Modelling velocity and retardation factor of a nonlinearly sorbing solute plume

Soil Research ◽  
2005 ◽  
Vol 43 (6) ◽  
pp. 735 ◽  
Author(s):  
M. A. Mojid ◽  
H. Vereecken
Keyword(s):  
Travel Time ◽  
Power Law ◽  
Transport Process ◽  
Breakthrough Curves ◽  
Retardation Factor ◽  
Sodium Fluorescein ◽  
Local Velocity ◽  
Steady State Condition ◽  
Travel Path ◽  
Non Equilibrium

This study, considering evidences of slower sorption rates of reactive solutes in the field than in laboratory, quantifies the velocity and retardation factor of a sodium fluorescein (uranin: C20H10Na2O5) plume over its travel path in a heterogeneous aquifer. The transport process of uranin was evaluated by batch experiments and from breakthrough curves (BTCs) by using solute-transport models. Method of time moments analysed BTCs of uranin and bromide to derive the velocity and retardation factor. A constant velocity of the bromide plume, 0.64 m/day, implies a spatially and temporally uniform velocity field where groundwater flows at steady-state condition. A large dimensionless index (195) of chemical non-equilibrium model and equilibrium distribution coefficient (0.32) of uranin are indicative of chemical non-equilibrium transport process. The travel time of uranin plume increases asymptotically, following power law, with travel path of the plume. Good agreement of the exponent of power law with that of Freundlich isotherm is a result of nonlinear sorption, and provides an independent way of estimating the exponent of the isotherm. The local velocity of the plume decreases asymptotically in time and is predicted by the derivative of the relationship between travel path and travel time of the plume. The retardation factor, which increases in time following power law, when estimated from the local velocity, is considerably larger than that estimated from travel time of the plume.

scholarly journals An Application of Safety Assessment for Radioactive Waste Repository: Non-Equilibrium Transport of Tritium, Selenium, and Cesium in Crushed Granite with Different Path Lengths

2021 ◽  
Vol 11 (20) ◽  
pp. 9750
Author(s):  
Chuan-Pin Lee ◽  
Dongyang Chen ◽  
Yanqin Hu ◽  
Yi-Lin Jan ◽  
Yunfeng Shi ◽  
...  
Keyword(s):  
Radioactive Waste ◽  
Safety Assessment ◽  
Breakthrough Curves ◽  
Retardation Factor ◽  
Suitable Model ◽  
Advection Dispersion ◽  
Crushed Granite ◽  
Path Lengths ◽  
High Level ◽  
Non Equilibrium

Advection-dispersion experiments (ADE) were effectively designed for inadequate transport models through a calibration/validation process. HTO, selenium (Se), and cesium (Cs) transport in crushed granite were studied using a highly reliable, dynamic column device in order to obtain the retardation factors (R) and the dispersion coefficients (D) by fitting experimental breakthrough curves (BTCs) for various path lengths. In order to conduct a safety assessment (SA) of a deep geological repository for high-level radioactive waste, radionuclide transport in rock systems is necessary to clarify and establish a suitable model. A dynamic column with a radiotracer (HTO, Se(IV), and Cs) was applied to 2, 4, and 8 cm path lengths using a STANMOD simulation. The results showed similar results between the BTCs of Se and Cs by fitting a non-equilibrium sorption model due to the retardation effect. In fact, there was a relatively obvious sorption of Se and Cs in the BTCs obtained by fitting a retardation factor (R) value higher than 1. In addition, a two-region (physical) and a two-site (chemical) non-equilibrium model with either the lowest sum of squared residuals (SSQ) or the root mean square error (RMSE) were applied to determine the Se and Cs sorption mechanisms on granite.

The extended transfer function model for the simulation of pesticides transport along the unsaturated zone

2021 ◽  
Author(s):  
Marialaura Bancheri ◽  
Antonio Coppola ◽  
Annachiara Colombi ◽  
Angelo Basile
Keyword(s):  
Transfer Function ◽  
Travel Time ◽  
Unsaturated Zone ◽  
Transfer Functions ◽  
Temporal Distribution ◽  
Absolute Error ◽  
Breakthrough Curves ◽  
Retardation Factor ◽  
Transfer Function Model ◽  
Function Model

<p><span lang="EN-US">The scope of this work is to present the extended transfer function model (TFM-ext) that allows to simulate the spatio-temporal distribution of nonpoint-source pollutants, e.g., pesticides, along the unsaturated zone, till the groundwater table depth.</span></p> <p><span lang="EN-US">The model is based on the transfer functions approach, i.e., on the travel time probability density functions (TT pdfs), which describe the leaching behavior in a given soil profile. The strength of the model, despite the important assumptions on time-invariant TT pdfs and steady-state input fluxes, is that it derives the TT pdfs from a physical quantity, i.e., the unsaturated hydraulic conductivity function k(</span>θ<span lang="EN-US">).  Moreover, the model extends the transport process to the generic depth z, where information on hydraulic properties could not be available, assuming a lognormal travel time pdf, whose parameters are scaled according to the generalized transfer function model. </span><span lang="EN-GB">In the case of reactive solutes, the model considers both the mass decay and the retardation factor.</span></p> <p><span lang="EN-US">The TFM-ext was validated in Valle Telesina, a hilly area of around 200 km<sup>2</sup><span class="apple-converted-space"> </span>in Italy. Forty-six soil profiles, completely characterized from the hydrological point of view, were used to evaluate the mean travel times and the breakthrough curves at the groundwater depth and then compared with the results of a physically based model, Hydrus 1D. Results gave very high correlation coefficients (above 0.8), a mean absolute error of around 40 days and a percent bias of -16%.</span></p> <p><span lang="EN-US">Moreover, a comprehensive sensitivity analysis to evaluate to which parameters the TFM-ext is more sensitive, was performed. Results shown that </span>τ <span lang="EN-US">anf θ<sub>s</sub> parameters related to the slope of the k(θ) are those affecting more the travel time. </span></p> <p><span lang="EN-US">The model was implemented as an operative tool for the specific groundwater vulnerability assessment within the geospatial Decision Support System developed for LANDSUPPORT H2020 project.</span></p>

Parameter Determination for Chloride and Tritium Transport in Undisturbed Lysimeters during Steady Flow

1992 ◽  
Vol 23 (2) ◽  
pp. 89-104 ◽  
Author(s):  
Ole H. Jacobsen ◽  
Feike J. Leij ◽  
Martinus Th. van Genuchten
Keyword(s):  
Experimental Data ◽  
Unsaturated Flow ◽  
Transport Model ◽  
Time Moment ◽  
Breakthrough Curves ◽  
Coarse Sand ◽  
Retardation Factor ◽  
Parameter Determination ◽  
Model Parameters ◽  
Water Fraction

Breakthrough curves of Cl and 3H2O were obtained during steady unsaturated flow in five lysimeters containing an undisturbed coarse sand (Orthic Haplohumod). The experimental data were analyzed in terms of the classical two-parameter convection-dispersion equation and a four-parameter two-region type physical nonequilibrium solute transport model. Model parameters were obtained by both curve fitting and time moment analysis. The four-parameter model provided a much better fit to the data for three soil columns, but performed only slightly better for the two remaining columns. The retardation factor for Cl was about 10 % less than for 3H2O, indicating some anion exclusion. For the four-parameter model the average immobile water fraction was 0.14 and the Peclet numbers of the mobile region varied between 50 and 200. Time moments analysis proved to be a useful tool for quantifying the break through curve (BTC) although the moments were found to be sensitive to experimental scattering in the measured data at larger times. Also, fitted parameters described the experimental data better than moment generated parameter values.

Transport of Microorganisms in the Underground – Processes, Experiments and Simulation Models

1991 ◽  
Vol 24 (2) ◽  
pp. 309-314 ◽  
Author(s):  
G. Teutsch ◽  
K. Herbold-Paschke ◽  
D. Tougianidou ◽  
T. Hahn ◽  
K. Botzenhart
Keyword(s):  
Simulation Models ◽  
Mass Conservation ◽  
Breakthrough Curves ◽  
Conservation Equation ◽  
Retardation Factor ◽  
Natural Systems ◽  
Laboratory Setup ◽  
Preliminary Model ◽  
Sand And Gravel ◽  
Mass Conservation Equation

In this paper the major processes governing the persistence and underground transport of viruses and bacteria are reviewed in respect to their importance under naturally occurring conditions. In general, the simulation of the governing processes is based on the macroscopic mass-conservation equation with the addition of some filter and/or retardation factor and a decay coefficient, representing the natural “die-off” of the microorganisms. More advanced concepts try to incorporate growth and decay coefficients together with deposition and declogging factors. At present, none of the reported concepts has been seriously validated. Due to the complexity of natural systems and the pathogenic properties of some of the microorganisms, experiments under controlled laboratory conditions are required. A laboratory setup is presented in which a great variety of natural conditions can be simulated. This comprises a set of 1 metre columns and an 8 metre stainless-steel flume with 24 sampling ports. The columns are easily filled and conditioned and therefore used to study the effects of different soil-microorganism combinations under various environmental conditions. In the artificial flume natural underground conditions are simulated using sand and gravel aquifer material from the river Neckar alluvium. A first set of results from the laboratory experiments is presented together with preliminary model simulations. The large variety of observed breakthrough curves and recovery for the bacteria and viruses under investigation demonstrates the great uncertainty encountered in microbiological risk assessment.

scholarly journals Stationary Non-equilibrium Solutions for Coagulation Systems

2021 ◽  
Vol 240 (2) ◽  
pp. 809-875
Author(s):  
Marina A. Ferreira ◽  
Jani Lukkarinen ◽  
Alessia Nota ◽  
Juan J. L. Velázquez
Keyword(s):  
Power Law ◽  
Source Term ◽  
Continuous Model ◽  
Stationary Solutions ◽  
Weight Functions ◽  
Equilibrium Solutions ◽  
Coagulation Rate ◽  
Diffusion Limited Aggregation ◽  
Coagulation Equations ◽  
Non Equilibrium

AbstractWe study coagulation equations under non-equilibrium conditions which are induced by the addition of a source term for small cluster sizes. We consider both discrete and continuous coagulation equations, and allow for a large class of coagulation rate kernels, with the main restriction being boundedness from above and below by certain weight functions. The weight functions depend on two power law parameters, and the assumptions cover, in particular, the commonly used free molecular and diffusion limited aggregation coagulation kernels. Our main result shows that the two weight function parameters already determine whether there exists a stationary solution under the presence of a source term. In particular, we find that the diffusive kernel allows for the existence of stationary solutions while there cannot be any such solutions for the free molecular kernel. The argument to prove the non-existence of solutions relies on a novel power law lower bound, valid in the appropriate parameter regime, for the decay of stationary solutions with a constant flux. We obtain optimal lower and upper estimates of the solutions for large cluster sizes, and prove that the solutions of the discrete model behave asymptotically as solutions of the continuous model.

scholarly journals A general real-time formulation for multi-rate mass transfer problems

2009 ◽  
Vol 6 (2) ◽  
pp. 2415-2449 ◽  
Author(s):  
O. Silva ◽  
J. Carrera ◽  
S. Kumar ◽  
M. Dentz ◽  
A. Alcolea ◽  
...  
Keyword(s):  
Mass Transfer ◽  
River Flow ◽  
Breakthrough Curves ◽  
Flow And Transport ◽  
Multiple Processes ◽  
Programming Effort ◽  
Non Local ◽  
Time Formulation ◽  
Transfer Problems ◽  
Non Equilibrium

Abstract. Many flow and transport phenomena, ranging from delayed storage observed in pumping tests to tailing in river or aquifer tracer breakthrough curves, display non-equilibrium behavior. Usually, they are modeled by non-local in time formulations, such as multi-porosity, multiple processes non equilibrium, continuous time random walk, memory functions, integro-differential equations, fractional derivatives or multi-rate mass transfer (MRMT), among others. We develop a MRMT algorithm that can be used to represent all these formulations. The method is accurate, computationally inexpensive and easy to implement in groundwater or river flow and transport codes. In fact, we present a module that can be linked to existing programs with minimal programming effort. Its accuracy is verified by comparison with existing solutions.

scholarly journals DETERMINATION OF TRANSPORT PARAMETERS FOR SOLUTES IN SALT-TREATED SOIL COLUMNS

2017 ◽  
Vol 48 (1) ◽  
Author(s):  
Bahia & Naser
Keyword(s):  
Sodium Chloride ◽  
Calcium Chloride ◽  
Peclet Number ◽  
Dispersion Coefficient ◽  
Breakthrough Curves ◽  
Retardation Factor ◽  
Transport Parameters ◽  
Péclet Number ◽  
Mixed Salts ◽  
Sodium And Potassium

A laboratory experiment was carried out at the Department of Soil Sciences and Water Resources, College of Agriculture, University of Baghdad. Silty clay soil was treated with three salt solutions (NaCl, CaCl2 and mixed NaCl–CaCl2). Homogeneously packed soil columns (10 cm, 40 cm) were leached six times using tap water. Effluent samples were collected to determine ion concentration Cl-, Ca++, Na+, K+ and Mg++. Breakthrough curves were used to estimate solute transport parameters (retardation factor, peclet number) using an analytical solution of convection-dispersion equation (CDE) by CXTFIT program. The results showed that relative concentration of chloride was increased rapidly with calcium chloride, which increased sodium leaching rate at starting of breakthrough curve. Sodium chloride increased water requirements for calcium displacement. Results indicated a good fitting of convection-dispersion equation with breakthrough curves data. The best-fit were used to calculate peclet number, retardation factor and dispersion coefficient. When soil was treated with calcium chloride, Peclet number of chloride was increased from 3.13 to 6.48, while it has been decreased for calcium, sodium and potassium. Sodium chloride decreased peclet numbers of chloride, calcium and sodium. Also mixed salts increased sodium peclet number from 1.01 to 9.02. Results showed, calcium chloride decreased retardation factor of chloride from 1.59 to 0.50, while it has been increased from 1.39, 1.58 to 175.00, 493.36 for each of sodium and potassium, respectively. Retardation factor of calcium was decreased when soil was treated with sodium chloride or mixed salts. Dispersion coefficient was decreased for chloride, and increased for calcium and magnesium. When soil was treated with calcium chloride, dispersion coefficients have been increased from 24.29, 25.56 to 40.51, 40.89 cm2hr-1 for sodium and potassium, respectively.

scholarly journals Short Term Effects of Salinization on Compound Release from Drained and Restored Coastal Wetlands

Water ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 1549 ◽  
Author(s):  
Haojie Liu ◽  
Bernd Lennartz
Keyword(s):  
Fresh Water ◽  
Coastal Wetlands ◽  
Saline Water ◽  
Breakthrough Curves ◽  
Water Salinity ◽  
Retardation Factor ◽  
Peat Soils ◽  
Exchange Processes ◽  
Nacl Concentration ◽  
Flow Through

Over the past two decades, great efforts have been made to restore coastal wetlands through the removal of dikes, but challenges remain because the effects of flooding with saline water on water quality are unknown. We collected soil samples from two adjacent coastal fen peatlands, one drained and diked, the other open to the sea and rewetted, aiming at assessing the mobility and export of various compounds. Microcosm experiments with constant flow-through conditions were conducted to determine the effluent concentrations of dissolved organic carbon (DOC), ammonium ( NH 4 + ), and phosphate ( PO 4 3 − ) during saline–fresh water cycles. Sodium chloride (NaCl) was used to adjust salinity (saline water, NaCl concentration of 0.12 mol L−1; fresh water, NaCl concentration of 0.008 mol L−1) and served as a tracer. A model analysis of the obtained chloride ( Cl − ) and sodium ( Na + ) breakthrough curves indicated that peat soils have a dual porosity structure. Sodium was retarded in peat soils with a retardation factor of 1.4 ± 0.2 due to adsorption. The leaching tests revealed that water salinity has a large impact on DOC, NH 4 + , and PO 4 3 − release. The concentrations of DOC in the effluent decreased with increasing water salinity because the combination of high ionic strength (NaCl concentration of 0.12 mol L−1) and low pH (3.5 to 4.5) caused a solubility reduction. On the contrary, saline water enhanced NH 4 + release through cation exchange processes. The PO 4 3 − concentrations, however, decreased in the effluent with increasing water salinity. Overall, the decommissioning of dikes at coastal wetlands and the flooding of once drained and agriculturally used sites increase the risk that especially nitrogen may be leached at higher rates to the sea.

Comparative analyses of alternative breakthrough curves from cumulative mass column testing of soil–bentonite backfills

2020 ◽  
Vol 57 (8) ◽  
pp. 1197-1214 ◽  
Author(s):  
Charles D. Shackelford ◽  
Catherine S. Hong
Keyword(s):  
Steady State ◽  
Solute Transport ◽  
Breakthrough Curves ◽  
Retardation Factor ◽  
Dimensionless Time ◽  
Mass Ratio ◽  
Column Tests ◽  
Cutoff Walls ◽  
Cumulative Mass ◽  
Linear Regressions

The results of eight cumulative mass column tests were analyzed via several different methods to evaluate the dispersion coefficient, D, and the retardation factor, Rd, governing the migration of chloride (Cl−), potassium (K), and zinc (Zn) through soil–bentonite backfills for vertical cutoff walls. Regression of the measured relative (effluent) concentration (RC) breakthrough curves (BTCs) resulted in relatively accurate determinations of Rd, but relatively inaccurate determinations of D for all three solutes. Values of Rd based on dimensionless time, T, corresponding to an RC of 0.5 were underestimated for all three solutes due to the significance of diffusion on solute transport. With a few exceptions, Rd for K and Zn based on analyses of the steady-state portions of measured cumulative mass ratio (CMR) BTCs and T – CMR BTCs were relatively accurate, whereas analysis of measured T – CMR BTCs was more accurate for determining Rd of Cl−. Overall, there is no advantage to analyzing the results of cumulative mass column tests in the form of RC BTCs, whereas the CMR and T – CMR BTCs offer the advantage of determining Rd based on simple linear regressions of the steady-state portions of the BTCs, i.e., provided steady-state solute transport has been established.

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