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Numerical simulation of reactive extraction of benzoic acid from wastewater via membrane contactors


Membrane-based non-dispersive solvent extraction is used in many chemical processes due to its significant benefits such as straightforward scale-up and low energy consumption. A mechanistic model was developed to predict recovery of benzoic acid (BA) from wastewater using membrane contactors. Model equations were derived for benzoic acid transport in the membrane module, and solved using FEM. The model findings were compared with experimental results, and an average deviation of 4% was observed between experimental and simulation results. Simulations showed that change in organic phase flowrate and initial concentration of BA does not have considerable effect on the removal efficiency of benzoic acid. In addition, increasing feed flowrate leads to the enhancement of convective mass transfer flux in the tube side of membrane contactor which decreases removal efficiency of benzoic acid.

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Correspondence to Saeed Shirazian.

Additional information

Responsible editor: Marcus Schulz



Mass transfer equations in three compartments of membrane contactor are expressed as follows

$$ {D}_{\mathrm{BA}\hbox{-} \mathrm{lumen}}\left[\frac{\partial^2{C}_{\mathrm{BA}\hbox{-} \mathrm{lumen}}}{\partial {r}^2}+\frac{1}{r}\frac{\partial {C}_{\mathrm{BA}\hbox{-} \mathrm{lumen}}}{\partial r}+\frac{\partial^2{C}_{\mathrm{BA}\hbox{-} \mathrm{lumen}}}{\partial {z}^2}\right]={U}_{\mathrm{z}\hbox{-} \mathrm{lumen}}\frac{\partial {C}_{\mathrm{BA}\hbox{-} \mathrm{lumen}}}{\partial z} $$
$$ {D}_{\mathrm{BA}\hbox{-} \mathrm{m}}\left[\frac{\partial^2{C}_{\mathrm{BA}\hbox{-} \mathrm{m}}}{\partial {r}^2}+\frac{1}{r}\frac{\partial {C}_{\mathrm{BA}\hbox{-} \mathrm{m}}}{\partial r}+\frac{\partial^2{C}_{\mathrm{BA}\hbox{-} \mathrm{m}}}{\partial {z}^2}\right]=0 $$
$$ {D}_{\mathrm{BA}\hbox{-} \mathrm{shell}}\left[\frac{\partial^2{C}_{\mathrm{BA}\hbox{-} \mathrm{shell}}}{\partial {r}^2}+\frac{1}{r}\frac{\partial {C}_{\mathrm{BA}\hbox{-} \mathrm{shell}}}{\partial r}+\frac{\partial^2{C}_{\mathrm{BA}\hbox{-} \mathrm{shell}}}{\partial {z}^2}\right]={U}_{\mathrm{z}\hbox{-} \mathrm{shell}}\frac{\partial {C}_{\mathrm{BA}\hbox{-} \mathrm{shell}}}{\partial z} $$

where D, C, and U denote diffusion coefficient, benzoic acid concentration, and velocity, respectively. Diffusion coefficient in the shell compartment is calculated as follows

$$ \begin{array}{l}{D}_{\left(\mathrm{BA}\hbox{-} \mathrm{shell}\right)}=1.55\times {10}^{-8}\left(\frac{T^{1.29}\left(\frac{P_{\mathrm{oct}}^{0.5}}{P_{\mathrm{BA}\hbox{--} {\mathrm{R}}_3\mathrm{N}}^{0.5}}\right)}{\eta_{\mathrm{oct}}^{0.92}{V}_{\mathrm{oct}}^{0.23}}\right)\\ {}{V}_{\mathrm{oct}}=0.28{V}_{\mathrm{oct}, C}^{1.048}\end{array} $$

where V oct is the molar volume of 1-octanol at the normal boiling temperature (cm3/mol). The symbol η oct denotes the viscosity of 1-octanol in centipoise, and T is absolute temperature (K). P oct and P BA–R3N are parachors for 1-octanol and BA–R3N, respectively (Agrahari et al. 2014).

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Ghadiri, M., Shirazian, S. Numerical simulation of reactive extraction of benzoic acid from wastewater via membrane contactors. Environ Sci Pollut Res 24, 11518–11527 (2017). https://doi.org/10.1007/s11356-017-8817-8

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  • Mechanistic model
  • Wastewater treatment
  • Separation
  • Membranes
  • Extraction