916 resultados para Pseudo-second-order kinetic models


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Adsorbents from coal fly ash treated by a solid-state fusion method using NaOH were prepared. It was found that amorphous aluminosilicate, geopolymers would be formed. These fly ash-derived inorganic polymers were assessed as potential adsorbents for removal of some basic dyes, methylene blue and crystal violet, from aqueous solution. It was found that the adsorption capacity of the synthesised adsorbents depends on the preparation conditions such as NaOH:fly-ash ratio and fusion temperature with the optimal conditions being at 121 weight ratio of Na:fly-ash at 250-350 degrees C. The synthesised materials exhibit much higher adsorption capacity than fly ash itself and natural zeolite. The adsorption isotherm can be fitted by Langmuir and Freundlich models while the two-site Langmuir model producing the best results. It was also found that the fly ash derived geopolymeric adsorbents show higher adsorption capacity for crystal violet than methylene blue and the adsorption temperature influences the adsorption capacity. Kinetic studies show that the adsorption process follows the pseudo second-order kinetics. (c) 2006 Elsevier Inc. All rights reserved.

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This study experimentally investigated methyl chloride (MeCl) purification method using an inhouse designed and built volumetric adsorption/desorption rig. MeCl is an essential raw material in the manufacture of silicone however all technical grades of MeCl contain concentrations (0.2 - 1.0 % wt) of dimethyl ether (DME) which poison the process. The project industrial partner had previously exhausted numerous separation methods, which all have been deemed not suitable for various reasons. Therefore, adsorption/desorption separation was proposed in this study as a potential solution with less economic and environmental impact. Pure component adsorption/desorption was carried out for DME and MeCl on six different adsorbents namely: zeolite molecular sieves (types 4 Å and 5 Å); silica gels (35-70 mesh, amorphous precipitated, and 35-60 mesh) and granular activated carbon (type 8-12 mesh). Subsequent binary gas mixture adsorption in batch and continuous mode was carried out on both zeolites and all three silica gels following thermal pre-treatment in vacuum. The adsorbents were tested as received and after being subjected to different thermal and vacuum pre-treatment conditions. The various adsorption studies were carried out at low pressure and temperature ranges of 0.5 - 3.5 atm and 20 - 100 °C. All adsorbents were characterised using Brunauer Emmett Teller (BET), thermogravimetric analysis (TGA), scanning electron microscopy (SEM) and energy dispersive x-ray analysis (EDXA) to investigate their physical and chemical properties. The well-known helium (He) expansion method was used to determine the empty manifold and adsorption cell (AC) regions and respective void volumes for the different adsorbents. The amounts adsorbed were determined using Ideal gas laws via the differential pressure method. The heat of adsorption for the various adsorbate-adsorbent (A-S) interactions was calculated using a new calorimetric method based on direct temperature measurements inside the AC. Further adsorption analysis included use of various empirical and kinetic models to determine and understand the behaviour of the respective interactions. The gas purification behaviour was investigated using gas chromatography and mass spectroscopy (GC-MC) analysis. Binary gas mixture samples were syringed from the manifold iii and AC outlet before and after adsorption/desorption analysis through manual sample injections into the GC-MS to detect and quantify the presence of DME and ultimately observe for methyl chloride purification. Convincing gas purification behaviour was confirmed using two different GC columns, thus giving more confidence on the measurement reliability. From the single pure component adsorption of DME and MeCl on the as received zeolite 4A subjected to 1 h vacuum pre-treatment, both gases exhibited pseudo second order adsorption kinetics with DME exhibiting a rate constant nearly double that of MeCl thus suggesting a faster rate of adsorption. From the adsorption isotherm classification both DME and MeCl exhibited Type II and I adsorption isotherm classifications, respectively. The strength of bonding was confirmed by the differential heat of adsorption measurement, which was found to be 23.30 and 10.21 kJ mol-1 for DME and MeCl, respectively. The former is believed to adsorb heterogeneously through hydrogen bonding whilst MeCl adsorbs homogenously via van der Waal’s (VDW) forces. Single pure component adsorption on as received zeolite 5A, silica gels (35-70, amorphous precipitated and 35-60) resulted in similar adsorption/desorption behaviour in similar quantities (mol kg-1). The adsorption isotherms for DME and MeCl on zeolite 5A, silica gels (35-70, amorphous precipitated and 35-60) and activated carbon 8-12 exhibited Type I classifications, respectively. Experiments on zeolite 5A indicated that DME adsorbed stronger, faster and with a slightly stronger strength of interaction than MeCl but in lesser quantities. On the silica gels adsorbents, DME exhibited a slightly greater adsorption capacity whilst adsorbing at a similar rate and strength of interaction compared to MeCl. On the activated carbon adsorbent, MeCl exhibited the greater adsorption capacity at a faster rate but with similar heats of adsorption. The effect of prolonged vacuum (15 h), thermal pre-treatment (150 °C) and extended equilibrium time (15 min) were investigated for the adsorption behaviour of DME and MeCl on both zeolites 4A and 5A, respectively. Compared to adsorption on as received adsorbents subjected to 1 h vacuum the adsorption capacities for DME and MeCl were found to increase by 1.95 % and 20.37 % on zeolite 4A and by 4.52 % and 6.69 % on zeolite 5A, respectively. In addition the empirical and kinetic models and differential heats of adsorption resulted in more definitive fitting curves and trends due to the true equilibrium position of the adsorbate with the adsorbent. Batch binary mixture adsorption on thermally and vacuum pre-treated zeolite 4A demonstrated purification behaviour of all adsorbents used for MeCl streams containing DME impurities, with a concentration as low as 0.66 vol. %. The GC-MS analysis showed no DME detection for the tested concentration mixtures at the AC outlet after 15 or 30 min, whereas MeCl was detectable in measurable amounts. Similar behaviour was also observed when carrying out adsorption in continuous mode. On the other hand, similar studies on the other adsorbents did not show such favourable MeCl purification behaviour. Overall this study investigated a wide range of adsorbents (zeolites, silica gels and activated carbon) and demonstrated for the first time potential to purify MeCl streams containing DME impurities using adsorption/desorption separation under different adsorbent pre-treatment and adsorption operating conditions. The study also revealed for the first time the adsorption isotherms, empirical and kinetic models and heats of adsorption for the respective adsorbentsurface (A-S) interactions. In conclusion, this study has shown strong evidence to propose zeolite 4A for adsorptive purification of MeCl. It is believed that with a technical grade MeCl stream competitive yet simultaneous co-adsorption of DME and MeCl occurs with evidence of molecular sieiving effects whereby the larger DME molecules are unable to penetrate through the adsorbent bed whereas the smaller MeCl molecules diffuse through resulting in a purified MeCl stream at the AC outlet. Ultimately, further studies are recommended for increased adsorption capacities by considering wider operating conditions, e.g. different adsorbent thermal and vacuum pre-treatment and adsorbing at temperatures closer to the boiling point of the gases and different conditions of pressure and temperature.

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Titanium dioxide (TiO2) nanoparticles with different sizes and crystalloid structures produced by the thermal method and doped with silver iodide (AgI), nitrogen (N), sulphur (S) and carbon (C) were applied as adsorbents. The adsorption of Methyl Violet (MV), Methylene Blue (MB), Methyl Orange (MO) and Orange II on the surface of these particles was studied. The photocatalytic activity of some particles for the destruction of MV and Orange II was evaluated under sunlight and visible light. The equilibrium adsorption data were fitted to the Langmuir, Freundlich, Langmuir-Freundlich and Temkin isotherms. The equilibrium data show that TiO2 particles with larger sizes and doped with AgI, N, S and C have the highest adsorption capacity for the dyes. The kinetic data followed the pseudo-first order and pseudo-second order models, while desorption data fitted the zero order, first order and second order models. The highest adsorption rate constant was observed for the TiO2 with the highest anatase phase percentage. Factors such as anatase crystalloid structure, particle size and doping with AgI affect the photocatalytic activity significantly. Increasing the rutile phase percentage also decreases the tendency to desorption for N-TiO2 and S-TiO2. Adsorption was not found to be important in the photocatalytic decomposition of MV in an investigation with differently sized AgI-TiO2 nanoparticles. Nevertheless C-TiO2 was found to have higher adsorption activity onto Orange II, as the adsorption role of carbon approached synchronicity with the oxidation role.

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The environmental pollution caused by industries has increased the concentration of pollutants in the environment, especially in water. Among the most diverse contaminants, there is the metals, who may or may not to be heavy/toxic, causing effluent of difficult treatment when in low concentrations. The search for alternative measures of wastewater effluent treatment has led to studies using phytoremediation technique through the various matrices (plant, fungi, bacteria) as means of polishing treatment to remove contaminants by means of biosorption/bioaccumulation. In order to use the phytoremediation technique for removing metals of the environmental, it have been performed bioassay with the macrophyte Pistia stratiotes. The bioassays were realized with healthy plants of P. stratiotes acclimatized in a greenhouse, at room temperature and lighting conditions during 28 days of cultivate. The cultivations were performed in glass vessels containing 1 L of the hydroponic solution with chromium (VI) in the potassium dichromate form with concentration range 0.10 to 4.90 mg L-1. The experiments were performed by Outlining Central Composite Rotational (OCCR), where the kinetics of bioaccumulation and chlorophyll a fluorescence were monitored in plants of P. stratiotes during cultivation. The collections of the samples and cultive solution were performed according to the OCCR. The chromium levels were measured in samples of P. stratiotes and the remaining solutions by the methodology of atomic absorption spectrometry by flame. The tolerance of P. stratiotes in relation to exposure to chromium (VI) was analyzed by parameters of physiological activity by means of chlorophyll a fluorescence, using the portable fluorometer PAM (Pulse Amplitude Modulation). The development of P. stratiots and their biomass were related to the time factor, while bioaccumulation capacities were strongly influenced by factors of time and chromium concentration (VI). The chlorophyll fluorescence parameters were affected by chromium and the exposure time at the bioassays. It was obtained an higher metal removal from the root in relation to the sheet, reaching a high rate of metal removal in solution. The experimental data removal kinetics were represented by kinetic models Irreversibly Langmuir, Reversible Langmuir, Pseudo-first Order and Pseudo-second Order, and the best fit for the culture solution was the Reversible Langmuir model with R² 0.993 and for the plant the best model was Pseudo-second order with R² 0.760.

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Na indústria têxtil grandes volumes de efluentes são gerados, os quais são caracterizados por serem coloridos e poluentes , devido à presença de corantes em sua composição. Com a necessidade de descontaminação, diferentes métodos são utilizados no tratamento, sendo um deles, a biossorção. Este consiste na remoção das substâncias tóxicas recorrendo a biossorventes obtidos a partir de resíduos agrícolas e sub-produtos de processos industriais. O objetivo principal deste trabalho foi estudar a remoção do corante Preto Reafix Super 2R em soluções aquosas por meio de biossorção com bagaço de malte. Baseando-se sobretudo no estudo da cinética e equilíbrio entre o biossorvente e o corante. Numa primeira fase foi estudada a influência dos parâmetros operacionais, como a influência do diâmetro médio das partículas do biossorvente, o pH da solução e a velocidade de agitação da solução. Sendo as condições ótimas de biossorção definidas a pH 2, velocidade de agitação de 150 rpm e biomassa sem peneiramento. Posteriormente, ajustaram-se os modelos cinéticos de Pseudo-primeira ordem, Pseudo-segunda ordem e de Difusão intrapartícula aos resultados experimentais obtidos pela cinética de adsorção avaliando também a influência da temperatura no tempo de contato para se alcançar o equilibrio. O modelo de Pseudo-segunda ordem conduziu ao melhor ajuste, com um coeficiente de correlação (R2) de apróximadamente 1. A partir dos testes de equilíbrio realizados com diferentes concentrações de corante, foram ajustadas as isotermas de Langmuir, Freundlich, Tempkin aos resultados experimentais tendo-se obtido parâmetros bastante significativos para o modelo Langmuir, cuja capacidade máxima de remoção (qmax) obtida foi de 40,16 mg.g-1. A análise dos parâmetros termodinâmicos permitiram avaliar que o processo de adsorção ocorre espontaneamente, sendo endotérmico e que ao longo do processo aumenta a aleatoriedade na interface sólido/solução, devido à desorganização do processo em virtude das interações que ocorrem.

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In this paper agricultural waste; Canarium schweinfurthii was explored for the sequestering of Fe and Pb ions from wastewater solution after carbonization and chemical treatment at 400oC. Optimum time of 30 and 150 min with percentage removal of 95 and 98% at optimum pH of 2 and 6 was obtained for Fe and Pb ions. Kinetics model followed pseudofirst order as sum of absolute error (EABS) between Qe and Qc greater than that of pseudo second order. Parameters evaluated from isothermal equation (Freundlich and Langmuir) showed that KL and QO for Fe > Pb and R2 for Langmuir> Freundlich. The study reveals the suitability of the adsorbent for sequestering of Fe and Pb ions from industrial wastewater.

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Heavy metals are used in many industrial processestheirs discard can harm fel effects to the environment, becoming a serious problem. Many methods used for wastewater treatment have been reported in the literature, but many of them have high cost and low efficiency. The adsorption process has been used as effective for the metal remoal ions. This paper presents studies to evaluate the adsorption capacity of vermiculite as adsorbent for the heavy metals removal in a synthetic solution. The mineral vermiculite was characterized by differents techniques: specific surface area analysis by BET method, X-ray diffraction, raiosX fluorescence, spectroscopy in the infraredd region of, laser particle size analysis and specific gravity. The physical characteristics of the material presented was appropriate for the study of adsorption. The adsorption experiments weredriveal finite bath metod in synthetic solutions of copper, nickel, cadmium, lead and zinc. The results showed that the vermiculite has a high potential for adsorption, removing about 100% of ions and with removal capacity values about 85 ppm of metal in solution, 8.09 mg / g for cadmium, 8.39 mg/g for copper, 8.40 mg/g for lead, 8.26 mg/g for zinc and 8.38 mg/g of nickel. The experimental data fit in the Langmuir and Freundlich models. The kinetic datas showed a good correlation with the pseudo-second order model. It was conducteas a competition study among the metals using vermiculiti a adsorbent. Results showed that the presence of various metals in solution does not influence their removal at low concentrations, removing approximat wasely 100 % of all metals present in solutions

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An unstructured mesh �nite volume discretisation method for simulating di�usion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume �nite-element method and it retains the local continuity of the ux at the control volume faces. A least squares function recon- struction technique together with a new ux decomposition strategy is used to obtain an accurate ux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it signi�cantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes, and appears independent of the mesh quality.

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We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.

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This paper gives a modification of a class of stochastic Runge–Kutta methods proposed in a paper by Komori (2007). The slight modification can reduce the computational costs of the methods significantly.

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In this paper, we consider a space Riesz fractional advection-dispersion equation. The equation is obtained from the standard advection-diffusion equation by replacing the ¯rst-order and second-order space derivatives by the Riesz fractional derivatives of order β 1 Є (0; 1) and β2 Є(1; 2], respectively. Riesz fractional advection and dispersion terms are approximated by using two fractional centered difference schemes, respectively. A new weighted Riesz fractional ¯nite difference approximation scheme is proposed. When the weighting factor Ѳ = 1/2, a second- order accurate numerical approximation scheme for the Riesz fractional advection-dispersion equation is obtained. Stability, consistency and convergence of the numerical approximation scheme are discussed. A numerical example is given to show that the numerical results are in good agreement with our theoretical analysis.

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Magnetic zeolite NaA with different Fe3O4 loadings was prepared by hydrothermal synthesis based on metakaolin and Fe3O4. The effect of added Fe3O4 on the removal of ammonium by zeolite NaA was investigated by varying the Fe3O4 loading, pH, adsorption temperature, initial concentration, adsorption time. Langmuir, Freundlich, and pseudo-second-order modeling were used to describe the nature and mechanism of ammonium ion exchange using both zeolite and magnetic zeolite. Thermodynamic parameters such as change in Gibbs free energy, enthalpy and entropy were calculated. The results show that all the selected factors affect the ammonium ion exchange by zeolite and magnetic zeolite, however, the added Fe3O4 apparently does not affect the ion exchange performance of zeolite to the ammonium ion. Freundlich model provides a better description of the adsorption process than Langmuir model. Moreover, kinetic analysis indicates the exchange of ammonium on the two materials follows a pseudosecond-order model. Thermodynamic analysis makes it clear that the adsorption process of ammonium is spontaneous and exothermic. Regardless of kinetic or thermodynamic analysis, all the results suggest that no considerable effect on the adsorption of the ammonium ion by zeolite is found after the addition of Fe3O4. According to the results, magnetic zeolite NaA can be used for the removal of ammonium due to the good adsorption performance and easy separation method from aqueous solution.

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This paper presents a higher-order beam-column formulation that can capture the geometrically non-linear behaviour of steel framed structures which contain a multiplicity of slender members. Despite advances in computational frame software, analyses of large frames can still be problematic from a numerical standpoint and so the intent of the paper is to fulfil a need for versatile, reliable and efficient non-linear analysis of general steel framed structures with very many members. Following a comprehensive review of numerical frame analysis techniques, a fourth-order element is derived and implemented in an updated Lagrangian formulation, and it is able to predict flexural buckling, snap-through buckling and large displacement post-buckling behaviour of typical structures whose responses have been reported by independent researchers. The solutions are shown to be efficacious in terms of a balance of accuracy and computational expediency. The higher-order element forms a basis for augmenting the geometrically non-linear approach with material non-linearity through the refined plastic hinge methodology described in the companion paper.