Numerical Study of Electrostatic Desalting Process Based on Droplet Collision Time
Abstract
:1. Introduction
2. Materials and Methods
2.1. Force Balance
2.2. Mathematical Modeling
2.2.1. Assumptions
- Isothermal system, i.e., there are no gradients of temperature.
- Constant physical properties, each fluid phase is Newtonian and incompressible.
- Non-slip and impermeable conditions were applied for all the internal walls and standard wall functions were used.
- Oil liquid phase is considered as a continuous primary phase and water is considered as the dispersed secondary phase.
- The multiphase system is modeled with a mixture approach which solves a single set of equations: the continuity, the turbulent Navier–Stokes equations and the realizable turbulence model, which showed the best convergence behavior and that is being used recently in many complex flow systems.
- A conservation equation for interfacial area concentration is used as an approximation to take into account the coalescence and break up of droplets due to the electrostatic and turbulence effects to compute a droplet t diameter distribution.
- Coalescence terms depend on the frequency of collision, which is taken as the inverse of the time between collisions, which in turn is obtained from the previous droplet collision study.
2.2.2. Governing Equations
2.2.3. Interfacial Area Concentration Model
2.2.4. Realizable Turbulence Model
2.2.5. Boundary Conditions and Solution
3. Results and Discussion
4. Conclusions
- The time of collision varies with an inverse relationship to the third power of the water content, which indicated to be the most significant variable, valid in the range of water content of 3–12%.
- The time of collision varies inversely to the square of the electrostatic field (0.1 < E < 3 kV/cm), while it has a proportional nearly linear relationship to the oil viscosity (0.017 < µo < 0.071 Pa s).
- The droplet size has no influence on the time of collision within the range of droplet sizes analyzed in this work (1 µm up to 20 µm).
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Reference | Correlation/Ranges | Notable Results |
---|---|---|
Bresciani et al. [7] Bresciani et al. [9] | tc = 3:57 lµo−2a−5 l0 = (1.613x−1/3 − 2) a E[0 0.1−3 kV/cm], x[0.02−0.08], a[1−100 µm] | Increase in operational variables promotes desalting |
Abdul-Wahab et al. [10] | η1 = β0 + β1X1 + β2X2 + β3X3 + β4X4 + β5X5 + β12X1X2 + β13X1X3 + β14X1X4 + β15X1X5 + β23X2X3 + β24X2X4 + β25X2X5 + β34X3X4 + β35X3X5 + β45X4X5 + β1212X1X2(X1 − X2) + β1313X1X3(X1 − X3) + β1414X1X4(X1 − X4) + β1515X1X5(X1 − X5) + β2323X2X3(X2 − X3) + β2424X2X4(X2 − X4) + β2525X2X5(X2 − X5) + β3434X3X4(X3 − X4) + β3535X3X5(X3 − X5) + β123X1X2X3 η1 = 50.277 + 8.040X2 + 1.863X3 + 0.679X5 (R2 = 0.7) µo[0.017–0.048 Pa s], X1[55–70 °C], X2[1–3 min], X3[1–9 min], X4[1–15 mg/kg ], X5[1–10%] | Depends on settling time, mixing time and rate of dilution |
Al-Otaibi et al. [2] | N/A | Increase in operational variables promotes desalting |
Aryafard et al. [12] | No correlation Δp[137.895–206.843 Pa] E[1–2 kV/cm] x[0.03–0.06] | Decrease in pressure drop, increase in electric field and inlet rate of fresh water promote desalting |
Mohammadi [20] | E[1.4–2.8 kV/cm], a[600 µm], µo[0.015 Pa s] | Strong electric field Small distance of separation of droplets |
Kakhki et al. [14] | No correlation T[50 °C], x[0.03−0.05], f[50−400 Hz] | Increase in frequency promotes desalting |
Alnaimat et al. [21] | No correlation, no ranges given | Low flow and charged particle velocities High electric and magnetic fields |
Process Variable | Quantity |
---|---|
Electric field | 1 kV/cm |
Lower droplet radius | 10 |
Upper droplet radius | 10 |
Water density | 943 kg/m3 |
Oil density | 892 kg/m3 |
Gravitational constant | 9.81 m/s2 |
Oil viscosity | 0.044 Pa s |
Water volume fraction | 0.07 |
Oil dielectric constant | 2.2 ε0 |
Process Variable | Quantity | Units |
---|---|---|
Water volume fraction | 0.03, 0.05, 0.07, 0.10, 0.12 | - |
Electric field | 0.1, 0.5, 1, 2, 3 | kV/cm |
Oil viscosity | 0.017, 0.027, 0.044, 0.071 | Pa s |
Lower droplet and upper droplet let radii | 1, 5, 10, 15, 20 |
Process Variable | Quantity |
---|---|
Length | 15.24 m |
Internal diameter | 3.66 m |
Water volume fraction | 0.10 |
Emulsion flow at inlet | 0.126 m3/s |
Electric field | 1 kV/cm |
Oil viscosity | 0.044 Pa s |
Interfacial tension | 4 mN/m |
Term | |
---|---|
Droplet size, a | −29.250 ± 733.2 |
Viscosity of oil, µo | 878.900 ± 733.2 |
Electric field, E | −1463.200 ± 733.2 |
Water content, x | −1436.200 ± 733.2 |
Double interaction, aµo | −17.528 ± 733.2 |
Double interaction, aE | 29.180 ± 733.2 |
Double interaction, ax | 28.640 ± 733.2 |
Double interaction, µoE | −877.000 ± 733.2 |
Double interaction, µox | −860.800 ± 733.2 |
Double interaction, Ex | 1433.100 ± 733.2 |
Triple interaction, aµoE | 17.490 ± 733.2 |
Triple interaction, aµox | 17.168 ± 733.2 |
Triple interaction, aEx | −28.580 ± 733.2 |
Triple interaction, µoEx | 858.9 ± 733.2 |
Quadruple interaction, aµoEx | −17.130 ± 733.2 |
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Ramirez-Argaez, M.A.; Abreú-López, D.; Gracia-Fadrique, J.; Dutta, A. Numerical Study of Electrostatic Desalting Process Based on Droplet Collision Time. Processes 2021, 9, 1226. https://doi.org/10.3390/pr9071226
Ramirez-Argaez MA, Abreú-López D, Gracia-Fadrique J, Dutta A. Numerical Study of Electrostatic Desalting Process Based on Droplet Collision Time. Processes. 2021; 9(7):1226. https://doi.org/10.3390/pr9071226
Chicago/Turabian StyleRamirez-Argaez, Marco A., Diego Abreú-López, Jesús Gracia-Fadrique, and Abhishek Dutta. 2021. "Numerical Study of Electrostatic Desalting Process Based on Droplet Collision Time" Processes 9, no. 7: 1226. https://doi.org/10.3390/pr9071226