Modeling of transport of radionuclides in beds of crushed crystalline rocks under equilibrium non-linear sorption isotherm conditions

AbstractA simple method for fitting the values of the experimental breakthrough curves in the form of pulse response obtained in dynamic flow column experiments is presented. It is based on the equation obtained by the analytical solution of a 1-D advection-dispersion equation (ADE) under defined conditions (equilibrium dynamics, linear sorption isotherm, constant bed height, pulse input), where the concentration (or activity) dependence on the number of pore volumes is expressed explicitly. It is shown that the method can be used in the case of validity of a non-linear Freundlich sorption isotherm if the experimental data are fitted by means of a Newton-Raphson multidimensional non-linear regression procedure in which the regression function consists of the above mentioned ADE equation and of the equation for a retardation coefficient including the first derivative of the Freundlich equation. Values of four parameters, namely, Freundlich equation parameters (

Download Full-text

Surface Resistance Limited Sorption Kinetics in Zeolite Crystals with a Non-Linear Sorption Isotherm

Zeitschrift für Physikalische Chemie ◽

10.1515/zpch-1986-26753 ◽

1986 ◽

Vol 267O (1) ◽

Cited By ~ 2

Author(s):

M. Kočiřík ◽

P. Struve ◽

M. Bülow

Keyword(s):

Sorption Isotherm ◽

Surface Resistance ◽

Sorption Kinetics ◽

Linear Sorption ◽

Non Linear ◽

Zeolite Crystals

Download Full-text

Determination of 137Cs and 85Sr transport parameters in fucoidic sand columns and groundwater system

Open Chemistry ◽

10.2478/s11532-011-0076-9 ◽

2011 ◽

Vol 9 (5) ◽

pp. 798-807 ◽

Cited By ~ 6

Author(s):

Štefan Palágyi ◽

Karel Štamberg

Keyword(s):

Solid Phase ◽

Breakthrough Curves ◽

Desorption Isotherm ◽

Hydrodynamic Dispersion ◽

Transport Parameters ◽

Constant Flow Rate ◽

Linear Sorption ◽

Non Linear ◽

Constant Distribution

AbstractThe determination is based on the evaluation of experimentally obtained breakthrough curves using the erfc-function. The first method is founded on the assumption of a reversible linear sorption/desorption isotherm of radionuclides on solid phase with constant distribution and retardation coefficients, whereas the second one is based on the assumption of a reversible non-linear sorption/desorption isotherm described with the Freundlich equation, i.e., with non-constant distribution and retardation coefficients. Undisturbed cores of 5 cm in diameter and 10 cm long were embedded in the Eprosin-type cured epoxide resin column. In this study the so-called Cenomanian background groundwater was used as transport medium. The groundwater containing radionuclides was introduced at the bottom of the columns at about 4 mL h−1 constant flow-rate. The results have shown that in the investigated fucoidic sands: (i) the sorption was in principle characterized by linear isotherms and the corresponding retardation coefficients of 137Cs and 85Sr, depending on the type of sample, were approximately 13 or 44 and 5 or 15, respectively; (ii) the desorption was characterized by non-linear isotherms, and the retardation coefficients of the same radionuclides ranged between 23–50 and 5–25, respectively. The values of the hydrodynamic dispersion coefficients of these radionuclides varied between 0.43–1.2 cm2 h−1.

Download Full-text

Application of linear and non-linear P-sorption models for describing phosphate transport.

Netherlands Journal of Agricultural Science ◽

10.18174/njas.v37i4.16625 ◽

1989 ◽

Vol 37 (4) ◽

pp. 387-390

Author(s):

S.E.A.T.M. van der Zee ◽

F. Leus ◽

M.J.P.F. Louer

Keyword(s):

Linear Model ◽

Phosphate Transport ◽

Breakthrough Curves ◽

Sorption Model ◽

P Sorption ◽

Simple Linear Model ◽

Precipitation Model ◽

Linear Sorption ◽

Non Linear ◽

Good Agreement

Phosphate transport in small columns was described using a two-site linear sorption model and a non-linear adsorption-precipitation model. Both approaches gave reasonable to good agreement with experimental breakthrough curves. This indicates the applicability of the simple linear model for engineering purposes, besides the general use of the more complex non-linear model. (Abstract retrieved from CAB Abstracts by CABI’s permission)

Download Full-text

A Simple Method for the Determination of Deposition Coefficient Using the Analytical Solution of Advection-Dispersion-Deposition Equation for Step Input

Water ◽

10.3390/w9060398 ◽

2017 ◽

Vol 9 (6) ◽

pp. 398

Author(s):

Nag-Choul Choi ◽

Jae-Woo Choi ◽

Kyu-Sang Kwon ◽

Sang-Gil Lee ◽

Bong-Ju Kim ◽

...

Keyword(s):

Analytical Solution ◽

Simple Method ◽

Step Input ◽

Advection Dispersion ◽

Deposition Coefficient

Download Full-text

Comparative analysis of linear and non-linear method of estimating the sorption isotherm parameters for malachite green onto activated carbon

Journal of Hazardous Materials ◽

10.1016/j.jhazmat.2005.09.018 ◽

2006 ◽

Vol 136 (2) ◽

pp. 197-202 ◽

Cited By ~ 83

Author(s):

K KUMAR

Keyword(s):

Activated Carbon ◽

Comparative Analysis ◽

Malachite Green ◽

Sorption Isotherm ◽

Linear Method ◽

Non Linear

Download Full-text

Mathematical Modeling of Sorption on Novel Sorbent Materials

10.5194/egusphere-egu21-10005 ◽

2021 ◽

Author(s):

Adna Koš ◽

Michal Kuráž

Keyword(s):

Metal Ions ◽

Programming Language ◽

Great Influence ◽

Langmuir Model ◽

Parameters Estimation ◽

Freundlich Model ◽

Error Functions ◽

Linear Sorption ◽

Non Linear ◽

Sorbent Materials

<p>The emission of metal ions in the environment has increased in recent times and since metal ions are not biodegradable, they belong to the cumulative toxins. Contamination of the environment with metal ions poses a serious danger to the entire ecosystem, agricultural production, quality of food and water, as well as to the health of humans and animals. This study investigates sorption as one of the processes which can be used for pollutants removal and efficiency of certain sorbent materials. Specifically, we focus on development and validation of non-linear Langmuir model and non-linear Freundlich model. Their application in sorption experiments is examined by applying different error functions and statistical methods which are employed to calculate the error divergence between observed data and predicted data of sorbate-sorbent system. Presented non-linear sorption models are developed by using programming language Fortran, and the data analysis is obtained by using different tools and packages in programming language R. Many authors are using linear sorption models in the way that they would linearize non-linear sorption models. It is evident that linear sorption models are used due to their simplicity in parameters estimation. We use approach of trying different algorithms and tools in programming language R in order to find the best objective function. This study shows that both non-linear Langmuir model and non-linear Freundlich model can be used for experimental data representation. The results also denote that better estimation and the better fit is given by Langmuir model due to divergence in error functions and graphical representation itself. The choice of sorption model has a great influence on the prediction of solute transfer and great care should be taken in selection of convenient approach.</p>

Download Full-text

An Overview of Stochastic Tools for Modeling Transport of Tracers in Heterogeneous Media

Applied Stochastic Hydrogeology ◽

10.1093/oso/9780195138047.003.0012 ◽

2003 ◽

Author(s):

Yoram Rubin

Keyword(s):

Spatial Variability ◽

Heterogeneous Media ◽

Breakthrough Curves ◽

Velocity Shear ◽

Numerical Dispersion ◽

Complex Flow ◽

Advection Dispersion ◽

Arbitrary Dimensions ◽

Flow Configurations ◽

Small Solute

Spatial variability and the uncertainty in characterizing the flow domain play an important role in the transport of contaminants in porous media: they affect the pathlines followed by solute particles, the spread of solute bodies, the shape of breakthrough curves, the spatial variability of the concentration, and the ability to quantify any of these accurately. This chapter briefly reviews some basic concepts which we shall later employ for the analysis of solute transport in heterogeneous media, and also points out some issues we shall address in the subsequent chapters. Our exposition in chapters 8-10 on contaminant transport is built around the Lagrangian and the Eulerian approaches for analyzing transport. The Eulerian approach is a statement of mass conservation in control volumes of arbitrary dimensions, in the form of the advection-dispersion equation. As such, it is well suited for numerical modeling in complex flow configurations. Its main difficulties, however, are in the assignment of parameters, both hydrogeological and geochemical, to the numerical grid blocks such that the effects of subgrid-scale heterogeneity are accounted for, and in the numerical dispersion that occurs in advection-dominated flow situations. Another difficulty is in the disparity between the scale of the numerical elements and the scale of the samples collected in the field, which makes the interpretation of field data difficult. The Lagrangian approach focuses on the displacements and travel times of solute bodies of arbitrary dimensions, using the displacements of small solute particles along streamlines as its basic building block. Tracking such displacements requires that the solute particles do not transfer across streamlines. Since such mass transfer may only occur due to pore-scale dispersion, Lagrangian approaches are ideally suited for advection-dominated situations. Let us start by considering the displacement of a small solute body, a particle, as a function of time. “Small” here implies that the solute body is much smaller than the characteristic scale of heterogeneity. At the same time, to qualify for a description of its movement using Darcy’s law, the solute body also needs to be larger than a few pores. The small dimension of the solute body ensures that it moves along a single streamline and that it does not disintegrate due to velocity shear.

Download Full-text

Experimental Evaluation of Distortion in Amplitude Modulation Techniques for Parametric Loudspeakers

Applied Sciences ◽

10.3390/app10062070 ◽

2020 ◽

Vol 10 (6) ◽

pp. 2070

Author(s):

Ricardo San Martín ◽

Pablo Tello ◽

Ana Valencia ◽

Asier Marzo

Keyword(s):

Frequency Response ◽

Amplitude Modulation ◽

Experimental Evaluation ◽

Harmonic Distortion ◽

Intermodulation Distortion ◽

Simple Method ◽

Modulation Techniques ◽

Audible Sound ◽

Non Linear

Parametric loudspeakers can generate a highly directional beam of sound, having applications in targeted audio delivery. Audible sound modulated into an ultrasonic carrier will get self-demodulated along the highly directive beam due to the non-linearity of air. This non-linear demodularization should be compensated to reduce audio distortion, different amplitude modulation techniques have been developed during the last years. However, some studies are only theoretical whereas others do not analyze the audio distortion in depth. Here, we present a detailed experimental evaluation of the frequency response, harmonic distortion and intermodulation distortion for various amplitude modulation techniques applied with different indices of modulation. We used a simple method to measure the audible signal that prevents the saturation of the microphones when the high levels of the ultrasonic carrier are present. This work could be useful for selecting predistortion techniques and indices of modulation for regular parametric arrays.

Download Full-text