Abstract
Direct contact membrane distillation (DCMD) is the most studied configuration for desalination and waste treatment, due to its ease of operation. Despite this, this technology has not been scaled for industrial use mainly because of its energy requirements. In this work, a mathematical model is presented in which the free surface approach is used to simulate a tube-and-shell module. The model was successfully validated with experimental data from the literature. The operational parameters were evaluated to determine its influence on the permeate flux. The recycling of concentrate as a strategy to increase water recovery was also studied. In addition, high recycling rates allowed to reduce the specific energy consumption (SEC) and achieve a higher water recovery (REC). Finally, aiming at the use of membrane distillation for desalination in a small-scale plant, various arrangements of modules were evaluated in terms of water recovery, final concentration reached and SEC. The Christmas Tree arrangement turned out to be the most efficient one using a smaller area of membranes allowing to achieve a high degree of water recovery (86.5%), a final concentration of 260 \(\mathrm{kg}/{\mathrm{m}}^{3}\) with a SEC of 1003 \(\mathrm{kWh}/{\mathrm{m}}^{3}\).
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Notes
The orthogonal collocation method as presented here is based on the family of the Jacobi polynomials given as \({P}_{n}^{\left(\alpha , \beta \right)}(x)\). Here, the parameters \(\alpha\) and \(\beta\) define the weight function associated with this family: \(w\left(x\right)={x}^{\beta }{\left(1-x\right)}^{\alpha }\) (Secchi et al. 1999).
Abbreviations
- AGMD:
-
Air gap membrane distillation
- CPC:
-
Concentration polarization coefficient
- DCMD:
-
Direct contact membrane distillation
- MD:
-
Membrane distillation
- REC:
-
Water recovery
- RO:
-
Reverse osmosis
- RR:
-
Recycle ratio
- SEC:
-
Specific energy consumption
- SGMD:
-
Sweep gas membrane distillation
- TPC:
-
Temperature polarization coefficient
- VMD:
-
Vacuum membrane distillation
- \(B\) :
-
Membrane permeability
- \({C}_{p}\) :
-
Heat capacity
- c:
-
Mass concentration
- C:
-
Molar concentration
- \({\mathcal{D}}_{ij}\) :
-
Diffusivity
- L:
-
Length
- \(\dot{m}\) :
-
Mass flow
- M:
-
Molecular weight
- N:
-
Permeate flux
- P:
-
Pressure
- \(q\) :
-
Flow rate
- r:
-
Radial coordinate
- r:
-
Radius
- R:
-
Universal gas constant
- Re:
-
Reynolds number
- T:
-
Temperature
- \(v\) :
-
Velocity
- x:
-
Liquid molar fraction
- Y:
-
Air molar fraction
- y:
-
Vapor molar fraction
- z:
-
Axial coordinate
- \(\Delta {H}_{v}\) :
-
Vaporization enthalpy
- \(\delta\) :
-
Thickness
- \(\kappa\) :
-
Thermal conductivity
- \(\rho\) :
-
Density
- \(\tau\) :
-
Membrane tortuosity
- \(\epsilon\) :
-
Membrane porosity
- \(\fancyscript{a}\) :
-
Lumen side
- A:
-
Volatile component
- B:
-
Non-volatile component
- \(\fancyscript{b}\) :
-
Shell side
- f:
-
Feed
- fs:
-
Free surface
- in:
-
Entry
- l:
-
Internal
- ln:
-
Logarithmic
- p:
-
Permeate
- P:
-
Pore
- r:
-
Radial
- s:
-
External
- w:
-
Water
- z:
-
Axial
- b:
-
Bulk
- c:
-
Concentration
- m:
-
Membrane
- sat:
-
Saturation
- t:
-
Thermal
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Acknowledgements
This research was financially supported by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico). The authors thank Professor Argimiro Secchi for his help in using EMSO software.
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Ferreiro, O.B., Kronemberger, F.A. & Borges, C.P. Assessment of module arrangements of a direct contact membrane distillation process for a small-scale desalination plant. Braz. J. Chem. Eng. 39, 773–787 (2022). https://doi.org/10.1007/s43153-021-00171-w
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DOI: https://doi.org/10.1007/s43153-021-00171-w