Numerical investigation of the velocity field and separation efficiency of deoiling hydrocyclones

Petroleum Science, Nov 2012

Three-dimensional simulation of a multiphase flow is performed using the Eulerian-Eulerian finite volume method in order to evaluate the separation efficiency and velocity field of deoiling hydrocyclones. The solution is developed using a mass conservation-based algorithm (MCBA) with collocated grid arrangement. The mixture approach of the Reynolds stress model is also employed in order to capture features of turbulent multiphase swirling flow. The velocity field and separation efficiency of two different configurations of deoiling hydrocyclones are compared with available experimental data. The comparison shows that the separation efficiency can be predicted with high accuracy using computational fluid dynamics. The velocity fields are also in good agreement with available experimental velocity measurements. Special attention is drawn to swirl intensity in deoiling hydrocyclones and it is shown that the differences in velocity and volume fraction fields of different configurations are related to swirl distribution.

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Numerical investigation of the velocity field and separation efficiency of deoiling hydrocyclones

International Journalof Multiphase Flow. 0 Center of Excellence in Energy Conversion, School of Mechanical Engineering, Sharif University of Technology , Tehran , Iran Three-dimensional simulation of a multiphase flow is performed using the Eulerianhydrocyclones. The solution is developed using a mass conservation-based algorithm (MCBA) with collocated grid arrangement. The mixture approach of the Reynolds stress model is also employed in of two different configurations of deoiling hydrocyclones are compared with available experimental data. The comparison shows that the separation efficiency can be predicted with high accuracy using velocity measurements. Special attention is drawn to swirl intensity in deoiling hydrocyclones and it is Deoiling hydrocyclone; numerical simulation; Eulerian-Eulerian approach; swirl intensity - to solid particles. Large droplets break down into smaller ones whenever the shear rate increases to a critical level. The than larger ones. On the other hand, if two droplets were close enough, they might coalesce. and deoiling hydrocyclones, the flow features of the continuous phase is not the same. the wall region in desander hydrocyclones while making oil droplets move to the center in the deoiling type. So the nearwall region is of high importance in desander hydrocyclones The use of common hydrocyclones for oil-water separation was first suggested by Simkin and Olney (1956) and Sheng et al (1974), but fundamental studies of deoiling hydrocyclones was started from 1980 by Colman and Thew. Several researchers (Colman et al, 1980; Colman, 1981; Colman and Thew, 1980; 1983; 1988) performed experiments to study deoiling hydrocyclones. Experimental results showed Moreover, the size distribution in the outlet is independent of The migration probability curves are also independent of the flow split. The problems of using hydrocyclones for water treatment were investigated by Thew (1986) and a new design and minimum instability and turbulence near the axis. MADDAHIAN Reza , ASADI Mohammad and FARHANIEH Bijan 1 Introduction Having an efficient and reliable system for oil-water separation especially in the offshore oil and gas industry is of crucial importance. Due to platform movement and space, weight and operating limitations in offshore industries, using common methods (e.g. gravity based vessels), for oilwater separation is ineffective. On the other hand, producing oil on offshore platforms is often accompanied by large discharge of oil-contaminated water into the sea, resulting in environmental pollution. Therefore, there is a need for high efficiency compact separators capable of operation in various operating conditions. One solution to the mentioned problem is the use of hydrocyclone separators. The advantages of hydrocyclones, compared to other methods, are those of simple design, easy installation and operation, lack of moving parts, low manufacturing and maintenance costs. The hydrocyclones are therefore an economical and effective way for produced water treatment (Van den Broek et al, 1991; Van den Broek and Plat, 1998) The main differences between the separation mechanisms of deoiling hydrocyclones and that of desanders are described below (Thew, 1986; Caldentey, 2000): encountered in deoiling hydrocyclones is smaller than solid The operational curves, principle of operations and the conducted by various researchers (Van den Broek and Plat, 1991; Van den Broek et al, 1998; Choi, 1990; Noort et al, 1990; Falnigan et al, 1989; Jones, 1993; Ditria and Hoyack, 1994) . The first attempt on optimizing hydrocyclones was conducted by Young et al (1994). They measured the flow behavior in a 35-mm hydrocyclone, designed by Colman and Thew (1980), and then compared the results with a newly modified design. They studied the effects of operational variables and geometrical parameters, such as inlet size, on their experimental results, a new geometry was proposed for hydrocyclones. Recent investigations on hydrocyclones focus on operational parameters (Belaidi and Thew, 2003; Husveg et oil droplets (Zhou et al, 2010) in deoiling hydrocyclones. Due to the difficulty of numerical simulations of focused on experimental investigations with only few studies concentrating on numerical simulations of deoiling hydrocyclones. Hargreaves and Silvester (1990) simulated the oil-water approach. They used the algebraic stress model to simulate the flow in a 2D cylindrical coordinate system. In the dispersed phase, they ignored the effect of particle-particle interaction, slip and droplet coalescence. The obtained results were in acceptable agreement with experimental data. The flow field, velocity distribution and separation efficiency of a 10-mm deoiling hydrocyclone was obtained by Grady et al (2003) using the algebraic slip mixture (ASM) multiphase model. In order to simulate the high swirling flow (swirl number 8.4) the Reynolds stress model (RSM) was used. Simulation of miniature hydrocyclones for downhole separation was conducted by Petty and Park (2004). Direct numerical simulation showed that the 3g centrifugal acceleration was created in a 5-mm miniature hydrocyclones respectively. Huang (2005) simulated the three dimensional Eulerian approach and the Reynolds stress model. Results showed accumulation of oil near the axis. The separation The separation curve for Colman type hydrocyclones was in good agreement with measured ones. It must be mentioned that no velocity distribution was reported by Huang. Noroozi and Hashemabadi (2009; 2011) investigated the effect of various inlet types and inlet chamber body profiles on the separation efficiency of deoiling hydrocyclones. The separation efficiency was improved 10% and 8% with the Kharoua et al (2010) conducted a complete review of hydrocyclones used for deoiling purposes. The literature review showed that nearly all conducted numerical studies done on deoiling hydrocyclones have mainly focused on separation efficiency of deoiling In other words, the more precise the determination of the The aim of this research is to introduce an appropriate multiphase model and demonstrate the capability of computational fluid dynamics in predicting separation efficiency, oil droplet distribution and the velocity field of multiphase flow using the general Eulerian-Eulerian multiphase model. The results also show the importance of swirl intensity in designing hydrocyclones. It should be mentioned that previous numerical investigations (Grady et al, 2003; Noroozi and Hashemabadi, 2009; 2011) considered the simple algebraic slip mixture model which could not correctly show the distribution of oil droplets in hydrocyclones. Optimization of hydrocyclones is not taken into consideration in this research and will be taken into account in future work. 2 Mathematical model and droplets. The modeling of instantaneous governing computationally intensive except for the case of ideal flow at low Reynolds numbers. Therefore, the local instantaneous derived based on ensemble-averaging of Navier-Stokes Details of the averaging procedure and assumptions can be found in (Drew, 1983; Enwald et al, 1996). 2.1 Governing equations (Enwald et al, 1996): U U 0 U U I F (1) (2) where (k) stands for the volume fraction of phase (k); (k) is the density of phase (k), kg/m3; U(k) denotes the averaged velocity of phase (k), m/s; , p and B(k) are the stress tensor (N/m2), pressure shared by all phases (kg/(m·s2)) and the body forces per unit volume of phase (k) (kg/(m2·s2)), respectively; F(k) the term includes all other forces such as lift and virtual mass, (kg/(m2·s2)). I is Fthe momentum transfer to phase (k) due to phase interaction and can be written as: I where 3·s); I is the momentum transfer to the phase (k), kg/(m2·s2); U(m) is the averaged velocity of phase (m), m/s; (m) stands for the volume fraction of phase (m). the averaging process and modeled using the eddy-diffusivity concept. The momentum exchange coefficient is defined as follows: where Vr is the relative slip velocity, m/s; d is the droplet diameter, m and CD is the drag coefficient. CD and function f( ) are obtained from Saboni and Alexandrova (2002) and Zuber (1964), respectively. with Molecular Turbulent The term ( ), the Reynolds stress tensor of the mixture, is modeled using an appropriate turbulence model. The phase while the Reynolds stress tensor is calculated for the mixture. 2.2 Turbulence model an appropriate turbulence model with high resolution scheme having acceptable and accurate results. Previous numerical the hydrocyclones (Grady et al, 2003; Huang, 2005). So the mixture approach of RSM Launder-Reece-Rodi (RSM-LRR) (Launder et al, 1975) model is adopted in this work. of the mixture is as follows (Wilcox, 1994): where P P Using Kolmogorov’s hypothesis of local isotropy, be modeled as (Wilcox, 1994): (10) 3/2 (11) (12) (13) (14) (16) C U U U 2 2 U Auxiliary relations (Wilcox, 1994): The pressure strain term, often referred as pressure-strain redistribution term ( ), is decomposed into the rapid and slow pressure strain terms and modeled according to (Wilcox, 1994): 1 ˆ D 3 Numerical method 3.1 Geometry of the problem and mesh generation Two different geometries used for numerical modeling of deoiling hydrocyclones are shown in Fig. 1. The numerical results of the separation efficiency and velocity distribution are obtained and compared to available experimental measurements. The geometrical parameters of these Three non-uniform structured grids are used to show the grid independency of the results. Nodal distributions in both (17) geometries for coarse, medium and fine grids are shown in Table 2. As shown in Fig. 2, the maximum differences in the tangential velocity in the radial direction, located at z/D=2.0 (z is the axial distance from the top wall, mm), - between the coarse and medium grids of case 1 and case 2 are 5% and 7%, respectively are 1% and 1%, respectively. Therefore, the medium grid is selected for numerical simulation in order to reduce the computational costs. The generated mesh for simulating the flow inside deoiling hydrocyclones is shown in Fig. 3. It can be seen that the mesh the wall and the core of hydrocyclone. 3.2 Boundary conditions There are three types of boundaries (inlet, outlet and wall) considered as follows: Inlet All of the variables are known in this region. Uniform velocity and volume fraction with turbulence intensity of 5% are employed. Wall No slip condition (U 0) is assumed on the walls. standard wall function. Outlet The gauge static pressure, determined based on the desired each outlet, i.e. the overflow and underflow. Velocities are (Ferziger and Peric, 2002). Operational parameters for both designs are shown in Table 3. 3.3 Solution methodology For numerical investigation of the flow field inside 12 10 /s 8 m , y it c o lve 6 l a it n e gn 4 a T 2 5.0 10.0 - Solve continuity of each phase to obtain the volume fractions. The above steps are repeated until convergence. For velocity calculations on the faces of the control volumes, the Rhie-Chow (Rhie and Chow, 1983) interpolation method is used and the modification of SIMPLEC for multifluid systems (Darwish et al, 2001) handles the linkage between the velocities and pressure. The partial elimination algorithm (PEA) (Darwish et al, 2001) is used to reduce the linkage between phases and accelerate the convergence. The global continuity phases, is normalized using ( k ) as a weighting factor in order to reduce the continuity error. The convergence rate is accelerated by solving two implicit volume fractions and then oil kg/m3 850 μwater kg/(m·s) μoil kg/(m·s) Rei is the Reynolds number at the inlet; R is the split ratio (Qo/Qi); is the viscosity. enforcing the geometric conservation constraints ( k 1) (Darwish et al, 2001). The Carver procedure (Carver, 1982) is also employed for bounding the volume fractions between 0 and 1. In order to calculate the convection and diffusion terms, high resolution SMART within the context of NVSF methodology (Darwish and Moukalled, 1994) and second order central difference scheme are used respectively. All of the simulations are performed in unsteady mode using implicit three time level (TTL) method (Ferziger and Peric, 2002). The time steps were changed from 10-3 to 5×10-5 The simulations are started with single phase k- model and after preliminary convergence, switched to the RSMintegration time needed to obtain a steady state result is about 1.2 seconds. The convergence is assessed by comparing the normalized sum of absolute residuals over all control volumes with some reference value. The residual in a convergence state is in the order of 10-4 for continuity and 10-5 The under relaxation factors are assumed as 0.2-0.4 for implemented at the start of simulations. 4 Results and discussion 4.1 Velocity distribution Fig. 4(a) depicts a comparison between simulated single phase tangential velocity for case 2 at different axial positions inside the hydrocyclone and velocities measured by Bai et al (2009). The numerical and experimental results are in good agreement. Small deviations can be seen for the location of maximum tangential velocity. Maximum tangential velocity occurs near the axis of hydrocyclone and decreases towards the wall. Tangential velocity distributions for case 1 (Colman's design) are also shown in Fig. 5(a). Tangential velocity has a shape of Rankine vortex, i.e. forced vortex near the axis of rotation and free vortex in outer region. This is also reported by other researchers (Hargreaves and Silvester, 1990; Bai et al, 2009). The width of free and forced regions is different between the two designs and is highly dependent on swirl intensity distribution along the hydrocyclone axis. Fig. 4(b) shows the radial variation of axial velocity of the single phase in case 2 at different axial positions for a split ratio of 5%. The experimental measurements and simulated results are in good agreement with each other. The axial vortex moves downward to the underflow of hydrocyclone The recirculation zones in case 1 are stronger than that in case 2. The maximum axial distance that has negative upward velocity occurs at the location of 1,000 mm and 210 mm in case 1 and 2, respectively. The negative upward velocity affects the distribution of oil in case 1 compared with case 2. z,mm160 0 20 40 60 80 100 120 140 180 200 220 240 260 280 300 320 0 5 r, mm 10 15 20 0 5 10 15 20 (b) Axial velocity Fig. 4 Comparison of velocity distribution between experimental data ( ) (Bai et al, 2009) and results of numerical simulations (-) for case 2 Separation efficiency of the standard Colman's design (case 1) is compared with available experiments (Young et al, 1994) in Fig. 6. It can be seen that numerical simulations can prediction of separation efficiency has occurred because of two reasons: 1) In numerical simulation, only the median diameter of droplets is used for calculating the inter-phase forces. diameter. However, droplets with various diameters, either larger or smaller than median, are found in experimental the hydrocyclones is over predicted in numerical simulations. 2) The wall shear stress and pressure drop in numerical simulations are smaller than the real operating condition and distance. So the location of negative axial velocity occurs in a longer axial distance in numerical simulations compared to r, mm 20 r, mm 20 0 10 30 40 0 10 30 40 0 50 100 150 200 250 350 400 450 500 550 600 mm300 z, 100 80 % , y c ine 60 c iff e w lfro 40 e d n U 20 experimental data. Therefore, more droplets are captured by 4.3 Oil distribution Distribution of oil inside hydrocyclones for both cases is shown in Fig. 7. As a result of the pressure difference in the droplets accumulate near the axis of the hydrocyclone. The radial distribution of oil volume fraction in three different axial distances from the top wall of hydrocyclones is shown in Fig. 8. As shown before (i.e. Figs. 4 and 5), the maximum tangential velocity in case 2 occurs closer to the axis, compared to case 1. The high value of tangential velocity in case 2 creates a region of oil volume fraction close to 1.0 near the axis and suddenly dipped to value of 0.05 in the immediate vicinity of the axis. The peak in distribution of oil volume fraction in case 1 is not as sharp as that in case 2. Variation of the axial velocity affects the distribution of oil inside the hydrocyclone. The negative upward velocity in case 1 creates a concentration valley near the axis. The oil concentration decreases gradually along the hydrocyclone axis for case 1, while in case 2, the peak in the oil volume fraction can be seen even in the axial distance of z/D=8.0 and it seems that the Young’s design (case 2) can It should be mentioned that previous researchers could achieve neither an accurate oil distribution inside deoiling hydrocyclones nor the separation efficiency, due to using weak multiphase models (ASM model). 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Oil volume fraction (a) Case 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Oil volume fraction (b) Case 2 Fig. 7 Distribution of oil droplets inside deoiling hydrocyclones 4.4 Swirl decay rate As discussed previously, the radial pressure gradient generated by swirling flow makes the lighter phase migrate toward the center. The migration velocity, also called slip velocity, is a function of density difference between dispersed 0 -1.00 -0.75 -0.50 -0.25 and continuous phase, radial pressure gradient, relaxation 1995). If the migration velocity is great enough so that the oil droplets arrive at locus of zero axial velocity before the bulk flow leaves the hydrocyclone, oil droplets can be separated (Wolbert et al, 1995). time by increasing the length to diameter ratio of deoiling hydrocyclones. On the other hand, the effects of wall shear stress and stream-wise friction reduce the spinning motion of flow. Therefore, in order to have a reasonable value of tangential velocity, the cross sectional area should be reduced along the axis. An increase in the tangential velocity is proportional to the inverse of radius, due to conservation of angular momentum, while the axial velocity is proportional of mass. Therefore, the area reduction decreases residence time of the flow and separation efficiency. These effects could be investigated using swirl number, defined as the ratio of axial flux of angular momentum to the axial flux of linear momentum. Many researchers tried to relate the velocity distribution and separation efficiency of deoiling hydrocyclones to the swirl number (Caldentey, 2000; Gomez, 2001). The swirl number variation along the hydrocyclone axis for both cases is shown in Fig. 9. The change in the cone angle of hydrocyclones results in the slope variation of the swirl decay rate. As a result of higher inlet flow rate, the inlet swirl number of case 1, i.e. Colman’s design, is greater than that of case 2. The swirl number in case 1, swiftly declines in the first conical section and continues to decrease gradually in the second conical and straight following sections. The swirl decay rate in the Young’s design, case 2, is not as steep as motion in the half of the hydrocyclone length. 5 4 1 0 0 y its 3 n e t n liiw 2 r S Fig. 9 Case 1 (Colman's design) Case 2 (Young's design) 0.2 0.4 0.6 0.8 1.0 z/Lh of deoiling hydrocyclones As a result of dissimilar swirl distribution between cases 1 and 2, the difference can be seen not only in velocities, both axial and tangential, but also in oil distribution inside deoiling hydrocyclones. Therefore, it seems that the design of the swirl chamber should be according to the amount of the swirl rate needed for proper separation. Designing a swirl chamber with appropriate swirl distribution is imperative in achieving 5 Conclusions Ve l o c i t y a n d o i l d i s t r i b u t i o n s i n s i d e d e o i l i n g hydrocyclones are obtained using a general code based on the Eulerian-Eulerian multiphase model. The turbulent stresses are approximated using the mixture approach of Reynolds stress model. The results of velocity distribution are validated using experimental data and showed that the RSM model is an appropriate choice for modeling multiphase flow inside deoiling hydrocyclones. A slight over prediction is also seen in the results of separation efficiency due to the fact that the median diameter of oil droplets is considered for the The distributions of oil droplets in various axial distances from the top wall of the hydrocyclone for two different designs are compared and it is shown that the swirl intensity distribution inside the hydrocyclone can affect the velocity distribution is introduced, which will be addressed in the development of present work. Acknowledgements The authors would like to thank Professor Marwan Darwish, American University of Beirut/Mechanical Engineering Department, for his guidance and help in developing the multiphase part of this research. References hydrocyclone. Miner. Eng. 2009. 22(4): 319-323 Belaidi A and Thew M T. The effect of oil and gas content on the controllability and separation in a de-oiling hydrocyclone. Chem. Eng. Res. Des. 2003. 81(3): 305-314 MS Thesis. The University of Tulsa. 2000 Carver M B. A method of limiting intermediate values of volume hydrocyclone based technology for water and crude processing. Paper Mech. 1983 . 15: 261-91 Experiment and modeling. MS Thesis. The University of Tulsa. 2001 Grady S A, Wesson G D, Abdullah M, et al. Prediction of 10-mm hydrocyclone separation efficiency using computational fluid dynamics. Filtr. Sep. 2003. 40(9): 41-46 to the analysis of deoiling hydrocyclone performance. Chem. Eng. Res. Des. 1990. 68(4): 365-383 Huang S. Numerical simulation of oil-water numerical simulation of oil-water hydrocyclone using Reynolds-stress model for Eulerian Husveg T, Rambeau O, Drengstig T, et al. Performance of a deoiling 368-379 24 : 221 -224 Choi M S. Hydrocyclone produced water treatment for offshore developments . Paper SPE 20662 presented at 65th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers , 1990 , New Orleans Colman D. The Hydrocyclone for Separating Light Dispersions . Ph.D. Thesis . Southampton University, UK. 1981 Colman D and Thew M. Hydrocyclone to give a highly concentrated sample of a lighter dispersed phase . Presented at International Conference on Hydrocyclones, 1980 , BHRA, Cambridge, United Kingdom 15 : 209 - 223 Colman D and Thew M. Correlation of separation results from light dispersion hydrocyclones . Chem. Eng. Res. Des . 1983 . 61 : 233 - 240 Colman D and Thew M. Cyclone Separator . U.S. Patent: 4764287 . 1988 Colman D , Thew M and Corney D . Hydrocyclones for oil/water separation . Presented at International Conference on Hydrocyclones, 1980 , BHRA, Cambridge, United Kingdom, 11 : 143 -165 Darwish M and Moukalled F . Normalized variable and space formulation methodology for high-resolution schemes . Numer. Heat Transfer B. Numer. Heat Transfer Part B. 2001 . 40 ( 2 ): 99 - 137 Davidson L and Farhanieh B. Manual of CALC-BFC . Chalmers University of Technology, Gothenburg, Sweden. 1991 Eyrolles Jones P S. A field comparison of static and dynamic hydrocyclones . Paper SPE 20701 presented at SPE Annual Technical Conference and Exhibition , 1993 , New Orleans Kharoua N, Khezzar L and Nemouchi Z. Hydrocyclones for de-oiling applications-A review . Pet. Sci. Tech . 2010 . 28 ( 7 ): 738 -755 Launder B E , Reece G J and Rodi W. Progress in the development of a Reynolds-stress turbulence closure . J. Fluid Mech . 1975 . 68 : 537 - 566 Lien F S and Leschziner M A . Assessment of turbulence-transport models including non-linear RNG eddy-viscosity formulation and second-moment closure for flow over a backward-facing step . Comput. Fluids. 1994 . 23 ( 8 ): 983 - 1004 Meldrum N. Hydrocyclones: A solution to produced-water treatment . Paper SPE 16642 presented at 19th Annual Conference on Offshore Technology , 1988 , Houston Heat Transfer Part B. 2004 . 45 ( 6 ): 495 - 522 Noort F J , Etten J P and Donders R S. Reduction of residual oil content in produced water at offshore gas production platform P/6A . Paper SPE 20882 presented at Europe's 90 Conference , 1990 , Netherlands Noroozi S and Hashemabadi S H. CFD simulation of inlet design effect 2009 . 32 ( 12 ): 1885 -1893 Noroozi S and Hashemabadi S H. CFD analysis of inlet chamber body Des . 2011 . 8 ( 7 ): 968 -977 Pett y C A a n d P a r k s S M . F l o w s t r u c t u r e s w i t h i n m i n i a t u r e hydrocyclones . Miner. Eng . 2004 . 17 ( 5 ): 615 - 624 an airfoil with trailing edge separation . AIAA J . 1983 . 21 ( 11 ): 1527 - 1532 Saboni A and Alexandrova S . Numerical study of the drag on a fluid sphere . AIChE J . 2002 . 48 ( 12 ): 2992 - 2994 a conventional hydrocyclone. Can. J. Chem. Eng . 1974 . 52 ( 4 ): 487 - 491 Simkin D J and Olney R B. Phase separation and mass transfer in a Chem . Engineer . 1986 . July/August: 17 -23 Van den Broek W M G T and Plat R. Characteristics and possibilities of presented at First International Conference on Health, Safety and Environmental. 1991. Netherlands Van den Broek W M G T , Plat R and Van der Zande M J. Comparison of plate separator, centrifuge and hydrocyclone . Paper SPE 48870 presented at SPE International Conference and Exhibition , 1998 , Beijing Wilcox C D. Turbulence Modeling for CFD . 1994 . DCW Industries Inc . 1395-1402 Young G A B , Wakley W D , Taggart D L , et al. Oil-water separation using hydrocyclones: An experimental search for optimum dimensions . J. Pet. Sci. Eng . 1994 . 11 ( 1 ): 37 -50 Zhou N , Gao Y , An W , et al. Investigation of velocity field and oil distribution in an oil-water hydrocyclone using a particle dynamics analyzer . Chem . Eng. J. 2009 . 157 ( 1 ): 73 - 79 Eng. Sci. 1964 . 19 ( 11 ): 897 - 917

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Reza Maddahian, Mohammad Asadi, Bijan Farhanieh. Numerical investigation of the velocity field and separation efficiency of deoiling hydrocyclones, Petroleum Science, 2012, 511-520, DOI: 10.1007/s12182-012-0236-3