Oily Water Treatment by Ceramic Membrane: Modeling and Simulation

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.


Introduction
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. [1], the water resulting from petroleum production is an undesirable by-product, which is always presented in crude oil extraction.
The oil concentration in the produced water can vary from relatively low values, ranging from 50 to 600 mg/L [2] [3] [4], to higher values, above 1000 mg/L [2] [5]. For this reason, and to obey environmental legislation, the contaminated water treatment is necessary for subsequent reuse or disposal.
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 [6] [7]. An alternative that has been studied is the use of membrane-based separation processes that is well indicated for particles with a diameter smaller than 10 µm. This is a clean and easy handling technique and at a low cost. Thus, the use of membranes is economically competitive when compared to other separation processes.
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. [8], membrane separation processes usually occur without phase change, and with energy saving. Their properties may be established according to the desirable application.
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 [9] A. B. Costa Pereira et al. Osmosis (RO) [12]. We state that microfiltration membranes are used in separation where particles with 0.1 to 10 µm diameter are present, ultrafiltration membranes for particles with diameter of 0.005 to 0.05 µm, nanofiltration for 0.0005 to 0.005 µm particle diameter, and finally reverse osmosis which is applied when particles with 0.0001 to 0.001 µm diameter are present in the fluid mixture.
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 [9], Vieira et al. [13], Souza [14], Cunha [15], Cunha et al. [16], Cunha et al. [17], Magalhães et al. [18], Souza et al. [19], Magalhães et al. [20], Oliveira [21] and Magalhães et al. [22].
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 ce-

Problem Description and Mesh Generation
The study domain basically is a separation module consisting of a tube with a porous wall (ceramic membrane), as shown in Figure 1(c). The water-oil mixture feeds the module through a duct of rectangular section positioned perpendicularly and tangentially to the membrane, as illustrated in Figure 1.

Advanced Mathematical Modeling
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: 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: 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) is a symmetric second-rank tensor, called the permeability tensor.
Momentum transfer equation  For the fluid phases where p is the pressure, M S 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: where p d is the particle diameter and D C 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: where e µ is the effective viscosity defined by the Equations (6)  In equation α µ is the dynamic viscosity and T µ 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: where µ is the dynamic viscosity and t µ is the eddy viscosity, which is given by where C µ is an empirical constant. In the Equations (7), (8) and (9), where η is defined as follows: where 0.085 RNG C µ = 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: where the term B P κ is the buoyant production, defined in Equation (15).
where g is gravity acceleration and kB P is Prandtl's number turbulent.

Boundary Conditions
For a complete mathematical modeling, different boundary conditions were previously defined, which can be observed in Table 1. Wall 0

Materials Parameters and Simulated Cases
The properties of fluid phases (water and oil) and porous media used in the simulations are shown in Table 2, and the studied cases are reported in Table 3.

Numerical Analysis Procedure
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 Figure 3.
In Figure 3, it is possible to verify that regardless of the iteration number proposed in the simulation, there is a similar response of the variable in the process, especially when observing the profiles obtained with 5000 and 8000 iterations. Thus, 5000 iterations were used in the present study, given that satisfactory results were obtained for the case studied (θ = 0.44, Table 3) with lower computational cost.
The velocity profiles shown in Figure 3(b) were obtained in the highlighted line in Figure 3(a). The choice of this location is due to the strong influence that the tangential inlet has on the flow behavior inside the membrane.    The behavior of the oil fraction concentration observed for the module's entry planes presented in Figure 4 showed similarity for the three membrane porosi-Open Journal of Fluid Dynamics ties. In the module's exit planes, shown in the aforementioned figure, different behavior is found, with lower oil volume fraction concentration for the membrane with minor porosity (θ = 0.35). Figure 5 illustrates the oil volume fraction distribution at the different XY transversal planes along the device. By analyzing Figure 5, it can be seen that as the flow occurs, there is a tendency to increase the oil volume fraction in the membrane and a more significant accumulation and/or passage of these particles at the ends of the membrane. This flow behavior occurs radially from the center of the device to the outer wall of the membrane.

The Effect of the Membrane Porosity
The oil behavior observed in Figure 5 can be explained by two factors: 1) the action of gravity, due to the horizontal positioning of the equipment, which has a direct influence on the oil particles deposition in the outer wall of the membrane, especially for the studied case with higher membrane porosity, and 2) the appearance of recirculation zones close to the tangential entrance, providing a bigger carrying of oil particles and, consequently, lower oil accumulation in this region.     Figure   9(a), caused a greater accumulation of oil in the external interface of the membrane or even filtered, as expected, considering that higher injection velocities can cause a greater fraction of oil to pass through the membrane, that is, less resistance of the membrane to the oil passage.
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 Figure 10. In this figure we can see that

Performance of the Ceramic Membrane
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 ( outlet m  ) and feed inlet ( inlet m  ), given as follows: Table 4 and Table 5 present the extracted data of the simulations and the calculations of membrane separation efficiency for each case. 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 Figure 8 for the oil fraction distribution inside the membrane.
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. Table 4. Oil mass flow rates and separation efficiency of the device for different membrane porosity (feed velocity 40 m/s).