Abstract
This paper provides a mathematical simulation model for the reverse osmosis (RO) process with series elements. A mathematical simulation model was developed based on the mass, material and energy balances considering the concentration polarization. The simulation model is open-source and easy to couple with other computational tools like optimization algorithms and SCADA1 applications. An RO laboratory pilot was also set up in the Hydraulic Lab of Shahid Chamran University of Ahvaz to validate the simulation results. Comparing the results of the simulation model with the experiments and ROSA commercial software, the proposed simulation model functions well and is reliable. The comparisons indicate that the simulation results are over 96% close to ROSA and over 80% close to experimental results.
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Abbreviations
- A:
-
membrane surface area [m2]
- Aeff :
-
effective surface area of membrane [m2]
- Am :
-
pure water permeability constant [m/s·kPa]
- C:
-
solution concentration [kg/m3]
- CF :
-
feed concentration [kg/m3]
- CP :
-
permeate concentration [kg/m3]
- CR :
-
retentate concentration [kg/m3]
- Cw :
-
concentration on the feed side of membrane wall [kg/m3]
- d:
-
membrane channel diameter [m]
- Ds:
-
solute diffusivity [m2/s]
- dsp :
-
spacer diameter [m]
- i:
-
stage counter
- j:
-
pressure vessel counter in stage
- jw :
-
water flux [m3/m2·s]
- k:
-
mass transfer coefficient [m/s]
- l ch :
-
length of the membrane channel [m]
- M:
-
molar concentration [mol/m3]
- n:
-
van’t Hoff factor
- Nei :
-
number of the membrane element in pressure vessel of the ith stage
- Ni:
-
number of membrane element in the ith stage
- NPVi :
-
number of pressure vessel in the ith stage
- Peff :
-
residual transmembrane pressure [kPa]
- P f :
-
feed pressure [kPa]
- Pp :
-
permeate pressure [kPa]
- QF :
-
feed flow rate [m3/s]
- QFPV :
-
feed flow rate in the pressure vessel [m3/s]
- Q F1 :
-
feed flow rate to the first stage [m3/s]
- Q F2 :
-
feed flow rate to the second stage [m3/s]
- QF3 :
-
feed flow rate to the third stage [m3/s]
- QP :
-
permeate flow rate [m3/s]
- QPPV :
-
permeate flow rate in the pressure vessel [m3/s]
- QR :
-
retentate flow rate [m3/s]
- QR1 :
-
retentate flow rate from the first stage [m3/s]
- QR2 :
-
retentate flow rate from the second stage [m3/s]
- R:
-
universal gases constant [8.314 m3·Pa/mol·°K]
- Re:
-
Reynolds number
- RE:
-
relative error
- rec1:
-
recovery in the first stage
- rec2:
-
recovery in the second stage
- rec3:
-
recovery in the third stage
- Sc:
-
schmidt number
- St:
-
spacer thickness [m]
- T:
-
temperature [°C]
- T0:
-
reference temperature [25 °C]
- TCF:
-
temperature’s correction factor
- TF :
-
feed water temperature [°C]
- VSP :
-
volume of the spacer [m3]
- VT :
-
total volume [m3]
- z:
-
element counter in the Pressure vessel
- μ :
-
feed water viscosity [Pa·s]
- α :
-
fraction of the stream branching to the left from a split point
- β :
-
fraction of the stream branching to the right from a split point
- γ :
-
fraction of the stream branching straight forward from a split point
- ΔPf :
-
pressure drop due to friction [kPa]
- ΔPin :
-
pressure drop at inlet [kPa]
- π :
-
osmotic pressure [kPa]
- π p :
-
osmotic pressure on the permeate side [kPa]
- π w :
-
osmotic pressure on the feed side of membrane wall [kPa]
- ρ :
-
density [kg/m3]
- ε :
-
Porosity
- f:
-
feed
- F:
-
feed split ratio
- p:
-
permeate
- r:
-
retentate
- R1:
-
retentate split ratio for first module
- R2:
-
retentate split ratio for second module
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Acknowledgements
The authors would like to thank Ghadir Khuzestan Water Company and Khuzestan Water and Power Authority for their financial and technical support.
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Hadadian, Z., Zahmatkesh, S., Ansari, M. et al. Mathematical and experimental modeling of reverse osmosis (RO) process. Korean J. Chem. Eng. 38, 366–379 (2021). https://doi.org/10.1007/s11814-020-0697-9
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DOI: https://doi.org/10.1007/s11814-020-0697-9