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Modeling Heavy Metal Sorption Kinetics Using Fractional Calculus

机译：使用分数演算建模重金属吸附动力学

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摘要

Heavy metals are commonly regarded as environmentally aggressive and hazardous to human health. Among the different metals, lead plays an important economic role due to its large use in the automotive industry, being an essential component of batteries. Different approaches have been reported in the literature aimed at lead removal, and among them a very successful one considers the use of water hyacinths for sorption-based operation. The modeling of the metal sorption kinetics is a fundamental step towards in-depth studies and proper separation equipment design and optimization. Fractional calculus represents a novel approach and a growing research field for process modeling, which is based on the successful use of derivatives of arbitrary order. This paper reports the modeling of the kinetics of lead sorption by water hyacinths (Eichhornia crassipes) using a fractional calculus. A general procedure on error analysis is also employed to prove the actual fractional nature of the proposed model by the use of parametric variance analysis, which was carried out using two different approaches (with the complete Hessian matrix and with a simplified Hessian matrix). The joint parameter confidence regions were generated, allowing to successfully show the fractional nature of the model and the sorption process.
机译：重金属通常被认为对环境有害，对人体健康有害。在各种金属中，铅由于在汽车工业中的大量使用而起着重要的经济作用，是电池的重要组成部分。在文献中已经报道了多种旨在去除铅的方法，其中非常成功的一种方法是考虑使用水葫芦进行基于吸附的操作。金属吸附动力学模型是深入研究以及适当的分离设备设计和优化的基本步骤。分数演算代表了一种新颖的方法以及一个不断发展的过程建模研究领域，该过程基于成功使用任意阶数的导数。本文报道了使用分数演算对凤眼兰（凤眼兰）吸附铅动力学的建模。还使用误差分析的一般程序通过使用参数方差分析来证明所提出模型的实际分数性质，该参数方差分析使用两种不同的方法（使用完整的Hessian矩阵和简化的Hessian矩阵）进行。生成了联合参数置信区域，从而可以成功显示模型的分数性质和吸附过程。

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  • 来源
    《Mathematical Problems in Engineering》 |2015年第6期|549562.1-549562.8|共8页
  • 作者

    Friesen V. C.; Leitoles D. P.; Goncalves G.; Lenzi E. K.; Lenzi M. K.;

  • 作者单位

    Univ Fed Parana, Dept Engn Quim, BR-81531980 Curitiba, PR, Brazil.;

    Univ Fed Parana, Dept Engn Quim, BR-81531980 Curitiba, PR, Brazil.;

    Univ Tecnol Fed Parana, Dept Engn Quim, BR-84016210 Ponta Grossa, PR, Brazil.;

    Univ Estadual Ponta Grossa, Dept Fis, BR-84030900 Ponta Grossa, PR, Brazil.;

    Univ Fed Parana, Dept Engn Quim, BR-81531980 Curitiba, PR, Brazil.;

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