Multi-step and two-step experiments in heterogeneous porous media to evaluate the relevance of dynamic effects

The determination of hydraulic properties in non-stationary experiments is suspected to be affected by dynamic effects. This is based on thermodynamic considerations on the pore scale displacement of wetting and non-wetting phase. But also macroscopic heterogeneities at the continuum scale may influence the dynamics of water during drainage and wetting. In this paper we investigate both aspects. Firstly, we present the results of typical multi-step outflow experiments in heterogeneous sand columns which are compared with two-step outflow experiments covering the same pressure range. The discrepancies caused by pressure steps of different size reveal the impact of dynamic effects due to the non-stationarity of the experiments.     

Validity limits for the van Genuchten–Mualem model and implications for parameter estimation and numerical simulation

The calculation of the relative hydraulic conductivity function based on water retention data is an attractive and widely used approach, since direct measurements of unsaturated conductivities are difficult. We show theoretically under which conditions an air-entry value for water retention data is definitely required when using the statistical approach of Mualem. Moreover we rigorously specify the conditions for which the classical van Genuchten–Mualem model leads to wrong predictions of relative hydraulic conductivity and, hence, an alternative formulation including an air-entry value should be used. Significant consequences are demonstrated for the inverse parameter estimation based on multistep outflow experiments. Furthermore it is shown that the use of a physically correct formulation of the water retention curve including an air-entry value and the derived hydraulic conductivity function influences not only the stability of numerical simulations but also their final results. This is especially grave as simulations with van Genuchten–Mualem parameters are frequently used to compare experiments and simulations and to draw conclusions on the correctness of Richards’ equation.     

Comparison of Galerkin-type discretization techniques for two-phase flow in heterogeneous porous media

A comparison of Standard Galerkin, Petrov-Galerkin, and Fully-Upwind Galerkin methods for the simulation of two-phase flow in heterogeneous porous media is presented. On the basis of the coupled pressure-saturation equations, a generalized formulation for all three finite element methods is derived and analysed. For flow in homogeneous media, the Petrov-Galerkin method gives excellent results. But this method fails miserably for problems with heterogeneous media. This is because it is not able to capture correctly processes that take place at interfaces when, for instance, the capillary pressure-saturation relationship after Brooks and Corey is assumed. The Fully-Upwind Galerkin method is superior to the Petrov-Galerkin approach because it is able to give correct results for flow in homogeneous and heterogeneous media for the two models of van Genuchten and Brooks-Corey. The widely used formulation which is correct for the homogeneous case cannot be used for heterogeneous media. Instead the straightforward approach of gradp_c in combination with a chord-slope technique must be utilized.     

Hydrologic response of engineered media in living roofs and bioretention to large rainfalls: experiments and modeling

The hydrologic response of engineered media plays an important role in determining a stormwater control measure's ability to reduce runoff volume, flow rate, timing, and pollutant loads. Five engineered media, typical of living roof and bioretention stormwater control measures, were investigated in laboratory column experiments for their hydrologic responses to steady, large inflow rates. The inflow, medium water content response, and outflow were all measured. The water flow mechanism (uniform flow vs. preferential flow) was investigated by analyzing medium water content response in terms of timing, magnitude, and sequence with depth. Modeling the hydrologic process was conducted in the HYDRUS‐1D software, applying the Richards equation for uniform flow modeling, and a mobile–immobile model for preferential flow modeling. Uniform flow existed in most cases, including all initially dry living roof media with bimodal pore size distributions and one bioretention medium with unimodal pore size distribution. The Richards equation can predict the outflow hydrograph reasonably well for uniform flow conditions when medium hydraulic properties are adequately represented by appropriate functions. Preferential flow was found in two media with bimodal pore size distributions. The occurrence of preferential flow is more likely due to the interaction between the bimodal pore structure and the initial water content rather than the large inflow rate.     

油水两相渗流多孔介质弹性波传播动力学模型研究

弹性波在储层渗流场中的传播与衰减规律是研究波场强化采油动力学机理的重要基础.基于等效流体理论和饱和静态流体弹性波传播Biot理论,建立油水两非混相流体渗流条件下储层多孔介质中弹性波传播的动力学模型,通过算例求解与分析,发现含油水两相渗流储层多孔介质中同时存在着3种纵波P1、P2、P3和1种横波S;受频率和含水饱和度的影响,各波波速和品质因子呈现出不同变化规律,4种体波波速与频率、饱和度正相关,P1、P2波品质因子与饱和度正相关,P3和S波品质因子与饱和度负相关;最后,通过与传统静态弹性波模型结果对比,进一步分析了宏观渗流场对弹性波传播特征的影响规律,为揭示低频人工地震波辅助强化采油技术的动力学机理和工艺参数优化提供了重要理论依据.

     

Models of sub-grid variability in numerical simulations of solute transport in heterogeneous porous formations: three-dimensional flow and effect of pore-scale dispersion

Modeling transport of contaminants in the earths subsurface relies on numerical solutions over grids with blocks larger than Darcys scale. The hydraulic conductivity is homogenized over the grid blocks and the plumes spreading is reduced as a consequence of the wiped-out variability. To compensate for this loss Rubin et al. (1999) proposed to augment mixing by block-effective dispersion coefficients, and Rubin et al. (2003) showed, by means of two dimensional simulations, how this concept can be applied in practice. In this paper, we present new solutions of the block-effective dispersion tensor for an axisymmetric exponential covariance model. In addition, we discuss the influence of pore-scale dispersion in both two- and three-dimensional applications.     

Wave-induced dynamic response of saturated multi-layer porous media: Analytical solutions and validity regions of various formulations in non-dimensional parametric space

In this paper, dynamic response of saturated-layered porous media under harmonic waves is evaluated through a semi-analytical solution. The coupled differential equations governing the dynamics of saturated or nearly saturated porous media such as soils containing all the inertial terms of solid and fluid phases are presented for a multi-layer system. Possible simplifications of the equations which are called formulations are introduced based upon the presence of inertial terms associated with the phases. The semi-analytical solutions to the response of multiple layers for all the formulations are presented in terms of pore water pressure and stress variations considering a set of non-dimensional parameters and their respective ratios. Validity of the formulations is presented in a non-dimensional parametric space. The maximum discrepancies in the pore pressure response of the formulations leading to validity regions are illustrated for typical dynamic problems. Subsequently, the effects of layering and drainage conditions on these regions are also presented. The proposed semi-analytical solution may be served as a benchmark one for validating the coupled numerical solutions, which can be used to deal with real scientific and geo-engineering problems in the emerging field of computational geomechanics.     

Dynamics of deformation and water flow in heterogeneous porous media and its impact on soil properties

The interaction of geomechanics and flow within a soil body induces deformation and pore pressure change. Deformation may change hydrogeological and elastic properties, which alters the mechanical behaviour and results in non‐linearity. To investigate this interaction effect in a heterogeneous porous medium, a stochastic poroelastic model is proposed. Monte Carlo simulations are performed to determine the mean and uncertainty of the parameter changes, displacement, and change in pore water pressure. Hydraulic conductivity is treated as the only random variable in the coupled geomechanics‐flow system due to its large variation compared to other mechanical and hydrogeological properties in natural environments. The three considered non‐linear models for the interaction between parameters and deformation are those that consider (1) porosity and hydraulic conductivity; (2) porosity and Young's modulus; and (3) a combined effect that includes porosity, hydraulic conductivity, and Young's modulus. Boundary effects on the coupled system are also explored. The relationships between changes of porosity, hydraulic conductivity, and Young's modulus are analytically shown to be non‐linear. Among the considered parameters, the deformation effect induces the largest reduction in hydraulic conductivity. The deformation‐induced change in hydraulic conductivity shows the most significant effect on the mean and variance of the change in pore water pressure and displacement, while changes in Young's modulus have the least effect. When the deformation effect is considered, the superposition relationship does not exist in the mean displacement and mean change in pore water pressure for the three scenarios considered; it exists for the case without deformation effects. Deformation also causes a reduction in the effective hydraulic conductivity for the whole domain. The scenario that considers both loading and discharge boundaries has larger changes in hydrogeological and geo‐mechanical parameters than those in scenarios that consider loading and discharge boundaries separately. The results indicate that the interaction between deformation and changes in parameters has a profound effect on the poroelastic system. The effect of deformation should thus be considered in modelling and practice. Copyright © 2009 John Wiley & Sons, Ltd.     

From the pore scale to the lab scale: 3-D lab experiment and numerical simulation of drainage in heterogeneous porous media

A well-controlled 3-D experiment with pre-defined block heterogeneities is conducted, where neutron tomography is used to map 3-D water distribution after two successive drainage steps. The material and hydraulic properties of the two sands are first measured in the laboratory with multistep outflow experiments. Additionally, the pore structure of the sands is acquired by means of image analysis of synchrotron tomography data and the structure is used for pore-scale simulation of one- and two-phase flow with Lattice-Boltzmann methods. This gives us another set of material and hydraulic parameters of the sands. The two sets of hydraulic properties (from the lab scale and from the pore scale) are then used in numerical simulations of the 3-D experiment.     

Analysis of runoff–storage relationships to evaluate the runoff-buffering potential of a sloping permeable domain

The runoff–storage relationship for a runoff system in a steady-state is analyzed as an indicator of the buffering potential of rainfall-runoff responses. In this relationship, a large storage increase in response to a given runoff increase indicates high buffering potential in the water balance equation. The evaluation method is applied to a sloping permeable domain. A two-dimensional form of the Richards equation is used to calculate runoff and storage. Macropore existence is represented by an enlargement effect of hydraulic conductivity near saturation. The runoff–storage relationship is controlled by the distribution of hydraulic quantities. The distribution of a pressure-head value is approximately classified into the following three zones: the I zone with vertical unsaturated flow, the U zone with unsaturated downslope flow, and the S zone with saturated downslope flow. The runoff-buffering potential is systematically evaluated by dependencies of the runoff–storage relationship on the classification of the pressure-head distribution. The potential is generally high for soil with a high permeability, but rather small in the range of low runoff rates where the S zone is not created. The macropore effect causes the range of high buffering potential to shift to high runoff rates through enlargement of the I zone. As a result, a moderate magnitude of the macropore effect gives the maximum increase in storage in response to a given increase in runoff.     

Divergence and flow direction as indicators of subsurface heterogeneity and stage‐dependent storage in alluvial floodplains

Assuming homogeneity in alluvial aquifers is convenient, but limits our ability to accurately predict stream‐aquifer interactions. Research is needed on (i) identifying the presence of focused, as opposed to diffuse, groundwater discharge/recharge to streams and (ii) the magnitude and role of large‐scale bank and transient storage in alluvial floodplains relative to changes in stream stage. The objective of this research was to document and quantify the effect of stage‐dependent aquifer heterogeneity and bank storage relative to changes in stream stage using groundwater flow divergence and direction. Monitoring was performed in alluvial floodplains adjacent to the Barren Fork Creek and Honey Creek in northeastern Oklahoma. Based on results from subsurface electrical resistivity mapping, observation wells were installed in high and low electrical resistivity subsoils. Water levels in the wells were recorded real time using pressure transducers (August to October 2009). Divergence was used to quantify heterogeneity (i.e. variation in hydraulic conductivity, porosity, and/or aquifer thickness), and flow direction was used to assess the potential for large‐scale (100 m) bank or transient storage. Areas of localized heterogeneity appeared to act as divergence zones allowing stream water to quickly enter the groundwater system, or as flow convergence zones draining a large groundwater area. Maximum divergence or convergence occurred with maximum rates of change in flow rates or stream stage. Flow directions in the groundwater changed considerably between base and high flows, suggesting that the floodplains acted as large‐scale bank storage zones, rapidly storing and releasing water during passage of a storm hydrograph. During storm events at both sites, the average groundwater direction changed by at least 90° from the average groundwater direction during baseflow. Aquifer heterogeneity in floodplains yields hyporheic flows that are more responsive and spatially and temporally complex than would be expected compared to more common assumptions of homogeneity. Copyright © 2012 John Wiley & Sons, Ltd.     

Anisotropy and depth‐related heterogeneity of hydraulic conductivity in a bog peat. II: modelling the effects on groundwater flow

Anisotropy and heterogeneity of hydraulic conductivity (K) are seldom considered in models of mire hydrology. We investigated the effect of anisotropy and heterogeneity on groundwater flow in bog peat using a steady‐state groundwater model. In five model simulations, four sets of K data were used. The first set comprised measured K values from an anisotropic and heterogeneous bog peat. These data were aggregated to produce the following simplified data sets: an isotropic and heterogeneous distribution of K; an isotropic and homogeneous distribution; and an anisotropic and homogeneous distribution. We demonstrate that, where anisotropy and heterogeneity exist, groundwater flow in bog peat is complex. Fine‐scale variations in K have the potential to influence patterns and rates of groundwater flow. However, for our data at least, it is heterogeneity and not anisotropy that has the greater influence on producing complex patterns of groundwater flow. We also demonstrate that patterns and rates of groundwater flow are simplified and reduced when measured K values are aggregated to create a more uniform distribution of K. For example, when measured K values are aggregated to produce isotropy and homogeneity, the rate of modelled seepage is reduced by 28%. We also show that when measured K values are used, the presence of a drainage ditch can increase seepage through a modelled cross‐section. Our work has implications for the accurate interpretation of hydraulic head data obtained from peat soils, and also the understanding of the effect of drainage ditches on patterns and rates of groundwater flow. Copyright © 2002 John Wiley & Sons, Ltd.     

Pore-scale characteristics of multiphase flow in porous media: A comparison of air–water and oil–water experiments

Studies of NAPL dissolution in porous media have demonstrated that measurement of saturation alone is insufficient to describe the rate of dissolution. Quantification of the NAPL–water interfacial area provides a measure of the expected area available for mass transfer and will likely be a primary determinant of NAPL removal efficiency. To measure the interfacial area, we have used a synchrotron-based CMT technique to obtain high-resolution 3D images of flow in a Soltrol–water–glass bead system. The interfacial area is found to increase as the wetting phase saturation decreases, reach a maximum, and then decrease as the wetting phase saturation goes to zero. These results are compared to previous findings for an air–water–glass bead study; The Soltrol–water interfacial areas were found to peak at similar saturations as those measured for the air–water system (20–35% saturation range), however, the peak values were in some cases almost twice as high for the oil-water system. We believe that the observed differences between the air–water and oil–water systems to a large degree can be explained by the differences in interfacial tensions for the two systems.     

Reactive transport in unsaturated soil: Comprehensive modelling of the dynamic spatial and temporal mass balance of water and chemical components

By implementing the moisture-based form of Richards’ equation into the geochemical modelling framework PHREEQC, a generic tool for the simulation of one-dimensional flow and solute transport in the vadose zone undergoing complex geochemical reactions was developed. A second-order, cell-centred, explicit finite difference scheme was employed for the numerical solution of the partial differential equations of flow and transport. In this scheme, the charge-balanced soil solution is treated as an assembly of elements, where changes in water and solute contents result from fluxes of elements across cell boundaries. Therefore, water flow is considered in terms of oxygen and hydrogen transport.     

On the use of finite‐difference and neural‐network models to evaluate the impact of underground water overexploitation

The purpose of this study is to include expert knowledge as one part of the modelling system and thereby offer the chance to create a productive interactive system between expert, mathematical model, ASM, and artificial neural networks (ANNs). An attempt to determine outflow‐influencing parameters in order to simulate spring flow is presented. The Bouteldja dune aquifer is fed by rains and streaming water on the sandy argillaceous relieves in the Est. The lateral passage to the gravel of the Bouteldja Plain is marked by numerous bogs that correspond to the piezometric level. These bogs have long been an environment for migratory birds and a natural reserve for many species. However, the continued exploitation of about 30 wells has negatively influenced the hydrodynamic equilibrium of the aquifer and has brought a diminution of the sources' capacity. In this study, we tried by using a hydrodynamic model and the neural network to ascertain the state of the resources and to identify the factors responsible for the decreasing flows of the three principal springs of the area (Bougles, Bourdim and Titteri) by using neural networks. The results obtained show a continued exhaustion of the reserve since 1986 with a large cone of depression. The ANNs show that the decrease in flows of the springs is not only due to the unfavourable climatic conditions, but also to the intensive exploitation of the aquifer. These results show that the groundwater reserves are decreasing over time, thus highlighting the need to take some urgent measures to stop this phenomenon. Copyright © 2006 John Wiley & Sons, Ltd.     

Hydraulic properties of concentrated flow of a bank gully in the dry‐hot valley region of southwest China

To quantify spatiotemporal variation in hydraulic properties of bank gully concentrated flow, a series of scour experiments were run under water discharge rates ranging from 30 to 120 l min^?1. Concentrated flows were found to be turbulent and supercritical in the upstream catchment area and downstream gully beds. As discharge increased, values of the soil erosion rate, Reynolds number (Re), shear stress, stream power, and flow energy consumption (ΔE) increased while values of the Froude number (Fr) and the Darcy–Weisbach friction factor (resistance f ) did not. With the exception of gully headcut collapse under discharge rates of 60, 90, and 120 l min^?1, a declining power function trend (P < 0.05) in the soil erosion rate developed in the upstream catchment area, headcuts, and downstream gully beds. However, increasing trends were observed in temporal variations of hydraulic properties for downstream gully beds and the upstream catchment area. Despite significant differences in temporal variation between the soil erosion rate and hydraulic property values, relative steady state conditions of the soil erosion rate and ΔE were attained following an initial period of adjustment in the upstream catchment area, headcuts, and downstream gully beds under different discharge rates. A logarithmic growth of flow energy consumption per unit soil loss (ΔE_u) was observed in bank gullies and the upstream catchment area as the experiment progressed, further illustrating the actual reason behind the discrepancy in temporal variation between soil erosion rates and ΔE. Results demonstrate that ΔE can be used to estimate headcut erosion soil loss, but further quantitative studies are required to quantify coupling effects between hydraulic properties and vertical variation in soil mechanical properties on temporal variation for bank gully soil erosion rates. Copyright © 2015 John Wiley & Sons, Ltd.     

Using a pore‐scale model to quantify the effect of particle re‐arrangement on pore structure and hydraulic properties

A pore‐scale model based on measured particle size distributions has been used to quantify the changes in pore space geometry of packed soil columns resulting from a dilution in electrolyte concentration from 500 to 1 mmol l^?1 NaCl during leaching. This was applied to examine the effects of particle release and re‐deposition on pore structure and hydraulic properties. Two different soils, an agricultural soil and a mining residue, were investigated with respect to the change in hydraulic properties. The mining residue was much more affected by this process with the water saturated hydraulic conductivity decreasing to 0·4% of the initial value and the air‐entry value changing from 20 to 50 cm. For agricultural soil, there was little detectable shift in the water retention curve but the saturated hydraulic conductivity decreased to 8·5% of the initial value. This was attributed to localized pore clogging (similar to a surface seal) affecting hydraulic conductivity, but not the microscopically measured pore‐size distribution or water retention. We modelled the soil structure at the pore scale to explain the different responses of the two soils to the experimental conditions. The size of the pores was determined as a function of deposited clay particles. The modal pore size of the agricultural soil as indicated by the constant water retention curve was 45 µm and was not affected by the leaching process. In the case of the mining residue, the mode changed from 75 to 45 µm. This reduction of pore size corresponds to an increase of capillary forces that is related to the measured shift of the water retention curve. Copyright © 2007 John Wiley & Sons, Ltd.     

Influence of aquifer properties and the spatial and temporal distribution of recharge and abstraction on sustainable yields in semi‐arid regions

This paper aims to contribute to understanding the importance of four factors on the determination of sustainable yields: (i) aquifer properties; (ii) temporal distribution of recharge; (iii) temporal distribution of groundwater pumping; and (iv) spatial distribution of pumping wells. It is important to comprehend how the present‐day and future vulnerability of groundwater systems to pumping activities depend on these critical factors and what the risks are of considering sustainable yield as a fixed percentage of mean annual recharge (MAR). A numerical model of the Querença–Silves aquifer in Portugal is used to develop hypothetical scenarios with which these factors are studied. Results demonstrate the aquifer properties, particularly the storage coefficient, have an important role in determining the resilience of an aquifer and therefore to which degree it is dependent on the spatial and temporal distribution of abstraction and recharge, as well as the occurrence of extreme events. Sustainable yields are determined for the developed scenarios based on specific criteria rather than a fraction of MAR. Under simplified current recharge and abstraction conditions, the sustainable yield was determined at approximately 73% of MAR or 76 million m³. When considering a concentration of rainfall in time, as predicted by climate scenarios for the region, sustainable yield could drop to ca 70% of MAR. However, a more even distribution of pumping volumes throughout the year could increase this value. The location of the pumping wells is seen to affect the distribution of hydraulic heads in the aquifer, albeit without significant changes in sustainable yield. Copyright © 2011 John Wiley & Sons, Ltd.     

Assessing the importance of seepage and springs to nitrate flux in a stream network in the Wisconsin sand plains

Evaluating the flow paths that contribute to solute flux in stream networks can lead to greater understanding of the linkages between biogeochemistry and hydrology. We compared the contributions of groundwater in spring brooks and in seepage through the streambed to nitrate flux in the Emmons Creek network in the Wisconsin sand plains. We predicted that spring brooks would contribute disproportionately to nitrate flux due to the presumed higher advection rates in springs and less opportunity for nitrate removal relative to seeps. Nitrate flux was measured in 15 spring brooks that entered Emmons Creek. Nitrate flux from seepage was measured at the locations of 30 piezometers, based on Darcy's Law, and by a reach‐scale injection of Rhodamine water tracing (RWT). When seepage discharge was estimated from the RWT release, groundwater inputs from seepage and springs accounted for the discharge gain in the Emmons Creek channel. Springs brooks and seepage (based on the RWT release) contributed 37% and 63%, respectively, to nitrate flux inputs in the study reach. Contrary to our prediction, seeps contributed disproportionately to nitrate flux relative to their discharge. Relatively high rates of seepage discharge and higher than anticipated nitrate concentrations in the shallow pore water at seepage locations contributed to the unanticipated result.