One-dimensional Convection-dispersion Model Research Articles

Analytical Solution of the One-Dimensional Transport of Ionic Contaminants in Porous Media with Time-Varying Velocity

The one-dimensional convection–dispersion equation has been widely used to describe the migration process of contaminant leachate through barriers. However, most of the existing solutions are limited to simple conditions. In this study, a one-dimensional convection–dispersion model with time-dependent velocity was established while considering the change in the permeability coefficient. The analytical solution of the model was obtained by using the integral transformation method. Based on the analytical model, three special conditions were assumed for comparison. The results showed that the concentration levels of pollutants inside the barrier would significantly increase with the increase in the flow velocity, and the pollutant concentrations inside the barrier would be increased by four times compared with the normal flow velocity when the flow rate increased by two times. The transports of heavy metal ions with variable velocities through soil–bentonite and soil–attapulgite barriers were predicted under field conditions. The predicted results showed that the breakthrough time would be reduced by as much as two times. In engineering practice, a barrier’s service performance can be improved by controlling the temperature of the seepage field and improving the chemical compatibility of the barrier materials.

Transport of imidazolium-based ionic liquids with different anion/cation species in sand/soil columns

Ionic liquids (ILs) have been widely used as environmentally friendly solvents to replace volatile organic solvents in the chemistry industries. They have a high water solubility and potential risk to organisms in the soil–water environment. At present, most studies focused on the batch sorption of ILs in soil and neglected the investigation of IL transports in soil, which results in a lack of understanding of the structure-dependent mobility of ILs in the environment. Laboratory-scale sand/soil column experiments were performed to study the transport of imidazolium-based ILs, such as [C4mim][OTF], [C4mim][TOS], [C4mim][MeSO3], [C4mim][BF4], [C2mim][BF4], and [C6mim][BF4] including different counteranions and alkyl chain lengths of IL cations. Batch experiments were also carried out to compare the difference of sorption distribution coefficient (Kd) between the batch and column experiments. A one-dimensional convective–dispersive model using CXTFIT code was created based on the measured breakthrough curves (BTCs) to estimate the column transport parameters. For the anion, [BF4-], the Kd of ILs in both batch and column experiments increased with increasing alkyl chain lengths of the IL cation. In batch tests, counteranions showed no influence on the Kd of [C4mim][OTF], [C4mim][TOS], [C4mim][MeSO3], [C4mim][BF4], [C2mim][BF4], and [C6mim][BF4]. However, in column tests, the BTCs of 1-butyl-3-methylimidazolium-based ILs were anion dependent as evidenced by the change of retardation factor (R) for different counteranions. Furthermore, the effects of transport distance (11cm, 15cm, 19cm, and 24cm) on the mobility of ILs were estimated. The longer distances signified an increase in the contact time and more binding sites for ILs and therefore, the smoother shapes of BTCs in column experiments.

Deposition and mobilization of functionalized multiwall carbon nanotubes in saturated porous media: effect of grain size, flow velocity and solution chemistry

Carbon nanotubes (CNTs) are widely manufactured nanoparticles which are utilized in a number of consumer products, such as sporting goods, electronics and biomedical applications. Due to their accelerating production and use, CNTs constitute a potential environmental risk if they are released to soil and groundwater systems. It is, therefore, essential to improve the current understanding of environmental fate and transport of CNTs. The current study systematically investigated the effect of solution chemistry (pH and ionic strength) and physical conditions (collector grain size and flow rate) on the deposition and mobilization of functionalized multiwall carbon nanotubes (MWCNTs) using a series of column experiments under fully saturated conditions. A one-dimensional convection–dispersion model including collector efficiency for cylindrical nanoparticles was used to simulate the transport of MWCNTs in porous media. It was observed that an increase in pH resulted in increased mobility of MWCNTs. However, the transport of MWCNTs was strongly dependent on ionic strength of the background solution and a critical deposition concentration was observed between 3 and 4 mM NaCl concentration, with more than 99 % filtration of MWCNTs at 4 mM. The finer sand grains were able to filter a significant amount of MWCNTs (15 % more than coarse sand) from the inflow solution; this was likely caused by grain-to-grain straining mechanisms in the finer sand. A decrease in pore water velocity also led to more deposition of MWCNTs due to lowering of the kinetic energy of the particles. The results from this study indicated that a weak secondary minimum existed under unfavorable conditions for deposition, but the particles were trapped at both primary and secondary minimum.

Biosorption of chromium, copper and zinc on rice wine processing waste sludge in fixed bed

Wine processing waste sludge (WPWS) has shown effective removal of heavy metals in batch studies, but the adsorption in a fixed-bed WPWS column has not been examined and the mass transport in this column remains unclear. This study aimed to investigate: (1) the retardation factor ( R) and the dispersion coefficient ( D) of WPWS, employing one-dimensional convective–dispersive model with breakthrough curve (BTC) and using chromium, copper and zinc as the adsorbates; and (2) explore the adsorption mechanism of WPWS column for heavy metals. The retardation factor for various metal treatments is shown in the following order: Cr(18.3) > Cu(13.0) > Zn(7.2), indicating their binding affinity toward WPWS. The dispersion coefficients were calculated to be 2.36 × 10 −6, 5.89 × 10 −7 and 6.83 × 10 −7 m 2 s −1 for Cr, Cu and Zn treatments, respectively. The high charge density for Cr 3+ ion makes it longer for the Cr column to attain exhaustion state, about 4.0 and 8.2 times the time required for the Cr and Zn columns. However, the least retardation and adsorption amount for Zn can be attributed to its full orbital in electronic configuration.

Applied tracers for the observation of subsurface stormflow at the hillslope scale

Abstract. Rainfall-runoff response in temperate humid headwater catchments is mainly controlled by hydrological processes at the hillslope scale. Applied tracer experiments with fluorescent dye and salt tracers are well known tools in groundwater studies at the large scale and vadose zone studies at the plot scale, where they provide a means to characterise subsurface flow. We extend this approach to the hillslope scale to investigate saturated and unsaturated flow paths concertedly at a forested hillslope in the Austrian Alps. Dye staining experiments at the plot scale revealed that cracks and soil pipes function as preferential flow paths in the fine-textured soils of the study area, and these preferential flow structures were active in fast subsurface transport of tracers at the hillslope scale. Breakthrough curves obtained under steady flow conditions could be fitted well to a one-dimensional convection-dispersion model. Under natural rainfall a positive correlation of tracer concentrations to the transient flows was observed. The results of this study demonstrate qualitative and quantitative effects of preferential flow features on subsurface stormflow in a temperate humid headwater catchment. It turns out that, at the hillslope scale, the interactions of structures and processes are intrinsically complex, which implies that attempts to model such a hillslope satisfactorily require detailed investigations of effective structures and parameters at the scale of interest.

Hydraulic characteristics of aerobic granules using size exclusion chromatography

Elution of poly(ethylene glycol) of molecular weight 200-20,000 Da from a size exclusion chromatography column packed with phenol-fed aerobic granules of three different nominal sizes (types I-III) has been investigated. The pore sizes of the three types of granules were evaluated based on the mean hydraulic times of the elution curves that decreased directly proportional to the increased logarithm of the molecular mass of a standard tracer and increased as granule size decreased. The corresponding exclusion limits for types I-III granules were 139,000, 123,000, and 54,500 Da, respectively. A one-dimensional convection-dispersion model described the effective dispersion coefficients of the tracers through the granule column. The intra-granular permeabilities and convective and diffusional transit times through the granule interior were evaluated by a dual porosity model. For small molecules of molecular mass <5,000 Da, intra-granular convection dominated transport mechanisms at fast moving velocity. For comparatively larger molecules, diffusion barrier existed to limit nutrient supply to the granules. The size exclusion test provided intra granular transport characteristics using detailed analysis on the elution data.

Tracing of water movement through the unsaturated zone of a coarse gravel aquifer by means of dye and deuterated water

To better understand the movement and transport of water and pollution through the coarse gravel unsaturated zone, the presented research was conducted to estimate water flow and transport processes with a tracing experiment in a lysimeter in the Selniska Dobrava. A combined tracing experiment was performed with deuterated water and the fluorescent dye—uranine. The fastest and dominant flow velocities were calculated based on injection time, the first tracer appearance time and the time of highest concentration. Mean flow velocity and vertical dispersion were estimated by an analytical best-fit method using one-dimensional convection–dispersion model. Deuterium was confirmed as an ideal conservative tracer and a more suitable tracer than dye (uranine) for the study of water flow in the unsaturated zone of a coarse gravel aquifer. The retardation factor of the dye as compared with deuterium was 1.13–1.75, which is in agreement with previously published results. Artificial tracers, especially deuterated water, were also identified as a very useful tool to assess other properties and differences in water flow in the unsaturated zone of a coarse gravel aquifer such as velocity and dispersion.

Transport of cadmium, nickel, and zinc in Taoyuan red soil using one-dimensional convective–dispersive model

Pollution of agricultural lands by heavy metals has become more serious with increasing pollutants emitted from electroplate plants of northern Taiwan. This study aimed to assess the retardation factor ( R) and the dispersion coefficient ( D) using one-dimensional convective–dispersive model by comparing the breakthrough curve (BTC) and least squares methods. An acrylic column, with an inner diameter of 9 cm and a length of 15 cm, was uniformly packed with soil for metal leaching experiments. An unpolluted surface (0–20 cm) of the Taoyuan red soil was collected for this study. In miscible displacement experiments, a mixture of 4 mg L − 1 CdCl 2, 20 mg L − 1 NiCl 2, and 60 mg L − 1 ZnCl 2 was leached from top of the column and the effluent was collected in increments with the aid of a fraction collector. The retardation factor ( R) calculated from the least squares method was close to the R value observed from breakthrough curves. The R value showed the trend: Cd>Zn>Ni, indicating the rate of metals transport in red soils: Ni>Zn>Cd. Their reactivity was assessed within the framework of the hard–soft acid–base principle (HSAB). From sequential extractions, most of the Cd remained in exchangeable fractions, and Ni and Zn were found to exist in residual Fe- or Mn-oxides, and organic matter fractions.

Solids mixing in the bottom zone of a circulating fluidized bed

Solids mixing in the bottom zone of a circulating fluidized bed was investigated by means of solid carbon dioxide as a tracer in combination with gas concentration and temperature measurements. The experiments were performed in a cold model CFB riser with a rectangular cross-section of 0.3×1.0 m and a height of 8.5 m at operating conditions which are typical of CFB combustors ( u=3 m/s, G s=20 kg/m 2 s, d p=150 μm). The measurements show a high extent of mixing in the vertical direction, whereas horizontal mixing in the bottom zone was found to be limited. If the tracer was injected into the solids return line, the observed horizontal temperature gradients were significantly lower, which is due to additional convection caused by externally circulating solids returned into the riser just above the bottom zone. A one-dimensional convection–dispersion model was used to calculate the temperature distribution within the bottom zone. The horizontal dispersion coefficient was found to be much higher in comparison to dispersion coefficients measured in bubbling fluidized beds as well as in the upper dilute zone of circulating fluidized beds.

Simulation of water flow and bromide transport in a water repellent sandy soil using a one-dimensional convection-dispersion model

Water repellent soils are known to inhibit water infiltration, ultimately forcing water to flow via preferential paths through the vadose zone. To study water flow and transport in a water repellent sandy soil, a bromide tracer experiment was carried out, which started in the fall, after winter wheat had been sown. Field average soil water content and bromide profiles were determined seven times during a 474d period. A one-dimensional convection–dispersion model was used to simulate observed flow and transport. It was found that water content and bromide profiles could be successfully simulated. The main reason was that despite water repellency no distinct preferential flow occurred within this particular experimental field. Only wavy wetting fronts were observed. This was due to a uniform vegetation cover and a relatively thick A-horizon (30cm), which contrasts with known water repellent sandy soils with thin (10cm) top layers in which typical fingered flow patterns had previously been found.

Evaluation of Rhodamine WT as an adsorbed tracer in an agricultural soil

Two column breakthrough tests and a series of 88 batch-equilibrium isotherms were conducted to quantify adsorption parameters for the fluorescent dye Rhodamine WT (Acid Red 388), in contact with a Nicollet loam soil. Results from batch-equilibrium isotherms performed at a 2:1 (water:soil) ratio showed that dye adsorption reached an equilibrium after 10 min on a shaker table. Regression equations were developed to predict distribution coefficients ( K d) for Rhodamine WT (RWT) adsorption to the soil based on soil organic carbon and the ionic strength of the RWT solution. A linear isotherm fitted the batchequilibrium data for RWT in the concentration range evaluated (25–8000 μg 1 −1). K d values obtained from the regression equation generated from the batch-equilibrium isotherms were input to a one-dimensional convection-dispersion model. The predicted results were compared with the experimental results obtained from two repacked column breakthrough curves. RWT adsorption was less than predicted in the first column (in which the breakthrough curve was terminated after 45 pore volumes), but greater than predicted for the second column (which was terminated after 420 pore volumes). The reason for the discrepancy was attributed to the plateau-shaped breakthrough curve observed for RWT and differences in the ionic compositions of the two RWT solutions used to conduct the two column breakthrough curves. RWT did not appear to be a reliable adsorbed tracer if quantitative prediction is needed. Breakthrough curves for atrazine and trifluralin, two herbicides present in the second column, showed atrazine adsorption to be less and trifluralin absorption greater as compared with RWT, as was predicted from their respective organic carbon partitioning coefficients ( K oc).

Derivation of gamma variate indicator dilution function from simple convective dispersion model of blood flow.

The gamma variate function, commonly used to analyze time-activity curves obtained in nuclear medicine flow studies, is shown to be related to the solution to the differential equation obtained from a one-dimensional convective dispersive model of blood flow.