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A simple and rapid approach to modeling chromium breakthrough in fixed bed adsorber
Chu, Khim Hoong Techno-Press 2018 Advances in environmental research Vol.7 No.1
A simple mathematical model for predicting fixed bed adsorption dynamics is described. The model is characterized by a linear adsorption isotherm and a linear driving force expression for mass transfer. Its analytic solution can be approximated with an algebraic equation in closed form which is easily evaluated by spreadsheet computation. To demonstrate one application of the fixed bed model, a previously published adsorption system is used as a case study in this work. The adsorption system examined here describes chromium breakthrough in a fixed bed adsorber packed with imidazole functionalized adsorbent particles and is characterized by a nonlinear adsorption isotherm. However, the equilibrium behavior of the fixed bed adsorber is in essence governed by a linear adsorption isotherm due to the use of a low influent chromium concentration. It is shown that chromium breakthrough is predicted reasonably well by the fixed bed model. The model's parameters can be easily extracted from independent batch experiments. The proposed modeling approach is very simple and rapid, and only Excel is used for computation.
Discrimination of rival isotherm equations for aqueous contaminant removal systems
Chu, Khim Hoong Techno-Press 2014 Advances in environmental research Vol.3 No.2
Two different model selection indices, the Akaike information criterion (AIC) and the coefficient of determination ($R^2$), are used to discriminate competing isotherm equations for aqueous pollutant removal systems. The former takes into account model accuracy and complexity while the latter considers model accuracy only. The five types of isotherm shape in the Brunauer-Deming-Deming-Teller (BDDT) classification are considered. Sorption equilibrium data taken from the literature were correlated using isotherm equations with fitting parameters ranging from two to five. For the isotherm shapes of types I (favorable) and III (unfavorable), the AIC favors two-parameter equations which can easily track these simple isotherm shapes with high accuracy. The $R^2$ indicator by contrast recommends isotherm equations with more than two parameters which can provide marginally better fits than two-parameter equations. To correlate the more intricate shapes of types II (multilayer), IV (two-plateau) and V (S-shaped) isotherms, both indices favor isotherm equations with more than two parameters.
Gang Yuan,Bin Zhao,Khim Hoong Chu 대한환경공학회 2020 Environmental Engineering Research Vol.25 No.5
A simple method is presented for extracting pore diffusion coefficients from batch adsorption kinetic data. The method employs the classic Langmuir kinetics model which is characterized by a single rate coefficient. An analytical solution in the form of a simple algebraic equation is available for this rate model. Fitting the algebraic equation to batch kinetic data to determine the rate coefficient is straightforward and can be conveniently accomplished using standard spreadsheet programs. The resultant rate coefficient can be converted to the pertinent pore diffusion coefficient via a separate algebraic expression. The proposed modeling approach provides accurate fits of experimental kinetic data taken from the literature and yields acceptable errors in the best estimates for pore diffusion coefficients. Specific examples discussed are the adsorption of fluoride by bone char and laterite adsorbents.
Sung Geun Kim,김의용,Khim Hoong Chu 한국화학공학회 2011 Korean Journal of Chemical Engineering Vol.28 No.1
Carotenoid production by Rhodotorula aurantiaca K-505 was optimized in shake-flask cultures using a central composite design. Quadratic polynomial models were used to correlate the relationships between six fermentation factors (pH, temperature, and the concentrations of glucose, yeast extract, peptone extract, and ammonium sulfate)and three response variables (cell mass yield, carotenoid content, and carotenoid production). Different optimum culture conditions were predicted by the models for maximizing the three response variables, indicating that there is no direct correlation between cell growth and carotenoid production. The maximum carotenoid production of 4.9 mg/L predicted by the relevant model under optimum culture conditions agreed well with the experimentally measured value of 5.3mg/L under the same culture conditions.