A very common practice during the parameter estimation of adsorption isotherms, including the well-known Langmuir and Freundlich isotherms, consists in manipulating the isotherm equation to obtain a linear equation and estimate the model parameters using a linear least squares method. This procedure is also usually used for estimating the thermodynamic adsorption parameters, despite the fact that personal computers and software are available for prompt implementation of non-linear solutions of the original parameterestimation problem. For this reason, the main purpose of this work is to show that the use of linear least-squares methods for estimating adsorption isotherm parameters leads to some serious drawbacks, which can be readily avoided through proper use of non-linear procedures and posterior statistical analyses of the parameter-estimation results, enhancing the quality of the obtained results.
Adsorption equilibrium is a fundamental concept in the adsorption science and relates the equilibrium between the quantity of the adsorbed material and its concentration in the bulk phase. Several models have been proposed for prediction of adsorption equilibrium and all models depend on parameters whose values must be estimated from available experimental data. Although linear parameter estimation procedures can be used for model fitting, through transformation of available experimental data and model parameters, non-linear parameter estimation procedures lead to more reliable results and allow for direct comparison of results obtained with different adsorption equilibrium models. The main objective of this work is to present and compare different non-linear procedures for parameter estimation of adsorption equilibrium models, based on theoretical arguments and also on the numerical estimation of adsorption equilibrium parameters, using available experimental data for adsorption of methylene blue onto activated carbon. The results obtained indicate that the best parameter estimation procedure is the one that relies on available equilibrium concentrations in the bulk phase as a function of the fluid volume, adsorbent mass and initial concentrations in the bulk phase, without transformation of measured experimental values and model parameters. Besides, it is shown that parameter estimates should be obtained through proper minimization of weighted least-squares objective function, in accordance with maximum likelihood procedures.
The global warming and energy crisis is motivating the search for sustainable power sources. The objective of this work is to analyze the economic return and quantify the reduction in the emission of pollutants, when low-cost solar collectors are used as a partial substitute for a boiler that uses fuel oil as the energy source, in order to heat water for the swimming pools of the Physical Education Center, Federal University of Santa Maria. The collectors are made from PVC and other easily acquired materials. The estimations for energy saving are based on a collecting area of 182 m 2 . From knowledge of the collectors' efficiency, the mathematical demonstration shows a fuel oil saving of 13,174 kg, representing 24% of the total amount consumed per annum. The investment required for the construction and installation of the collectors is US$ 6,445 and the estimated useful live is five years. The internal rate of return is 30%. The emission of pollutants is reduced by a considerable amount of 41,213 kg CO 2 equivalent/year. The use of direct sun energy as an alternative power source represents a significant economic interest as well as contributing to the mitigation of greenhouse gases.
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