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The separation process of oily water using membranes has attracted the attention of researchers and engineers. The greater problem in the use of membrane separation process is the reduction in permeate flux due to clogged pores by oil deposition inside the membrane or by the effect of the concentration polarization. For this purpose, a theoretical study of a water/oil separation module was performed. This device consists of a tubular ceramic membrane provided with a rectangular inlet section. Numerical simulations were performed using Ansys CFX software to solve the mass and momentum conservation equations in the fluid and porous domains. Here was adopted the RNG k-ε turbulence model. The effect of the membrane porosity and the inlet velocity of the fluid mixture on the two-phase flow behavior inside the separation module were evaluated. Results of the volumetric fraction, velocity and pressure fields of the oil and water phases are presented and analyzed. The results indicate a higher oil concentration within the membrane for the cases of higher porosity, and that the inlet fluid mixture velocity does not substantially affect the velocity profile within the separation module. It is found that the maximum separation efficiency of the module was obtained with feed velocity of 40 m/s and membrane porosity of 0.44.

The effects of technological advancement have provided countless socio-economic benefits. However, the misuse of such technology and the disregard for its imminent risks might lead to environmental degradation. Several cases of water contamination as well as the reduction in the volume of drinking water have been reported. The most reasonable conclusions point to the need for wastewater treatments, whether residential or industrial, in order to minimize the environmental damage caused by polluted effluents, such as oily water.

Along with the standard oil production process, there is a simultaneous production of oil, gas, sand, and water, consequently requiring adequate separation systems. According to Moraes et al. [

The oil concentration in the produced water can vary from relatively low values, ranging from 50 to 600 mg/L [

There are some separation processes commonly used by the oil industry for the treatment of oily water, such as: flotation equipment, clarifiers, and absorbers, settling tanks, hydro-cyclones and centrifuges. However, these devices are restricted to separate particles with a diameter of 10 µm [

Membranes act as selective barriers to particle transportation. They perform the separation into two phases and control the flow of particles in each of them. The membrane filtration results in permeate flux (liquid driven through the membrane) and concentrated fluid (retained liquid containing the feed contaminants). According to Thomas et al. [

The flow setting is an important feature in membrane-based filtration processes and it may occur in two different ways: Cross-flow filtration (also known as tangential flow filtration) and dead-end filtration (the conventional method for perpendicular flow). The feed mixture flux in the dead-end filtration method is frontally forced against the membrane, which causes the retained particles to rapidly coagulate on the membrane surface, gathering solute (suspended solids). This phenomenon is called Concentration Polarization and it is responsible to reduce the separation performance. In the cross-flow filtration method, the tangential flux reduces the solute accumulation due to the particle movements. For this reason, tangential flow operations are chosen for industrial applications which deal mainly with higher concentrations of suspended solids [

Depending on the nature and type of solutes and presence of suspended particles, membranes with different sizes and pores distribution can be classified as MicroFiltration (MF), UltraFiltration (UF), NanoFiltration (NF) and Reverse Osmosis (RO) [

The modeling and simulation of problems involving oily water separation by membranes is complex, requiring a deep theoretical basis. The separation process occurs over time thus, some changes in the characteristics and properties of the membrane can be observed. Besides, solute accumulation at interface membrane/solution is inevitable. Because of the importance, several studies involving the membrane separation process with computer codes’ aid based on CFD tools (Computational Fluid Dynamics) have been conducted, for example, Porciúncula [

As a complement to these studies, this work aims to simulate the oily water treatment by a new configuration of the ceramic membrane using CFD tools. Based on the earlier discussions, the present work is motivated by the growing importance of separation processes using membranes, especially that using ceramic membranes, and by the fact that most of the experimental and numerical works reported in the literature have used polymeric membranes. The contribution of this research is directed to answer some questions involved in effluent treatment by ceramic membranes not yet well understand, such as membrane geometry, 3D fluid flow behavior and oil concentration inside the membrane which strongly affect the separation performance.

The study domain basically is a separation module consisting of a tube with a porous wall (ceramic membrane), as shown in

Different simulations were performed to identify the non-dependence of the results with the mesh and number of interactions (5000, 8000, 11,000, 14,000, and 17,000), directly related to the computational time used in solving the

simulations for the studied separation phenomenon. Then, three membrane porosities were assumed, (0.35, 0.40 and 0.44) and three input velocities of the mixture, (U_{feed} = 35, 40 and 45 m/s) in the separation module. All simulations of the fluid separation process were performed using the Ansys CFX software.

The mathematical model defined to describe an oil/water flow separating process is based on the generalized equations mass and momentum conservation of the RNG k-ε model turbulence. The following considerations were adopted:

1) Newtonian and incompressible fluid;

2) Steady-state flow regime;

3) Isothermal flow;

4) Constant physical and chemical properties of the fluids;

5) The chemical reaction, mass transfer between the phases, and mass source are disregarded;

6) The interfacial drag force was considered;

7) The oil droplets are spherical and non-deformable.

The mathematical model does not predict the phenomenon of retention of molecules or particles in the porous medium, however, it considers the difficulty or resistance to the passage of the phases (oil and water) into porous media. Based on the considerations cited earlier and using an Eulerian-Eulerian approach, the following equations are given:

Mass conservation equation

• For the fluid phases

∇ ⋅ ( f α ρ α U → α ) = 0 (1)

where α is the phase (water or oil), f, ρ and U → represent volumetric fraction, density and velocity vector, respectively.

• For the porous medium (ceramic membrane)

∇ ⋅ ( f α ρ α K U → α ) = 0 (2)

where K = ( K i j ) is a symmetric second-rank tensor, called the permeability tensor.

Momentum transfer equation

• For the fluid phases

∇ ⋅ [ f α ( ρ α U → α ⊗ U → α ) ] = − f α ∇ p α + ∇ ⋅ { f α μ e [ ∇ U → α + ( ∇ U → α ) T ] } + S → M α + M → α (3)

where p is the pressure, S → M α it is the term of external forces acting on the system per unit volume, M → α describes the overall strength per unit volume on the α phase due to interaction with the β phase. This parameter is given as follows:

M α = M α β D = 3 C D 4 d p f β ρ α | U α − U β | ⋅ ( U α − U β ) (4)

where d p is the particle diameter and C D is drag coefficient, which was assumed to be equal to 0.44.

• For the porous media

The following equation defines the momentum conservation for the porous media:

∇ ⋅ [ f α ρ α ( K ⋅ U → ) ⊗ U → ] = − ∇ p + ∇ ⋅ { f α μ e K ⋅ [ ∇ U + ( ∇ U → i ) T ] } + S → i M (5)

where μ e is the effective viscosity defined by the Equations (6) and S → i M is the linear momentum source term:

μ e = μ α + μ T (6)

In equation μ α is the dynamic viscosity and μ T represents the turbulent viscosity given by Equation (9).

Turbulence model

In this research, it was used the RNG k-ε turbulence model. In this model, the transport equations for estimating the variables, k, turbulent kinetic energy (dimensions L^{2}∙T^{−2}) and, ε, turbulent dissipation rate (dimensions L^{2}∙T^{−3}) are given as follows:

∂ ( ρ k ) ∂ t + ∇ ( ρ U j k ) = ∇ ⋅ [ ( μ + μ t σ k R N G ) ∇ κ ] + P k − ρ ε (7)

∂ ( ρ ε ) ∂ t + ∇ ⋅ ( ρ U j ε ) = ∇ ⋅ [ ( μ + μ t σ ε R N G ) ∇ ε ] + ε k ( C ε 1 R N G P k − C ε 2 R N G ρ ε ) (8)

where μ is the dynamic viscosity and μ t is the eddy viscosity, which is given by:

μ t = C μ ρ k 2 ε (9)

where C μ is an empirical constant. In the Equations (7), (8) and (9),

C μ = σ ε R N G = σ κ R N G = 0. 7179 (10)

C ε 2 R N G = 1.68 (11)

C ε 1 R N G = 1.42 − η ( 1 − η 4.38 ) 1 + η 3 β R N G (12)

where η is defined as follows:

η = P κ ρ ε C μ R N G (13)

where C μ R N G = 0.085 is the constant that appears in the RNG κ-ε turbulence model (ANSYS CFX 12.1), P κ is the production of turbulence due to the viscosity and shear forces, defined as follows:

P κ = μ t ∇ U ⋅ ( ∇ U + ∇ U ) T + P κ B (14)

where the term P κ B is the buoyant production, defined in Equation (15).

P k B = − μ t ρ σ µ g ⋅ ∇ ρ (15)

where g is gravity acceleration and P k B is Prandtl’s number turbulent.

For a complete mathematical modeling, different boundary conditions were previously defined, which can be observed in

Location | Type (Ansys CFX) | Boundary conditions |
---|---|---|

Feeding | Inlet | f_{oil} = 0.05 |

U x = U z = 0 | ||

U y = U f e e d _{ } | ||

Permeated outlet | Outlet | ∂ U i ∂ x i = 0 |

P = 99,000 Pa | ||

Wall (non-slip condition) | Wall | U x = U y = U z = 0 |

Concentrated outlet | Outlet | ∂ U i ∂ x i = 0 |

The properties of fluid phases (water and oil) and porous media used in the simulations are shown in

On the simulation study is very important to perform mesh refinement and number of iterations studies, in order to obtain confiability and precision in the obtained results. The aim is to obtain results with lower computational cost and great precision. As a first step, a numerical analysis to determine the effect of the number of iterations in the obtained results was performed. In the study, five variations on the number of iterations (5000, 8000, 11,000, 14,000 and 17,000 iterations) were established and, thus, the direct relation between the simulation runs and generation of results was verified.

The set of studies was carried out the principle of superposition of the water velocity profile curves near the tangential entrance along the membrane, as defined in

In

The velocity profiles shown in

Material | Property | Value |
---|---|---|

Water | Density (kg/m^{3}) | 997 |

Viscosity (Pa/s) | 8.89 × 10^{−4} | |

Oil | Density (kg/m^{3}) | 868.7 |

Viscosity (Pa/s) | 7.6 × 10^{−2} | |

Ceramic membrane | Porosity | θ (Available in _{ } |

Permeability (m^{2}) | 2.29 × 10^{−10} |

Case | Feed velocity (U_{feed}) (m/s) | Porosity (θ) (-) |
---|---|---|

1 | 40 | 0.35 |

2 | 40 | 0.40 |

3 | 40 | 0.44 |

4 | 35 | 0.35 |

5 | 45 | 0.35 |

planes that pass through the center of the membrane and on the transverse planes at the inlet and outlet of the separation module for different porosity (Cases θ = 0.35, θ = 0.40 and θ = 0.44). By analyzing

The behavior of the oil fraction concentration observed for the module’s entry planes presented in

The oil behavior observed in

and XY longitudinal planes). By analyzing the XY transversal plane, it is observed a similarity in the results for the three cases of membrane porosity in terms of the pressure distribution except for the plane closest to the tangential inlet (XY plane at z = 0.0 m), where turbulence is more pronounced. This existing eddy contributes to the presence of greater pressure in the regions close to the inner wall of the membrane, and sometimes the pressure drops in the innermost regions of the module.

Despite different values scales, pressure fields at the membrane surface and transversal planes, illustrated in

vector field for the condition of 35 m/s (

The zero value on the abscissa axis shown in the graphs corresponds to the center of the inner pipe. At this point it can be seen the minor velocity values and rising in direction to the membrane surface reaching the “spikes” can be explained by the recirculation zones. For minor distance to the membrane surface velocities values tend to be reduced drastically.

In

The second analysis concerns the pressure profiles for the three analyzed cases of the feed water-oil mixture velocity for the membrane with porosity of 0.35 m. In

The region highlighted in

Despite the small difference between the values of oil distribution in the membrane for the three velocity cases, an injection velocity of 35 m/s,

It is interesting to note that the distribution of the volume oil fraction throughout the module showed a similar behavior regardless of the feed velocity of the fluid mixture, as observed in

despite the swirling zone observed in the initial section of the modules, the permeate flux occurred over the entire length of the module being more intense in the region close to the module’s outlet.

The membrane performance for water-oil separation was also analyzed for each case studied. The calculation of the separation efficiency was performed by the ratio between the oil mass flow rates at the concentrate outlet ( m ˙ outlet ) and feed inlet ( m ˙ inlet ), given as follows:

η = m ˙ outlet / m ˙ inlet (15)

Upon analyzing these tables, it is clear the influence of both the membrane porosity and mixture feed velocity on the membrane module performance. Concerning porosity, it can be seen that the higher the membrane porosity, the greater the water-oil separation efficiency, due to less resistance to flow through the membrane. Unlike behavior was verified for the feed velocity. The higher the feed velocity, the higher the pressure gradient in the device and the higher resistance to oil passage, a complementary result to that observed in

The maximum performance of 70% was verified for the operating condition: feed velocity of 40 m/s and membrane porosity of 0.44. This efficiency can be considered like moderate, and can be improved changing membrane permeability and membrane thickness, for example.

θ = 0.35 | m ˙ inlet | 0.348 kg/s | η = 60.2% |
---|---|---|---|

m ˙ outlet | 0.209 kg/s | ||

θ = 0.40 | m ˙ inlet | 0.347 kg/s | η = 66.8% |

m ˙ outlet | 0.232 kg/s | ||

θ = 0.44 | m ˙ inlet | 0.347 kg/s | η = 70.0% |

m ˙ outlet | 0.242 kg/s |

v = 35 m/s | m ˙ inlet | 0.304 kg/s | η = 67.0% |
---|---|---|---|

m ˙ outlet | 0.205 kg/s | ||

v = 40 m/s | m ˙ inlet | 0.347 kg/s | η = 60.2% |

m ˙ outlet | 0.209 kg/s | ||

v = 45 m/s | m ˙ inlet | 0.391 kg/s | η = 56.0% |

m ˙ outlet | 0.219 kg/s |

This paper evaluated a fluid dynamic analysis and separation performance of a ceramic membrane module with tangential inlet of rectangular cross section used in oily water treatment. From the simulated results (Ansys CFX software) the following conclusions can be given: 1) The fluid mixture flow inside the separation module presented a strong three-dimensional behavior, mainly near the feed duct inlet; 2) The velocity profiles inside the membrane showed a significant similarity in all cases and recirculation zones immediately after the feed duct inlet; 3) The higher the membrane porosity the higher the oil volume fraction, the lower pressure inside the membrane, and the higher the separation efficiency of the device; 4) The higher the feed mixture velocity the lower the oil volume fraction inside the membrane, the higher the pressure gradient close to the inner membrane surface, and the lower the separation efficiency of the device; 5) An axisymmetric behavior of the pressure inside the module at each cross section was verified in all studied cases, and 6) The maximum separation efficiency of the module (70%) was obtained when feed velocity of 40 m/s and membrane porosity of 0.44 were applied.

The authors thank CNPq, CAPES and FINEP (Brazilian Research Agencies) for the financial support.

The authors declare no conflicts of interest in this paper.

Costa Pereira, A.B., Magalhães, H.L.F., Silva, L.P.L., Passos, C.A., Gomez, R.S., Correia, B.R.B., Farias Neto, S.R. and Lima, A.G.B. (2021) Oily Water Treatment by Ceramic Membrane: Modeling and Simulation. Open Journal of Fluid Dynamics, 11, 1-19. https://doi.org/10.4236/ojfd.2021.111001