Theory Of Solute Transport Research Articles

DFNSC: A particle tracking discrete fracture network simulator considering successive spatial correlation

Discrete fracture network (DFN) models are currently a suitable tool representing the anisotropic and discontinuity features of fractured media. Literatures has shown that it is challenging to obtain accurate DFN considering the quantitative spatial correlation in DFN modeling. This study proposes a particle tracking simulator for DFN modeling considering the successive spatial correlation of fracture distribution (DFNSC) by coupling fracture generating method, groundwater flow and solute transport theory, graph theory, and random walk method. By carrying out simulation calculations of seepage field and particle tracking on four DFNs with different distributions, more detailed conclusions have been obtained: The areas with dense fracture distribution have smaller hydraulic gradient than areas with sparse fracture distribution. The high flow velocity basically appears in the areas where the fractures are relatively sparse. Dense areas of fractures hinder the migration of particles. In essence, dense fractures create a low velocity zone, which makes the transport speed of solute particles slower. In the DFN with uniformly distribution and centralized distribution of fractures, the proportion of penetrating particles reaches 100%, whereas it is only 62% in the DFN with fractures gathered on one side. This study can provide reliable technology for the calculation of the seepage field of fractured media and the study of the pollutant migration process.

Flow, Transport, and Reaction in Porous Media: Percolation Scaling, Critical‐Path Analysis, and Effective Medium Approximation

AbstractWe describe the most important developments in the application of three theoretical tools to modeling of the morphology of porous media and flow and transport processes in them. One tool is percolation theory. Although it was over 40 years ago that the possibility of using percolation theory to describe flow and transport processes in porous media was first raised, new models and concepts, as well as new variants of the original percolation model are still being developed for various applications to flow phenomena in porous media. The other two approaches, closely related to percolation theory, are the critical‐path analysis, which is applicable when porous media are highly heterogeneous, and the effective medium approximation—poor man's percolation—that provide a simple and, under certain conditions, quantitatively correct description of transport in porous media in which percolation‐type disorder is relevant. Applications to topics in geosciences include predictions of the hydraulic conductivity and air permeability, solute and gas diffusion that are particularly important in ecohydrological applications and land‐surface interactions, and multiphase flow in porous media, as well as non‐Gaussian solute transport, and flow morphologies associated with imbibition into unsaturated fractures. We describe new applications of percolation theory of solute transport to chemical weathering and soil formation, geomorphology, and elemental cycling through the terrestrial Earth surface. Wherever quantitatively accurate predictions of such quantities are relevant, so are the techniques presented here. Whenever possible, the theoretical predictions are compared with the relevant experimental data. In practically all the cases, the agreement between the theoretical predictions and the data is excellent. Also discussed are possible future directions in the application of such concepts to many other phenomena in geosciences.

Analytical Solution of Advection-Dispersion Equation with Spatially Dependent Dispersivity

AbstractIn the dispersion theory of solute transport in groundwater flow, the dispersion coefficient is regarded as proportional to the nth power of groundwater velocity, where n varies from 1 to 2...

Visualization of three pathways for macromolecule transport across cultured endothelium and their modification by flow.

Transport of macromolecules across vascular endothelium and its modification by fluid mechanical forces are important for normal tissue function and in the development of atherosclerosis. However, the routes by which macromolecules cross endothelium, the hemodynamic stresses that maintain endothelial physiology or trigger disease, and the dependence of transendothelial transport on hemodynamic stresses are controversial. We visualized pathways for macromolecule transport and determined the effect on these pathways of different types of flow. Endothelial monolayers were cultured under static conditions or on an orbital shaker producing different flow profiles in different parts of the wells. Fluorescent tracers that bound to the substrate after crossing the endothelium were used to identify transport pathways. Maps of tracer distribution were compared with numerical simulations of flow to determine effects of different shear stress metrics on permeability. Albumin-sized tracers dominantly crossed the cultured endothelium via junctions between neighboring cells, high-density lipoprotein-sized tracers crossed at tricellular junctions, and low-density lipoprotein-sized tracers crossed through cells. Cells aligned close to the angle that minimized shear stresses across their long axis. The rate of paracellular transport under flow correlated with the magnitude of these minimized transverse stresses, whereas transport across cells was uniformly reduced by all types of flow. These results contradict the long-standing two-pore theory of solute transport across microvessel walls and the consensus view that endothelial cells align with the mean shear vector. They suggest that endothelial cells minimize transverse shear, supporting its postulated proatherogenic role. Preliminary data show that similar tracer techniques are practicable in vivo.NEW & NOTEWORTHY Solutes of increasing size crossed cultured endothelium through intercellular junctions, through tricellular junctions, or transcellularly. Cells aligned to minimize the shear stress acting across their long axis. Paracellular transport correlated with the level of this minimized shear, but transcellular transport was reduced uniformly by flow regardless of the shear profile.

3D Transport of Solute in Deformable Soils with Different Adsorption Modes

Additional loading due to the weight of the waste in landfills results in consolidation and deformation of clay liners beneath, which will induce changes in the inner structure and permeability of the clay liners. Based on combination of Biot consolidation theory and solute transport theory, a three-dimensional coupled model describing solute transport in deforming soil has been proposed, taking account of the effect of consolidation on solute transport processes. The consolidation and transport equations are linked by choosing the permeability coefficients as the coupled parameter. The effects of different adsorption modes on solute transport processes in deforming soil under two conditions are studied: the solute source concentration remains constant or degrades with time. The solute concentration versus space with degraded-concentration source increases gradually and reaches a peak value at a certain depth in the vertical section or at a certain position in the horizontal section, and then decreases, which is very different from that with the constant-concentration source.

Damköhler Number Input to Transport-Limited Chemical Weathering Calculations

Chemical weathering of the silicate minerals in the Earth’s crust is the dominant influence on variability of atmospheric carbon on time scales of about 1 Ma and up, lending significance to the ability to predict such weathering rates. Field weathering rates at such large time scales tend to be much slower than laboratory values, however. It has been proposed that the discrepancy occurs because field weathering rates are solute-transport-limited rather than reaction-kinetic-limited. To assess the relative importance of reaction kinetics and solute transport, the Damkohler number, DaI, a ratio of a transport time to a reaction time can be used. Unfortunately, even in those experiments that suggest importance of transport limitations, the traditional calculation of DaI yields values close to 1 and an extreme sensitivity of experimental reaction rates on DaI. We develop a new method of calculating DaI based on the theory of non-Gaussian solute transport, appropriate for heterogeneous porous media. Our result...

Analysis of the dynamic impact of Three-Gorge Project on regime of soil water and salt in Yangtze River Delta

The topography is low and flat in the estuarine region of the Yangtze River, where waterlog and salt-affected soil are all through a latent threat to the agricultural development for long time. After the Three-Gorge Project is built up, the Three-Gorge Reservoir adjusts seasonably runoff will impact on the dynamic of soil water and salt in the region. These influence relations are very complicated. Based on the theory of solute transport and the principle of soil water dynamics, the model of soil water and salt transport was created, which involved root water extraction, adsorption---desorption, mobile---immobile region. To overcome numerical dispersion, the paper solved the convection---dispersion equation by Bresler algorithm, the term of time derivative used the approximate difference formula of quadratic differential coefficient based on central difference. Then, the impact of Three-Gorge Project on the regime of soil water and salt in the estuarine region by numerical simulation was studied in. The numerical simulation indicates that electric conductivity of soil one meter thick of each observed section will go down by 0.005---0.174 mS/cm as discharge increases in spring after building the Three-Gorge Reservoir, and up by 0.004---0.416 mS/cm as discharge decreases in autumn---winter. The elementary predicted result of numerical simulation shows that salification will be bigger in autumn than desalinization in spring. The impact degree of the project on the regime of soil salt will be gradually weakened along the river up from the estuary, the nearer to the sea, the bigger the impact, and from cross profiles, the nearer to the river, the bigger the impact. Especially within the range of 4 km of the river, it is more possible that the soil will produce salification or secondary salinization.

Solute dynamics and the Ontario nitrogen index: I. Chloride leaching

The nitrogen (N) index for humid temperate southern Ontario, Canada (Ontario N index) incorporates previous and current crop type, fertilizer and (or) manure management, and hydrologic soil group (HSG) to estimate risk for contamination of tile drainage water and groundwater by nitrate leached below the primary crop root zone (top 60 cm of soil). The Ontario N index has received limited ground-truthing, and the leaching component was assessed using chloride tracer (ClTR) on five soils (one sandy loam, two loams, and two clay loams) representing four HSG-based risk levels (HSG-A, high risk; HSG-B, medium risk; HSG-C, low risk; HSG-D, very low risk). A square-wave pulse of ClTR was applied to the soil surfaces in fall 2007 as KCl, and movement and loss of ClTR was tracked over 1–1.2 years using monthly soil core samples collected from the top 60–80 cm. For all five soils, 60–96% of ClTR was leached out of the primary crop root zone (below 60 cm depth) during the noncropping period (October 2007 to March 2008 inclusive), and >80% was leached out of the root zone within 1 year. The percentage of ClTR that leached did not correlate with precipitation or HSG designation, but produced significant (P < 0.05) power function regressions with minimum and harmonic mean saturated soil hydraulic conductivity (Ksat) measured in the top 50–60 cm. ClTR leaching rate appeared to be controlled primarily by Ksat in a manner consistent with infiltration and solute transport theory. It was consequently proposed that solute leaching loss versus Ksat relationships may improve N index risk estimates for both southern Ontario and other humid temperate regions.

Numerical Simulation of Coupled Water and Salt Transfer in Soil and a Case Study of the Expansion of Subgrade composed by Saline Soil

Salt expansion is one of the major problems of subgrade involving saline soils. Salt expansion is induced by the crystallization of salt when the soil water content or temperature decreases. A case of salt expansion in subgrade composed by saline soil is introduced. It is located in G314 Road, which is one of the national highways in China, from Urumqi to Khunjerab. There is 3.40 ∼5.91% salt within 1.0 depth in the ground surface of the G314 (K587 + 035), which belongs to strong sulphate salty soil. The maximum salt expansion is up to 20cm in G314 Road, which has a serious impact on the road. Salt expansion is majorly controlled by the salt crystallization and the transmission of water and salt. Based on the solute transport theory in porous media, the water flow theory and thermal conduction theory, the govern differential equations of coupled salt crystallization, salt transmission and water flow are established in this paper. The coupled water and salt transfer problem of saline soil is solved by a software named as COMSOL with the use of a secondary development module. To verify the method for simulating the coupled water and salt transmission process, the water and salt transfer process in a 1D soil column is simulated and the results are compared with the theoretical solution. The results show that coupled model of water and salt established in this paper can accurately predict salt migration and crystallization of saline soil.

Scaling of geochemical reaction rates via advective solute transport.

Transport in porous media is quite complex, and still yields occasional surprises. In geological porous media, the rate at which chemical reactions (e.g., weathering and dissolution) occur is found to diminish by orders of magnitude with increasing time or distance. The temporal rates of laboratory experiments and field observations differ, and extrapolating from laboratory experiments (in months) to field rates (in millions of years) can lead to order-of-magnitude errors. The reactions are transport-limited, but characterizing them using standard solute transport expressions can yield results in agreement with experiment only if spurious assumptions and parameters are introduced. We previously developed a theory of non-reactive solute transport based on applying critical path analysis to the cluster statistics of percolation. The fractal structure of the clusters can be used to generate solute distributions in both time and space. Solute velocities calculated from the temporal evolution of that distribution have the same time dependence as reaction-rate scaling in a wide range of field studies and laboratory experiments, covering some 10 decades in time. The present theory thus both explains a wide range of experiments, and also predicts changes in the scaling behavior in individual systems with increasing time and/or length scales. No other theory captures these variations in scaling by invoking a single physical mechanism. Because the successfully predicted chemical reactions include known results for silicate weathering rates, our theory provides a framework for understanding changes in the global carbon cycle, including its effects on extinctions, climate change, soil production, and denudation rates. It further provides a basis for understanding the fundamental time scales of hydrology and shallow geochemistry, as well as the basis of industrial agriculture.

Effect of multiple lateral cavities on stream solute transport under non-Fickian conditions and at the Fickian asymptote

Summary In field studies of solute transport, transient storage within lateral cavities and other stream features generates breakthrough curves (BTCs) with pronounced and persistent skewness. Current solute transport theory requires that the coefficient of skewness ( CSK ) decrease over time because the system eventually reaches Fickian conditions. However, published data show that CSK is constant in time. To aid development of solute transport theory that explains field observations, we quantify the effect of lateral cavities on solute transport under non-Fickian and Fickian conditions. Six hydrodynamics models were developed: one with no lateral cavities, three with lateral cavities in series, and two with lateral cavities in parallel. Results reveal that lateral cavities in series have longer tails and smaller peak concentrations compared to lateral cavities in parallel. Lateral cavities in series cause greater dispersion and require larger distances to reach Fickian conditions ( x Fick ) compared to lateral cavities in parallel. Cavity configuration has a greater influence on longitudinal dispersion and x Fick than the number of cavities present. CSK changes with monitoring location and maximum CSK (= 10–20) near lateral cavities is higher than empirical estimates (≈1.18). We postulate that adding more transient storage zones would increase channel complexity and yield closer results between simulated and empirical CSK , and testing this hypothesis warrants future research. Finally, while current models can obtain good fits to measured BTCs by parameterizing mass exchange rates and volume ratios, these parameters do not adequately describe the fundamental fluid mechanics driving exchange.

Scaling and predicting solute transport processes in streams

We investigated scaling of conservative solute transport using temporal moment analysis of 98 tracer experiments (384 breakthrough curves) conducted in 44 streams located on five continents. The experiments span 7 orders of magnitude in discharge (10−3 to 103 m3/s), span 5 orders of magnitude in longitudinal scale (101 to 105 m), and sample different lotic environments—forested headwater streams, hyporheic zones, desert streams, major rivers, and an urban manmade channel. Our meta‐analysis of these data reveals that the coefficient of skewness is constant over time ( , ). In contrast, the of all commonly used solute transport models decreases over time. This shows that current theory is inconsistent with experimental data and suggests that a revised theory of solute transport is needed. Our meta‐analysis also shows that the variance (second normalized central moment) is correlated with the mean travel time ( ), and the third normalized central moment and the product of the first two are very strongly correlated ( ). These correlations were applied in four different streams to predict transport based on the transient storage and the aggregated dead zone models, and two probability distributions (Gumbel and log normal).

Dispersion of solutes in porous media

A recently introduced theory of solute transport in porous media is tested by comparison with experiment. The solute transport is predicted using an adaptation of the cluster statistics of percolation theory to critical path analysis together with knowledge of how the structure of such percolation clusters affects the time of transport across them. Only the effects of a single scale of medium heterogeneity are incorporated, and a minimal amount of information regarding the structure of the medium is required. This framework is used to find effectively the distributions of solute velocities and travel distances and thus generate arrival time distributions. The comparison with experiment focuses on the dispersivity (the ratio of the second to the first moment of the spatial solute distribution). The predictions of the theory in the absence of diffusion are verified by comparing with over 2200 experiments over length scales from a few microns to 100 km. At larger length scales (centimeters on up) about 95% of the data lie within our predicted bounds. At smaller length scales approximately 99.8% of the data lie where we predict. These comparisons are not trivial as the typical values of the dispersivity increase by ten orders of magnitude over ten orders of magnitude of length scale. Noteworthy is that the classical advection-dispersion (ADE) equation predicts that the dispersivity should be independent of length scale! This agreement with experiment requires rethinking of the relevance of diffusion and multi-scale heterogeneity and would also appear to signal the complete inappropriateness of using the classical ADE or any of its derivatives to model solute transport.

Systematic construction of hidden nonlocal symmetries for the inhomogeneous nonlinear diffusion equation

We consider a class of inhomogeneous nonlinear diffusion equations (INDE) that arise in solute transport theory. Hidden nonlocal symmetries that seem not to be recorded in the literature are systematically determined by considering an integrated equation, obtained using the general integral variable, rather than a system of first-order partial differential equations (PDEs) associated with the concentration and flux of a conservation law. Reductions for the INDE to ordinary differential equations (ODEs) are performed and some invariant solutions are constructed.

Explicit and implicit coupling during solute transport through clay membrane barriers

Simulations of salt (KCl) flux through a 1-m-thick clay membrane barrier (CMB) based on coupled solute transport theory are compared to simulated fluxes based on traditional advective–dispersive transport theory. The simulations are based on measured values for the effective salt-diffusion coefficient ( D s*) and chemico-osmotic efficiency coefficient ( ω) for a bentonite-based barrier material subjected to KCl solutions. The results indicate that the exit salt flux is reduced due to both explicit coupling (hyperfiltration and chemico-osmotic counter-advection) and an implicit coupling effect resulting from the decrease in D s* due to a decrease in the apparent tortuosity factor, τ a, with an increase in ω. Implicit coupling is shown to be more significant than explicit coupling for reducing and retarding salt flux through a CMB under diffusion-dominated conditions. Failure to account for the implicit coupling effect may result in unrealistic results, such as the existence of salt flux through a perfect (ideal) clay membrane (i.e., ω=1).

A review of some tracer-test design equations for tracer-mass estimation and sample-collection frequency

Determination of necessary tracer mass, initial sample-collection time, and subsequent sample-collection frequency are the three most difficult aspects to estimate for a proposed tracer test prior to conducting the tracer test. To facilitate tracer-mass estimation, 33 mass-estimation equations have been developed over the past century. These 33 equations are reviewed here, 32 of which were evaluated using previously published tracer-test design examination parameters. Comparison of the results produced a wide range of estimated tracer mass, but no means is available by which one equation may be reasonably selected over the others. Each equation produces a simple approximation for tracer mass. Most of the equations are based primarily on estimates or measurements of discharge, transport distance, and suspected transport times. Although the basic field parameters commonly employed are appropriate for estimating tracer mass, the 33 equations are problematic in that they were all probably based on the original developers experience in a particular field area and not necessarily on measured hydraulic parameters or solute-transport theory. Suggested sampling frequencies are typically based primarily on probable transport distance, but with little regard to expected travel times. This too is problematic in that tracer sampling remains a haphazard process that tends to result in false negatives or data aliasing. Simulations from the recently developed efficient hydrologic tracer-test design methodology (EHTD) were compared with those obtained from 32 of the 33 published tracer-mass estimation equations and suggested sampling frequencies. EHTD applies functional relationships developed from hydrologic measurements in a solute-transport model to develop a preliminary tracer-breakthrough curve that has been shown to reasonably predict actual tracer-test results.

Validation of classical density-dependent solute transport theory for stable, high-concentration-gradient brine displacements in coarse and medium sands

A series of careful laboratory soil column experiments was carried out for the purpose of providing data for testing recently presented theories of miscible density-dependent flow and transport. In particular, modifications to the standard theory involve extensions to both Darcy's (for flow) and Fick's laws (for diffusive/dispersive solute flux). Both coarse- and medium-grained sands were used in the experiments. All experiments concerned upward (i.e., stable) displacement of fresh water within the soil by a brine solution, under either constant head or constant volume flux conditions. The experimental data were analysed using accurate numerical solutions of the standard governing flow and transport model, as well as models with modified Darcy's and Fick's laws. Model parameters were determined by a step-wise fitting procedure based on the least-squares criterion. The results show clearly that, for large density contrasts, an extended Darcy's law was not necessary. On the other hand, an extension to Fick's Law was needed to model the experimental data accurately.

Microforces and the theory of solute transport

A generalized continuum framework for the theory of solute transport in fluids is proposed and systematically developed. This framework rests on the introduction of a generic force balance for the solute, a balance distinct from the macroscopic momentum balance associated with the mixture. Special forms of such a force balance have been proposed and used going back at least as far as Nernst's 1888 theory of diffusion. Under certain circumstances, this force balance yields a Fickian constitutive relation for the diffusive solute flux, and, in conjunction with the solute mass balance, provides a generalized Smoluchowski equation for the mass fraction. Our format furnishes a systematic procedure for generalizing convection-diffusion models of solute transport, allowing for constitutive nonlinearities, external forces acting on the diffusing constituents, and coupling between convection and diffusion.

Measurement of Hydraulic Properties During Constant Flux Infiltration Field Average

Accurate measurement of in situ soil hydraulic properties is important for developing, testing, and applying water and solute transport theory. A method of measuring hydraulic conductivity (K), soil matric pressure head (ψ), and water content (θ) relationships is presented. The procedure uses a series of multipurpose time domain reflectometry (TDR) probes that measure both θ and ψ. The TDR probes are installed vertically and measure the rate of change of local soil water storage (q) along the probe during constant rate water application. The values of q are equal to local soil water flux, and assuming unit gradient, are set equal to K at the steady state θ and ψ measured at long times. The measured values of K, θ, and ψ from different water application rates are combined to obtain average K(θ) and θ(ψ) functions. To test the procedure, multipurpose TDR probes were installed vertically in a sandy soil every 0.15 m in a 7.5‐m‐long transect for a total of 50 probes per depth. This was repeated in parallel transects 0.1 m apart for four depths (0.2 m, 0.4 m, 0.6 m, 0.8 m) and a total of 200 probes. Six different water application rates were applied with subsequent drainage. Average K(θ) and θ(ψ) functions were obtained and used in an analytical solution for constant rate infiltration. Transient water storage changes were accurately predicted for all application rates.

Technical comment on: “On the stochastic theory of solute transport by unsteady and steady groundwater flow in heterogeneous aquifers”, by M.L. Kavvas and A. Karakas (Journal of Hydrology Vol. 179 (1996) 321–351)

In this note, we demonstrate that statements made in a recent paper by Kavvas and Karakas (1996) (J. Hydrol., 179: 321–351), concerning the assumptions underlying the stochastic model of solute transport in spatially-heterogeneous aquifers developed by Kabala and Sposito (1991) (Water Resour. Res., 25: 341–350), are incorrect.