In the last decade a growing interest was observed in low-cost adsorbents for heavy metal ions. Clinoptilolite is a mineral sorbent extracted in Poland that is used to remove heavy metal ions from diluted solutions. The experiments in this study were carried out in a laboratory column for multicomponent water solutions of heavy metal ions, i.e. Cu(II), Zn(II) and Ni(II). A mathematical model to calculate the metals' concentration of water solution at the column outlet and the concentration of adsorbed substances in the adsorbent was proposed. It enables determination of breakthrough curves for different process conditions and column dimensions. The model of process dynamics in the column took into account the specificity of sorption described by the Elovich equation (for chemical sorption and ion exchange). Identification of the column dynamics consisted in finding model coefficients β, KE and Deff and comparing the calculated values with experimental data. Searching for coefficients which identify the column operation can involve the use of optimisation methods to find the area of feasible solutions in order to obtain a global extremum. For that purpose our own procedure of genetic algorithm is applied in the study.
The latest achievements in the field of mathematical modelling include the application of artificial neural networks (ANN). A growing interest in the ANN is confirmed by the number of publications devoted to the applicability of ANN in chemical, process and environmental engineering. A recent dynamic development of ANN provided an efficient and universal tool that is used to solve many tasks, including modelling, approximation and identification of objects. The initial step of applying the network to a given process consists in the determination of weights of the proposed neural network structure. This is performed on the basis of training data. A network that is properly trained allows correct information to be obtained on the basis of other data which have not been used in the network training. In most cases the network training is performed on the basis of a known mathematical model. However, the training of a network can be also performed using experimental data. In this paper, the sorption isotherms were predicted by means of a multilayer perceptron (MLP). Calculations were made using a training program written in Matlab, which took advantage of the Lavenberg-Marquardt procedure. In the last decade a growing interest is observed in inexpensive and very cheap adsorbents to remove heavy metal ions. Clinoptilolite is the mineral sorbent extracted in Poland used to remove heavy metal ions from diluted solutions. Equilibrium experiments were carried out to estimate sorptivity of a clinoptilolite and its selectivity towards Cu(II), Zn(II) and Ni(II) ions for multicomponent solution. Calculations with the use of MLP enabled description of sorption isotherms for one, two and three ions which were present at the same time in the solution. The network also enabled an analysis of sorption of the single ion, taking into account the effect of its concentration.
PL
W ostatnich dekadach obserwuje się rosnące zainteresowanie zastosowaniem tanich adsorbentów w celu usuwania zanieczyszczeń z roztworów wodnych. Klinoptylolit jest sorbentem mineralnym wydobywanym w Polsce, stosowanym do usuwania jonów metali ciężkich z rozcieńczonych roztworów. Eksperymenty równowagi przeprowadzono w celu oszacowania efektywności sorpcji klinoptylolitu i jego selektywności wobec Cu(II), Zn(II) i Ni(II) w roztworach wieloskładnikowych. SSN umożliwiają obliczenia izoterm sorpcji dla jednego, dwóch lub trzech jonów jednocześnie obecnych w roztworze. W pracy izotermy sorpcji przewidywano za pomocą wielowarstwowego perceptronu (MLP). Obliczenia prowadzono za pomocą własnych algorytmów zgodnie z procedurą Matlaba z zastosowaniem metody uczenia Lavenberga-Marquardta.
Azo dye-plant sorbent system was investigated in the paper. Direct Orange 26 and Reactive Blue 81 azo dyes were sourced from Boruta-Zachem Kolor Sp. z o.o. Mechanically and chemically modified rye straw was used as a “low-cost” biosorbent. During experiments, dye concentration changes in the solution and sorbent in time were measured at constant temperature until equilibrium was reached. Sorption equilibrium was described by 2-parameter (Freundlich, Langmuir) and 3-parameter (Redlich-Peterson and Radke-Prausnitz) equations widely used in adsorption studies. Characteristic coefficients of equations were determined and the proposed approximations of the results of experimental studies were evaluated statistically. Higher sorption capacity was obtained for Direct Orange 26 than for Reactive Blue 81.
PL
W pracy prowadzono badania dla układu barwnik azowy - sorbent roślinny. Barwniki azowe Direct Orange 26 i Reactive Blue 81 pochodziły z Zakładu Boruta - Zachem Kolor Sp. z o.o. Jako biosorbenta użyto modyfikowanej fizycznie i chemicznie słomy żytniej, materiału taniego i łatwo dostępnego. Wykonano eksperymenty, kontrolując w czasie zmiany stężenia barwników w roztworze i sorbencie. Eksperymenty prowadzono w stałej temperaturze do ustalenia równowagi procesu. Opisu równowagi sorpcyjnej dokonano za pomocą równań dwu- i trójparametrowych szeroko stosowanych w adsorpcji. Wyznaczono charakterystyczne współczynniki równań i dokonano oceny statystycznej proponowanych aproksymacji wyników badań eksperymentalnych. Większą pojemność sorpcyjną uzyskano dla Direct Orange 26 niż dla Reactive Blue 81.
It was examined if buckwheat hull has a potential to be used to adsorb heavy metal ions Zn(II), Cd(II), Co(II), Cu(II), Ni(II) from water. The research involved experiments aimed at the determination of sorption kinetics taking into consideration changes of concentration in a solution and sorbent over time. According to the literature data, kinetics is described with the use of pseudo first-order equations. Application of fractional derivatives for the description of sorption kinetics enables the development of the generalised sorption kinetics equation. Result analysis with this concept requires making a computational procedure using gamma functions and infinite series. Kinetics description using fractional derivatives will be equations with two parameters ie fraction of derivative α and the kinetics constant K dependent on the analysed sorbent-adsorbate system.
PL
W pracy wykorzystano łuskę gryki do procesu sorpcji jonów metali ciężkich Cu(II), Ni(II), Zn(II), Co(II) i Cd(II) z roztworów wodnych. Wyznaczone zostały maksymalne pojemności sorpcyjne oraz stałe kinetyczne i równowagowe. Obliczone wartości pozwoliły na zastosowanie równań różniczkowych ułamkowych do opisu kinetyki sorpcji oraz uzyskania uogólnionego równania kinetyki sorpcji. Opracowanie wyników według tej koncepcji wymaga napisania procedury obliczeniowej wykorzystującej funkcje gamma oraz szeregi nieskończone. Równania kinetyki z wykorzystaniem pochodnych ułamkowych są równaniami o dwóch parametrach. Są to ułamek pochodnej i stała kinetyczna zależne od analizowanego układu sorbent - adsorbat.
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