Equilibrium two-parameter isotherms of acid dyes sorption by activated carbons: Study of residual errors

The adsorption of two acid dyes Acid Black 1 (AB1) and Acid Blue 113 (AB113) onto mesoporous granular pine-cone derived activated carbon and the adsorption of three acid dyes Acid Black 80 (AB80), Acid Red 114 (AR114) and Acid Yellow 117 (AY117) onto microporous Granular Activated Carbon (GAC) type F400, from aqueous solution, has been studied in a batch system. Seven two-parameter isotherm models – Langmuir, Freundlich, Dubinin–Radushkevich, Temkin, Halsey, Jovanovic and Harkins–Jura – were used to correlate the experimental data. Adsorption isotherm modeling shows that the interaction of dye with activated carbon surface is by localized monolayer adsorption. In order to determine the best fit isotherm for each system, nine error analysis methods, namely, chi-square (χ2), log-likelihood (G2), residual root mean square error (RMSE), sum of the squares of the errors (ERRSQ), composite functional error (HYBRD), derivative of Marquardt's percent standard deviation (MPSD), average relative error (ARE), sum of absolute error (EABS) and average percentage error (APE) were used to evaluate the data.In order to facilitate decision making for the best fit data set, a procedure of normalizing and combining the error results was adopted producing a “sum of the normalized errors” for each parameter set from which the “lowest normalized error set” is selected.