scholarly journals Searching for optimum adsorption curve for metal sorption on soils: comparison of various isotherm models fitted by different error functions

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
Péter Sipos
Keyword(s):  
Experimental Data ◽  
Error Function ◽  
Isotherm Models ◽  
Metal Sorption ◽  
Error Functions ◽  
Sorption System ◽  
Geochemical Properties ◽  
Function Combination ◽  
Soil Metal ◽  
Sorption Curve

AbstractStudies comparing numerous sorption curve models and different error functions are lacking completely for soil-metal adsorption systems. We aimed to fill this gap by studying several isotherm models and error functions on soil-metal systems with different sorption curve types. The combination of fifteen sorption curve models and seven error functions were studied for Cd, Cu, Pb, and Zn in competitive systems in four soils with different geochemical properties. Statistical calculations were carried out to compare the results of the minimizing procedures and the fit of the sorption curve models. Although different sorption models and error functions may provide some variation in fitting the models to the experimental data, these differences are mostly not significant statistically. Several sorption models showed very good performances (Brouers-Sotolongo, Sips, Hill, Langmuir-Freundlich) for varying sorption curve types in the studied soil-metal systems, and further models can be suggested for certain sorption curve types. The ERRSQ error function exhibited the lowest error distribution between the experimental data and predicted sorption curves for almost each studied cases. Consequently, their combined use could be suggested for the study of metal sorption in the studied soils. Besides testing more than one sorption isotherm model and error function combination, evaluating the shape of the sorption curve and excluding non-adsorption processes could be advised for reliable data evaluation in soil-metal sorption system.

scholarly journals Heavy Metal Sorption by Sludge-Derived Biochar with Focus on Pb2+ Sorption Capacity at μg/L Concentrations

Processes ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 1559
Author(s):  
Ida Sylwan ◽  
Hanna Runtti ◽  
Lena Johansson Westholm ◽  
Henrik Romar ◽  
Eva Thorin
Keyword(s):  
Experimental Data ◽  
Heavy Metals ◽  
Heavy Metal ◽  
Sorption Capacity ◽  
Municipal Wastewater ◽  
Metal Removal ◽  
Metal Exposure ◽  
Isotherm Models ◽  
Metal Sorption ◽  
Heavy Metal Sorption

Municipal wastewater management causes metal exposure to humans and the environment. Targeted metal removal is suggested to reduce metal loads during sludge reuse and release of effluent to receiving waters. Biochar is considered a low-cost sorbent with high sorption capacity for heavy metals. In this study, heavy metal sorption to sludge-derived biochar (SDBC) was investigated through batch experiments and modeling and compared to that of wood-derived biochar (WDBC) and activated carbon (AC). The aim was to investigate the sorption efficiency at metal concentrations comparable to those in municipal wastewater (<1 mg/L), for which experimental data are lacking and isotherm models have not been verified in previous works. Pb2+ removal of up to 83% was demonstrated at concentrations comparable to those in municipal wastewater, at pH 2. SDBC showed superior Pb2+ sorption capacity (maximum ~2 mg/g at pH 2) compared to WDBC and AC (<0 and (3.5 ± 0.4) × 10−3 mg/g, respectively); however, at the lowest concentration investigated (0.005 mg/L), SDBC released Pb2+. The potential risk of release of other heavy metals (i.e., Ni, Cd, Cu, and Zn) needs to be further examined. The sorption capacity of SDBC over a metal concentration span of 0.005–150 mg Pb2+/L could be predicted with the Redlich–Peterson model. It was shown that experimental data at concentrations comparable to those in municipal wastewater are necessary to accurately model and predict the sorption capacity of SDBC at these concentrations.

scholarly journals Evaluation of the Microsoft Excel Solver Spreadsheet-Based Program for Nonlinear Expressions of Adsorption Isotherm Models onto Magnetic Nanosorbent

2021 ◽  
Vol 11 (16) ◽  
pp. 7432
Author(s):  
Kowit Suwannahong ◽  
Surachai Wongcharee ◽  
Torpong Kreetachart ◽  
Chadrudee Sirilamduan ◽  
Javier Rioyo ◽  
...  
Keyword(s):  
Experimental Data ◽  
Wastewater Treatment ◽  
Function Analysis ◽  
Error Function ◽  
Isotherm Models ◽  
Microsoft Excel ◽  
Water And Wastewater Treatment ◽  
Water And Wastewater ◽  
Excel Solver ◽  
Magnetic Nanosorbent

The sorption of basic dyes onto magnetic nanosorbent is commonly used as a novel material to combat powdered activated carbon, which is difficult to handle and separate during water and wastewater treatment. This adsorption method is commonly implemented in water and wastewater treatment due to its low cost and high performance. To explore the feasibility of adsorption, six different nonlinear isotherm models were applied and introduced to evaluate the performance and adsorption mechanisms via Microsoft Excel, and they were then compared to those of MATLAB and OriginPro. The Langmuir best provided the sorption of methylene blue adsorbed for a two-parameter isotherm model. The three-parameter model Toth gave a goodness of fit indicating a heterogeneous sorbent surface. Error function analysis found that the Residual Sum of Squares Error, Chi-square, Coefficient of determination, Average Relative Error, Hybrid Fractional Error Function, Marquardt’s Percent Standard Deviation and Root Mean Square Error provided the best overall results. In comparison, it could be concluded that six isotherm models showed the confidence interval that is simply the best fit at all experimental data points provided by the three software tools. All error function results indicated that the Microsoft Excel Solver function spreadsheet method satisfied all the statistic measures to predict the real variance of the probability of experimental data for all six isotherm models of adsorption of basic dye removal. One added benefit of this Microsoft Excel software tool is the built-in function associated with the desired type of application, which designates the desired type of error/statistical functions not mentioned in this research to the adsorbent materials used.

scholarly journals Determination of best-fit isotherm model for the sorption of Lead (II) and Manganese (II) ions onto acid-activated shale using selected non-linear error functions

2021 ◽  
Vol 5 (1) ◽  
pp. 11-19
Author(s):  
I. R. Ilaboya ◽  
J. S. Okpoko
Keyword(s):  
Standard Deviation ◽  
Error Function ◽  
Surface Characteristics ◽  
Isotherm Model ◽  
Isotherm Models ◽  
Error Functions ◽  
Function Computation ◽  
Normalized Error ◽  
Non Linear ◽  
Best Fit

The focus of this research is to apply the selected error function equation to establish the equilibrium isotherm model that best describes the adsorption of Pb2+ and Mn2+ onto acid-activated shale.  Data collected from the batch experiment were analyzed using selected isotherm models (Langmuir, Freundlich, Temkin, Dubinin-Radushkevich, Sips and Redlich-Peterson). To compute the isotherm parameters used in choosing the best-fit isotherm model, selected non-linear error functions, namely, error sum of the square, normalized standard deviation, hybrid error function, root mean square error and Marquardt’s percent standard deviation were employed. From the scanning electron microscope results, it was observed that the surface characteristics of the shale change considerably with calcination and acid treatment but the acid-treated shale shows better uneven porous surface characteristics. Error function computation shows that the Dubinin-Radushkevich isotherm model had the least sum of normalized error of 0.3623 for Pb2+ adsorption and 0.5465 for Mn2+ adsorption; hence, it was selected as the best isotherm model for explaining the sorption of Pb(II) and Mn(II) ions unto acid-activated shale.

An extension of q-starlike and q-convex error functions endowed with the trigonometric polynomials

2020 ◽  
Vol 70 (3) ◽  
pp. 599-604
Author(s):  
Şahsene Altinkaya
Keyword(s):  
Error Function ◽  
Trigonometric Polynomials ◽  
Error Functions ◽  
The Family ◽  
Coefficient Inequalities

AbstractIn this present investigation, we will concern with the family of normalized analytic error function which is defined by$$\begin{array}{} \displaystyle E_{r}f(z)=\frac{\sqrt{\pi z}}{2}\text{er} f(\sqrt{z})=z+\overset{\infty }{\underset {n=2}{\sum }}\frac{(-1)^{n-1}}{(2n-1)(n-1)!}z^{n}. \end{array}$$By making the use of the trigonometric polynomials Un(p, q, eiθ) as well as the rule of subordination, we introduce several new classes that consist of 𝔮-starlike and 𝔮-convex error functions. Afterwards, we derive some coefficient inequalities for functions in these classes.

scholarly journals Multi-Component Adsorption of Benzene, Toluene, Ethylbenzene, and Xylene from Aqueous Solutions by Montmorillonite Modified with Tetradecyl Trimethyl Ammonium Bromide

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
H. Nourmoradi ◽  
Mehdi Khiadani ◽  
M. Nikaeen
Keyword(s):  
Experimental Data ◽  
Aqueous Solutions ◽  
Structural Changes ◽  
Freundlich Isotherm ◽  
Isotherm Models ◽  
Ammonium Bromide ◽  
Order Kinetic ◽  
Multicomponent Adsorption ◽  
Benzene Toluene ◽  
Kinetic And Isotherm Models

Multicomponent adsorption of benzene, toluene, ethylbenzene, and xylene (BTEX) was assessed in aqueous solutions by montmorillonite modified with tetradecyl trimethyl ammonium bromide (TTAB-Mt). Batch experiments were conducted to determine the influences of parameters including loading rates of surfactant, contact time, pH, adsorbate concentration, and temperature on the adsorption efficiency. Scanning electron microscope (SEM) and X-ray diffractometer (XRD) were used to determine the adsorbent properties. Results showed that the modification of the adsorbent via the surfactant causes structural changes of the adsorbent. It was found that the optimum adsorption condition achieves with the surfactant loading rate of 200% of the cation exchange capacity (CEC) of the adsorbent for a period of 24 h. The sorption of BTEX by TTAB-Mt was in the order ofB<T<E<X. The experimental data were fitted by many kinetic and isotherm models. The results also showed that the pseudo-second-order kinetic model and Freundlich isotherm model could, respectively, be fitted to the experimental data better than other available kinetic and isotherm models. The thermodynamic study indicated that the sorption of BTEX with TTAB-Mt was achieved spontaneously and the adsorption process was endothermic as well as physical in nature. The regeneration results of the adsorbent also showed that the adsorption capacity of adsorbent after one use was 51% to 70% of original TTAB-Mt.

Preparation of crosslinked chitosan magnetic membrane for cations sorption from aqueous solution

2017 ◽  
Vol 75 (9) ◽  
pp. 2034-2046 ◽  
Author(s):  
Adnan Khan ◽  
Samina Begum ◽  
Nauman Ali ◽  
Sabir Khan ◽  
Sajjad Hussain ◽  
...  
Keyword(s):  
Experimental Data ◽  
Aqueous Solution ◽  
Adsorption Capacity ◽  
Magnetic Particles ◽  
Isotherm Models ◽  
Chitosan Membrane ◽  
Dilute Aqueous Solution ◽  
Chitosan Membranes ◽  
The Fourier Transform ◽  
Time Required

A chitosan magnetic membrane was prepared in order to confer magnetic properties to the membrane, which could be used for the removal of cations from aqueous solution. The crosslinked magnetic membrane was compared with pristine chitosan membrane in term of stability, morphology and cation adsorption capacity. The fabricated magnetic materials are thermally stable as shown by thermogravimetric curves. The membrane containing nickel magnetic particles (CHNiF-G) shows high thermal stability compared to the other membranes. The Fourier transform infrared spectroscopy showed successful preparation of chitosan magnetic membrane. Scanning electron microscopy micrographs showed the rough surface of the membrane with increased porosity. The prepared chitosan membranes were applied to cations of copper, nickel and lead in dilute aqueous solution. The chitosan membrane showed the following adsorption order for metallic cations: Cu2+ &gt; Ni2+ &gt; Pb2+, while CHNiF-G showed higher capacity, 3.51 mmol g−1 for copper, reflecting the improvement in adsorption capacity, since the amount of copper on pristine chitosan gave 1.40 mmol g−1. The time required for adsorption to reach to the equilibrium was 6 h for the selected cations using different chitosan membranes. The kinetic study showed that adsorption followed pseudo-second order kinetics. The most commonly used isotherm models, Freundlich, Langmuir and Temkin, were applied to experimental data using linear regression technique. However, The Temkin model fits better to experimental data.

scholarly journals Thermodynamic properties and moisture sorption isotherms of two pharmaceutical compounds

2018 ◽  
Author(s):  
Amel Zammouri ◽  
M. Ben Zid ◽  
N. Kechaou ◽  
N. Boudhrioua Mihoubi
Keyword(s):  
Experimental Data ◽  
Thermodynamic Properties ◽  
Moisture Content ◽  
Equilibrium Moisture Content ◽  
Water Sorption ◽  
Pharmaceutical Preparations ◽  
Sorption Isotherms ◽  
Integral Enthalpy ◽  
Isotherm Models ◽  
Water Sorption Isotherms

This investigation examines and compares the water sorption isotherms and the thermodynamic properties of two pharmaceutical preparations (Hypril and Azix) intended to be manufactured with the same process plant and equipment. The moisture equilibrium isotherms were determined at 50, 60 and 70 °C using a gravimetric technique. Five isotherm models were explored for their fitting to the experimental data. Azix showed sigmoid type II isotherms while Hypril showed type III isotherms according to the BET classification. All investigated models fitted well the water sorption isotherms of Hypril. By contrast, only GAB and Adam and Shove equations gave appropriate fit to the experimental data of Azix. For both formulations, the isosteric heat and the differential entropy decreased sharply with the increase of equilibrium moisture content to minimum values and thereafter remain constant. In the case of Azix, the integral enthalpy decreased with equilibrium moisture content while the integral entropy increased until reaching a constant value. Contrariwise, Hypril showed decreasing of the integral enthalpy and entropy with the equilibrium moisture content. Keywords: sorption isotherm, enthalpy, entropy, spreading pressure, pharmaceutical formulations  

scholarly journals Adsorption of propan-1-ol vapour on Sorbonorit 4 activated carbon – equilibrium and dynamic studies

2017 ◽  
Vol 19 (4) ◽  
pp. 59-64 ◽  
Author(s):  
Dorota Downarowicz ◽  
Katarzyna Ziętarska
Keyword(s):  
Experimental Data ◽  
Activated Carbon ◽  
Energy Requirement ◽  
Isosteric Heat ◽  
Breakthrough Curves ◽  
Isotherm Models ◽  
Column Studies ◽  
Temperature Isotherm ◽  
Electrothermal Desorption ◽  
Temperature Swing Adsorption

Abstract The study examined the adsorption of propan-1-ol (1PN) vapour on Sorbonorit 4 (S4) activated carbon in cyclic Electrothermal Temperature Swing Adsorption (ETSA) process. Dynamic adsorption capacity and breakthrough time were determined based on column studies. Thomas model was used to describe experimental breakthrough curves. Adsorption isotherms for 1PN vapour on S4 activated carbon were tested at 293 to 413 K. The experimental data were examined by using three multi-temperature isotherm models: Toth, Sips and hybrid Langmuir-Sips. Results indicate that S4 activated carbon is a heterogeneous adsorbent and the hybrid Langmuir-Sips model provides the best-fit experimental data. The energy requirement for 1PN electrothermal desorption from S4 bed (ca. 170–200 kJ/mol) was about 3 to 3.5 times larger than the isosteric heat of adsorption (56.8 kJ/mol), which was calculated using Toth adsorption isotherm.

scholarly journals Adsorption of UV254 in Kerian River water onto ZeliacTM: Analysis using linear and non-linear forms of isotherm models

2017 ◽  
Vol 19 (1) ◽  
pp. 74-81 ◽  
Keyword(s):  
River Water ◽  
Function Analysis ◽  
Low Cost ◽  
Error Function ◽  
Linear Regression Analysis ◽  
Freundlich Isotherm ◽  
Linear Analysis ◽  
Isotherm Models ◽  
Freundlich Isotherms ◽  
Non Linear

<p>The composite media, Zeliac<sup>TM</sup> was developed with the initial aim to provide low cost adsorbent with promising adsorption capacity. This study was conducted to investigate the removal of UV absorbance at 254 nm (UV<sub>254</sub>) in Kerian river water using Zeliac<sup>TM</sup> as the media. Batch experiments study was carried out to determine the optimum removal of UV<sub>254</sub> by Zeliac<sup>TM</sup>. The experimental data were fitted to Langmuir and Freundlich isotherms to investigate the adsorption mechanism. The results from batch study exhibit that Zeliac<sup>TM</sup> is capable to remove 74.4% UV<sub>254</sub> at the dosage of 7g/100 ml. Linear isotherm analysis suggests that the best fitting linear line is Freundlich isotherm with R<sup>2</sup> values of 0.9294 indicating multilayer adsorption. Similarly, non-linear regression analysis reveals that the adsorption of UV<sub>254</sub> by Zeliac<sup>TM</sup> is attributed by physisorption. The non-linear Freundlich isotherm gives a better fit to the adsorption of UV<sub>254</sub> than Langmuir isotherm with R<sup>2</sup> values of 0.9488. The results are supported with low values of X<sup>2</sup>, ARE, HYBRID and MPSED from the error function analysis.&nbsp; Additionally, it is noted that the linear analysis overestimates the constant parameters’ values for Freundlich isotherm, which cause larger errors as estimated by the error function analysis. Hence, non-linear analysis is more appropriate in explaining the batch experiment data.</p>

scholarly journals Some Discussions about the Error Functions on SO(3) and SE(3) for the Guidance of a UAV Using the Screw Algebra Theory

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Yi Zhu ◽  
Xin Chen ◽  
Chuntao Li
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Error Function ◽  
Elliptic Cylinder ◽  
General Situation ◽  
3 Dimensional ◽  
Error Functions ◽  
Aerial Vehicle ◽  
Algebra Theory ◽  
In The Beginning

In this paper a new error function designed on 3-dimensional special Euclidean group SE(3) is proposed for the guidance of a UAV (Unmanned Aerial Vehicle). In the beginning, a detailed 6-DOF (Degree of Freedom) aircraft model is formulated including 12 nonlinear differential equations. Secondly the definitions of the adjoint representations are presented to establish the relationships of the Lie groups SO(3) and SE(3) and their Lie algebras so(3) and se(3). After that the general situation of the differential equations with matrices belonging to SO(3) and SE(3) is presented. According to these equations the features of the error function on SO(3) are discussed. Then an error function on SE(3) is devised which creates a new way of error functions constructing. In the simulation a trajectory tracking example is given with a target trajectory being a curve of elliptic cylinder helix. The result shows that a better tracking performance is obtained with the new devised error function.

Sign in / Sign up

Export Citation Format

Share Document