scholarly journals Mathematical modeling on non-dispersive extraction of germanium from aqueous solutions using Aliquat 336

2018 ◽  
Vol 78 (12) ◽  
pp. 2489-2499
Author(s):  
Hossein Kamran Haghighi ◽  
Mehdi Irannajad ◽  
Agustin Fortuny ◽  
Ana Maria Sastre
Keyword(s):  
Mathematical Modeling ◽  
Mass Transfer ◽  
Correlation Coefficients ◽  
Aliquat 336 ◽  
Transfer Coefficients ◽  
Extraction Equilibrium ◽  
Flat Sheet ◽  
Flat Sheet Membrane ◽  
Error Bias ◽  
And Diffusion

Abstract In this work, the mathematical modeling of the facilitated transport of germanium (non-dispersive extraction) through a flat sheet membrane with an Aliquat 336 carrier was described. The flat sheet supported liquid membrane (FSSLM) experiments were performed under conditions germanium ≈ 100 mg/L, tartaric acid concentration of 2.76 mmol/L, and carrier concentrations of 2.5–10%v/v. The extraction equilibrium, mass transfer, and diffusion equations based on Fick's law were the principles of modeling. Modeling was carried out by programming in Matlab mathematical software to obtain the extraction (Kex) and mass transfer constants (Km) as the objective parameters. According to the model resolution, Kex and Km were found to be 0.178 and 9.25 × 10−2 cm/s, respectively. The correlation coefficients between model and experimental data relating to the Aliquat 336 concentrations of 2.5, 5, 7.5, and 10%v/v were found as 0.96, 0.98, 0.99, and 0.92. The parameters of root mean square error, bias, and scatter index showed the model accuracy. In addition, diffusion coefficients relating to Aliquat 336 concentrations of 2.5, 5, 7.5, and 10%v/v were calculated using mass transfer coefficients to be 2.4 × 10−4, 2.23 × 10−4, 1.91 × 10−4, and 1.79 × 10−4 cm2/s, respectively.

scholarly journals MATHEMATICAL MODELING OF THERMOGRAVITATIONAL AND THERMOCA-PILLARY CONVECTION IN GAS-LIQUID PROCESSES

2021 ◽  
Vol 2021 (1) ◽  
pp. 58-66
Author(s):  
Evgeniy Podoplelov ◽  
Aleksey Bal'chugov ◽  
Anatoliy Dement'ev ◽  
Anatoliy Glotov
Keyword(s):  
Mathematical Modeling ◽  
Mass Transfer ◽  
Phase Boundary ◽  
Mass Exchange ◽  
Exchange Process ◽  
Transfer Coefficients ◽  
Mass Exchange Process ◽  
Convective Flows ◽  
Liquid Phases ◽  
Turbulent Pulsations

. The interaction of gas and liquid phases in some cases is accompanied by the spontaneous occur-rence of convective flows and turbulent pulsations at the phase boundary and in adjacent areas. Hy-drodynamic instability allows to accelerate the interfacial transfer of matter and leads to an increase in mass transfer coefficients. Research in this field is not only theoretical, but also practical, since sur-face convection can be artificially created in apparatus for intensifying the mass exchange process.

Mathematical Modeling of Gas Separation in Flat-sheet Membrane Contactors

2012 ◽  
Vol 28 (1) ◽  
pp. 13-18 ◽  
Author(s):  
Azam Marjani ◽  
Saeed Shirazian ◽  
Mahmoud Ranjbar ◽  
Mitra Ahmadi
Keyword(s):  
Mathematical Modeling ◽  
Gas Separation ◽  
Flat Sheet ◽  
Flat Sheet Membrane ◽  
Membrane Contactors ◽  
Sheet Membrane

Chromium (VI) removal by Aliquat-336 in a novel multiframe flat sheet membrane contactor

2020 ◽  
Vol 147 ◽  
pp. 107765 ◽  
Author(s):  
Hassina Semghouni ◽  
Said Bey ◽  
Aberto Figoli ◽  
Alessandra Criscuoli ◽  
Mohamed Benamor ◽  
...  
Keyword(s):  
Aliquat 336 ◽  
Membrane Contactor ◽  
Chromium Vi ◽  
Flat Sheet ◽  
Flat Sheet Membrane ◽  
Sheet Membrane

RESEARCH OF THERMAL AND MASS-EXCHANGE PROCESSES IN GAS-LIQUID FILM ABSORBERS IN SURFACE-ACTIVE TECHNOLOGY

2021 ◽  
pp. 3-16
Author(s):  
O. Dzevochko ◽  
M. Podustov ◽  
A. Dzevochko
Keyword(s):  
Mathematical Modeling ◽  
Heat Transfer ◽  
Mass Transfer ◽  
Heat Transfer Coefficient ◽  
Liquid Phase ◽  
Transfer Coefficient ◽  
Sulfur Trioxide ◽  
Cooling Water ◽  
Transfer Coefficients ◽  
The Heat Transfer Coefficient

The article states that surfactants have an asymmetrically constructed molecule that contains hydrophilic and hydrophobic groups. The main department of surfactant production is the process of sulfation of organic matter with gaseous sulfur trioxide. It is shown that the process of sulfation in gas-liquid film absorbers consists of the following stages: the process of mass transfer of sulfur trioxide from the gas stream to the liquid phase; the process of absorption of sulfur trioxide by organic matter with the passage of an exothermic chemical reaction; the process of heat exchange between the liquid phase and the gas stream; the process of heat exchange between the liquid phase and the flow of cooling water. Studies of heat and mass transfer processes at these stages make it possible to select the necessary equations for the calculation of heat transfer coefficients, heat transfer coefficients and mass transfer coefficient. It is recommended to calculate the heat transfer coefficient from liquid to gas by the equation when the diffusion and thermal Prandtl numbers are close to unity. The use of the classical equation to calculate the heat transfer coefficient from the liquid phase to the wall of the reaction tube did not give the desired result. Therefore, an equation was used that takes into account the properties of the gas-liquid flow as a whole. It is recommended to calculate the heat transfer coefficient from the reaction pipe wall to the cooling water flow according to the classical Nusselt equation. Experimental data processing data for calculating the density and dynamic viscosity of the reaction mass along the length of the reactor are presented. The equation for calculating the mass transfer coefficient was obtained by analyzing 6 equations of different authors who were engaged in the process of sulfation of organic substances. A mathematical description of the sulfation process in a film absorber was developed for analysis. During the development of the mathematical description, the balance equations of mass and heat transfer for the reaction tube were compiled. Based on the results of mathematical modeling, an equation was chosen that includes the tangential stress at the gas-liquid interface. The results of mathematical modeling were compared with Gutierrez's experimental data and the results of Dabir's mathematical modeling. The obtained results will be used in mathematical modeling of the sulfation process in a film absorber.

scholarly journals Chromium(VI) Removal by Polyvinyl Chloride (PVC)/Aliquat-336 Polymeric Inclusion Membranes in a Multiframe Flat Sheet Membrane Module

2019 ◽  
Vol 9 (15) ◽  
pp. 2994
Author(s):  
Hassina Semghouni ◽  
Said Bey ◽  
Alberto Figoli ◽  
Alessandra Criscuoli ◽  
Francesca Russo ◽  
...  
Keyword(s):  
Polyvinyl Chloride ◽  
Operating Conditions ◽  
Effect Of Temperature ◽  
Separation Performance ◽  
Aliquat 336 ◽  
Chromium Vi ◽  
Flat Sheet ◽  
Feed Phase ◽  
Flat Sheet Membrane ◽  
Sheet Membrane

A new multiframe flat sheet membrane contactor module containing several flat membranes was designed and implemented. Each frame contains a chamber (central hole) in which the feed and the receiving phases are put in contact with polyvinyl chloride (PVC)/Aliquat-336 polymeric flat sheet membranes for Cr(VI) removal from aqueous solutions (feed phase). To evaluate the efficiency of the system, the experimental design methodology was used to analyze the effect of temperature (T, °C), PVC/Aliquat-336 ratio, and Cr (VI) concentration in the feed phase and the concentration of sodium chloride (NaOH-NaCl) in the receiving phase. Two representative mathematical models of the two responses (extraction and back-extraction) were respectively obtained. A good correlation between the experimental results and those predicted (RS2 = 97.77 and RR2 = 97.87) was achieved, allowing the optimization of the different factors selected for each response, separately. The proposed system showed a good separation performance, leading to Cr(VI) extractions up to 93% when working at the optimized operating conditions.

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