# Impact of Permeable Membrane on the Hydrocyclone Separation Performance for Oily Water Treatment

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Problem Description

#### 2.2. Computational Domain Generation

^{®}software was used. Besides this, to ensure that the mesh leads to coherent numerical results and at the same time requires a lower computational effort, three structured meshes were made with different refinement degrees, aiming at a good distribution of the elements on the study domain. A mesh refining test was carried out, using the mesh convergence index (ICM) method as proposed by [22].

#### 2.3. Mathematical Modeling

- Incompressible and Newtonian fluid with constant physical–chemical properties;
- Steady-state and isothermal flow;
- Mass transfer, interfacial momentum, and mass source are disregarded;
- The non-drag interfacial forces (lift forces, wall lubrication, virtual mass, turbulent dispersion and solid pressure) were neglected;
- Constant drag coefficient equal to 0.44, due to the established turbulent flow;
- The geometry walls are static and there is null wall roughness.
- The water stream is a multicomponent mixture of water and oil (solute);
- The composition of the multicomponent water/oil mixture is variable;
- The viscosity and density of the mixture are constant;
- The mass diffusion coefficient of the oil in the water is constant;
- The porous medium (ceramic membrane) has constant permeability and isotropic distribution of it pores;
- The pore obstruction by the solute was neglected (constant porosity);
- The concentration polarization layer is present and its thickness is considered uniform and homogeneous, thus the resistance resulting from the presence of this layer was defined at the fluid–membrane interface (concentration polarization resistance);
- The rate of local permeation is determined by the series resistance theory;
- The non-slip condition on the membrane surface was adopted;
- There is no reaction or adsorption of the solute on the contact surface in the porous medium.

#### 2.3.1. The Governing Equations

- (a)
- Mass Conservation Equation:

- (b)
- Momentum Conservation Equation:

_{D}is the drag coefficient and d

_{p}represents the particle diameter. The term $\nabla \xb7\left\{{f}_{\alpha}{\mathsf{\mu}}_{ef}\left[\nabla {\overrightarrow{U}}_{\alpha}+{\left(\nabla {\overrightarrow{U}}_{\alpha}\right)}^{T}\right]\right\}$ corresponds to the momentum transfer induced by the interfacial mass transfer, and ${\mathsf{\mu}}_{ef}$ is the effective viscosity, defined by:

- (c)
- Turbulence Model:

- (d)
- Separation Efficiency:

#### 2.3.2. Boundary Conditions

- (a)
- Input:

- (b)
- Porous Wall (Permeate):

_{h}is the hydraulic diameter, given by:

_{C}is the cylinder diameter, and D

_{TC}is the diameter of the tapered trunk.

_{E}= u

_{E}·S

_{E}, u

_{E}is the inlet fluid velocity and S

_{E}is the section area of the feed duct.

- (c)
- Outputs (Concentrated and Diluted):

- (d)
- Non-porous walls:

#### 2.4. Studied Cases

^{®}15.0 software (15, Ansys, Inc., Canonsburg, PA, USA). For the calculations, machines with Intel Core I7-3770 3.40 GHz processor and 16 GB of RAM were used. The simulations were performed using the fixed convergence criterion concerning the residual error–Root Mean Square (RMS) of ${10}^{-7}kg/s$ for the additional and flow variables.

## 3. Results and Discussion

#### 3.1. Mesh Quality Assessment

#### 3.2. Comparative Study between the Conventional Cyclonic Separator and the Cyclonic Filter Separator

^{−1}to 50 mg·L

^{−1}, depending on the country. In Brazil, the permitted value is 29 mg·L

^{−1}(simple monthly arithmetic mean), with a maximum daily value of 42 mg·L

^{−1}[37]. To comply with environmental legislation, the oil industry has used certain equipment, such as air floats, hydrocyclones (offshore installations), bed coalescers, and gravitational separators (onshore installations). Despite being used today, these processes have some disadvantages, such as long residence time, the use of high-cost special chemicals, the generation of solid waste, and their low efficiencies, especially when the oil drops have diameters in the order of micrometers, and tensioactive agents are present, which are very common in emulsions.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Water and oil streamlines inside the separation equipment. (

**a**) Conventional cyclonic separator, (

**b**) filtering cyclonic separator, (

**c**) detail of the conventional cyclonic separator outlet, and (

**d**) detail of the filtering cyclonic separator outlet.

**Figure 5.**Pressure field on the xy and xz planes. (

**a**) Conventional cyclonic separator and (

**b**) filtering cyclonic separator.

**Figure 6.**Pressure profile in conventional and filtering hydrocyclones at positions (

**a**) y = 0.15 m, (

**b**) y = 0.45 m and (

**c**) y = 0.75 m.

**Figure 7.**Water tangential velocity field in the yz plane. (

**a**) Conventional hydrocyclone and (

**b**) filtering hydrocyclone.

**Figure 8.**Tangential velocity profile in conventional and filtering hydrocyclones at the positions (

**a**) y = 0.15 m, (

**b**) y = 0.45 m and (

**c**) y = 0.75 m.

**Figure 9.**Water axial velocity field in the yz plane. (

**a**) Conventional hydrocyclone and (

**b**) filtering hydrocyclone.

**Figure 10.**Axial velocity profile in the conventional and filtering hydrocyclones at the positions (

**a**) y = 0.15 m, (

**b**) y = 0.45 m and (

**c**) y = 0.75 m.

**Figure 11.**Oil concentration field in the yx and xz planes at positions y = 0.15 m, y = 0.45 m and y = 0.75 m. (

**a**) Conventional cyclonic separator and (

**b**) filtering cyclonic separator.

**Figure 12.**Oil concentration profile in conventional and filtering hydrocyclones at the positions (

**a**) y = 0.15 m, (

**b**) y = 0.45 m and (

**c**) y = 0.75 m.

Tangential Inlets (mm) | Height (A_{1}) | 50 |

Length (C_{1}) | 50 | |

Width (L_{1}) | 5 | |

Upper Conical Part (mm) | Height (A_{2}) | 75 |

Width (L_{2}) | 5 | |

Top Diameter (D_{1}) | 65 | |

Bottom Diameter (D_{2}) | 18 | |

Cylindrical Section (mm) | Height (A_{2}) | 75 |

Diameter (D_{5}) | 70 | |

Conical Section (mm) | Height (A_{3}) | 725 |

Annular Outlet (mm) | Diameter (D_{3}) | 18 |

Tubular Outlet (mm) | Diameter (D_{4}) | 10 |

Height (A_{4}) | 50 |

**Table 2.**Thermal, physical, chemical and geometrical parameters of the porous wall and mixture fluids (T = 293.15 K).

Membrane | Permeability | $1.39\times {10}^{-15}{m}^{2}$ [16] |

Polarization layer thickness | $0.255mm$ [16] | |

Porosity | 0.4 | |

Water | Density | $997kg/{m}^{3}$ |

Viscosity | $8.889\times {10}^{-4}Pa\xb7s$ | |

Molar mass | $18.05kg/kmol$ | |

Oil | Density | $868.7kg/{m}^{3}$ |

Viscosity | $0.985Pa\xb7s$ | |

Molar mass | $873kg/kmol$ | |

The average oil drop diameter | $0.1mm$ |

Case | Input Velocity (m/s) | Oil Volumetric Fraction (%) | Membrane Rejection Index R (-) |
---|---|---|---|

01 | 5 | 5.0 | - |

02 | 15 | 7.5 | - |

03 | 5 | 5.0 | 1 |

04 | 15 | 7.5 | 1 |

Mesh | Number of Elements | Simulation Time | |
---|---|---|---|

Cyclonic Separator | Filtering Separator | ||

M1 | 337.360 | 1 d 4 h 17′26″ | 3 d 8 h 4′2″ |

M2 | 71,352 | 3 h 10′44’’ | 21 h 38′40″ |

M3 | 10,571 | 23′22″ | 17′4″ |

Separator | Mass Flow Rate (kg/s) | |||||||
---|---|---|---|---|---|---|---|---|

Water | Oil | Water | Oil | |||||

Input | Input | Annular Output | Tubular Outlet | Membrane | Annular Output | Tubular Outlet | ||

Conventional Cyclonic | 6.91 | 0.48 | 5.19 | 1.72 | - | 2.02 × 10^{−4} | 0.48 | |

Filtering Cyclonic | 6.91 | 0.48 | 4.41 | 1.76 | 0.74 | 1.99 × 10^{−4} | 0.46 |

Separator | Total Efficiency (%) | Liquid Ratio (%) | Reduced Efficiency (%) |
---|---|---|---|

Conventional Cyclonic | 99.95 | 24.94 | 99.94 |

Filtering Cyclonic | 96.07 | 25.46 | 94.72 |

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**MDPI and ACS Style**

Nunes, S.A.; Magalhães, H.L.F.; de Farias Neto, S.R.; Lima, A.G.B.; Nascimento, L.P.C.; Farias, F.P.M.; Lima, E.S.
Impact of Permeable Membrane on the Hydrocyclone Separation Performance for Oily Water Treatment. *Membranes* **2020**, *10*, 350.
https://doi.org/10.3390/membranes10110350

**AMA Style**

Nunes SA, Magalhães HLF, de Farias Neto SR, Lima AGB, Nascimento LPC, Farias FPM, Lima ES.
Impact of Permeable Membrane on the Hydrocyclone Separation Performance for Oily Water Treatment. *Membranes*. 2020; 10(11):350.
https://doi.org/10.3390/membranes10110350

**Chicago/Turabian Style**

Nunes, Sirlene A., Hortência L. F. Magalhães, Severino R. de Farias Neto, Antonio G. B. Lima, Lucas P. C. Nascimento, Fabiana P. M. Farias, and Elisiane S. Lima.
2020. "Impact of Permeable Membrane on the Hydrocyclone Separation Performance for Oily Water Treatment" *Membranes* 10, no. 11: 350.
https://doi.org/10.3390/membranes10110350