Clogging of saturated porous media by silt‐sized suspended solids under varying physical conditions during managed aquifer recharge

Managed aquifer recharge is an effective method for utilizing excess flood flows, but clogging of porous media is a limiting factor in the implementation of this water storage technique. In recent years, much research on the physical clogging of porous media during artificial recharge has been conducted. However, the understanding of clogging due to silt‐sized suspended solids (SS) is still inadequate, especially under varying physical conditions. Here, we subjected sand columns to controlled rates of flow and SS suspensions to investigate the influence of media size, SS size, SS concentration, and flow velocity on the clogging of porous media by silt‐sized SS. The results show that the diameter ratio of SS particles to sand grains is the dominant factor influencing the position of physical clogging. As pore velocity increased, the mobility of silt‐sized SS was enhanced and retention in the porous media decreased noticeably. The spatial retention profiles in the porous media were found to vary greatly at different flow velocities. The SS concentration of the infiltrating suspension also dramatically influenced the mobility and deposition of silt‐sized SS particles, such that high concentrations accelerated the clogging process. As the different physical factors changed, the breakthrough curves and retention profiles of silt‐sized SS particles changed obviously and the mechanisms of retention differed. On the whole, clogging position is mainly determined by particle size ratio, but clogging rate is dominated by a variety of factors including particle size ratio, SS concentration, and flow velocity.     

Approaches for modeling longitudinal dispersion in pore-networks

The purpose of this study is to quantify the dispersivity in the longitudinal direction by upscaling pore scale mixing over a network domain and to verify the dispersivity with that obtained through the more rigorous upscaling technique, the Brownian particle tracking model (BPTM). We model a porous medium with a network of pore-units that are comprised of pore bodies and bonds of finite volume. Such a pore-unit is assumed to be a mixing cell with the steady state flow condition for a single fluid. Dispersivity can be obtained by solving the mixing cell model (MCM) for the concentration in each pore-unit and by averaging the concentrations for a large number of pore units (as a function of time and space). A minimal size of network that ascertains an asymptotic value of dispersivity was determined and verified with large size pore networks. This numerically computed dispersivity is compared with the results from the BPTM for the same porous medium and flow conditions. We show that the dispersivity obtained from the MCM is equally reliable for the heterogeneous pore-networks and can be estimated as a function of pore size heterogeneity. For homogeneous networks with the MCM, the iteration time step plays an important role. On the other hand, for networks with the BPTM, the assumption of intra-bond velocity profile affects the results.     

Experimental investigation of suspended particles transport in porous medium under variable temperatures

This paper presents a study on suspended particle transport in porous medium with the aid of a sand layer transportation–deposition testing system to determine the kinetic characteristics of particles in porous medium under variable temperatures. Quartz sand and quartz powder were chosen as the porous medium and particle in the tests, respectively. Four size compositions and two operational modes, that is, temperature reduction mode (changing from 18°C to 5°C) and temperature increment mode (changing from 18°C to 35°C), were adopted. The turbidity and concentration of quartz powder were measured under various conditions. We observed a high temperature‐independent correlation between them. Breakthrough curves under different conditions were analysed using this testing system. The results showed that changes in temperature affected the particle transport process to some extent, and the degree of influence was closely related to the time moment of the temperature change onset. Moreover, we found a hysteresis phenomenon in the breakthrough curve under both temperature reduction and increment conditions. The results also indicated that the temperature effect was particularly significant for smaller particles. The typical curves to represent particle transport process under variable temperatures were put forward according to the results. To explain the test results, four factors, that is, water viscosity, adsorption effect, double layer force, and particle kinetic energy, were considered and categorized as promotion or constraining factors.     

Estimation of water saturation dependence of dispersion in unsaturated porous media: experiments and modelling analysis

In the dispersion theory, a linear relationship has been verified between the coefficient of hydrodynamic dispersion and water velocity, both in saturated and in unsaturated porous media. But for unsaturated soils the variability of flow directions and microscopic velocities can be larger than in saturated soils because of the lower degree of water saturation. This leads to an increased dispersion. Therefore, relationships between water content and relative water velocity fluctuations and water content together with the coefficient of dispersivity in unsaturated porous media respectively have been investigated systematically by displacement experiments in glass beads and coarse-textured sandy soil columns. The breakthrough curves (BTCs) of chloride showed that an increase of solute mixing with a decrease of water content was caused by an increase of flow velocity fluctuations for different pathways. In order to explain the observed tailing effect in unsaturated flow, two mathematical models were used to fit theoretically derived nonlinear functions of water content dependent dispersivities for both porous media. The close agreement between the observed and computed results suggests that the theoretical model of hydrodynamic dispersion can be extended to transport in unsaturated porous media, providing that BTCs of the effluent water are used to estimate representative dispersivity parameters of soils.     

Nonlocal transport models for capturing solute transport in one-dimensional sand columns: Model review,applicability, limitations and improvement

Modelling pollutant transport in water is one of the core tasks of computational hydrology, and various physical models including especially the widely used nonlocal transport models have been developed and applied in the last three decades. No studies, however, have been conducted to systematically assess the applicability, limitations and improvement of these nonlocal transport models. To fill this knowledge gap, this study reviewed, tested and improved the state-of-the-art nonlocal transport models, including their physical background, mathematical formula and especially the capability to quantify conservative tracers moving in one-dimensional sand columns, which represents perhaps the simplest real-world application. Applications showed that, surprisingly, neither the popular time-nonlocal transport models (including the multi-rate mass transfer model, the continuous time random walk framework and the time fractional advection-dispersion equation), nor the spatiotemporally nonlocal transport model (ST-fADE) can accurately fit passive tracers moving through a 15-m-long heterogeneous sand column documented in literature, if a constant dispersion coefficient or dispersivity is used. This is because pollutant transport in heterogeneous media can be scale-dependent (represented by a dispersion coefficient or dispersivity increasing with spatiotemporal scales), non-Fickian (where plume variance increases nonlinearly in time) and/or pre-asymptotic (with transition between non-Fickian and Fickian transport). These different properties cannot be simultaneously and accurately modelled by any of the transport models reviewed by this study. To bypass this limitation, five possible corrections were proposed, and two of them were tested successfully, including a time fractional and space Hausdorff fractal model which minimizes the scale-dependency of the dispersion coefficient in the non-Euclidean space, and a two-region time fractional advection-dispersion equation which accounts for the spatial mixing of solute particles from different mobile domains. Therefore, more efforts are still needed to accurately model transport in non-ideal porous media, and the five model corrections proposed by this study may shed light on these indispensable modelling efforts.     

Applicability of the Dual‐Domain Model to Nonaggregated Porous Media

More theoretical analysis is needed to investigate why a dual‐domain model often works better than the classical advection‐dispersion (AD) model in reproducing observed breakthrough curves for relatively homogeneous porous media, which do not contain distinct dual domains. Pore‐scale numerical experiments presented here reveal that hydrodynamics create preferential flow paths that occupy a small part of the domain but where most of the flow takes place. This creates a flow‐dependent configuration, where the total domain consists of a mobile and an immobile domain. Mass transfer limitations may result in nonequilibrium, or significant differences in concentration, between the apparent mobile and immobile zones. When the advection timescale is smaller than the diffusion timescale, the dual‐domain mass transfer (DDMT) model better captures the tailing in the breakthrough curve. Moreover, the model parameters (mobile porosity, mean solute velocity, dispersivity, and mass transfer coefficient) demonstrate nonlinear dependency on mean fluid velocity. The studied case also shows that when the Peclet number, Pe, is large enough, the mobile porosity approaches a constant, and the mass transfer coefficient can be approximated as proportional to mean fluid velocity. Based on detailed analysis at the pore scale, this paper provides a physical explanation why these model parameters vary in certain ways with Pe. In addition, to improve prediction in practical applications, we recommend conducting experiments for parameterization of the DDMT model at a velocity close to that of the relevant field sites, or over a range of velocities that may allow a better parameterization.     

Probabilistic sensitivity and modeling of two-dimensional transport in porous media

A reliability approach is used to develop a probabilistic model of two-dimensional non-reactive and reactive contaminant transport in porous media. The reliability approach provides two important quantitative results: an estimate of the probability that contaminant concentration is exceeded at some location and time, and measures of the sensitivity of the probabilistic outcome to likely changes in the uncertain variables. The method requires that each uncertain variable be assigned at least a mean and variance; in this work we also incorporate and investigate the influence of marginal probability distributions. Uncertain variables includex andy components of average groundwater flow velocity,x andy components of dispersivity, diffusion coefficient, distribution coefficient, porosity and bulk density. The objective is to examine the relative importance of each uncertain variable, the marginal distribution assigned to each variable, and possible correlation between the variables. Results utilizing a two-dimensional analytical solution indicate that the probabilistic outcome is generally very sensitive to likely changes in the uncertain flow velocity. Uncertainty associated with dispersivity and diffusion coefficient is often not a significant issue with respect to the probabilistic analysis; therefore, dispersivity and diffusion coefficient can often be treated for practical analysis as deterministic constants. The probabilistic outcome is sensitive to the uncertainty of the reaction terms for early times in the flow event. At later times, when source contaminants are released at constant rate throughout the study period, the probabilistic outcome may not be sensitive to changes in the reaction terms. These results, although limited at present by assumptions and conceptual restrictions inherent to the closed-form analytical solution, provide insight into the critical issues to consider in a probabilistic analysis of contaminant transport. Such information concerning the most important uncertain parameters can be used to guide field and laboratory investigations.     

Probabilistic sensitivity and modeling of two-dimensional transport in porous media

A reliability approach is used to develop a probabilistic model of two-dimensional non-reactive and reactive contaminant transport in porous media. The reliability approach provides two important quantitative results: an estimate of the probability that contaminant concentration is exceeded at some location and time, and measures of the sensitivity of the probabilistic outcome to likely changes in the uncertain variables. The method requires that each uncertain variable be assigned at least a mean and variance; in this work we also incorporate and investigate the influence of marginal probability distributions. Uncertain variables includex andy components of average groundwater flow velocity,x andy components of dispersivity, diffusion coefficient, distribution coefficient, porosity and bulk density. The objective is to examine the relative importance of each uncertain variable, the marginal distribution assigned to each variable, and possible correlation between the variables. Results utilizing a two-dimensional analytical solution indicate that the probabilistic outcome is generally very sensitive to likely changes in the uncertain flow velocity. Uncertainty associated with dispersivity and diffusion coefficient is often not a significant issue with respect to the probabilistic analysis; therefore, dispersivity and diffusion coefficient can often be treated for practical analysis as deterministic constants. The probabilistic outcome is sensitive to the uncertainty of the reaction terms for early times in the flow event. At later times, when source contaminants are released at constant rate throughout the study period, the probabilistic outcome may not be sensitive to changes in the reaction terms. These results, although limited at present by assumptions and conceptual restrictions inherent to the closed-form analytical solution, provide insight into the critical issues to consider in a probabilistic analysis of contaminant transport. Such information concerning the most important uncertain parameters can be used to guide field and laboratory investigations.     

Experimental study of ERT monitoring ability to measure solute dispersion

This paper reports experimental measurements performed to test the ability of electrical resistivity tomography (ERT) imaging to provide quantitative information about transport parameters in porous media such as the dispersivity α, the mixing front velocity u, and the retardation factor R(f) associated with the sorption or trapping of the tracers in the pore structure. The flow experiments are performed in a homogeneous porous column placed between two vertical set of electrodes. Ionic and dyed tracers are injected from the bottom of the porous media over its full width. Under such condition, the mixing front is homogeneous in the transverse direction and shows an S-shape variation in the flow direction. The transport parameters are inferred from the variation of the concentration curves and are compared with data obtained from video analysis of the dyed tracer front. The variations of the transport parameters obtained from an inversion performed by the Gauss-Newton method applied on smoothness-constrained least-squares are studied in detail. While u and R(f) show a relatively small dependence on the inversion procedure, α is strongly dependent on the choice of the inversion parameters. Comparison with the video observations allows for the optimization of the parameters; these parameters are found to be robust with respect to changes in the flow condition and conductivity contrast.     

Significance of particle interaction to the modelling of cohesive sediment transport in rivers

Aggregation processes of fine sediments have rarely been integrated in numerical simulations of cohesive sediment transport in riverine systems. These processes, however, can significantly alter the hydrodynamic characteristics of suspended particulate matter (SPM), modifying the particle settling velocity, which is one of the most important parameters in modelling suspended sediment dynamics. The present paper presents data from field measurements and an approach to integrate particle aggregation in a hydrodynamic sediment transport model. The aggregation term used represents the interaction of multiple sediment classes (fractions) with corresponding multiple deposition behaviour. The k–ε–turbulence model was used to calculate the coefficient of vertical turbulent mixing needed for the two‐dimensional vertical‐plane simulations. The model has been applied to transport and deposition of tracer particles and natural SPM in a lake‐outlet lowland river (Spree River, Germany). The results of simulations were evaluated by comparison with field data obtained for two levels of river discharge. Experimental data for both discharge levels showed that under the prevailing uniform hydraulic conditions along the river reach, the settling velocity distribution did not change significantly downstream, whereas the amount of SPM declined. It was also shown that higher flow velocities (higher fluid shear) resulted in higher proportions of fast settling SPM fractions. We conclude that in accordance with the respective prevailing turbulence structures, typical aggregation mechanisms occur that continuously generate similar distribution patterns, including particles that settle toward the river bed and thus mainly contribute to the observed decline in the total SPM concentration. In order to determine time‐scales of aggregation and related mass fluxes between the settling velocity fractions, results of model simulations were fitted to experimental data for total SPM concentration and of settling velocity frequency distributions. The comparison with simulations for the case of non‐interacting fractions clearly demonstrated the practical significance of particle interaction for a more realistic modelling of cohesive sediment and contaminant transport. Copyright © 2004 John Wiley & Sons, Ltd.     

冷泉形成的数值模拟研究

海底冷泉形成的一种可能机制是海平面下降引起天然气水合物的分解.本文基于对冷泉渗漏特征的分析,建立了二维轴对称模型,利用有限元方法定量分析了南海区域海平面下降对冷泉形成的影响.结果表明,末次冰盛期(26.5~19.0ka BP)海平面下降引起的冷泉活动可以持续到现在,但是从水合物停止分解至今,超孔隙压力的极值在持续减小,而流体向海底的渗漏达西速度先快速减小、然后缓慢减小.同时发现,流体向海底的渗漏达西速度与管状通道的渗透率、通道周围介质的渗透率以及通道的半径等有关,估计目前的冷泉活动还可以持续10000年以上.海平面下降引起的天然气水合物分解,可能是影响全球气候变化的一个重要因素.     

An equivalent medium model for wave simulation in fractured porous rocks

Seismic wave propagation in reservoir rocks is often strongly affected by fractures and micropores. Elastic properties of fractured reservoirs are studied using a fractured porous rock model, in which fractures are considered to be embedded in a homogeneous porous background. The paper presents an equivalent media model for fractured porous rocks. Fractures are described in a stress‐strain relationship in terms of fracture‐induced anisotropy. The equations of poroelasticity are used to describe the background porous matrix and the contents of the fractures are inserted into a matrix. Based on the fractured equivalent‐medium theory and Biot's equations of poroelasticity, two sets of porosity are considered in a constitutive equation. The porous matrix permeability and fracture permeability are analysed by using the continuum media seepage theory in equations of motion. We then design a fractured porous equivalent medium and derive the modified effective constants for low‐frequency elastic constants due to the presence of fractures. The expressions of elastic constants are concise and are directly related to the properties of the main porous matrix, the inserted fractures and the pore fluid. The phase velocity and attenuation of the fractured porous equivalent media are investigated based on this model. Numerical simulations are performed. We show that the fractures and pores strongly influence wave propagation, induce anisotropy and cause poroelastic behaviour in the wavefields. We observe that the presence of fractures gives rise to changes in phase velocity and attenuation, especially for the slow P‐wave in the direction parallel to the fracture plane.     

Virtual velocity of sand transport in water

Using the 160‐m‐long flume at Tsukuba University we undertook an experiment to provide a first estimate of the virtual velocity of sand in the size range 0.5–2.0 mm. For the flow velocity used in our experiment this sediment‐size range would conventionally be regarded as suspended sediment. The virtual velocity was found to be 37–41% of the flow velocity. Paradoxically, virtual velocity decreases as particle size decreases. Such a lower virtual velocity of finer sediment is not inconceivable. First, trapping of the sediment appears to be a function of bed roughness, and there is a probable relationship between bed roughness and trapping efficiency for particles of different sizes. Second, finer particles are more likely to find sheltered positions on a rough bed and thus experience lower mobility, relative to the more exposed coarser grains, as observed for bedload transport. Third, the virtual velocity of particles undergoing bedload transport has been found, in some instances, to be lower for finer clasts. We combine our data with previous studies of virtual velocity of bedload to develop, for the first time, a hypothesis for a holistic analysis of sediment movement in rivers. Copyright © 2017 John Wiley & Sons, Ltd.     

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。     

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.     

Observations of bedload transport in a gravel bed river during high flow using fiber‐optic DTS methods

The question: ‘how does a streambed change over a minor flood?’ does not have a clear answer due to lack of measurement methods during high flows. We investigate bedload transport and disentrainment during a 1.5‐year flood by linking field measurements using fiber optic distributed temperature sensing (DTS) cable with sediment transport theory and an existing explicit analytical solution to predict depth of sediment deposition from amplitude and phase changes of the diurnal near‐bed pore‐water temperature. The method facilitates the study of gravel transport by using near‐bed temperature time series to estimate rates of sediment deposition continuously over the duration of a high flow event coinciding with bar formation. The observations indicate that all gravel and cobble particles present were transported along the riffle at a relatively low Shields Number for the median particle size, and were re‐deposited on the lee side of the bar at rates that varied over time during a constant flow. Approximately 1–6% of the bed was predicted to be mobile during the 1.5‐year flood, indicating that large inactive regions of the bed, particularly between riffles, persist between years despite field observations of narrow zones of local transport and bar growth on the order ~3–5 times the median particle size. In contrast, during a seven‐year flood approximately 8–55% of the bed was predicted to become mobile, indicating that the continuous along‐stream mobility required to mobilize coarse gravel through long pools and downstream to the next riffle is infrequent. Copyright © 2017 John Wiley & Sons, Ltd.     

Shear dispersion in a fracture with porous walls

We present an analytical expression for the shear dispersion during solute transport in a coupled fracture–matrix system. The dispersion coefficient is obtained in a fracture with porous walls by taking into account an accurate boundary condition at the interface between the matrix and fracture, and the results were compared with those in a non-coupled system. The analysis presented identifies three regimes: diffusion-dominated, transition, and advection-dominated. The results showed that it is important to consider the exchange of solute between the fracture and matrix in development of the shear dispersion coefficient for the transition and advection-dominated regimes. The new dispersion coefficient is obtained by imposing the continuity of concentrations and mass fluxes along the porous walls. The resulting equivalent transport equation revealed that the effective velocity in a fracture increases while the dispersion coefficient decreases due to mass transfer between the matrix and fracture. A larger effective advection term leads to greater storage of mass in the matrix as compared with the classical double-porosity model with a non-coupled dispersion coefficient. The findings of this study can be used for modeling of tracer tests as well as fate, transport, and remediation of groundwater contaminants in fractured rocks.     

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.     

Field studies on factors affecting very fine and ultra fine particulate organic matter deposition in low‐gradient sand‐bed streams

The knowledge on particle deposition in streams is mainly based on investigations in mountain streams. No data exist from low‐gradient sand‐bed streams that largely differ in the morphological and hydraulic factors proposed to affect deposition. To identify physical control on particle deposition in low‐gradient streams, we assessed deposition of very fine and ultra fine organic particulate matter in 18 sand‐bed stream reaches. We added particles derived from lake sediment and assessed the mean transport distance S_P and the deposition velocity v_dep. Additionally, reach hydraulics were estimated by injections of a conservative solute tracer (NaCl). Among the low‐gradient streams, particle deposition kinetics were variable but similar to deposition in mountain streams. S_P was solely related to the flow velocity. This relation was confirmed when comprising published data on deposition of fine organic particles. An association between particle deposition and transient storage factors was insignificant. We found significance of the transient storage to S_P only for repeated measures within a single reach, when flow velocity and benthic conditions were nearly constant. Measured v_dep/v_fall ratios were much larger than unity in most reaches. Evidence from this relation suggests that the vertical transport of very fine and ultra fine organic particulate matter through the water column was caused mainly by vertical mixing. Copyright © 2006 John Wiley & Sons, Ltd.