Evaluation of Linear Regression Equations and Methods of Solving Linear Equations: Adsorption Kinetics Model

Abstract

As a follow up on previous studies such as Kumar (2006);  Oke (2013), Ho (2014), Guasian et al., (2014) Oke et al. (2014) and Fehintola et al., (2015), this paper presents a report on the comparison between linear regression methods and linear equation of the pseudo second kinetics model. Selected materials (clay soil, activated carbon, egg shells, corn cobs and used dry batteries) were collected from selected locations in Nigeria. The materials collected were washed with distilled water, air-dried, ground into powder (powdered corn cob, PCC; powdered eggshell, PES and powdered carbon rod, PCR) as the case may be and classified using British Standard sieve. The mineral contents of these materials (adsorbents) were determined.  Linear equations of adsorption kinetics models were derived. Adsorption capacities of powdered adsorbents were examined on synthetic lead solution prepared by using standard methods. Adsorption kinetics models (pseudo second) parameters were determined using linear regression methods (least squared, graphical, iteration, Gaussian elimination and Microsoft excel Solver methods) and linear equations. The methods and linear equations derived were evaluated statistically using a model of the selection criterion, total error, coefficient of determination, correlation coefficient (R)  and mean The study revealed that these materials are good error.

adsorbents based on the adsorption capacities. The linear pseudo second-order kinetics and the adsorption theory were found of getting violated by linear regression B

See the full pdf 

Statistical evaluation revealed that Microsoft excels solver method is the best method to be used for analysis adsorption pseudo second kinetics model based on the highest average Model of selection criterion (3.6584) and average Coefficient of Determination (0.9729); R (0.9875); low average total error (0.0190) and mean error (0.0383). It was concluded that in the determination of engineering parameters Microsoft excels solver should be used for linear pseudo second order kinetics parameter determination to prevent failure of adsorption reactors and processes. The equation

See the full pdf 

which has been in use by many researchers is wrong.

Key words: Pb²⁺ removal, PCC, PES; PCR, aqueous solution, regression methods, environmental pollution control.