Hydrodynamic Dispersion Coefficient Research Articles

Effect of Biochar on NO3--N Transport in Loessial Soil and Its Simulation

The objective of this study was to explore the effects of different amounts of biochar on the migration process and characteristics of NO3--N in loessial soil. In this study, six groups of mixed soil samples with biochar and loessial soil mass ratios of 0% (T0), 1% (T1), 2% (T2), 3% (T3), 4% (T4), and 5% (T5) were used as research objects. NO3--N was used as the tracer. Through the indoor soil column solute transport simulation tests, the effects of different biochar application amounts on the NO3--N transport process in loessial soil were simulated and studied. The results showed that the breakthrough curve of NO3--N in loessial soil shifted to the right with the increasing of biochar application, and the peak value gradually decreased. The initial penetration time, complete penetration time, and total penetration time increased with the increasing of biochar application amount. The total penetration time of NO3- in the T1, T2, T3, T4, and T5 treatments was 1.26, 2.31, 2.72, 3.22, and 3.57 times that of T0, respectively. The R2 was > 0.997 and RMSE was < 2.083 of the two-zone model (TRM). Compared with the convection-dispersion equation (CDE), the TRM model had higher fitting accuracy and could better simulate the NO3--N migration process in loessial soil after the application of different contents of biochar. The analysis of the fitting parameters of the TRM model showed that the average pore velocity, hydrodynamic dispersion coefficient, and water content ratio in the movable zone gradually decreased with the increasing of biochar application, whereas the dispersion and mass exchange coefficient showed an increasing trend. The results showed that biochar application could effectively enhance the ability of loessial soil to fix NO3--N, reduce the leakage of NO3--N to groundwater, and play an important role in maintaining soil fertility and preventing groundwater pollution.

DEVELOPMENT OF A MATHEMATICAL MODEL FOR ANALYSING THE HAZARDOUS IMPACT ON THE STATE OF GROUNDWATER IN CITY AGGLOMERATIONS FROM MISSILE AND ARTILLERY ATTACKS

The authors have developed a mathematical model for analysing the hazardous impact on the groundwater in urban agglomerations from missile and artillery attacks. The mathematical model consists of a system of four analytical dependencies. The first analytical dependence describes determining the area of groundwater intake from the groundwater level, considering the presence of artificial coatings, infiltration, evaporation, and transpiration, as well as the effect of evapotranspiration. The second dependence determines the area of influence of the missile and artillery danger from the type of weapon, the explosive charge, calibre (diameter), and territorial conditions, the key indicators of the content of which in the territory of the critical infrastructure object, which suffered damage, are further determined by expert calculation using natural samples of soils and groundwater. The third dependence determines the impact of harmful (polluting) substances on groundwater in the territory of the critical infrastructure object, which suffered damage, depending on the process of groundwater movement in the area of the emergency, taking into account the hydraulic pressure and water yield coefficient; the process of distribution of chemically dangerous substances in groundwater, taking into account the coefficient of hydrodynamic dispersion and the velocity of groundwater; convective diffusion of chemically hazardous substances, taking into account the kinetics of sorption. The fourth dependency allows us to choose an efficient concept for the organisation of groundwater monitoring on the territory of a critical infrastructure object that suffered damage based on the variation of formalised parameters for solving individual problems. The initial conditions of the mathematical model are related to the presence of chemically dangerous compounds in groundwater at the maximum permissible concentration level. The boundary conditions of the mathematical model relate to the non-overgrowth of consequences beyond the object level in terms of the number of victims. Keywords: mathematical model, groundwater, missile and artillery damage, critical infrastructure object, emergency prevention.

Transport of nZVI/copper synthesized by green tea extract in Cr(IV)-contaminated soil: modeling study and reduced toxicity.

In this study, nano-zero-valent iron/copper was synthesized by green tea extracts (GT-nZVI/Cu) and produced a stable suspension than nano-zero-valent iron synthesized by green tea extracts (GT-nZVI) injected into Cr(VI)-containing soil column. The equilibrium 1D-CDE model was successfully used to fit the penetration curves of Fe(tot), Fe(aq), and Fe(0) in order to determine the relevant parameters. The hydrodynamic dispersion coefficient of chromium-contaminated soil was 0.401 cm2·h-1, and the pore flow rate was 0.144cm·h-1. The stable C/C0 of Fe(tot), Fe(aq), and Fe(0) in the effluent were retarded to 0.39, 0.79, and 0.11, respectively, compared to a ratio of 1 for the concentration of the tracer Cl- in the effluent to the concentration in the influent. Additionally, the 1D-CDE model describes the migration behavior of Cr(VI) with a high R2 (> 0.97). The obtained blocking coefficients declined gradually with increasing concentration of GT-nZVI/Cu suspension and decreasing concentration of Cr(VI). The content of reduced chromium in the soil decreased from 2.986 to 1.121 after remediation, while the content of more stable oxidizable chromium and residual chromium increased from 2.975 and 20.021 to 16.471 and 27.612. The phytotoxicity test showed that mung bean seeds still had a germination rate of 90% (control of 100%), root length of 29.63mm (control of 35.25mm), and stem length of 17.9cm (control of 18.96cm) after remediation with GT-nZVI/Cu. These indicated that GT-nZVI/Cu was effective in immobilizing Cr(VI) in the soil column and reduced the ecological threat. This study provides an analytical basis and theoretical model for the migration of chromium-contaminated soil in practical application.

Transport of graphene oxide in the capillary fringe: Insights from sandbox experiments and numerical simulation

Studying contaminant transport in the capillary fringe (CF), a crucial part of the vadose zone, offers insights into the mechanisms controlling pollution in soils and groundwater aquifers. This paper investigated contaminant transport in the CF by continuously injecting a conservative tracer (NaCl) and graphene oxide nanoparticle (GONP), an adsorptive contaminant, into a sandbox. After entering the CF from the unsaturated zone, both NaCl and GONP underwent lateral transport. The breakthrough curves (BTCs) for NaCl and GONP were derived from water samples collected at predetermined sampling holes. Subsequently, contaminant transport in the CF was modeled using a one-dimensional–two-dimensional (1D-2D) coupled hydrodynamic model. This model incorporated lateral dispersivity (αL = 1.198 cm) and longitudinal dispersivity (αT = 0.286 cm), calculated using a point-by-point method. The hydrodynamic dispersion coefficients obtained were then applied to the Brooks and Corey (BC) and the van Genuchten (VG) parametric models. The BC model more accurately simulated the NaCl migration compared to the VG model, leading to its application in simulating GONP transport in the CF. However, the simulated BTCs for GONP showed a lag behind the measured data, especially at high ionic strengths. This discrepancy was attributed to the variable adsorption partition coefficient of GONP under different ionic conditions. During the experiment, GONP adsorption onto the porous media's surface altered the capillary dynamics, notably increasing capillary rise height, decreasing seepage velocity, and reducing GONP dispersion. Therefore, it is necessary to consider the adsorption capacity of the contaminants in order to accurately assess their transport within the vadose zone.

Pre-asymptotic dispersion revisited

We develop a new approach to formulation and solution of mathematical models of one-dimensional advective–dispersive transport that specifies the hydrodynamic dispersion coefficient as a function of time since the solute has entered the flow field, termed ‘age.’ This approach addresses Taylor’s concern about the use of time-dependent dispersion coefficients to model pre-asymptotic dispersion by replacing time-dependence with age-dependence, where age of solute is exposure-time to the flow. We show closed form solutions obtained for transport on the −∞<x<∞ and a numerical solution for transport on the 0<x<∞ domain. We demonstrate how this works by application to an in-silico experiment recently published in a study addressing the same issue in a different manner. Our simple and intuitive approach matches the simulated pre-asymptotic data without additional terms or parameter fitting. The same principle applies to pre-asymptotic dispersion in other important upscaled one-dimensional transports e.g., in river corridor or groundwater flows.

Bimolecular reactive transport in a filled single fracture-matrix system considering the nonequilibrium sorption

Comprehending the transport mechanism of bimolecular reactive solutes in fracture-matrix systems is crucial for improving the efficiency of collaborative remediation using hydraulic fracturing and in-situ chemical oxidation in low-permeability contaminated sites. Previous studies have neglected the effects of physical nonequilibrium (PNE) caused by sedimentation and chemical nonequilibrium (SNE) caused by rete-limited sorption. In this study, a two-dimensional numerical model that considers mobile-immobile mass transfer in the fracture and two-site nonequilibrium sorption in both fracture and matrix is established to investigate the behavior of bimolecular reactive solutes in a filled fracture-matrix system. The results indicate that the PNE and SNE lead to two-stage characteristics and severe tailing effects in contaminant remediation. High tailing occurs when the equilibrium sorption fraction and fracture-mobile/fracture-immobile porosity ratio are relatively small and the longitudinal hydrodynamic dispersion coefficient is relatively large, requiring consideration of multi-nonequilibrium processes. Additionally, the solute concentration in the matrix is most sensitive to the matrix porosity (θk), less sensitive to fracture aperture (2b), and reagent bulk diffusivity (DOA). The remediation area (Sr) in the matrix has an exponential relationship with θk and a linear relationship with 2b and DOA. The quantitative relationship between Sr and key parameters facilitates the prediction of remediation effectiveness.

Hyper-gravity experiment of solute transport in fractured rock and evaluation method for long-term barrier performance

Hyper-gravity experiment enable the acceleration of the long-term transport of contaminants through fractured geological barriers. However, the hyper-gravity effect of the solute transport in fractures are not well understood. In this study, the sealed control apparatus and the 3D printed fracture models were used to carry out 1 ​g and N g hyper-gravity experiments. The results show that the breakthrough curves for the 1 ​g and N g experiments were almost the same. The differences in the flow velocity and the fitted hydrodynamic dispersion coefficient were 0.97–3.12% and 9.09–20.4%, indicating that the internal fractures of the 3D printed fracture models remained stable under hyper-gravity, and the differences in the flow and solute transport characteristics were acceptable. A method for evaluating the long-term barrier performance of low-permeability fractured rocks was proposed based on the hyper-gravity experiment. The solute transport processes in the 1 ​g prototype, 1 ​g scaled model, and N g scaled model were simulated by the OpenGeoSys (OGS) software. The results show that the N g scaled model can reproduce the flow and solute transport processes in the 1 ​g prototype without considering the micro-scale heterogeneity if the Reynolds number (Re) ​≤ ​critical Reynolds number (Recr) and the Peclet number (Pe) ​≤ ​the critical Peclet number (Pecr). This insight is valuable for carrying out hyper-gravity experiments to evaluate the long-term barrier performance of low-permeability fractured porous rock.

Analytical solution of three-dimensional particle transport in porous media considering a dual deposition mode

Based on the classical one-dimensional particle transport model, a three-dimensional particle transport model with a dual deposition mode considering sieving and adsorption effects was established. Through Laplace and Fourier transforms, general solutions for particle transport in saturated semi-infinite porous media under one-dimensional seepage and three-dimensional dispersion conditions were derived. According to the basic solution in the case of a point source injection on the surface of a semi-infinite body, the analytical expression in the case of a circular surface source injection was obtained by the integration method. The analytical solution is verified using two well-established numerical simulation solvers. The influence of parameters such as the hydrodynamic dispersion coefficient, sieving coefficient, adsorption coefficient, and desorption coefficient, on the mechanism of the particle transport process was analyzed under the conditions of constant concentration and circulating concentration injection of the circular surface source. The results showed that the hydrodynamic dispersion effect accelerated the transport of particles, shortened the breakthrough time, and increased the peak concentration. Moreover, a larger sieving coefficient and particle adsorption coefficient meant a smaller particle release coefficient, and more particles deposited on the solid matrix with a smaller peak particle concentration in the pores.

Geometry‐Based Prediction of Solute Transport Process in Single 3D Rock Fractures Under Laminar Flow Regime

AbstractSubsurface substance migration in the fractured rock aquifer is mainly controlled by fractures, and prediction of solute transport in fractures is important to many geophysical processes and engineering activities. This study explores the possibility of predicting transport process in single rock fractures from measurable physical properties. For this purpose, we conducted a large number of pore‐scale simulations of solute transport in single 3D rock fractures with different apertures and various degrees of roughness. The numerically‐obtained breakthrough curves under laminar flow regime were reproduced with high fidelity by the classic analytical solution within the framework of macroscopic advection‐dispersion theory. The fitted transport coefficients (hydrodynamic dispersion coefficient and transport velocity) were normalized by the parallel‐plate model's values, and were further parameterized by aperture b and roughness parameter σ/b in form of ωeb/ψ + λ(mσ/b − 1)/bn and 1 − α(σ/b)/βb, respectively. By incorporating these parameterized transport coefficients and the modified cubic law into the classic analytical solution, we proposed a new transport predictive model. This model was adaptively degenerated into the classic analytical solution of parallel‐plate model, and was proved to be capable of predicting macroscopic solute transport only relying on arithmetic‐mean mechanical aperture and its standard deviation, without solving the velocity and concentration fields. By the established model, we quantitatively revealed the impacts of aperture and roughness on the breakthrough curve under laminar flow regime. This study puts a step toward predicting solute transport process in fractured rock aquifers with measurable geometric properties.

Intrapore Geometry and Flow Rate Controls on the Transition of Non‐Fickian to Fickian Dispersion

AbstractHydraulic heterogeneity leads to non‐Fickian transport characteristics, which cannot be entirely accounted for by the continuum‐scale advection‐dispersion equation. In this pore‐scale computational study, we investigate the combined effects of flow rate (i.e., Peclet number, Pe) and first‐order hydraulic heterogeneity, that is, resulting from intrapore geometry exclusively, on the transition from non‐Fickian to Fickian dispersion. A set of intrapore geometries is designed and quantified by a dimensionless pore geometry factor (β), which accounts for a broad range of pore shapes likely found in nature. Navier‐Stokes and Advection‐Diffusion equations are solved numerically to study the transport phenomenon using velocity variance, residence time distribution, and coefficients of hydrodynamic dispersion and dispersivity. We determine the length scale (i.e., the linear distance in flow direction) for each pore shape and Pe when non‐Fickian features transition to the Fickian transport regime by incrementally extending the length, that is, the linear array of pores. We show how velocity distribution and variance (σ2) depend on β, and directly control the transition to Fickian dispersion. Pores with a larger β, that is, complex pore shapes with constricted pore‐body or with “slit‐type” attributes, result in a substantial non‐Fickian characteristics. The magnitude of non‐Fickian characteristics gets amplified with an increase in Pe requiring a significantly longer length scale, that is, up to 1 m or a linear array of 500 pores to transition to the Fickian transport regime. We find the hydrodynamic dispersion coefficient (Dh) exponentially depends on the pore shape factor β, with its exponent dependent on flow rate or Pe. We determine constitutive relations to quantify how σ2, β, and Pe, contribute to the degree of non‐Fickian characteristics, the length scale needed for the transition to Fickian transport regime, asymptotic Dh, and the length‐scale dependence of longitudinal dispersivity.

Effect of a Superabsorbent Polymer (Poly-Gamma-Glutamic Acid) on Water and Salt Transport in Saline Soils under the Influence of Multiple Factors.

In order to effectively suppress the negative effects of salt ions contained in saline soils on agricultural soil quality and crop growth, this study took advantage of the water-saving properties and better soil improvement properties of poly-γ-glutamic acid (γ-PGA). By carrying out various experiments, the following relationships have been found. (1) The lab experiment studies the effect of the γ-PGA application on the infiltration of sandy loam soil. The application rates of γ-PGA are 0%, 0.1%, 0.2%, and 0.3%, respectively. (2) HYDRUS-1D is used to simulate water infiltration of sandy loam soil under multiple factors (bulk density, γ-PGA application rate, and the application depth of γ-PGA). (3) The effect of γ-PGA on soil solute (Cl−) transport is also explored in this paper. The results show that bulk density and the application depth of γ-PGA (p < 0.01) have higher effects on cumulative infiltration than the application amount of γ-PGA (p < 0.05). A lower γ-PGA application rate will increase the proportion of unavailable soil water by 3%. The established empirical models have good results. Furthermore, when the γ-PGA application rate is 0.3% (0.02-cm2 min−1), the Cl− hydrodynamic dispersion coefficient is the highest. The study recommends applying the γ-PGA at 1.4 g cm−3, 5–20 cm, and 0.2%. The results of this study are conducive to an in-depth understanding of the physicochemical properties of poly-γ-glutamic acid, improving the utilization rate of salinized land, achieving agricultural water and fertilizer conservation and yield enhancement, and guaranteeing sustainable land use and sustainable development of agroecological environment.

Development of water quality management strategies based on multi-scale field investigation of nitrogen distribution: a case study of Beiyun River, China.

Accurately quantifying the distribution of nitrogen (N) contaminants in a river ecosystem is an essential prerequisite for developing scientific water quality management strategy. In this study, we have conducted a series of field investigations along the Beiyun River to collect samples from multiple scales, including surface water, riverbed sediments, vadose zone, and aquifer, for evaluating the spatial distribution of N; besides, column simulation experiments were carried out to characterize the transport behavior of N in riverbed sediments. The surface water of the Beiyun River was detected to be eutrophic because of its elevated total N concentration, which is 33 times of the threshold value causing the potential eutrophication. The hydrodynamic dispersion coefficient (D) of riverbed sediments was estimated by CXTFIT 2.1, demonstrating that the D of upstream section was lower than that of midstream and downstream sections (Dupstream < Dmidstream < Ddownstream), with the estimated annual N leaching volume of 130,524, 241,776, and 269,808 L/(m2·a), respectively. The average total N concentration in vadose zone and aquifer of upstream Sect.(297.88mg/kg) was obviously lower than that of midstream Sect.(402.62mg/kg) and downstream Sect.(447.02mg/kg). Based on multi-scale investigation data, subsequently, water quality management strategies have been achieved, that is, limiting the discharge of N from the midstream and downstream banks to the river and setting up the impermeable layer in the downstream reaches to reduce infiltration. The findings of this study are of great significance for the improvement of river environmental quality and river management.

Linking mixing and flow topology in porous media: An experimental proof.

Transport processes in porous media are controlled by the characteristics of the flow field which are determined by the porous material properties and the boundary conditions of the system. This work provides experimental evidence of the relation between mixing and flow field topology in porous media at the continuum scale. The setup consists of a homogeneously packed quasi-two-dimensional flow-through chamber in which transient flow conditions, dynamically controlled by two external reservoirs, impact the transport of a dissolved tracer. The experiments were performed at two different flow velocities, corresponding to Péclet numbers of 191 and 565, respectively. The model-based interpretation of the experimental results shows that high values of the effective Okubo-Weiss parameter, driven by the changes of the boundary conditions, lead to high rates of increase of the Shannon entropy of the tracer distribution and, thus, to enhanced mixing. The comparison between a hydrodynamic dispersion model and an equivalent pore diffusion model demonstrates that despite the spatial and temporal variability in the hydrodynamic dispersion coefficients, the Shannon entropy remains almost unchanged because it is controlled by the Okubo-Weiss parameter. Overall, our work demonstrates that under highly transient boundary conditions, mixing dynamics in homogeneous porous media can also display complex patterns and is controlled by the flow topology.

Semi-analytical solution for reactive contaminant transport in a filled-fractured system with intervening rock matrices: Case examples of tritium and uranium

While fractures are commonly filled in the subsurface, they have received little attention in terms of flow and solute transport. This study presents a semi-analytical solution for a reactive contaminant in a five-layer fracture-matrix groundwater system characterized by a thin rock matrix separating the fractures, which are taken to be filled with sediments. Under conditions of steady groundwater flow using the Laplace transform for two scenarios of two-dimensional unilateral and three-dimensional radial flows, the solutions have obtained that account for longitudinal advective transport in the mobile portion of fractures and transverse diffusion in the adjacent matrices. The mathematical models in the real-time domain are derived by numerically inverting the solutions from the Laplace domain and validated against both the numerical and existing semi-analytical solutions. Examples of the solution behavior are presented, which demonstrate an increase in the fracture-mobile/fracture-immobile porosity ratio tends to increase the solute concentration in the adjacent matrices, particularly under unilateral flowrate, because in addition to the groundwater velocity, Peclet number, and hydrodynamic dispersion coefficient, the ratio of retardation factor to hydrodynamic dispersion coefficient also plays a significant role in solute transport. Compared to the fracture, the solute behavior in the matrices, particularly under the unilateral flow case, is more sensitive to changes in the parameters. The porosity of the rock matrix has a twofold effect since as porosity is increased, the retardation factor decreases while storage capacity increases. A thinner middle matrix in addition to a lower peak in tritium and uranium concentrations inside the whole system over long-time periods, is further accompanied by a quick overlapping the concentration penetration depth of adjacent fractures. The diffusion process in the rock matrix has been further identified as important as advection in the fracture for those repositories that are planned to safely dispose wastes for a long-time. The idea of combining multiple fractures as a single one with a double aperture is found to be only reasonable for the conservative solute under the steady-state or long-time conditions while it is not to be useful for the cases of sorptive solutes under the unsteady-state solute transport. The findings of this study can assist for simulating tracer tests as well as fate, transport, and remediation of groundwater contaminants in fractured rocks to better evaluate the safety degree of deep reservoirs in regard to disposal of nuclear and chemical wastes.

Enhanced contaminant retardation by novel modified calcium bentonite backfill in slurry trench cutoff walls

This study aimed at assessing containment properties of slurry wall backfill containing sodium hexametaphosphate (SHMP) modified calcium bentonite to contaminated groundwater. Free swell index and flexible-wall hydraulic conductivity (k) tests were conducted to investigate swelling and hydraulic performances of this novel backfill. The relative concentration (RC) and cumulative mass ratio (CMR) methods were adopted to assess transport parameters including hydrodynamic dispersion coefficient (D) and the retardation factor (Rd) of calcium ion (Ca2+) through the backfills. The results showed negligible to moderate decrease in the swell index of the modified bentonite and the modified backfill when exposed to 5 mM and 1 M calcium chloride (CaCl2) solution. Permeation with CaCl2 solutions increased the short-term k of the backfill by a factor of 0.9 to 1.1 as compared to the tap water permeation. The D values varied from 1.44 × 10–10 m2/s to 2.89 × 10–10 m2/s regardless of the CaCl2 concentration, whereas Rd was vulnerable to CaCl2 concentration. The CMR method yielded a higher coefficient of determination than the RC method, but it showed no particular advantage in evaluating the transport parameters. The SHMP-modification delayed the breakthrough time of Ca2+ by a factor of 15 to 199 in a model slurry trench wall.

Numerical dispersion of solute transport in an integrated surface–subsurface hydrological model

Integrated surface–subsurface hydrological models (ISSHMs) are increasingly being used for the assessment of contaminant transport in the environment, in addition to their more common use in water flow applications. However, the subsurface solute transport solvers in these models are prone to numerical dispersion errors. Numerical dispersion is a well-known issue in groundwater modeling, but its impacts on the results of ISSHM simulations are still poorly understood. In this study, the CATchment HYdrology (CATHY) model is used to assess the potential impacts of numerical dispersion on the simulation of coupled surface–subsurface solute transport. We first simulate the subsurface transport of a nonreactive tracer in two soil column test cases (1D and 3D) with known analytical solutions. The subsurface solute transport solver in CATHY adopts a computationally efficient time-splitting technique whereby the advection component of the governing equation is solved on elements and the hydrodynamic dispersion component is solved on nodes. Comparison between simulation results and analytical solutions with different mesh discretizations and different values for the hydrodynamic dispersion coefficients allows for accurate quantification of the numerical dispersion error and yields insights into the parameters and other factors that control it. It is shown that, taken alone, the advection and dispersion solvers are very robust, but their combination can result in significant numerical dispersion, stemming from the exchange of concentration information from elements to nodes and vice versa in the time-splitting procedure. The tests also show that these errors can be kept under control by ensuring that the grid Péclet number is in the range 0.5-1.0 or smaller. We then apply CATHY in a third test case involving two synthetic hillslopes (concave and convex) in fully coupled surface–subsurface mode, in order to examine the impact of this subsurface numerical dispersion on simulated streamflow hydrographs, in particular with reference to pre-event water contributions to runoff. Here as well the results show that the effect of numerical dispersion can be controlled by keeping the grid Péclet number sufficiently small. This work provides a new set of benchmark test cases for integrated surface–subsurface hydrological models, extending to solute transport the flow-only suite of benchmarks recently published in two intercomparison studies.

Transport of silica encapsulated DNA microparticles in controlled instantaneous injection open channel experiments

Surface water tracing is a widely used technique to investigate in-stream mass transport including contaminant migration. Recently, a microparticle tracer was developed with unique synthetic DNA encapsulated in an environmentally-friendly silica coating (Si-DNA microparticle). Previous tracing applications of such tracers reported detection and quantification, but a massive loss of tracer mass. However, the transport behavior of these DNA-tagged microparticle tracers has not been rigorously quantified and compared with that of solute tracers. Therefore, we compared the transport behavior of Si-DNA microparticles to the behavior of solute NaCl in 6 different, environmentally representative water types using breakthrough curves (BTCs), obtained from laboratory open channel injection experiments, whereby no Si-DNA microparticle tracer mass was lost. Hereafter, we modelled the BTCs using a 1-D advection-dispersion model with one transient storage zone (OTIS) by calibrating the hydrodynamic dispersion coefficient D and a storage zone exchange rate coefficient. We concluded that the transport behavior of Si-DNA microparticles resembled that of NaCl in surface-water relevant conditions, evidenced by BTCs with a similar range of D; however, the Si-DNA microparticle had a more erratic BTC than its solute counterpart, whereby the scatter increased as a function of water quality complexity. The overall larger confidence interval of DSi-DNA was attributed to the discrete nature of colloidal particles with a certain particle size distribution and possibly minor shear-induced aggregations. This research established a solid methodological foundation for field application of Si-DNA microparticles in surface water tracing, providing insight in transport behavior of equivalent sized and mass particles in rivers.

The hydrodynamic mechanism of rainfall runoff from loess slopes treated with incorporated straw

AbstractThe hydrodynamic parameters of rainfall runoff are important for those studying hillslope water flow, which in turn affects soil erosion, chemical pollutant migration, and diffusion. Straw incorporation into the cultivated soil layer may affect soil properties, resulting in different hydrodynamic behaviours of hillslope runoff. The objective of this study was to evaluate the influences of straw incorporation, rainfall intensity, and slope gradient on hydraulic parameters, such as the Reynolds number (Re), Froude number (Fr), Darcy‐Weisbach friction factor (f), and hydrodynamic dispersion coefficient (DH). Laboratory experiments were conducted under four straw incorporation rates (SRs: 0, 2, 4, and 8 t ha−1), three rainfall intensities (RIs: 80, 120, and 160 mm hr−1), and three slope gradients (SGs: 10, 15, and 20°) to examine the hydrodynamic characteristics. The results show that the increase in SR significantly reduces the DH. Compared with bare soil slope (0.020 m2 s−1), the mean DH decreased by half (0.011 m2 s−1) at an SR of 2 t ha−1 and approximately three‐quarters (0.005 m2 s−1) at an SR of 8 t ha−1. Both Re and Fr decreased with a rise in the SR; however, the slope roughness increased, which caused a significant increase in frictional force compared to results observed for the bare soil. A rise in RI and SG increased the driving force on the farmland slope. The Re and Fr decreased with RI and SR, while f increased with RI and SG. Therefore, this study elucidates that the incorporation of straw in the soil can alter the hydrodynamic parameters, thus influencing water flow velocity and soil erosion.

Effect of X-ray $$\mu$$CT Resolution on the Computation of Permeability and Dispersion Coefficient for Granular Soils

X-ray micro-computed tomography ( $$\mu$$ CT) can produce realistic 3D-images of the pore structure of a material. Extracting its geometry enables the computation of effective properties of the material—such as the permeability (k) and the hydrodynamic dispersion coefficient ( $$D_h$$ )—, through the solutions of the Stokes equation (SE) and Advection-Diffusion equation (ADE), respectively. In this study, the effect of the image resolution on these properties is discussed. For such purpose, four different resolutions are evaluated for both a real sample of Fontainebleau sand and a numerically generated sample created by degrading the Fontainebleau image with highest resolution. The SE was computed using the commercial software GeoDict. To solve the ADE, a Finite Volume software was developed which includes a high order total variation diminishing scheme for advection. The analysis of dispersion was based on numerical breakthrough curves. Our model was tested in a large range of Peclet numbers (Pe) and travel distances, accurately describing the transition between diffusion and advection dominated regimes of dispersion. The $$D_h$$ exhibits a linear increase with travel distance for Pe $$> 10$$ . This classical effect increases with increasing Pe. The percentage change on k and $$D_h$$ increases with decreasing resolution in agreement with the corresponding behavior of porosity, specific surface and pore size distributions. The images directly scaled with the $$\mu$$ CT showed more discrepancy than the numerically scaled images. The criteria to estimate the quality of permeability from the pore size distribution proposed on our previous study remains valid. The $$D_h$$ is less sensitive to resolution than k.

Experimental and numerical study of bimolecular reactive transport in a single rough-wall fracture

In order to test the performance of the incomplete mixing model including the advection-dispersion-reaction equation (IM-ADRE) in simulating bimolecular reactive transport in fractured media, the laboratory-controlled experiments and numerical modeling were conducted in a single rough-wall fracture. Bimolecular reaction of aniline (AN) + 1, 2-napthoquinone-4-sulfonic acid (NQS) → 1, 2-naphthoquinone-4-aminobenzen (NQAB) was employed. Three different flow rates (0.15, 0.825 and 1.5 mL/s) and three fracture apertures (2, 3 and 4 mm) were considered in the experiment. The numerical simulation was analyzed and discussed based on the Péclet (Pe) number and Damköhler (Da) number. The results showed that although the spatial distribution of product concentration varied with the Pe number, the IM-ADRE model could simulate it well. The discrepancy between the simulated and measured peak product concentrations was less than 0.7%, which was far less than the value of 5% in previous study (Qian et al., 2015) produced by the IM-ADRE model used to modeling the reactive transport in porous media. This meant that the IM-ADRE model was effective for simulating and predicting the experimental results of bimolecular reactive transport in a single rough-wall fracture. Due to the instability of the product, the simulated value of the peak product concentration was always higher than the experimental value. Through further analysis of the model parameters, it was found that the hydrodynamic dispersion coefficient (D) changed significantly with the change of Pe number. The parameters m and β0 were linearly correlated with the Pe number. In addition, the IM-ADRE model was more sensitive to the parameters m and β0 but less sensitive to D.