Tailing Of Breakthrough Curves Research Articles

Mercury transport through a porous medium in presence of natural organic matter

Natural organic matter (NOM), derived from degradation of living organism matter, can significantly control the fate and transport of chemical components, particularly metal ions, by forming organometallic complexes in aquatic systems. Column experiments were performed to study the mobility of humic acids (HA) and Hg. Single component (HA or Hg) and multicomponent (Hg and HA) experiments were conducted to assess transport behaviour of Hg in the presence of HA. A natural quartz sand was used as porous sorbing medium. HA breakthrough curves (BTCs) showed a first step with a sharp front followed by an important tailing over a long period of time. The tailing of HA BTCs is assumed to be due to slow sorption kinetics of HA onto the quartz sand and the non linear nature of the sorption isotherms. The time required to get steady-state concentration for organic C depended on the inlet HA concentration. HA sorption depends also on pH, the highest HA sorption being observed at pH<pH pzc due to electrostatic attractions. The Hg transport is strongly enhanced in the presence of HA and the Hg BTCs are quite similar to the HA BTCs. These results suggest strong aqueous complexation between Hg and HA and the formation of ternary surface complexes of type B.

Measurement and analysis of non-Fickian dispersion in heterogeneous porous media

Contaminant breakthrough behavior in a variety of heterogeneous porous media was measured in laboratory experiments, and evaluated in terms of both the classical advection–dispersion equation (ADE) and the continuous time random walk (CTRW) framework. Heterogeneity can give rise to non-Fickian transport patterns, which are distinguished by “anomalous” early arrival and late time tails in breakthrough curves. Experiments were conducted in two mid-scale laboratory flow cells packed with clean, sieved sand of specified grain sizes. Three sets of experiments were performed, using a “homogeneous” packing, a randomly heterogeneous packing using sand of two grain sizes, and an exponentially correlated structure using sand of three grain sizes. Concentrations of sodium chloride tracer were monitored at the inflow reservoir and measured at the outflow reservoir. Breakthrough curves were then analyzed by comparison to fitted solutions from the ADE and CTRW formulations. In all three systems, including the “homogeneous” one, subtle yet measurable differences between Fickian and non-Fickian transport were observed. Quantitative analysis demonstrated that the CTRW theory characterized the full shape of the breakthrough curves far more effectively than the ADE.

A stochastic interpretation of the tailing effect in solute transport

The advection-dispersion equation (ADE) is inadequate for describing tails in solute breakthrough curves. Re-examination of solute breakthrough curves from one-dimensional experiments in porous media and channel flow literature shows a consistent discrepancy compared with solutions to the ADE. The leading tail of breakthrough curves is sharper, and the trailing tail is longer and smoother, than best fitting, least-squares ADE solutions. A random particle simulation exercise shows that the ADE may firstly be erroneous because of the assumption of time steps over which random solute movements are considered independent. Definition of such time steps hinges upon the slowest random movements, such as those predominantly by molecular diffusion. A second potential source of error is the highly skewed nature of the inverse distribution of underlying, micro-scale velocities, which causes slow convergence to normality under the central limit theorem.

Artificial colloid tracer tests: development of a compact on-line microsphere counter and application to soil column experiments

Multi-tracer tests with both solutes and particles allow to parametrise heterogenous porous media on the basis of the dual porosity model. In soil column experiments both solute and particle tracers were measured on-line at the outflow of the column. For the on-line measurement of particles we developed a flow cytometer with a sensitivity of one single microsphere in 1 ml of water. The microspheres used are latex spheres of 1 μm diameter, labeled with a fluorescent dye. The technique is based on the excitation of microspheres with a small diode laser. If a microsphere passes the laser focus the incorporated dye molecules emit fluorescent light. These photons are sampled by a Single-Photon-Counting Avalanche-Diode. The maximum flow rate through the instrument is 1 ml/min with a detection efficiency of up to 90%. The instrument is working stably over a time period of several weeks and has been tested under field conditions. The solute tracer we use is uranine, which is detected with a sensitive fluorimeter. Extreme sensitivity of the detectors is necessary to resolve tails of breakthrough curves which contain information on the structure of the medium. Laboratory columns were filled with a mixture of quartzsand (250–500 μm) and cellpore filter cylinders with an internal pore size of ∼35 μm. The measured breakthrough curves show, that because of the highly reduced matrix diffusion of colloids, their first breakthrough can be up to 2.25 times faster than the first breakthrough of uranine.

A Laplace transform solution for tracer tests in a radially convergent flow field with upstream dispersion

When tracers are introduced into an injection borehole, noticeable concentration gradients at the injection well may cause a backward spreading of the initial plume during radially convergent tracer tests. Based on this concept a non-rigorous mathematical model is developed to estimate the effect of backward spreading. The injection well with an instantaneous slug input is treated as a mathematical source and the initial plume at the injection well is allowed to move upstream. The model assumes that advection and longitudinal dispersion are the transport mechanisms in a radially converging flow field. The Laplace transform solution for solute concentration in an infinite porous medium is obtained using the method of Green's function. Breakthrough curves are computed by numerically inverting the Laplace transform solution. As compared with the solution of Moench, it is concluded that the presence of backward movement of initial plume yields a decrease of peak concentration and spreading out of breakthrough curve tails. This effect is significant for small Peclet numbers and can be neglected for large Peclet numbers. A field tracer test is carried out to demonstrate the applicability of the model. The experimental data are fitted with the type curves of this study, and those of Moench's study, to determine dispersivity and aquifer porosity. The results show that dispersivity values estimated by matching the two type curves are different. Because it neglects backward dispersion, Moench's solution overestimates the dispersivity and effective aquifer porosity.

Pore and surface diffusion in multicomponent adsorption and liquid chromatography systems

AbstractA generalized parallel pore and surface diffusion model for multicomponent adsorption and liquid chromatography is formulated and solved numerically. Analytical solution for first‐ and second‐order central moments for a pulse on a plateau input is used as benchmarks for the numerical solutions. Theoretical predictions are compared with experimental data for two systems: ion‐exchange of strontium, sodium, and calcium in a zeolite and competitive adsorption of two organics on activated carbon. In a linear isotherm region of single‐component systems, both surface and pore diffusion cause symmetric spreading in breakthrough curves. In a highly nonlinear isotherm region, however, surface diffusion causes pronounced tailing in breakthrough curves; the larger the step change in concentration, the more pronounced tailing, in contrast to relatively symmetric breakthroughs due to pore diffusion. If only a single diffusion mechanism is assumed in analyzing the data of parallel diffusion systems, a concentration‐dependent apparent surface diffusivity or pore diffusivity results; for a convex isotherm, the apparent surface diffusivity increases, whereas the apparent pore diffusivity decreases with increasing concentration. For a multicomponent nonlinear system, elution order can change if pore diffusion dominates for a low‐affinity solute, whereas surface diffusion dominates for a high‐affinity solute.

Nonequilibrium Transport of Atrazine through Large Intact Soil Cores

AbstractPreferential flow in heterogeneous soils may result in more rapid leaching of pollutants through soils than would be predicted using transport models based on the local equilibrium assumption (LEA). Our objectives were to evaluate nonequilibrium processes important to the transport of tritiated water (3H2O) and atrazine under varying pore water velocities and soil water contents, and to distinguish between transport‐related nonequilibrium (TNE) and sorption‐related nonequilibrium (SNE). Column experiments were performed using a 3H2O‐14C‐labeled atrazine pulse through intact soil cores (15.24‐cm diam., 30‐cm length) at pore water velocities of 0.12, 0.69, and 2.16 cm h−1 (θv ≈ 0.39) and at 0.74 cm h−1 (θv ≈ 0.44). The asymmetrical shape and the left‐handed displacement of 3H2O breakthrough curves (BTCs) as a function of pore water velocity and soil water content (θv) indicated that 3H2O was subject to TNE at only the 0.74 (θv = 0.44) and 2.16 cm h−1 pore water velocities. The asymmetrical shape and increased tailing of atrazine BTCs at all pore water velocities indicated that atrazine was influenced primarily by SNE at pore water velocities of 0.12 and 0.69 cm h−1, and a combination of both TNE and SNE at pore water velocities of 0.74 (θv ≈ 0.44) and 2.16 cm h−1. The convection‐dispersion equation based on the LEA was unable to predict atrazine BTCs at any pore water velocity. Although the nonequilibrium bicontinuum (two‐site/two‐region) model provided excellent fit to all atrazine BTCs, fits to the model cannot be used to separate between TNE and SNE when both mechanisms are operative. Results of this study confirm that TNE and SNE are important transport processes in naturally structured soils under conditions of relatively high pore water velocities and volumetric water contents.

The equations of miscible flow with negligible molecular diffusion

A set of equations with ‘generalized permeability’ functions has been proposed by de la Cruz and Spanos, Whitaker, and Kalaydjian to describe three-dimensional immiscible two-phase flow. We have employed the zero interfacial tension limit of these equations to model two phase miscible flow with negligible molecular diffusion. A solution to these equations is found; we find the generalized permeabilities to depend upon two empirically determined functions of saturation which we denote asA andB. This solution is also used to analyze how dispersion arises in miscible flow; in particular we show that the dispersion evolves at a constant rate. In turn this permits us to predict and understand the asymmetry and long tailing in breakthrough curves, and the scale and fluid velocity dependence of the longitudinal dispersion coefficient. Finally, we illustrate how an experimental breakthrough curve can be used to infer the saturation dependence of the underlying functionsA andB.

Adsorptive solute transport in fractured rock: analytical solutions for delta-type source conditions

Solutions for adsorptive solute transport equations in a single fracture-rock system were derived under two different delta-type source conditions. One was the delta-type, flux injection condition. The correspondent solution can be used for the analysis of experimental column breakthrough curves obtained by injecting the tracer into the rock fracture. The other was the delta-type, resident fluid injection condition. The solution can be used for the crude estimation of pollutant migration from the underground radioactive waste repository. In formalizing the resident fluid injection, an initial distribution of solute between solution and solid phase was assumed in order to satisfy the mass balance between injected and detected solute. Each of the two solutions was also expressed in two ways reflecting the flux and the resident fluid detection. Solutions expressed in terms of the flux detection correspond to the effluent concentration measured experimentally by a fraction collector system. On the other hand, solutions expressed in terms of the resident fluid detection describe spatial distribution of the solute in the fluid. Since considerably long tailings of breakthrough curves are often observed in column tracer experiments using fractured rocks effects of some parameter values on the tailing were also discussed. It was shown that the adsorption of solute rock matrix caused longer tailing. It was also shown that the resident fluid injection caused longer tailing of breakthrough curves than the flux injection condition.