Convective-dispersive Transport Research Articles

Analytical solution of volatile active ingredient release and subsequent dispersion in wind tunnel

This paper proposes a new mathematical model describing the diffusion-controlled release of an active ingredient (AI) from a cylindrical product, followed by convection-dispersion transport in a wind tunnel through which air flows. The model aims to support the development of products with targeted AI release profiles. It was motivated by the particular case of a new product formulation releasing phytochemicals with insecticide activity. The well-known analytical solution for the AI transient release from the product is coupled with the analytical solution for the convection-dispersion transport along the tunnel through a simple approximation that introduces a negligible error. An overall analytical solution is thus obtained, having obvious advantages against numerical approximations, particularly for intensive computational tasks such as model fitting to experimental data, uncertainty analysis and product composition optimization.

Approximate analytical solutions for multispecies convection-dispersion transport equation with variable parameters

Multispecies pollutant migration often occurs in polluted groundwater systems. Most of the multispecies problems that have been dealt in the literature assume constant transport parameters, primarily because analytical solutions for varying parameters become a challenge. The present study analytically solves a two-species convection-dispersion transport equation, considering spatially varying dispersion coefficient and seepage velocity, which corresponds to the steady migration in a steady flow domain. Indeed, the methodology can be adopted for other cases, such as the transient migration in a steady flow domain and transient migration in an unsteady flow domain, without any difficulty. Three kinds of homotopy-based methods, namely the homotopy perturbation method (HPM), homotopy analysis method (HAM), and optimal homotopy asymptotic method (OHAM), are used to derive approximate analytical solutions in the form of truncated series. In homotopy analysis method, the convergence-control parameter ℏ plays a key role in the convergence of the series solution. It is observed that for a specific case of this parameter, namely ℏ=−1, the HAM-based solution recovers the HPM-based solution. For the verification of homotopy-based solutions, we utilize the MATLAB routine pdepe, which efficiently solves a class of parabolic PDEs (single/system). An excellent agreement is found between the derived analytical solutions and the numerical solutions for all three methods. Further, a quantitative assessment is carried out for the derived solutions. Also, convergence theorems are proposed for the series solutions obtained using HAM and OHAM.

Developing convective–dispersive transport model to characterize fixed-bed adsorption of lead (II) over activated tea waste biosorbent

Developing convective–dispersive transport model to characterize fixed-bed adsorption of lead (II) over activated tea waste biosorbent

Application of divided convective-dispersive transport model to simulate variability of conservative transport processes inside a planted horizontal subsurface flow constructed wetland

This paper offers a novel application of our model worked out in Maple environment to help understand the very complex transport processes in horizontal subsurface flow constructed wetland with coarse gravel (HSFCW-C). We made tracer measurements: Inside a constructed wetland, we had 9 sample points, and samples were taken from each point at two depths. Our model is a divided convective-dispersive transport (D-CDT) model which makes a fitted response curve from the sum of two separate CDT curves showing the contributions of the main and side streams. Analytical solutions of CDT curves are inverse Gaussian distribution functions. This model was fitted onto inner points of the measurements to demonstrate that the model gives better fitting to the inner points than the commonly used convective-dispersive transport model. The importance of this new application of the model is that it can resemble transport processes in these constructed wetlands more precisely than the regularly used convective-dispersive transport (CDT) model. The model allows for calculations of velocity and dispersion coefficients. The results showed that this model gave differences of 4–99% (of velocity) and 2–474% (of dispersion coefficient) compared with the CDT model and values were closer to actual hydraulic behavior. The results also demonstrated the main flow path in the system.

Influence of metal cation and surface iron oxide on the transport of sulfadiazine in saturated porous media

Sulfadiazine (SDZ) is an antibiotic frequently detected in soil and groundwater. The transport of SDZ in subsurface environment is a critical process affecting its retention in soil. To date, the effects of iron oxide and metal cation on the transport of SDZ remain largely unknown, so we investigated the transport properties of SDZ in cleaned and iron oxides coated quartz sand, as affected by the presence of conventional cations (Ca2+, Mg2+, K+, and Na+) and Cd2+ through column experiments and simulation. We found that iron oxide coating on sand surface inhibited the transport of SDZ, mainly due to hydrophobic effect, complexation, and electrostatic attraction. The inhibitory effect became more marked with increasing concentration of Cd2+. It favors the transport of Cd2+ due to the electrostatic repulsion between positively charged iron oxide and Cd2+. Ca2+ promoted the transport of SDZ in coated sand, while all the conventional cations had no effect on the transport of SDZ in cleaned sand. The increase in the concentration of Cd2+ favors the transport of SDZ in cleaned sand. However, in iron oxide coated sand, the influence of Cd2+ on the transport of SDZ was dependent on the concentration of Cd2+. At lower concentration of Cd2+ and by competition, the transport is favored. At high concentration, the transport is inhibited mainly due to the formation of ternary surface complexes. A convective–dispersive transport model was applied to simulate and interpret experimental data. Breakthrough curves fitted well with a one-site model (OSM), indicating that SDZ adsorption on the sand experiences reversible kinetic. A low level of KF values with nearly linear sorption isotherm shows high mobility of SDZ and a high potential risk of surface and groundwater contamination. However, such high mobility can be reduced by increasing the content of iron oxides in porous media.

Analysis of conservative tracer measurement results inside a planted horizontal subsurface flow constructed wetland filled with coarse gravel using Frechet distribution

We worked out a method in Maple environment to help understand the difficult transport processes in horizontal subsurface flow constructed wetlands filled with coarse gravel (HSFCW-C). With this process, the measured tracer results of the inner points of a HSFCW-C can be fitted more accurately than with the conventionally used distribution functions (Gaussian, Lognormal, Fick (Inverse Gaussian) and Gamma). This research outcome only applies for planted HSFCW-Cs. The outcome of the analysis shows that conventional solutions completely stirred series tank reactor (CSTR) model and convection-dispersion transport (CDT) model do not describe the internal transport processes with sufficient accuracy. This study may help us develop better process descriptions of very complex transport processes in HSFCW-Cs. Our results also revealed that the tracer response curves of planted HSFCW-C conservative inner points can be fitted well with Frechet distribution only if the response curve has one peak.

Cry1Ab Adsorption and Transport in Humic Acid-Coated Geological Formation of Alumino-Silica Clays

Genetically modified agricultural products have been introduced to increase food supply by enhancing their resistance to pests and diseases, along with easily adapting to environmental conditions. Due to the modification of DNA, public objections are prevalent, including concerns on the impact on the ecosystem. In this research, adsorption and transport of Cry1Ab, a toxin exuded by the transgenic Bt maize in alumino-silica clays, were evaluated in laboratory columns under steady-state flow conditions. Since Cry1Ab fate and transport were very responsive to animal waste field applications, during which humic acids were released, Cry1Ab adsorption and transport in humic acid-coated alumino-silica clays were also investigated. Cry1Ab breakthrough curves were simulated using the convection-dispersion transport models. It was discovered that the humic acid coating increased Cry1Ab deposition during the transport. Based on analysis of the breakthrough curves, adsorption isotherms of Cry1Ab in alumino-silica clays were obtained and compared with those of batch experiments. The humic acid coating changed the bonding energy between Cry1Ab and the adsorption receptor sites on alumino-silica clay surfaces, thereby changing Cry1Ab partition between the aqueous phase and the solid phase.

Visualization and simulation of density driven convection in porous media using magnetic resonance imaging

Magnetic resonance imaging is used to observe solute transport in a 40cm long, 26cm diameter sand column that contained a central core of low permeability silica surrounded by higher permeability well-sorted sand. Low concentrations (2.9g/L) of Magnevist, a gadolinium based contrast agent, produce density driven convection within the column when it starts in an unstable state. The unstable state, for this experiment, exists when higher density contrast agent is present above the lower density water. We implement a numerical model in OpenFOAM to reproduce the observed fluid flow and transport from a density difference of 0.3%. The experimental results demonstrate the usefulness of magnetic resonance imaging in observing three-dimensional gravity-driven convective-dispersive transport behaviors in medium scale experiments.

Simulating the Fate and Transport of Coal Seam Gas Chemicals in Variably-Saturated Soils Using HYDRUS

The HYDRUS-1D and HYDRUS (2D/3D) computer software packages are widely used finite element models for simulating the one-, and two- or three-dimensional movement of water, heat, and multiple solutes in variably-saturated media, respectively. While the standard HYDRUS models consider only the fate and transport of individual solutes or solutes subject to first-order degradation reactions, several specialized HYDRUS add-on modules can simulate far more complex biogeochemical processes. The objective of this paper is to provide a brief overview of the HYDRUS models and their add-on modules, and to demonstrate possible applications of the software to the subsurface fate and transport of chemicals involved in coal seam gas extraction and water management operations. One application uses the standard HYDRUS model to evaluate the natural soil attenuation potential of hydraulic fracturing chemicals and their transformation products in case of an accidental release. By coupling the processes of retardation, first-order degradation and convective-dispersive transport of the biocide bronopol and its degradation products, we demonstrated how natural attenuation reduces initial concentrations by more than a factor of hundred in the top 5 cm of the soil. A second application uses the UnsatChem module to explore the possible use of coal seam gas produced water for sustainable irrigation. Simulations with different irrigation waters (untreated, amended with surface water, and reverse osmosis treated) provided detailed results regarding chemical indicators of soil and plant health, notably SAR, EC and sodium concentrations. A third application uses the HP1 module to analyze trace metal transport involving cation exchange and surface complexation sorption reactions in a soil leached with coal seam gas produced water following some accidental water release scenario. Results show that the main process responsible for trace metal migration in soil is complexation of naturally present trace metals with inorganic ligands such as (bi)carbonate that enter the soil upon infiltration with alkaline produced water. The examples were selected to show how users can tailor the required model complexity to specific needs, such as for rapid screening or risk assessments of various chemicals nder generic soil conditions, or for more detailed site-specific analyses of actual subsurface pollution problems.

Polyethylenimine-functionalized pyroxene nanoparticles embedded on Diatomite for adsorptive removal of dye from textile wastewater in a fixed-bed column

In this study, polyethylenimine-functionalized pyroxene nanoparticles (PEI-PNPs) were embedded into Diatomite (D4500), a commonly used filter aid, at <5wt% to remove a dissolved commercial textile red dye (CRD) from wastewater in batch and continuous flow column experiments. An array of characterization techniques, such as XRD, BET, HRTEM, and SEM was carried out for the Diatomite embedded nanoparticles. The filter aid was mainly composed of macroporous diatomaceous earth, its adsorption surface area and capacity for the CRD were improved significantly via embedding more PEI-PNPs. The adsorption isotherms in the batch studies were fairly explained by the Sips model. The adsorption performance of the fixed-bed column was tested for D4500, before and after embedding it with virgin and PEI-functionalized pyroxene nanoparticles, to determine the breakthrough curves under different operational conditions (e.g., inlet concentration of CRD, inlet flow rate, bed height, and nanoparticle concentration in Diatomite, %nps). The convection-dispersion transport equation was used to describe the obtained breakthrough curves, which enabled the determination of the axial dispersion coefficient (DL) and the Peclet number (Pe). Additionally, the breakthrough data was analyzed using the equivalent length of unused bed (HUNB) approach. In this approach Pe was correlated with HUNB with a good accuracy with the correlation: HUNB=0.013Pe+1.25 when Q and Co are the operational control parameters, while the correlation: HUNB=4.08e−0.002Pe when Z and %nps are the operational control parameters. These correlations can be helpful and useful for scaling up our proposed process for real industrial applications.

E. coli interactions, adhesion and transport in alumino-silica clays

Bacterial adhesion and transport in the geological formation are controlled by their mutual complex interactions, which have been quantified by the traditional and extended Derjaguin–Landau–Verwey–Overbeek (DLVO) theory as well as direct atomic force microscopy (AFM) measurements. In this research, the DLVO forces calculated based on the independently determined bacterial and porous media surface thermodynamic properties were compared with those of AFM measurements. Although differences in the order of several magnitudes existed, forces obtained from both ways could explain the observations of E. coli attachment to alumino-silica clays evaluated in laboratory columns under saturated and steady-state flow conditions. E. coli deposition in alumino-silica clays was simulated using a two-site convection-dispersion transport model against E. coli transport breakthrough curves, which was then linked to the interactions forces. By exploring the differences of the two force measurements, it was concluded that the thermodynamic calculations could complement the direct force measurements in describing bacterial interactions with the surrounding environment and the subsequent transport in the porous media.

Transport Characteristics of Nitrite in a Shallow Sedimentary Aquifer in Northwest China as Determined by a 12-Day Soil Column Experiment

The transport behaviour of nitrite in a shallow sedimentary aquifer in northwest China was investigated in the laboratory by conducting a soil column experiment under flow velocity and temperature conditions likely to be encountered in field situations. The transport characteristics of nitrite are not well known scientifically and the purpose of the study was to provide data that are considered essential for the development of programs for aquifer remediation and groundwater quality protection. The soil column experiment was performed at a constant flow rate for a period of 12 days using a 40 cm column. It involved a 1.5 mmol/L solution of sodium nitrite to which sodium bromide had been added as a chemically conservative tracer. The data were analysed using the CXTFIT 2.0 model code for the one-dimensional convective–dispersive transport of solutes. The breakthrough curve (BTC) for bromide revealed an average linear flow velocity of 0.3445 cm/h for the experiment and a longitudinal dispersivity of 4.16 cm for the sediment. The effective porosity was determined to be 29 %. The BTC for nitrite showed a significant delay compared to the bromide BTC, presumably due to some form of chemical reaction. Significantly, outflow concentrations of nitrite approached 1.5 mmol/L (the input value) towards the end of the experiment (after 10 days) indicating that the nitrite emerging at that time had not undergone significant chemical transformation during its passage through the column. Curve matching showed that nitrite behaviour could be represented by invoking chemical retardation using a retardation factor that begins at 2.5 and gradually decreases over time to a value of 1. However, the BTC for nitrite is better explained by the pH-dependent, chemical transformation of nitrite, presumably to nitrate or nitrogen gas, at the leading edge of the advancing chemical front that gives the appearance that nitrite is being retarded. Nitrite in more alkaline conditions behind the advancing front is significantly less affected by chemical transformation such that the apparent retardation effect diminishes. Further work is required to provide details on the nature of the reactions taking place and the constraints under which they operate.

Application of divided convective-dispersive transport model to simulate conservative transport processes in planted horizontal sub-surface flow constructed wetlands.

We have created a divided convective-dispersive transport (D-CDT) model that can be used to provide an accurate simulation of conservative transport processes in planted horizontal sub-surface flow constructed wetlands filled with coarse gravel (HSFCW-C). This model makes a fitted response curve from the sum of two independent CDT curves, which show the contributions of the main and side streams. The analytical solutions of both CDT curves are inverse Gaussian distribution functions. We used Fréchet distribution to provide a fast optimization mathematical procedure. As a result of our detailed analysis, we concluded that the most important role in the fast upward part of the tracer response curve is played by the main stream, with high porous velocity and dispersion. This gives the first inverse Gaussian distribution function. The side stream shows slower transport processes in the micro-porous system, and this shows the impact of back-mixing and dead zones, too. The significance of this new model is that it can simulate transport processes in this kind of systems more accurately than the conventionally used convective-dispersive transport (CDT) model. The calculated velocity and dispersion coefficients with the D-CDT model gave differences of 24-54% (of velocity) and 22-308% (of dispersion coeff.) from the conventional CDT model, and were closer to actual hydraulic behaviour.

Analysis of conservative tracer measurement results using the Frechet distribution at planted horizontal subsurface flow constructed wetlands filled with coarse gravel and showing the effect of clogging processes.

A mathematical process, developed in Maple environment, has been successful in decreasing the error of measurement results and in the precise calculation of the moments of corrected tracer functions. It was proved that with this process, the measured tracer results of horizontal subsurface flow constructed wetlands filled with coarse gravel (HSFCW-C) can be fitted more accurately than with the conventionally used distribution functions (Gaussian, Lognormal, Fick (Inverse Gaussian) and Gamma). This statement is true only for the planted HSFCW-Cs. The analysis of unplanted HSFCW-Cs needs more research. The result of the analysis shows that the conventional solutions (completely stirred series tank reactor (CSTR) model and convection-dispersion transport (CDT) model) cannot describe these types of transport processes with sufficient accuracy. These outcomes can help in developing better process descriptions of very difficult transport processes in HSFCW-Cs. Furthermore, a new mathematical process can be developed for the calculation of real hydraulic residence time (HRT) and dispersion coefficient values. The presented method can be generalized to other kinds of hydraulic environments.

Bacterial interactions and transport in geological formation of alumino-silica clays

Bacterial transport in the subsurface is controlled by their interactions with the surrounding environment, which are determined by the surface properties of the geological formation and bacterial surfaces. In this research, surface thermodynamic properties of Escherichia coli and the geological formation of alumino-silica clays were characterized based on contact angle measurements, which were utilized to quantify the distance-dependent interactions between E. coli and the geological formation according to the traditional and extended Derjaguin, Landau, Verwey and Overbeek (DLVO) theory. E. coli attachment to alumino-silica clays was evaluated in laboratory columns under saturated and steady-state flow conditions. E. coli deposition coefficient and desorption coefficient were simulated using convection–dispersion transport models against E. coli breakthrough curves, which were then linked to interactions between E. coli and the geological formation. It was discovered that E. coli deposition was controlled by the long-ranged electrostatic interaction and E. coli desorption was attributed to the short-ranged Lifshitz–van der Waals and Lewis acid–base interactions. E. coli transport in three layers of different alumino-silica clays was further examined and the breakthrough curve was simulated using E. coli deposition coefficient and desorption coefficient obtained from their individual column experiments. The well-fitted simulation confirmed that E. coli transport observations were interaction-dependent phenomena between E. coli and the geological formation.

Modeling the effects of water velocity on TiO2 nanoparticles transport in saturated porous media

The transport of manufactured titanium dioxide (TiO2, rutile) nanoparticles (NP) in porous media was investigated under saturated conditions. Experiments were carried out with different fluid velocities, with values in the range of observed velocities in alluvial aquifers. As reported on the literature for different kinds of NPs, the amount of retained NPs decreased when the water velocity increased. Moreover, no retention was observed for ionic strength values smaller than 5mM.A transport model coupling convective–dispersive transport with a Langmuirian kinetic deposition was used to fit the BTCs. Empirical linear equations were developed to estimate the attachment rate ka and the maximal solid phase concentration smax. Both parameters were found to be linearly depending on the collector efficiency (η0). It was also observed that attachment efficiency (α) did not change with increase of water velocity under the given experimental conditions and that the model had a low sensitivity to α. Based on these estimates of the retention parameters, the classical dispersion–convection model coupled with a Langmuir type adsorption model was able to reproduce quite well the observed TiO2 breakthrough curves for every fluid velocity used in the experiments.

Imaging and quantification of preferential solute transport in soil macropores

Despite significant advances during the last decades, there are still many processes related to nonequilibrium flow and transport in macroporous soil that are far from completely understood. The use of X-rays for imaging time-lapse 3-D solute transport has a large potential to help advance the knowledge in this field. We visualized the transport of potassium iodide (20 g iodide l−1 H2O) through a small undisturbed soil column (height 3.8 cm, diameter 6.8 cm) under steady state hydraulic conditions using an industrial X-ray scanner. In addition, the electrical conductivity was measured in the effluent solution during the experiment. We attained a series of seventeen 3-D difference images which we related to iodide concentrations using a linear calibration relationship. The solute transport through the soil mainly took place in two cylindrical macropores, by-passing more than 90% of the bulk soil volume during the entire experiment. From these macropores the solute diffused into the surrounding soil matrix. We illustrated the properties of the investigated solute transport by comparing it to a 1-D convective-dispersive transport and by calculating the temporal evolution of the dilution index. We furthermore showed that the tracer diffusion from one of the macropores into the surrounding soil matrix could not be exactly fitted with the cylindrical diffusion equation. We believe that similar studies will help establish links between soil structure and solute transport processes and lead to improvements in models for solute transport through undisturbed soil.

Numerical modelling of an oil spill in the northern Adriatic

Hypothetical cases of oil spills, caused by ship failure in the northern Adriatic, are analysed with the aim of producing three-dimensional models of sea circulation and oil contaminant transport. Sea surface elevations, sea temperature and salinity fields are applied as a forcing argument on the model’s open boundaries. The Aladin-HR model with a spatial resolution of 8km and a time interval of 3hours is used for atmospheric forcing. River discharges along the coastline in question are introduced as point source terms and are assumed to have zero salinity at their respective locations. The results of the numerical modelling of physical oceanography parameters are validated by measurements carried out in the ‘Adriatic Sea monitoring programme’ in a series of current meter and CTD stations in the period from 1 January 2008 to 15 November 2008.The oil spill model uses the current field obtained from a circulation model. Besides the convective dispersive transport of oil pollution (Lagrangian model of discrete particles), the model takes into account a number of reactive processes such as emulsification, dissolution, evaporation and heat balance between the oil, sea and atmosphere. An actual event took place on 6 February 2008, when the ship ‘Und Adriyatik’ caught fire in the vicinity of the town of Rovinj (Croatia) en route from Istanbul (Turkey) to Trieste (Italy). At the time the fire broke out, the ship was carrying around 800 tons of oil. Thanks to the rapid intervention of the fire department, the fire was extinguished during the following 12hours, preventing possible catastrophic environmental consequences. Based on this occurrence, five hypothetical scenarios of ship failure with a consequent spill of 800 tons of oil over 12hours were analysed. The main distinction between the simulated scenarios is the time of the start of the oil spill, corresponding to the times when stronger winds were blowing (>7ms−1) with a minimum duration of 24h within the timeframe. Each scenario includes a simulation of oil transport for a period of two months after the beginning of the oil spill.The results show that the coastal belt between the towns of Poreč and Rovinj is seriously exposed to an oil pollution load, especially a few days after a strong and persistent bora (NE wind).

Adsorption of Asphaltenes in Porous Media under Flow Conditions

Asphaltene adsorption on minerals induces wettability alteration in porous media, which, in turn, affects capillary pressure, relative permeability, and residual oil saturations. The majority of existing work addresses the adsorption of asphaltenes on minerals under static conditions, where adsorption isotherms are measured and modeled. Very little work currently exists on the adsorption kinetics of asphaltenes under dynamic conditions, which are more relevant to laboratory-scale experiments, specifically those involving dynamic wettability alteration of minerals. In this study, we propose to investigate the dynamic adsorption of different asphaltenes on various minerals using UV−vis spectroscopy. The experimental setup consists of a core holder containing crushed minerals with comparable mesh size. Asphaltene solutions in toluene are then flown though the mineral pack with a constant flow rate, and their concentrations are recorded with time at the outlet. Preliminary results indicate that adsorption is largely controlled by the type of mineral rather than the asphaltene itself. The highest adsorption amounts per unit area are found on calcite. Furthermore, the effect of several parameters, such as concentration, asphaltene composition, and flow rate, are considered. The theory of activated adsorption/desorption (TAAD) approach (Rudzinski, W.; Plazinski, W. J. Phys. Chem. C 2007, 111, 15100−15110) is incorporated into the convection-dispersion transport equation to model the flow of asphaltenes inside the porous medium. The resulting equation is then solved numerically using Barakat−Clark finite difference technique (Satter, A.; Shum, Y.; Adams, W.; Davis, L. SPE J. 1980, 20, 129−138). We find that kinetics and not equilibrium governs asphaltene adsorption in porous media. Levenberg−Marquardt’s optimization algorithm is used to derive kinetic parameters, such as Γm, ka, and kd. Once these concentration-independent parameters are found, the model is able to predict with reasonable accuracy the effect of concentration on asphaltene adsorption in porous media.

Comparison of Heterogeneous Transport Processes Observed with Electrical Resistivity Tomography in Two Soils

Preferential flow in soils can manifest itself in several ways. To illustrate this, we analyzed solute transport during a step tracer experiment in two soils expected to differ in their governing transport processes: a loamy sand and a silty soil. By combining electrical resistivity tomography (ERT), time domain reflectometry, and effluent measurements, we observed different preferential flow phenomena. The transport process was characterized using voxel‐ and column‐scale effective convective–dispersive equation (CDE) parameters, local velocities, and leaching surfaces. At the column scale, transport in the loamy sand was dominated by a homogenous convective–dispersive transport behavior, but at the scale of the voxel, preferential transport was observed. Transport in the silty soil was considerably more heterogeneous. Preferential flow was identified using ERT, voxel‐ and column‐scale effective CDE parameters, local velocities, and leaching surfaces. In these soils, a clear influence of soil layering on solute transport was observed.