Results were obtained using both rigid and compressible soil theories, thus allowing comparison of the two techniques. Compressible soil theory gives values for hydraulic conductivity that are typically a factor of five times less than rigid soil calculations. Hydraulic conductivity is often assumed to decrease with depth in upland peats, but at the study site in the northern Pennines it was not found to vary significantly with depth within the range of peat depths sampled. The variance within depth categories was not significantly different to the variance between depth categories showing that individual peat layers did not have characteristic hydraulic conductivity values. Thus, large lateral and vertical differences in hydraulic conductivity over short distances create problems for modelling but may help account for the high frequency of preferential flow pathways within what is otherwise a low matrix hydraulic conductivity peat. Hydraulic conductivity was found to vary significantly between sampling sites, demonstrating that hillslope‐ or catchment‐scale variability may be more important than plot‐scale variability. Values for compressibility of the peats are also reported. These generally decline with depth, and they also vary significantly between sampling sites. There are implications for the way in which measurements of hydraulic conductivity and other properties of blanket peat are interpreted, as the effects of environmental change in one part of a peat catchment may be very different to those in another. Copyright © 2002 John Wiley & Sons, Ltd.     

Synergistic effects of water repellency and macropore flow on the hydraulic conductivity of a burned forest soil,south‐east Australia

Research shows that water repellency is a key hydraulic property that results in reduced infiltration rates in burned soils. However, more work is required in order to link the hydrological behaviour of water repellent soils to observed runoff responses at the plot and hillslope scale. This study used 5 M ethanol and water in disc infiltrometers to quantify the role of macropore flow and water repellency on spatial and temporal infiltration patterns in a burned soil at plot (<10 m²) scale in a wet eucalypt forest in south‐east Australia. In the first summer and winter after wildfire, an average of 70% and 60%, respectively, of the plot area was water repellent and did not contribute to infiltration. Macropores (r > 0·5 mm), comprising just 5·5% of the soil volume, contributed to 70% and 95%, respectively, of the field‐saturated and ponded hydraulic conductivity (K_p). Because flow occurred almost entirely via macropores in non‐repellent areas, this meant that less than 2·5% of the soil surface effectively contributed to infiltration. The hydraulic conductivity increased by a factor of up to 2·5 as the hydraulic head increased from 0 to 5 mm. Due to the synergistic effect of macropore flow and water repellency, the coefficient of variation (CV) in K_p was three times higher in the water‐repellent soil (CV = 175%) than under the simulated non‐repellent conditions (CV = 66%). The high spatial variability in K_p would act to reduce the effective infiltration rate during runoff generation at plot scale. Ponding, which tend to increase with increasing scale, activates flow through macropores and would raise the effective infiltration rates at larger scales. Field experiments designed to provide representative measurements of infiltration after fire in these systems must therefore consider both the inherent variability in hydraulic conductivity and the variability in infiltration caused by interactions between surface runoff and hydraulic conductivity. Copyright © 2010 John Wiley & Sons, Ltd.