Coupling of CFD and semiempirical methods for designing threephase condensate separator: case study and experimental validation
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Abstract
This study presents an approach to determine the dimensions of threephase separators. First, we designed different vessel configurations based on the fluid properties of an Iranian gas condensate field. We then used a comprehensive computational fluid dynamic (CFD) method for analyzing the threephase separation phenomena. For simulation purposes, the combined volume of fluid–discrete particle method (DPM) approach was used. The discrete random walk (DRW) model was used to include the effect of arbitrary particle movement due to variations caused by turbulence. In addition, the comparison of experimental and simulated results was generated using different turbulence models, i.e., standard k–ε, standard k–ω, and Reynolds stress model. The results of numerical calculations in terms of fluid profiles, separation performance and DPM particle behavior were used to choose the optimum vessel configuration. No difference between the dimensions of the optimum vessel and the existing separator was found. Also, simulation data were compared with experimental data pertaining to a similar existing separator. A reasonable agreement between the results of numerical calculation and experimental data was observed. These results showed that the used CFD model is well capable of investigating the performance of a threephase separator.
Keywords
Threephase separator CFD Semiempirical design method Multiphase flow model Discrete random walk methodList of symbols
 \( C_{\text{D}} \)
Drag coefficient
 \( C_{\text{F}} \)
Inertial resistance coefficient, \( L^{  1} \) (\( {\text{m}}^{  1} \))
 \( C_{1 } , C_{2} ,C_{M} \)
Constants in turbulent transport equations
 \( d_{\text{p}} \)
Liquid droplet diameter, \( L \) (μm)
 \( \overline{d} \)
Rosin–Rammler diameter, \( L \) (μm)
 \( D \)
Separator diameter, L (m)
 \( F_{\text{D}} \)
Drag function
 \( F_{\text{s}} \)
Momentum transfer term exerted by discrete particles, \( {\raise0.7ex\hbox{${ m}$} \!\mathord{\left/ {\vphantom {{ m} {t^{2} L^{2} }}}\right.\kern0pt} \!\lower0.7ex\hbox{${t^{2} L^{2} }$}} \) (N/m^{3)}
 \( G \)
Unit variance normally a distributed random number
 \( g \)
Gravity acceleration, \( {\raise0.7ex\hbox{$L$} \!\mathord{\left/ {\vphantom {L {t^{2} }}}\right.\kern0pt} \!\lower0.7ex\hbox{${t^{2} }$}} \) (m/s^{2})
 \( L_{\text{e}} \)
Eddy length scale, \( L \) (m)
 \( L_{\text{eff}} \)
Effective length of the vessel, L (m)
 \( L_{\text{ss}} \)
Seam to seam length of the vessel, L (m)
 \( \left( {\frac{{L_{\text{ss}} }}{D}} \right) \)
Slenderness ratio
 \( P \)
Vessel operation pressure, m/Lt^{2} (\( {\text{kPa}} \))
 \( Q_{\text{o}} \)
Oil flow rate, L^{3}/t (m^{3}/s)
 \( Q_{\text{g}} \)
Gas flow rate, L^{3}/t (scm/h)
 \( Q_{\text{w}} \)
Water flow rate, L^{3}/t (m^{3}/s)
 \( S_{\text{m}} \)
Mass source term, \( {\raise0.7ex\hbox{$m$} \!\mathord{\left/ {\vphantom {m {t \cdot L^{3} }}}\right.\kern0pt} \!\lower0.7ex\hbox{${t \cdot L^{3} }$}} \) (kg/s m^{3})
 \( r \)
Particle relaxation time,\( t \) (s)
 \( t_{\text{cross}} \)
Eddy crossing time of the particles, \( t \) (s)
 \( t_{\text{ro}} \)
Theoretical residence time of oil, \( t \) (min)
 \( t_{\text{rw}} \)
Theoretical residence time of water, \( t \) (min)
 \( T \)
Operating temperature, \( \theta \) (K)
 \( t_{\text{e}} \)
Eddy lifetime, \( t \) (s)
 \( t_{\text{L}} \)
Particle Lagrangian integral time, \( t \) (s)
 \( \vec{U} \)
Average fluidphase velocity, L/t (m/s)
 \( u \)
Fluidphase velocity, L/t (m/s)
 \( u_{\text{p}} \)
Particle velocity, L/t (m/s)
 \( u^{\prime} \)
Velocity fluctuation of the continuous phase, L/t (m/s)
 \( \vec{U}_{\text{m}} \)
Velocity of phase m, L/t (m/s)
 \( \left {\vec{U}} \right \)
Velocity magnitude, L/t (m/s)
 \( Z \)
Gas compressibility factor
Greek symbols
 \( \alpha_{\text{l}} \)
Ratio of liquid area to total area of the separator
 \( \alpha_{\text{m}} \)
Volume fraction of phase m
 \( {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 \alpha }}\right.\kern0pt} \!\lower0.7ex\hbox{$\alpha $}} \)
Viscous resistance coefficient, \( L^{  2} \) (\( {\text{m}}^{  2} \))
 \( \beta \)
Production term of turbulence kinetic energy due to velocity gradients, m/L⋅(kg/m s^{3})
 \( \beta_{\text{l}} \)
Ratio of liquid height to total height of the separator
 \( \varepsilon \)
Turbulent dissipation rate, L^{2}/t^{3} (m^{2}/s^{3})
 \( k \)
Turbulent kinetic energy, L^{2}/t^{2} (m^{2}/s^{2})
 \( \mu \)
Molecular viscosity, m/Lt (Pa s)
 \( \mu_{\text{t}} \)
Turbulent viscosity, m/Lt (Pa s)
 \( \rho \)
Density, m/L^{3} (kg/m^{3})
 \( \rho_{\text{g}} \)
Gas density, m/L^{3} (kg/m^{3})
 \( \rho_{\text{l}} \)
Liquid density, m/L^{3} (kg/m^{3})
 \( \rho_{m} \)
Density of phase m, m/L^{3} (kg/m^{3})
 \( \sigma_{k} ,\sigma_{\varepsilon } \)
Constants in turbulent transport equations
 \( \varpi \)
Rosin–Rammler exponent
Abbreviations
 CFD
Computational fluid dynamic
 DPM
Discrete particle method
 DRW
Discrete random walk
 FBRM
Focus beam reflectance measurement
 NIOC
National Iranian Oil Company
 PBM
Population balance model
 RSM
Reynolds stress model
 VOF
Volume of fluid
Introduction
On production units, a multiphase separator is the first surface equipment which is used to separate the produced wellhead fluid into the liquid and gas fractions. Inappropriate design of threephase separators is a major obstacle to stable hydrocarbon processing and leads to reduce the efficiency of the entire surface equipment such as: heaters, exchangers and pressure maintenance equipment. When sizing a horizontal separator, it is necessary to choose a seam to seam vessel length and a diameter (Stewart and Arnold 2008). In the semiempirical method, the separator length and diameter are chosen, in order to allow different phases to separate from each other and reach an equilibrium. Much work has been conducted to investigate the aspects of designing threephase separators (GPSA 1998; Smith 1987; Gerunda 1981 and Watkins 1967). Bothamley (2013a, b, c) conducted a complete study for quantifying the separation performance. The effects of different types of momentum breaker and mist extractor device, feed pipe velocity, particlesize distribution and the main vessel dimensions were discussed in their work.
Although useful guidelines are provided by the semiempirical approach, the essential data that affect the separator performance are not always considered (Kharoua et al. 2013). The semiempirical method does not, for example, consider the effects of liquid reentrainment and recirculation within the liquid layers (Viles 1993; Shaban 1995). In addition, this method uses a single representative particle size for oil and water phases. This is not always the case since previous studies stressed the importance of the secondaryphase distribution in predicting the performance of threephase separators (Monnery and Svrcek 1994; Kharoua et al. 2013). It should also be emphasized that the semiempirical method could not forecast the separation efficiency since it is based on 100% separation (Stewart and Arnold 2008). These fundamental limitations of a semiempirical method illustrate the need for a more detailed method to investigate the threephase separation phenomena. CFD simulations will be able to investigate the threephase separation phenomena and provide some useful guidelines for optimization of dimensions.
There are two methods for dealing with multiphase flow, the Eulerian–Lagrangian approach and the Eulerian–Eulerian approach. The Eulerian–Lagrangian method deals with the continuous fluid phase as a continuum by solving the Navier–Stokes equation, while the secondaryphase particles are tracked in their movements through space and time. The Eulerian–Lagrangian approach is preferred over the Eulerian–Eulerian approach when information about particle locations is needed. The other advantage of the Eulerian–Lagrangian approach is physically concrete modeling of fluid–particle interaction. Nevertheless, the computing time of Eulerian–Lagrangian method significantly increases by increasing the number of tracked particles. Therefore, the main detraction of using the Eulerian–Lagrangian approach is the computational expense (Chrigui 2005; Mpagazehe 2013). Conversely, the Eulerian–Eulerian method mathematically focuses on the fluid motion in a specific location in space. The VOF model, the mixture model and the Eulerian model belong to the Eulerian–Eulerian approach. The VOF model is used when the position of the interface between fluids is important. The mixture model is used to model homogeneous multiphase flows where the phases move at almost same velocities. The Eulerian multiphase model is used to model separate but yet interacting phases. It should be noted that in the Eulerian multiphase model a single pressure is shared by all phases (Mahmud et al. 2018; Zakerian et al. 2018; Fluent Theory Guide 2016; Sun et al. 2014).
Previously, numerical studies of threephase separators mostly used the Eulerian–Eulerian method. Vilagines and Akhras (2010) used the CFD model to evaluate the effect of new internals on the efficiency of a threephase separator. They used the shear stress transport turbulence model and threephase Eulerian model to simulate the multiphase flow. In that study, the results of the CFD simulation and the experimental data were not compared. Kharoua et al. (2012) used a CFD model to modify a production separator. The wellknown k–ε turbulence model and the Eulerian–Eulerian multiphase approach were used to study the threephase separation phenomena. Again, in that study, the numerical calculation results were not compared with the experimental data.
Kharoua et al. (2013) used the CFD model to analyze the performance and internal multiphase flow behavior in a threephase separator. To deal with complex phenomena such as size distribution, coalescence and breakup of secondary phases, the population balance model (PBM) was used. Three different liquid particle distributions were used to determine the effect of size distribution of the secondary phase on the performance of the separator. The simulation results stressed the importance of the secondaryphase distribution in predicting the performance of the internal flow behavior. However, the PBM model was applied to one liquid phase and the other liquid phase was represented by a monodispersed distribution. In that study, the results of numerical calculation were compared with industrial data. A very poor agreement between the outcomes of the CFD simulation and the experimental data was observed. In addition, the details of the sampling procedures and experimental methods were not presented in their study.
There are also a few publications that made use of the Eulerian–Lagrangian method. Laleh et al. (2011) applied numerical calculations to study the fluid flow behavior in twophase separators. In their paper, two simulation approaches, the DPM model and a combination of VOF and DPM model, were used to simulate the multiphase flow. In addition, the k–ε turbulence model was used because of its simplicity and achieved accuracy. Their simulation results demonstrated that the combination of VOF and DPM models was more reliable than the DPM model with respect to predicted separation efficiency. Laleh et al. (2012a, b, 2013) used DPM, VOF and k–ε turbulence models to develop a realistic CFD simulation in order to debottleneck a threephase separator. In that study, the flowdistributing baffles and the mist extractor were modeled as porous media. However, the results of the CFD simulation and the experimental data were not compared in their work.
This study presents an approach to determine the dimensions of threephase separators. First, based on the Arnold and Stewart semiempirical procedure, we developed a computer code to design several configurations with varying slenderness ratios for one of the Iranian south gas condensate reservoirs. We then devised a comprehensive CFD model to investigate the threephase separation phenomena.
In this study, the commercial CFD code ANSYS Fluent version 16.2 was utilized. For simulation purposes, two multiphase models, VOF and DPM, were combined with the k–ε turbulence model, while the DRW model was implemented to include the effect of arbitrary particle movement due to velocity variations caused by turbulence. The results of numerical calculations in terms of fluid profiles, separation performance and DPM particle behavior were used to choose the optimum vessel configuration. To evaluate the proposed method, the optimized length and diameter of the separator were compared with those of one currently used by National Iranian Oil Company (NIOC). No difference between the dimensions of the optimum vessel and the existing separator was found. Also, simulation data were compared with experimental data pertaining to a similar existing separator. A reasonable agreement between the experimental data and the simulation results was observed.

The quality of computational grid systems was not validated in previous studies. In addition, many previous studies used the general mesh qualities such as the maximum aspect ratio to validate the computational grid systems. However, the results of this study will show that the general mesh qualities are not sufficient to investigate the computational mesh. Therefore, the mesh independence test is an important aspect of simulating the threephase separators.

Comparison of numerical simulation results and experimental data is an important aspect of the CFD study. However, most of the CFD studies on threephase separators did not validate the CFD simulations with the experimental or field test data. This is presumably because of the high cost required for conducting such tests. In the present study, simulation results are compared with industrial data pertaining to a similar existing separator. In addition, this study presents the details of the sampling procedures used to collect fluids and the experimental methods used to evaluate the efficiency of threephase separators.

The effect of arbitrary particle movement due to variations caused by the turbulence was ignored in previous studies. However, the results of this study underline the importance of this factor in predicting the performance of threephase separators.

The present study is meant for establishing a suitable methodology, including turbulence model selection for simulating the threephase separation phenomena. As a result, the comparison of experimental and simulated results was generated using different turbulence models, i.e., standard k–ε, standard k–ω and RSM.

One important parameter that has received inadequate attention thus far in designing separators is the change in input water and gas flow rates. This negligence can eventuate in problems such as rising of the water level in separator, difficulties in operational threephase separation, increasing volumetric water fraction in natural condensate and gas outlets and finally reducing efficiency of separators. In this work, the effect of input gas and water flow rates on the threephase separation performance is investigated.

Previous studies have defined different ranges of slenderness. These guidelines for the slenderness ratio are mainly determined by economic analysis without thorough investigation of the threephase separation phenomena (Laleh et al. 2012a, b). In this study, the effect of the slenderness ratio on the threephase separation phenomena and behavior of secondaryphase particles are investigated. In addition, the slenderness ratio of the optimum vessel is compared with the slenderness ranges proposed in the literature.

Finally, most of the CFD studies on threephase separators only provided the overall steps of CFD modeling. However, this study presents the details of the used CFD model.
Implemented semiempirical approach
In the semiempirical method, the separator length and diameter are chosen, in order to allow the water and condensate droplets to separate from the continuous gas phase and reach an equilibrium. Several semiempirical methods for sizing two and threephase separators have been presented before (Arnold and Stewart 1998; Stewart and Arnold 2008; Monnery and Svrcek 1994; Dokianos 2015; HernandezMartinez and Martinez Ortiz 2014). Of all the previous methods, the Arnold and Stewart procedure is the most suitable for designing a threephase separator, due to its robustness and simplicity (Olotu and Osisanya 2013; Ghaffarkhah et al. 2017).
The software developed in our study was based on the Arnold and Stewart procedure for calculating the dimensions of threephase separators. This software eliminates the risk of mistakes and increases the reliability of the semiempirical procedure. The most important equations of this software are summarized below.
Gas capacity formula
Liquid capacity formula
Seam to seam length formula
The seam to seam length of the separator is given by the following equations (Stewart and Arnold 2008).
Eventually, several separator configurations with different slenderness ratios \( \left( {\frac{{L_{\text{ss}} }}{D}} \right) \) were computed by our software. Note that in this study, the design of the vessel is based on the gas capacity constraint. It should also be emphasized that the separator seam to seam dimensions were reported in multiples of 100 mm, while the vessel diameters were in multiples of 50 mm.
Slenderness ranges proposed in the literature
Computational methodology
A 3D, transient mathematical model is developed to simulate the threephase separation phenomena. The VOF model was used to create the background of the computational domain, while the DPM model was used to describe the properties of fluid droplets that were injected at the separator inlet. In addition, the DRW model was used to include the effect of arbitrary particle movement due to variations caused by turbulence. Note that in the DRW model, the interaction of a particle with a series of fluidphase turbulent eddies is simulated (Fluent Theory Guide 2016; Gosman and Loannides 1983).
Mathematical formulation
The VOF multiphase model belongs to the Eulerian–Eulerian approach. In this model, a single set of momentum equations is solved and the resulting velocity field is shared among the phases. In this study, the gas and liquid phases are treated as incompressible. In addition, the gas phase is defined as the primary phase, while the condensate and water phases are defined as the secondary phases.
In the present study, the DPM model with fourway coupling calculation was used to investigate the statistics of particle trajectories. In this model, the momentum transfer from the continuous phase to the discrete phase is calculated through interchange terms such as drag force. In addition, the momentum gained or lost by the particle stream (condensate and water droplets) is incorporated into the subsequent continuousphase calculations. Coalescence of particles and their breakup are also modeled by using the DPM model with fourway coupling. When the particle trajectory is calculated, a proper model within the spray model theory (Taylor analogy breakup (TAB) model or wave model) is used to compute the droplet breakup based on the particle Weber number. In addition, the outcomes of the collision model are used for modeling droplet coalescence (Laleh et al. 2012a, b).
Material definition
Flow rates and physical properties of fluids
Density (kg/m^{3})  Viscosity (kg/m s)  Mass flow rate (kg/h)  

Gas  96.5  1.6E−5  117,343 
Condensate  624.7  1.24E−4  16,300 
Water  1186.70  8E−4  9450 
Gas compressibility (Z)  0.88 
Hallanger et al. (1996) utilized a secondary water particle distribution with an average diameter of 250 μm and a Rosin–Rammler exponent of 3 for seven different particle classes. Based on the maximum stable droplet size, Laleh et al. (2012a, b, 2013) generated the particle distribution with a Rosin–Rammler exponent of 2.6 and a maximum diameter of about 2270 and 4000 μm for oil and water phases, respectively. Note that the abovementioned studies were combined with the actual fluid data provided by NIOC, based on the focus beam reflectance measurement (FBRM), to choose the proper particle distribution model. The maximum, minimum and average diameters for the water phase were set at 2000, 150 and 500 μm. For condensate phase, the maximum, minimum and average diameters of 560, 140 and 50 μm were selected. The Rosin–Rammler exponent, \( \varpi \), at 2.6 was used for both the condensate and water phases.
In the present study, the diameter ranges of the condensate and water droplets are divided into 35 subintervals. Each of these discrete intervals is represented by a mean diameter for which trajectory calculations are performed (Zhang 2009). It should be mentioned that Eq. 21 is used to calculate the mass fraction of each of these subintervals based on its mean diameter. Eventually, the number of injected particles for each of these subintervals is calculated.
Computational domain
Vessel dimensions and location of the internals
Configuration number  Seam to seam length (mm)  Diameter (mm)  Slenderness ratio (mm)  The longitudinal location from the inlet side seam  Other vessel properties  

Gas outlet (mm)  Condensate outlet (mm)  Condensate weir (mm)  Water outlet (mm)  
Case 1  4800  2500  1.92  3832  3351  3678  4449  The semispherical inlet diverter has a diameter of 696 mm, while the inlet, gas outlet, condensate outlet and water outlet have the diameters of 508, 609.6, 203.2 and 203.2 mm, respectively 
Case 2  4900  2150  2.28  3932  3452  3779  4550  
Case 3  5000  1850  2.7  4021  3541  3868  4639  
Case 4  5300  1550  3.42  4330  3849  4176  4947  
Case 5  6000  1250  4.8  5069  4590  4918  5688  
Case 6  5000  1850  2.7  4021  3541  3868  4639  The vanetype inlet diverter has 12 curved vanes. This internal has a length of 648 mm. The inlet is a 90° SR elbow with a 254 mm radius. The diameters of the gas, condensate and water outlets are equal to 609.6, 203.2 and 203.2 mm, respectively 
Case 7—data validation  5000  1850  2.7  3750  3175  3500  4370  The vanetype inlet diverter has 12 curved vanes. This internal has a length of 648 mm. The mist extractor box has a length of 540 mm—there are two perforated plates at 500 and 3550 mm, respectively, from the inlet side seam. The inlet is a 90° SR elbow with a 254 mm radius. The diameters of the gas, condensate and water outlets are equal to 609.6, 203.2 and 203.2 mm, respectively 
As can be seen in Table 3, Cases 3, 6 and 7 have the same seam to seam length and diameter. However, these vessels are equipped with different internals. A spherical inlet diverter is used for Case 3, while Case 6 is equipped with a vanetype inlet diverter. In addition, Case 7 is equipped with a vanetype inlet diverter, perforated plates and a highefficiency mist extractor device. The comparison between these cases could highlight the effect of different internals on the threephase separation performance. It should also be emphasized that Case 7 has the dimensions and internals quite similar to those of an industrial separator currently in use for one of the Iranian oil fields. The results obtained from this vessel were reviewed in a CFD evaluation. The overall arrangement of this separator (Case 7) is shown in Fig. 1b. Note that the mist extractor device and perforated plates were modeled as the porous zone, while the curved plates were used for modeling of the vanetype inlet diverter.
The original mist extractor is a type E wire mesh demister. In this study, based on Helsør and Svendsen (2007) work, the porosity, viscosity resistance coefficient and the inertial resistance coefficient of the mist extractor were set at 97.7%, 3.84e6 m^{−2} and 126 m^{−1}, respectively. Moreover, the flow distribution baffle was modeled as a perforated plate with a free area of 40% and an inertial resistance factor of 1822.1 m^{−1}. Note that the properties of internals were taken from the configuration of the existing NIOC separator for validation purposes.
Boundary conditions
Implemented simulation boundary conditions
Location  Description 

Inlet  Boundary type: velocity inlet Fluid velocity (m/s): 7.209 Turbulence intensity (%): 2.16 Hydraulic diameter (m): 0.254 Discretephase BC type: escape Condensate volume fraction: 0.028 Water volume fraction: 0.0061 
Gas outlet  Boundary type: pressure outlet Gauge pressure (Pascal): 1.235e+7 Turbulence intensity (%): 2.2 Backflow hydraulic diameter (m): 0.3048 Backflow discretephase BC type: escape 
Oil outlet  Boundary type: velocity outlet Oil velocity (m/s): 0.9465 Turbulence intensity (%): 3.1 Backflow hydraulic diameter (m): 0.1016 Backflow discretephase BC type: escape 
Water outlet  Boundary type: velocity outlet Water velocity (m/s): 0.29 Turbulence intensity (%): 5.658 Backflow hydraulic diameter (m): 0.1016 Backflow discretephase BC type: escape 
Walls of oil and water zones  Boundary type: wall Noslip condition Discretephase BC type: reflect Discretephase reflection coefficients: Normal: 0.1 Tangential: 0.05 
Other walls  Boundary type: wall Noslip condition Discretephase BC type: reflect 
Mesh generation and grid independency
Global mesh quality for different meshing system of Case 3
Skew factor range  

Generated mesh  0–0.2  0.2–0.4  0.4–0.6  0.6–0.8  0.8–1 
Mesh number one  21.83%  45.51%  24.16%  8.11%  0.39% 
Mesh number two  23.48%  44.58%  23.86%  7.69%  0.39% 
Mesh number three  23.12%  44.82%  24.18%  7.51%  0.37% 
Mesh number four  25.51%  43.68%  23.27%  7.23%  0.31% 
Maximum aspect ratio  Maximum squish factor  Total number of cells  

Mesh number one  21.1  0.94  593,796 
Mesh number two  16.7  0.95  923,687 
Mesh number three  14.8  0.94  1,392,721 
Mesh number four  14.1  0.92  1,812,732 
Discretization and numerical solution
In this study, the multiphase partial differential equations were discretized using the finite volume method, while the SIMPLE algorithm was used as the pressure–velocity coupling scheme (Patankar and Spalding 1972). Moreover, the firstorder upwind approximation was chosen for the discretization of the turbulent kinetic energy, turbulent dissipation rate and momentum equations, while the PRESTO discretization scheme was employed to interpolate the pressure values at the faces of computational cells (Patankar 1980; Peyret 1996). The GeoReconstruct interpolation scheme was used for the discretization of the volume fraction. It should be noted that the GeoReconstruct interpolation scheme is used whenever the timeaccurate transient behavior of the interface between phases is important (Fluent Theory Guide 2016).
Three different time step sizes, i.e., 0.005, 0.001 and 0.0005 s, were tested. The time step 0.005 s is proven to be too large for all cases since it caused several simulation instabilities. Comparison between the other two time steps showed little difference. As a result, the time step size at 0.001 s was used for both the DPM and VOF models. It should be noted that the time step 0.001 s fulfills the Courant–Friedrichs–Lewy (CFL) criterion (CFL < 1). As a result, this time step size does not affect convergence negatively (Fluent Theory Guide 2016). Since the dimensions and the total number of cells were different for Cases 1 to 7, the PC run time was also different for them. For Case 7, a PC run time of 47 h was required to simulate the continuous and discrete phases on two 4.2 GHz CPUs running the 64bit version of ANSYS Fluent. It should be emphasized that solving multiphase problems is a timeconsuming process, which can be hindered by many factors such as the large number of grids and complex computational domains. For this reason, the proper underrelaxation factors for pressure, density, body forces, momentum, turbulent group and discretephase sources were accurately chosen at 0.3, 0.9, 1, 0.005, 0.8 and 0.5, respectively, to improve the stability of the solutions. Finally, in this study, the convergence criteria for different equations were set to 10e−4.
Experimental
Fluid sampling
Apparatus setup and measurement method
Determining the amount of water in condensate and gas outlets
In the present study, the gas sample was directed through the Coulometric Karl Fischer vessel to determine the amount of water in the gas outlet. As can be seen from Fig. 5a, a flow meter and a control valve were placed between the titration cell and the highpressure gas cylinder to control the flow rate of the injected gas. The gas flow rate was kept at a constant value of 50 ml/min for 3 min. The control valve was then closed and titration continued until all amounts of water consumed.
On the other hand, to determine the amount of water in the condensate outlet, the water evaporator accessory was installed upstream of the titration vessel. In accordance with ASTM D6304, 5 g of the condensate sample was accurately weighed and added to a volumetric flask. The volume was then made up to 10 ml with dry hexane. After this, 1 ml of the dissolved sample was injected into an oven (APD513 of KEM, Japan). The vaporized sample was then transferred into the titration cell by using dry nitrogen gas with a flow rate of 300 ml/min. Eventually, the titration process continued until all amounts of water consumed. It should be noted that only a small amount of water in the injected nitrogen gas will cause an enormous error in the results. As a result, a highefficiency gas drying system (Fig. 5b) was used to eliminate the moisture of the injected nitrogen gas.
Determining the amount of condensate in water outlet
In this method, an oily water sample is acidified and extracted with hexane. The extracted sample is then purified by passing over a drying agent and injected into the FID injection port of chromatograph. Eventually, different groups of hydrocarbons will leave the column and be detected by the FID section (Yang 2011). For further investigation, the results are continuously transferred to a desktop computer.
Result and discussion
Data validation and experimental outputs
As mentioned before, Case 7 has the dimensions and internals quite similar to those of an industrial separator currently in use for one of the Iranian oil fields. Note that the properties of internals were taken from the configuration of existing NIOC separator. In this section, the results of the used CFD model are compared with the experimental data.
Experimental results
Comparison between CFD results and experimental data
Comparison of field and simulation data for Case 7
Experimental data (Volumetric ppm)  Simulation data with standard k–ε turbulence model and DRW model (volumetric ppm)  Simulation data with standard k–ε turbulence model and without DRW model (volumetric ppm)  Simulation data with standard k–ω turbulence model and DRW model (volumetric ppm)  Simulation data with RSM turbulence model and DRW model (volumetric ppm)  

Condensate in water  1980  2419  1191  2983  2502 
Water in condensate  1994  1502  983  2142  3406 
Water in gas  51  39  21  103  50 
Condensate in gas  –  634  474  1021  851 
Choosing the optimum vessel configuration
To choose the optimum vessel configuration, the results of numerical calculations in terms of separation performance, secondaryphase particle behavior and fluid profiles are presented in this section.
Separation performance
Secondaryphase particle behavior
Fluid flow profiles
Simulation results in terms of density profiles
Case number  Fluid density at the gas outlet (kg/m^{3})  Fluid density at the condensate outlet (kg/m^{3})  Fluid density at the water outlet (kg/m^{3}) 

Case 1  109.19  628.02  1176.58 
Case 2  109.57  628.04  1176.54 
Case 3  110.13  628.11  1176.56 
Case 4  111.69  629.36  1176.12 
Case 5  113.76  631.01  1175.67 
In this study, an inefficient condensate–water separation was predicted for Cases 4 and 5 with a higher condensate density in the condensate outlet and a lower water density in the water outlet. As can be seen from Table 7, the fluid density at the condensate outlet of Cases 4 and 5 is higher than other cases. This is mainly because more water droplets are being carried out into the gas outlet of these two cases.
Effect of gas and water flow rates on separator’s efficiency
One important parameter that has received inadequate attention thus far in designing separators is the change in input water and gas flow rates. This change can range from small to large values. This negligence can eventuate in problems such as rising of the water level in separator, difficulties in operational threephase separation, increasing volumetric water fraction in natural condensate and gas outlets and finally reducing efficiency of separators. Hence, these changes must be brought into account when performing an optimal design for separators. Regarding field observations, the production history of adjacent wells as well as information gathered from the NIOC, the mass flow rate range of 105,608–129,078 kg/h was used for the gas phase, while the mass flow rate range of 9450–18,900 kg/h was used for the water phase.
Considering the abovementioned results in conjunction with the total cost of the separator, it was decided to opt for Case 3 as the best configuration. It should be mentioned that the smaller the diameter, the less the vessel will weigh and therefore the lower it cost (Stewart and Arnold 2008; Mulyandasari 2011). A high condensate–water separation performance along with a low water content at the condensate outlet was predicted for this case. In addition, the high condensate percentage at the gas outlet in this case could have been decreased by using a suitable mist extractor. It should also emphasize that vessel number three can effectively handle increasing the gas and water flow rates. The dimensions of this vessel were compared with the length and diameter of the existing threephase separator of NIOC, which was a threephase horizontal separator with a seam to seam length of 5000 mm and a diameter of 1850 mm. No difference in dimensions of the Case 3 and existing vessel was observed.
In addition, even the range proposed by Smith (1987) could not guarantee designing the optimum vessel configuration. This is mainly because choosing different slenderness ratios in this range resulted in different vessel dimensions. As can be seen from Fig. 20, the slenderness ratios of Cases 2–5 are in the range proposed by Smith (1987). The semiempirical model could not investigate the efficiency of these vessels and choose the optimum configuration. However, as mentioned before, the used CFD model is well capable of investigating the threephase separation phenomena and choosing the optimum vessel configuration. This again shows the benefits of the used CFD model in designing threephase separators.
Effect of different internals on the separation performance
As we mentioned before, a perforated plate and a mist extractor were modeled inside the gas zone of Case 7 (ref. Figure 1a). In the mist extractor, liquid droplets coalesce and fall to the liquid zone (Stewart and Arnold 2008). In addition, perforated plates are used to improve the flow distribution, increase the liquid residence time and enhance the separation (Lu et al. 2007; Laleh et al. 2012a, b). As a result, the mass distribution of the condensate and water droplets slightly reduced after passing through the abovementioned internals of Case 7.
Comparing the results of Cases 6 and 7 showed that the mass distribution of the condensate droplets near the water outlet of Case 7 was less than Case 6. Similarly, the amount of water near the condensate outlet of Case 7 was less than Case 6. This is mainly because the liquid residence time was increased due to installation of the perforated plates. It should be noted that increasing the condensate residence time indicates that the water phase provides more time for condensate droplets to rise up and join the condensate phase. In addition, increasing the water residence time indicates that the condensate phase provides more time for the water droplets to settle down and join the water phase.
As mentioned before, the coalescence and breakup of particles were considered in the present study. The simulation results showed that the droplet coalescence happened at a very low rate of less than 0.5% in Cases 3, 6 and 7. However, the droplet breakup was more common. For Cases 3, 6 and 7, the droplet breakup occurred at a significant rate of 15.10, 17.94 and 18.37%, respectively. As a result, it can be concluded that the installation of the vanetype momentum breaker and perforated plates increased the number of breakups.
Conclusion
 1.
The general mesh qualities are not sufficient to investigate the computational mesh. Therefore, the mesh independence test is an important aspect of simulating the threephase separators.
 2.
The results underlined the importance of the DRW model and showed that without applying this model the computational setup tends to overestimate the separation efficiency.
 3.
The results showed that the threephase separation performance reduces by increasing the slenderness ratio.
 4.
The optimum vessel configuration can effectively handle increasing the gas and water flow rates.
 5.
No difference between the dimensions of the optimum vessel and the existing separator was found.
 6.
The slenderness ratio of the optimum vessel was compared with the slenderness ranges proposed in the literature. The results showed that the slenderness ratio of the optimum vessel was just in the range proposed by Smith (1987).
 7.
Among the used turbulence models, the simulation results, adopting k–ε model is found to have better predictions with experimental results.
 8.
The results of numerical calculation were compared with industrial data. A reasonable agreement between the outcomes of the CFD simulation with DRW model and the experimental data was observed.
 9.
The efficiency of the optimum vessel configuration (Case 3) was improved due to installation of a vanetype inlet diverter, perforated plates and a highperformance mist extractor.
Notes
Acknowledgements
The authors thank NIOC for permission to publish these data. We would also like to thank Dr. Nasiri A. (Research Institute of Petroleum Industry) for his valuable discussion in the experimental part of this work. The authors also thank the anonymous referees for comments on this manuscript.
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