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

Abstract

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.

Modelling the Adsorption of Arsenic from Water and Wastewater using Microsoft Excel Solver and SPSS

“…Table 7, which is ANOVA results for AIC revealed that there was no significant difference between the methods (MES and SPSS) at the 95 % confidence level (F 1,21 = 2.50; p =0.129), but between the adsorption isotherm models there were significant difference (F 21,21 = 6.80; p = 0.000). The results from these tables agree with the literature (Nameni et al, 2008;Wongcharee et al, 2017;2018;Henley et al, 2019;Jasper et al, 2020;Suwannahong et al, 2021;Olaosebikan et al, 2022), which highlighted that adsorption equilibrium isotherm models are significantly different in expressions and in magnitude.…”

“…Tay et al (2014) offered solutions to nonlinear equations by Newton Raphson, but none of the literature and researches dealt with a system of nonlinear and linear equations in adsorption isotherm equilibria and statistical evaluations were not conducted by these studies. Suwannahong et al (2021) studied the evaluation of the Microsoft Excel Solver Spreadsheet-Based program for nonlinear expressions of adsorption isotherm models, which was limited to nonlinear models without linear expressions. More information on adsorption can be found in literature such as Wongcharee et al (2017Wongcharee et al ( , 2018, Ng et al (2014), Bastami and Entezari (2012), Cheng et al (2012), Chincholi et al (2014), Kumar andSivanesan (2006), andJasper et al (2020).…”

Strongly Basic Anion Exchange Resin Based on a Cross-Linked Polyacrylate for Simultaneous C.I. Acid Green 16, Zn(II), Cu(II), Ni(II) and Phenol Removal

“…The parameters characteristic for selected isotherm models as well as Marquardt’s percent standard deviation ( MPSD ), determination coefficient ( R 2 ) and adjusted R-squared ( ) [ 58 ], which are essential for the evaluation of the best fitting model using linear (L) and non-linear regression (NL), are presented in Table 1 .…”

C.I. Basic Red 46 Removal from Sewage by Carbon and Silica Based Composite: Equilibrium, Kinetic and Electrokinetic Studies

“…The following were used as substrates for the synthesis of the composite: pyrogenic silica A-300 (pilot plant of Institute of Surface Chemistry NAN of Ukraine, Kalush, Ukraine) and phenol-formaldehyde resin of novolac type (JSC ‘Ukrainian resins’). The substrates were mixed in a 1:1 weight ratio and grinded by a porcelain ball mill for 2 h. The next step was their pyrolysis for 2 h in argon flow at 1073 K. The adsorbent was thoroughly characterized in terms of composition and structure using appropriate methods and analytical techniques, as described in [ 9 , 46 ]. Analysis of the microscopic images (with a scanning electron microscope (SEM) QuantaTM 3D FEG (FEI Company, Hillsboro, OR, USA) and transmission electron microscope (TEM) TecnaiTM G2 20 (FEI Company)) revealed that the composite had a disordered structure in which the individual components were randomly distributed.…”

“…To validate the best-fitting isotherm model to experimental data, four statistic error functions, namely determination coefficient ( R 2 ), residual sum of squares error ( ERRSQ / SSE ), Chi-square ( χ 2 ) and sum of squares regression ( SSR ) were assessed based on the following Equations (11)–(14) [ 28 , 46 ]: where n —number of experimental data points, q e,cal (mg/g)—theoretically calculated adsorption capacity and q e,exp (mg/g)—experimental adsorption capacity.…”