Proceedings of the ASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting FEDSM2014 August 3-7, 2014, Chicago, Illinois, USA FEDSM2014-21289 CFD STUDY OF HYDRODYNAMICS AND SEPARATION PERFORMANCE OF A NOVEL CROSSFLOW FILTRATION HYDROCYCLONE (CFFH) Abdul Motin Mechanical Engineering Michigan State University East Lansing, MI, USA Volodymyr V. Tarabara Civil and Environmental Engineering Michigan State University East Lansing, MI, USA André Bénard* Mechanical Engineering Michigan State University East Lansing, MI, USA ABSTRACT This research addresses various hydrodynamic aspects and the separation performance of a novel cross-flow filtration hydrocyclone (CFFH) using computational fluid dynamics. A CFFH is a device that combines the desirable attributes of a cross-flow filter and a vortex separator into one unit to separate oil from water. The velocity and pressure fields within the CFFH are estimated by numerically solving the filtered NavierStokes equations (by using a Large Eddy Simulation (LES) approach). The Lagrangian approach is employed for investigating the trajectories of dispersed droplets based on a stochastic tracking method called the Discrete Phase Model (DPM). The mixture theory with the Algebraic Slip Model (ASM) is also used to compute the dispersed phase fluid mechanics and for comparing with results obtained from the DPM. In addition, a comparison between the statistically steady state results obtained by the LES with the Wall Adaptive Local Eddy-Viscosity (WALE) subgrid scale model and the Reynolds Average Navier-Stokes (RANS) closed with the Reynolds Stress Model (RSM) is performed for evaluating their capabilities with regards to the flow field within the CFFH and the impact of the filter medium. Effects of the Reynolds number, the permeability of the porous filter, and droplet size on the internal hydrodynamics and separation performance of the CFFH are investigated. Results indicate that for low feed concentration of the dispersed phase, separation efficiency obtained based on multiphase and discrete phase simulations is almost the same. Higher Reynolds number flow simulations exhibit an unstable core and thereby numerous recirculation zones in the flow field are observed. Improved separation efficiency is observed at a lower Reynolds number and for a lower permeability of the porous filter. INTRODUCTION Separation of oil from water is a critical aspect of produced water treatment and oil spills cleanup. It is also important in refining petroleum products. Produced water is the largest byproduct stream associated with oil and gas production. The US Department of Energy‟s Argonne National Laboratory estimates a volume of produced water in the United States at 21 billion barrels a year [1]. Additional production from the rest of the world is estimated at a volume of more than 50 billion barrels a year [1]. As a field becomes depleted, the amount of produced water typically increases. Several challenges exist in the oil industry with respect to the treatment of produced water for re-use in the underground injection or discharge to surface water. In the United States, the U.S. Environmental Protection Agency issued standards for underground injection [2], and discharges to surface water [3]. Depending on the country and location of offshore platforms the allowable concentration of oil in the water to be discharged is in the range of 15 to 40 mg/L [4]. Many technologies are currently used for produced water treatment. Common techniques available for treating the oilwater mixture and the removal capacity of existing technologies are given in Table 1.1 ________________________________ * Corresponding author; [email protected] 1 Copyright © 2014 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/conferences/asmep/82001/ on 02/14/2017 Terms of Use: http://www.asme.org/abo Table 1 Common technologies used for produced water treatment and their removal capacity [5] Technology API gravity separator Corrugated plate separator Induced gas flotation without chemical addition Induced gas flotation with chemical addition Hydrocyclones Mesh coalescer Media filter Centrifuge Membrane filter Removal capacity by particle size (micron) 150 40 25 3-5 10-15 5 5 2 0.01 Gravity separation and gas flotation are the primary treatments used for separation of oil from water in highly concentrated mixtures. Produced water is dilute and the typical concentration of oil ranges from 100 to 5,000 mg/L [6]. The density difference between the phases can be very small (less than 150 kg/m3) [7]. Secondary treatments may use hydrocyclones and centrifuges, where breakdown of oil-water emulsion occurs and most of the free oil is removed, are widely used in industries for produced water treatment. Filtration is capable of separating very fine droplets but membranes can easily be fouled by oil droplets. Hydrocyclones are simple devices having no moving parts, compact in size, and insensitive to orientation. However, existing hydrocyclone technology is only effective for a droplet size larger than 10 microns [8]. Moreover, existing de-oiling hydrocyclones have a finite turndown ratio [9] i.e. they exhibit acceptable separation efficiency only for a certain range of feed flow rate. A filtering hydrocyclone is a potential technology for produced water treatment. The filtering hydrocyclone is a swirling flow device in which the solid wall of the swirl chamber or the tail pipe section is replaced by a filtering medium (e.g. a membrane). The filtering hydrocyclone for solid-liquid separation was first patented in 1991 and it consisted of a Bradley‟s class hydrocyclone whose conical section was replaced by a conical filtering wall [10]. For solidliquid separation, the filtration hydrocyclone increases the inlet volumetric flow rate and decreases the energy consumption in comparison with a conventional hydrocyclone [11-15]. The dependency of the underflow to throughput ratio on the filtering medium resistance was investigated by Souza et al. [15]. Based on experimental results, they developed empirical expressions to account for the influence of the filtering medium resistance on the separation performance. Vieira et al. [10] and Barbosa et al. [14] replaced the conical section of both Rietema‟s and Bradley‟s hydrocyclones by filtering walls. They observed that the overall efficiency for the Bradley‟s filtering hydrocyclone decreases, but the Rietemas‟ filtering hydrocyclone shows an increase in the overall efficiency. However, based on experimental results, Rodrigues et al. [16] mentioned that the overall separation efficiency of the filtering hydrocyclone is similar to the conventional hydrocyclone, but with a reduced energy cost due to a reduction in pressure drop. CFD simulations performed by Vieira et al. [17] on the solid/liquid filtering hydrocyclone demonstrated that the incorporation of the filtering wall reduces the mixing effect and the radial drag on solid particles. A majority of earlier research on the filtration hydrocyclone was conducted for solid-liquid separation only. The first study on a Crossflow Filtration Hydrocyclone (CFFH) for liquid-liquid separation was conducted by Gaustad et al. [18]. Simulation results of the CFFH showed poor separation performance. Motin et al. [19] investigated the internal hydrodynamics of the single inlet CFFH by solving the RANS equations closed with the RSM. They observed that the swirling flow loses its intensity quickly in the filtering zone. This research further examines the hydrodynamics within a dual inlet CFFH based on the LES with the WALE subgridscale model to identify favorable operating conditions. Effects of the Reynolds number and permeability of the porous filter on the internal flow structures are analyzed. Trajectories of oil droplets and the volume fraction in the flow filed determined based on the DPM and ASM, respectively are also investigated to evaluate the separation performance of the CFFH. Effects of dispersed droplet size, permeability of porous filter, and the Reynolds number on the trajectories of dispersed droplets, grade fouling, and cut size are also examined. NOMENCLATURE A a CD D 𝒟 d F G L p 𝒫 Q R Re S U u VC 2 Area (m2) Acceleration (m/s2) Drag coefficient of droplet Diameter (m) Turbulent Diffusion Droplet diameter (µm) Grade fouling Grade efficiency Length (m) Pressure (Pa) Turbulent production Flow rate (m3/s) Flow ratio Reynolds number Rate of strain (1/s) Velocity (m/s) Fluctuating velocity (m/s) Cell volume (m3) Copyright © 2014 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/conferences/asmep/82001/ on 02/14/2017 Terms of Use: http://www.asme.org/abo Greek symbols µ α κ ν ρ τ χ Π Overflow: “dirty” water Dynamic viscosity (Pa.s) Permeability (m2) Von Karman constant Kinematic viscosity (m2/s) Density (kg/m3) Stress (Pa) Dissipation (m2/s3) Droplet position Pressure strain QF ,PF ,cF Feed: oil in water Subscripts C D F O t U V S P ‘ sgs T Residual component Sub-grid scale Transpose Operators <> Filtered component Ensemble average Vector Second order tensor CROSSFLOW FILTRATION HYDROCYCLONE The CFFH combines the desirable attributes of a cross-flow filter and those of a vortex separator (i.e., hydrocyclone) into one unit to separate dispersed droplets from produced water. It has the potential of removing smaller droplets that a conventional hydrocyclone cannot remove; the filter‟s (or membrane) pore size controls how small a droplet can be removed. The swirling flow has the advantage of keeping the dispersed droplets away from the filter medium by hydrodynamic separation, thus possibly mitigating fouling of the membrane. A CFFH illustration showing inflows and outflows is presented in Fig. 1. The spiral structures inside the CFFH represent the streamlines of the swirling flow. The spiraling streamlines in the outer region (near the wall) form the outer vortex and the spiraling lines at the core form the inner vortex. The outer vortex transports the oil-water mixture downstream while the inner vortex drives the separated oil-rich core to the overflow orifice. Vortex finder Filter Continuous phase Disperse phase Feed Overflow Turbulent Underflow Vortex finder Swirl chamber Porous filter Superscripts QO ,PO ,cO Underflow: “clean” water QU ,PU ,cU Figure 1 Illustration of feed and effluents in a crossflow filtration hydrocyclone. Lines inside the CFFH represent the flow streamlines. The arrow at the feed, underflow and overflow represents the flow direction. The main difference between the CFFH and a conventional de-oiling hydrocyclone is that the CFFH has a radial outlet of the underflow clean water instead of an axial outlet. Due to the presence of the radial outlet of underflow in the CFFH, the hydrodynamic features inside the CFFH greatly differ from those of the conventional hydrocyclone. In the conventional deoiling hydrocyclone, the pressure drop ratio (PDR = (PFPO)/(PF-PU)) is generally greater than one [8], while the CFFH maintains that ratio equal to or less than one. Typically, the underflow ratio (RU = QU/QF) in the de-oiling hydrocyclone is more than 0.90 [8, 9]. In the CFFH, because of the use of a porous filter, the underflow rate depends on the transmembrane pressure as well as the permeability of the porous filter. The underflow rate in the CFFH is generally less than that of the de-oiling hydrocyclone. To achieve the rule of thumb of the underflow ratio (more than 0.90), a staging operation can be utilized. A diagram with the front and top views of the CFFH is provided in Fig. 2. Eight dimensionless geometric groups can describe the relevant features of the CFFH (Table 2). The feed diameter DF is the hydraulic diameter of the rectangular inlet, which is defined as DF = 4AF ⁄P , where AF = a×b. a, b, and P represent the thickness, height and perimeter of the rectangular inlet, respectively. z and r are the axial and the radial coordinates of the CFFH. 3 Copyright © 2014 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/conferences/asmep/82001/ on 02/14/2017 Terms of Use: http://www.asme.org/abo is achieved by solving the continuity and momentum equations for the mixture based on the Eulerian-Eulerian approach. (a) In a first set of continuous phase simulations, the velocity and pressure fields inside the CFFH are calculated by solving the filtered Navier-Stokes equations using the LES approach. A low-pass filter is applied to decompose the velocity into the resolved and residual components. After the decomposition and filtering process, the Navier-Stokes equation can be written as [20] ̅=0 ∇∙U (1) ̅ 1 ∂U 2̅ sgs ̅ ̅ = U ∙ ∇U = − ∇p̅ + ν∇ U − ∇ ∙ τ (b) ρ ∂t ̅ = U − U ′ is the resolved component and U ′ is the where U residual component of velocity. τsgs is the residual stress tensor, which requires an appropriate subgrid scale turbulence model. The τsgs is modeled using the eddy-viscosity approach as ̅ + ∇T U ̅ ) is the rate of strain τsgs = −2νt S̅ where S̅ = 0.5(∇U tensor for the resolved scale. Numerous issues are known to arise with such a model [21, 22]. The turbulent kinematic viscosity is approximated using Wall-Adapting Local EddyViscosity (WALE) subgrid scale model [23] as νt = L2s (S ∗S ) (S̅∗S̅) (2) +(S ∗S ) ̅ [24]. Here 𝜅 is where Ls = min(κ , 0.325Vc1 3 ) and S ≡ ∇U Figure 2 Schematic of the CFFH; a) top view; b) front sectional. The shaded region of thickness δ is the porous filter. Table 2 Dimensionless groups for the CFFH geometry and their magnitude. The swirl chamber diameter is D = 20 mm. Do/D a/D b/D Ls/D Lp/D Lo/D Lv/D δ/D 0.25 0.15 0.5 4 4 1 1 0.25 SIMULATION APPROACH Two different simulation approaches are utilized in this research: Eulerian-Lagrangian and Eulerian-Eulerian. The continuous phase (water) and the dispersed phase (oil droplets) are calculated separately in the Eulerian-Lagrangian approach. The velocity and pressure fields of the continuous phase are obtained using the Eulerian approach based on the LES and the RANS equations. The motion of the dispersed phase is then measured by tracking a large number of dispersed (oil) droplets through the calculated flow field using the Lagrangian approach. The multiphase flow simulation of oil-water mixture the von Karman constant, is the distance to the closest wall, and VC is the volume of the computational cell. The WALE subgrid scale model provides correct wall asymptotic behavior for wall bounded flows and returns a zero turbulent viscosity for laminar shear flows [25]. WALE allows the treatment of laminar zone (porous medium) of the CFFH. In the second set of continuous phase simulations, the RANS equation closed with the RSM is solved. The Reynolds average continuity and momentum equations for a constant density and a constant viscosity can be written as [20] ∇ ∙< U >= 0 (3) ρ ∂<U> + ρ < U >∙ ∇< U >= −∇< p > +μ∇2 < U > −ρ∇ ∙< uu > ∂t The unclosed kinematic Reynolds momentum flux, < uu > is modeled by solving the transport equation given by [20] as ∂<u u> ρ + ρ < U >∙ ∇< u u >= 𝒟 + 𝒫 + Π − ε (4) ∂t where the pressure/rate of strain tensor coupling, Π , is closed using the Liner Pressure-Strain Model (LPSM) proposed by Gibson and Launder [26], Fu et al. [27] and Launder [28]. The details of the diffusion tensor, 𝒟, Production tensor, 𝒫, Strain tensor, Π, and dissipation tensor, ε are not presented here for the sake of brevity and see Pope [20] and Ansys fluent theory guide, 2013 [24] for details. 4 Copyright © 2014 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/conferences/asmep/82001/ on 02/14/2017 Terms of Use: http://www.asme.org/abo Motion of the oil droplets is estimated by tracking their trajectories in the calculated flow field. The trajectories of the oil droplets denoted as χD (t) are predicted from the kinematic equation of droplet motion, shown in Eq. (5), which is written in the Lagrangian frame of reference as ∂χ (t) = UD (t) (5) where subscript „D‟ represents the dispersed phase. At any instant, the position of an oil droplet can be estimated by integrating Eq. (5) over a time period as t+∆t χD (t + ∆t) = χD (t) + ∫t (6) UD (t′)dt′ The dispersed phase velocity in the right hand side of Eq. (6) is calculated by solving the following equation: ∂t ∂U (t) ∂t = ρ U ρ (t) τ + ∑N n=1 a n (t) (7) or UD (t + ∆t) = UD (t) + where τD = 4d C ‖U CD = f(ReD ) , ‖ t+∆t U (t ) * ∫t τ ρ ρ Table 4 Test cases and corresponding operating conditions. + ∑N n=1 a n (t′)+ dt′ , Udrift = UC − UD , and ReD ≡ ρ ‖U BOUNDARY CONDITIONS AND TEST CASES A plug flow profile is specified at the inlet. The inflow velocities for different test cases are given in Table 4. The average gauge pressures at the overflow and underflow outlets are set to zero. The turbulence intensity implemented at the inlet is 5%. For the RANS simulations, the Reynolds stresses at the inlet boundaries are specified by the turbulent intensity, I as < uF uF >: ei ej = (UF I)2 for i = j and < uF uF >: ei ej = 0 for i ≠ j [35]. The solid wall boundary conditions were set as no-slip. The boundary between the fluid field and the porous medium is specified as an interior region. The volume fraction and the droplet size of the dispersed phase at the inlet for the multiphase simulation are 0.05 and 15 microns, respectively. The operating conditions for different test cases are presented in Table 4. Test Cases 1 ‖d μ a n above represents the acceleration of oil droplets due to the effect pressure gradient and of virtual mass force as shown in Table 3. The oil droplets are assumed to be spherical and the drag coefficient, CD, is calculated by applying the spherical drag law proposed by Mosi and Alexander [29]. The approach has been used successfully in a variety of settings [30-32]. Table 3 Additional accelerations included in the analyses of the droplet trajectory are shown below Accelerations Definition Acceleration due to pressure a1 = UD ∙ ∇UC gradient force DUdrift Acceleration due to virtual a2 = mass force Dt Multiphase flow simulations of oil-water mixture are also performed by solving the continuity and momentum equations for the mixture, and the volume fraction equation for the dispersed phase. Governing equations for the mixture are solved using the LES approach with the WALE subgrid scale model. Filtered equations for the mixture and the volume fraction are not presented here for the sake of brevity (see Ansys fluent theory guide, 2013 for detail [24]). The algebraic slip model (ASM) is applied for the calculation of dispersed phase velocity relative to the velocity of continuous phase [33]. The drag coefficient of the oil droplets is calculated using the Schiller and Naumann formula [34]. There is no coalescence or breakup considered for this simulation. ReF RU α (m2) LES UF (m/s) 6 27690 0.41 2×10-13 2 LES 4 18460 0.43 2×10-13 3 LES 2 9230 0.48 2×10-13 4 5 6 LES RANS Multiphase 4 4 4 18460 18460 18460 0.87 0.34 0.46 1×10-12 2×10-13 2×10-13 Approach NUMERICAL METHOD The filtered Navier-Stokes equations are solved using a pressure-based segregated solver available with Fluent 6.0. A converged statistically steady state solution using the standard k-ε model is used as a precondition for the transient calculation based on both the LES with the WALE and the RANS with RSM. The Semi-Infinite Method for Pressure Linked Equation (SIMPLE) algorithm [36] was used to achieve pressure-velocity coupling between the continuity and the momentum equations. A good stability of the numerical computations was achieved by setting the under-relaxation factors for pressure and momentum to 0.3 and 0.5 respectively [25]. The transient simulations are continued until a statistically steady-state solution is obtained. The time dependency of the mass flow rates at the overflow and the underflow outlets are monitored during the simulations for determining the statistically steady state conditions of the simulation results. Simulation times required to achieve the statistically steady-state results for all the cases is approximately 0.5 second. At every time step the residual levels for continuity and momentum are in the order of 10-4. The time step is set to 1x10-5 s, which provides a stable and accurate solution for these flow conditions [25]. Pressure interpolation is performed using the PREssure STaggering Option (PRESTO) scheme [36]. The PRESTO scheme provides improved results for high speed swirling flows and flows in 5 Copyright © 2014 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/conferences/asmep/82001/ on 02/14/2017 Terms of Use: http://www.asme.org/abo strongly curved domain [25, 37]. The momentum equation is discretized using Quadratic Upstream Interpolation for Convective Kinetics (QUICK) scheme [38] since it provides better accuracy and is suitable for hexahedral mesh [25, 37]. The transient calculations are performed using a bounded second order implicit discretization since it provides stable numerical solutions [25]. Bulk flow domain For simulating the motion of oil droplets, Eqs. (6) and (7) are integrated using the 5th order Runge-Kutta scheme derived by Cash and Karp [39]. There are five integration steps used for each grid cell. About 2700 uniformly distributed mono sized droplets with a specific gravity 0.85 mimicking the crude oil are injected from the inlet surfaces. For each group with a uniform droplet size, the total number of droplets escaping from the overflow and the underflow orifice are tracked to estimate grade fouling. In the numerical calculations, the droplets are allowed to reflect from the solid wall and to pass through the porous medium. Any droplet passing through the porous medium is considered as fouling the filter. The accuracy of the solution is controlled by specifying a residual value of 10-6. The maximum number of time steps is set as 1x106, which is sufficient to ensure that there are no droplets with incomplete trajectories in the flow domain. GRID A structured hexahedral O-grid was generated using ANSYS ICEM CFD and is shown in Fig. 3. A finer mesh is generated at the core region because of the higher sensitivity of the internal flow structure due to the core flow patterns. A finer mesh is also generated near the wall region to capture the near-wall flow properties without deteriorating the accuracy of the numerical solution. A fine mesh in the porous medium near the inner wall is created to maintain a small aspect ratio between adjacent cells. About 650,000 cells with an orthogonal quality of 0.45 were generated. This grid size is chosen based on a grid refinement study. The dependency of the numerical results on the grid size is examined by comparing the results for different meshes (400, 500, and 650 thousands). The grid convergence index [40] is calculated for the tangential velocity component. The tangential velocity is observed to be monotonically increasing with grid refinement. The maximum numerical uncertainty in the finest grid (650,000 cells) for the tangential velocity is around 4.2%. Hence, the 650,000 cells mesh was deemed to be sufficiently fine. The same mesh is used for both the LES and RANS approach. The non-dimensional wall distance (y+) of the centroid of the first cell is less than 0.7. Therefore, the grid near the wall is sufficiently fine for the LES and no wall function is used since (y+ < 1) [20]. For the RANS simulation, a Scalable Wall Function [25] is used since it provide good accuracy for y+ < 11 for high Reynolds number and wall bounded flow. Porous domain Figure 3 Structured hexahedral O-grid mesh generated using Ansys ICEM CFD. A finer grid resolution is created near the wall and at the core. Based on the grid refinement study, this mesh appears sufficiently fine and of good quality for the numerical simulations. RESULTS AND DISCUSSION A comparison between simulation results found using the LES with the WALE model and the RANS equation closed with the RSM is shown in Fig. 4. The results obtained from the LES/WALE model (Fig. 4a) show that the swirling motion continues to the bottom of the CFFH. However, the swirling motion dies off quickly in the filter region in the case of the RANS/RSM (Fig. 4b). The wall reflection term in the RSM (the LPSM) redistributes the normal stress near the wall, i.e. it tends to damp the normal stress perpendicular to wall, while enhancing the stress parallel to the wall [20]. The interface between the bulk flow domain and porous medium is specified as an interior region for the numerical simulation based on the RSM and a viscous resistance is imposed in the filter domain to mimic a porous medium. However, the inner surface of a very low permeable porous medium acts as a solid wall which is overlooked in the simulation bases on the RSM. Moreover, the RSM requires wall function for the near wall treatment, but the present simulation method has no capability to impose a wall function at the interface. Therefore, the wall reflection term in the RSM cannot redistribute the normal stress at the interface, which may be the possible cause of the immediate drops of the swirl intensity in the filter region. In the LES with WALE model, no wall function is used because of high resolution of 6 Copyright © 2014 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/conferences/asmep/82001/ on 02/14/2017 Terms of Use: http://www.asme.org/abo grid near the wall and at the interface between bulk flow and porous medium. It appears that as a consequence of this, the LES approach provides improved results near the interface between the bulk flow and filter domain. The results presented in the remaining part of the paper are calculated based on the flow field obtained using the LES approach. Inner vortex Outer vortex recirculation zones near the porous filter eventually block the pores because of the radial outflow. On the other hand, droplets suspended within a recirculation in the solid cylindrical region have higher residence time. Because of the higher residence time and of the lack of radial outflow, the suspended droplets at z/D > 4 eventually migrate to the core and move to the overflow orifice. Fig. 5d shows flow streamlines for a higher magnitude of permeability (α = 1x10-12). A large number of recirculation zones are generated in the core flow, which may breakdown the oil rich core and provide resistance against the movement of oil droplets to the overflow orifice. Velocity 20.00 15.00 Porous filter 10.00 5.00 0.00 [ms^-1] LES with WALE RANS with RSM (a) (b) Figure 4 Three dimensional streamlines calculated using a) the LES with the subgrid WALE model b) the RANS equations with the RSM for ReF = 18460 and α = 2x10-13. The color map represents the velocity magnitude. The swirl intensity drops off rapidly in the filter region in the case of results obtained by solving the RANS equation combined with the RSM. The time-averaged velocity streamlines obtained using the LES approach are shown in Fig. 5 for the test cases of 1 to 4. At a high Reynolds number (ReF = 27690) the inner core is “strong” but unstable. Moreover, a large number of recirculation zones are generated in the filter region (z/D < 4). However, the flow recirculation zones in the outer vortex at z/D > 4 are fewer than that in the filter region. With a decrease in the Reynolds number, the core gets “thicker and weaker” but more stable. The number of recirculation zone decreases in the filter region (z/D < 4) with a reduction in the Reynolds number. The trend is opposite in the solid cylindrical region (z/D > 4). For the low Reynolds number (ReF = 9230) the core appears straight and stable. The recirculation in the flow field suspends oil droplets and provides a resistance against droplets‟ movement towards the core. Droplets suspended in the ReF=27690 ReF=18460 ReF=9230 ReF=18460 α =2x10-13 α =2x10-13 α =2x10-13 α =1x10-12 (a) (b) (c) (d) Figure 5 Plane view of time averaged velocity streamlines on the A-B plane, as shown in Fig. 2a. A higher Reynolds number shows more recirculation in the filter region. The opposite is true in the solid cylindrical region. The core flow regime appears more unstable for a higher Reynolds number. The effect of the Reynolds number on the underflow grade fouling is shown in Fig. 6. The grade fouling (FU) is calculated as FU = (1 − GO )⁄R U where GO = ṁDO ⁄ṁDF [30, 31] is the overflow grade recovery and R U = Q U ⁄Q F is the underflow ratio. Here ṁD is the mass flow rate of dispersed droplets. The grade fouling represents a mass fraction of oil droplets deposits on the filter surface for a given operating condition. Figure 6 indicates that all the droplets having a size less than one micron deposit on the filter. In other word, the vortex motion cannot separate any droplets smaller than one micron. The grade fouling decreases with an increase in the droplet size. According to Stokes‟ law, a larger droplet creates a greater 7 Copyright © 2014 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/conferences/asmep/82001/ on 02/14/2017 Terms of Use: http://www.asme.org/abo FU centrifugal force which in turns increases the migration of oil droplets towards the core. It is interesting that the grade fouling increases with an increase in the Reynolds number. The lowest grade fouling is observed for the ReF = 9230. The grade fouling should increase again for a Reynolds number below a specific value. An insufficient swirling intensity due to a small Reynolds number lessens the migration probability of droplets towards the core. The unstable core (see Fig. 5) for the higher Reynolds number redirects the migrated droplets in the outer flow field. Moreover, the larger number of recirculation zones for a higher Reynolds number trap droplets near the filter surface. These suspended droplets eventually are deposited on the filter surface and foul the membrane. For ReF = 9230, there is no fouling of porous filter found for oil droplets greater than 20 microns. 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Re= 27690 Re = 18460 Re = 9230 0 20 25 30 35 40 dD (μm) Figure 6 Grade fouling versus droplet size plot for the different Reynolds number. The fraction of oil droplets deposited on the porous wall increases with the Reynolds number. FU correspond to permeability values of 2x10 -13 m2 and 1x10-12 m2 respectively. The grade fouling increases with an increase in the permeability of porous filter. For a higher magnitude of the permeability, a larger number of recirculation zones found in both the inner core and outer vortex (see Fig. 5d) destroy the oil rich core as well as move oil droplets in random directions. As a consequence, grade fouling increases with an increase in the underflow rate. 5 10 15 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Ru = 0.43 Ru = 0.87 0 10 20 30 40 50 60 dD (μm) Figure 7 Grade fouling versus droplet size plot for different underflow ratio. RU = 0.43 and 0.87 correspond to permeability values of 2x10-13 m2 and 1x10-12 m2 respectively. Higher radial outlet through the porous filter increases the grade fouling. Effect of the underflow ratio on the grade fouling is presented in Fig. 7. The underflow ratios of 0.43 and 0.87 Figure 8 Contours of volume fraction of the dispersed phase for ReF = 18460 and dD = 15 μm. The feed volume fraction of dispersed phase is 0.05. An oil-rich core is developed in the filter region (z/D < 4). The calculated grade fouling is 0.5. Contours of the volume fraction of the oil phase in the flow field for ReF = 18460 are shown in Fig. 8. The inlet volume fraction of the dispersed phase is 5% of the total mixture at the feed. The results obtained using the multiphase flow simulations support the single phase flow pattern as shown in Fig. 5b. An oil-rich core is generated in the filter region. In the lower half of the solid cylindrical section, there is no considerable oil-rich core developed. In the filter region, the inner vortex core is stronger and more stable than that in the upstream region (Fig. 5b). Oil droplets can easily move and stay in a stable core. Flow structures in the core in both the filter and upstream regions, obtained from single phase simulations, correlated with the patterns of volume fraction distributions calculated using multiphase flow simulations. In the solid cylindrical section, the recirculation and the unstable core (Fig. 5b) create a mixing effect in the flow field. As a consequence, oil droplets randomly distribute over the domain and no considerable oil-rich core is observed in the solid cylindrical section. The normalized volume fraction of the dispersed phase at the middle of the filter region (z/D = 2) is shown in Fig. 9. At the oil rich core (2r/D = 0) the volume fraction of the dispersed phase is less than the feed volume fraction. It indicates that a fraction of the dispersed phase volume separates in the solid cylindrical section. However the normalized volume fraction decreases in the outer periphery of the inner vortex (2r/D ≈ 0.4). It again increases near the filter surface (2r/D ≈ 0.9). It appears that the recirculation near the filter surface (Fig. 5b) suspends oil droplets which yield a higher volume fraction near the filter surface. 8 Copyright © 2014 by ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/conferences/asmep/82001/ on 02/14/2017 Terms of Use: http://www.asme.org/abo resistance against the movement of oil droplets towards the core and enable the stable oil-rich core to move easily to the overflow orifice. 1 ϕ/ϕF 0.9 0.8 0.7 0.6 0.5 0 0.2 0.4 0.6 0.8 1 2r/D Figure 9 Normalized volume fraction of dispersed phase at z/D = 2. ϕF = 0.05 is the feed volume fraction. The concentration of dispersed droplets is higher at the core and near the filter wall. CONCLUSIONS Based on the results presented above the following observations can be made i) Flow disturbances and recirculation increase with an increase in the feed Reynolds number. ii) The core flow becomes unstable at high values of the feed Reynolds number, which destroys an oil-rich core and redirects oil droplets in the outer flow field. iii) Recirculation and an unstable core generate a mixing effect in the flow field which reduces the separation performance of the CFFH iv) Grade fouling decreases with an increase in the size of oil droplet. v) Grade fouling also decreases with a reduction of the feed Reynolds number up to a certain value. vi) A higher permeability as well as a higher underflow ratio increases the grade fouling. vii) The LES with the WALE subgrid scale model appears to provide improved simulations of swirling turbulent flow in the CFFH when compared to the RANS equation closed off with the RSM. viii) For the operating conditions simulated, the CFFH appears to be very efficient device. However, high pressure is required due to the low permeability of the filter. ACKNOWLEDGMENTS Support for this research from the U.S Environmental Protection Agency (award no. RC-83518301), the U.S. National Science Foundation (award no. IIA-1243433), and MSU Foundation (Strategic Partnership Grant no. 71-1624) is gratefully acknowledged. ReF=27690 ReF=18460 ReF=9230 (a) (b) (c) Figure 10 Trajectories of oil droplets for dD=15 µm for different Reynolds numbers. Five droplets are injected from an inlet surface. The color code is used to identify individual droplets. No droplets foul the filter for ReF = 9230 for dD = 15 µm which corresponds to result shown in Fig. 6. Trajectories of oil droplets for different operating conditions are shown in Fig. 10. A total of five uni-sized oil droplets (dD = 15 μm) having a specific gravity of 0.85 are released from an inlet surface. Different colors in the trajectories indicate distinct oil droplets. Figure 10 shows oil droplets rotating in the outer vortex for ReF = 27690. The migration probability of oil droplets toward the core increases with a decrease in the Reynolds number. The unstable core and a larger number of recirculation zones for higher Reynolds number reduce the migration of oil droplets toward the core. Fewer disturbances in the flow field for a lower Reynolds number provide less REFERENCES [1] Clark, C.E., Veil, J.A., 2009, “Produced Water Volumes and Management Practices in the United States,” ANL/EVS/R09/1, prepared by the Environmental Science Division, Argonne National Laboratory for the U.S. Department of Energy, Office of Fossil Energy, National Energy Technology Laboratory. [2] Environmental Protection Agency (EPA), 2012, “National pollutant discharge elimination system: industrial and commercial facilities,” Washington, DC. [3] Environmental Protection Agency (EPA), 2012, “Underground Injection Control Program: Regulations,” Washington, DC. 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