Performance evaluation of a multibranch gas–liquid pipe separator using computational fluid dynamics
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Abstract
The present paper aims to evaluate the performance of a multibranch gas–liquid pipe separator by means of 3D computational fluid dynamics. This type of separator is attractive for deepwater subsea hydrocarbon fields due to its compactness and reduced weight when compared against traditional gravity vessel separators. The focus of this paper is on studying the internal flow dynamics, the separation efficiency, and the performance with changing and transient operating conditions. Numerical simulations were performed on a numerical prototype of the separator using the inhomogeneous mixture model and assuming that both phases are continuous. Sensitivity analyses were performed on gas volume fraction, outlet pressures, and considering slug flow at the inlet with periods of 2 s and 8 s. The separation efficiency was quantified by calculating the liquid carryover and gas blowby. For most of the operational conditions studied, separation occurred primarily in pipe branches closer to the inlet while those closer to the outlet exhibited a static liquid level. Reducing the gas outlet pressure caused the height of the liquid in the branches to be reduced. The inlet gas volume fraction did not affect significantly the separation performance, the flow distribution, nor the liquid level inside the separator. Separation efficiencies were not affected significantly with the presence of slugs; however, the liquid level in the branches oscillated significantly. The results and numerical models produced by this study could potentially be used to improve the understanding of this type of separators and improve its efficiency and systemlevel design.
Keywords
Gas–liquid separation Subsea processing Computational fluid dynamicsList of symbols
Variables
 \(\Delta y\)
Thickness of cell closest to wall (m)
 \(u_{*}\)
Friction velocity (m/s)
 \(t\)
Time (s)
 \(\varvec{U}\)
Velocity vector
 \(U\)
Velocity component (m/s)
 p
Pressure (Pa, bara)
 g
Gravitational acceleration (m/s^{2})
 M_{p}
Momentum interphase (N/m^{3})
 C_{D}
Drag coefficient
 \(d_{\text{og}}\)
Oil–gas interfacial length (m)
 \(\mu_{\text{t}}\)
Turbulent viscosity (Pa s)
 \(k\)
Kinetic energy (m^{2}/s^{2})
 \(p_{k}\)
Turbulent production (kg/m s^{3})
Greek symbols
 ρ
Density (kg/m^{3})
 μ
Dynamic viscosity (Pa s)
 \(\alpha\)
Volume fraction
 \(\varepsilon\)
Turbulent dissipation rate (m^{2}/s^{3})
Subscripts
 o
Oil
 g
Gas
 OG
Outlet of gas
 OL
Outlet of liquid
 p
Generic phase “p”
 j
Generic spatial coordinate
 i
Generic spatial coordinate
 m
Mixture
Superscripts
 o
Oil
 g
Gas
Abbreviations
 CFD
Computational fluid dynamics
 GCU
Gas carry under
 GLCC
Gas liquid cylindrical cyclone
 GVF
Gas volume factor
 LCO
Liquid carryover
 RSM
Reynolds stress model
 VOF
Volume of fluid
Introduction
There are challenges when moving processing equipment to subsea, especially in deepwater fields with high hydrostatic pressure. Conventional separator vessels with a large diameter require thick walls; hence, the equipment is heavy and expensive to build and to deploy. Reducing the diameter on separators gives a more compact solution compared to conventional vessels, as they require a thinner wall and can be designed and manufactured using pipecode guidelines.
A Harp is currently installed subsea as part of the SSAO Marlim system (SSAO is short for Separação Submarina de ÁguaÓleo in Portuguese, which means Subsea Oil–Water Separation) in the Marlim field in Brazil (Orlowski et al. 2012). Marlim is a brownfield producing with a high water cut (Euphemio et al. 2007). Topside processing and disposing of water are expensive and bottlenecks oil production; hence, a subsea water separation station was implemented. The Harp is placed at a water depth of 876 m and at the inlet of a pipe separator for oil–water separation, which is designed for a liquid flow rate of 3500 Sm^{3}/day. The water is further processed and reinjected into the formation while the oil and gas are mixed and transported to surface facilities through a 2.4kmlong pipe. The main intention of the Harp is slug catching and bulk separation of gas to allow using a small diameter in the oil–water pipe separator downstream of the liquid outlet.
The Harp multibranch pipe separator could be used for different applications that require bulk gas or liquid removal, e.g., before gas or liquid boosters. Gas compression systems, for instance, are very sensitive to the liquid content in the gas stream, compromising the equipment performance and reliability. Liquid boosting, on the other hand, can tolerate very high void fraction in the liquid stream, but at expense of efficiency and boosting capability. Gas–liquid separation may enable better operating conditions and allow higher boosting efficiency in both cases. The Harp separator could also be suitable for cases where decentralized subsea processing (at well or cluster level) is desired.
Unfortunately, there is limited information in the literature available to the public about the separation performance of the Harp, especially regarding operational envelope, flow dynamics in the separator, separation efficiency, slughandling capabilities, etc. This, to the authors’ opinion, limits the understanding about the technology and inhibits further implementation, development and improvement in the design.
In this work, a prototype of the Harp separator is studied in detail using twophase computational fluid dynamics (CFD). The focus is to study the internal flow dynamics, the separation efficiency, and the performance with changing and transient operating conditions. This will hopefully clarify the operating principle of the technology and will serve as a useful reference for future researchers and industry people that wish to improve further or use and deploy this technology. Unfortunately, there are no experimental data available to the public on the performance of this separator to compare the results of the numerical simulations against, which is an important limitation of the present study.
Bulk gas–liquid separation has been studied extensively and successfully in the past by several researchers using computational fluid dynamic simulations. In CFD simulation software, typically the user must specify the topology of the phase beforehand (either continuous or dispersed). This modeling assumption is used further when formulating expressions of the momentum, mass, and energy transfer terms between the phases.
For example, Afolabi and Lee (2014) used the commercial CFD package ANSYS Fluent with the particle model and Reynolds stress turbulence model (RSM) to study air–water flow in a GLCC (Gas–Liquid Cylindrical Cyclone) separator. The air was treated as the dispersed phase, characterized by a representative bubble diameter, in a continuous water phase. Phase segregation in a helical pipe was analyzed experimentally and numerically by da Mota and Pagano (2014), using the commercial CFD software ANSYS CFX. The Kepsilon turbulence model was used, and the water and gas were treated as dispersed phases (droplet and bubbles) with the oil as the continuous phase. The results of the numerical simulations were in agreement with experimental measurements. Monesi et al. (2013) conducted numerical simulations to evaluate the performance of a slug catcher. Two different models were created in ANSYS CFX for the liquid and the gasdominated stream. Simulations of the liquiddominated stream were conducted with the particle model using kepsilon as turbulence model. The model was able to predict the performance of the slug catcher for the corresponding operating conditions.
Ghaffarkhah et al. (2018) used CFD to model threephase separation in a horizontal vessel to evaluate different vessel configurations and choosing the best. The volume of fluid (VOF) model was used for the continuous phase and a Lagrangian approach for tracking the movement of droplets and bubbles. The Kepsilon turbulence model was employed. Ghaffarkah et al. (2019) also used CFD to study threephase separation in a horizontal vessel to determine its optimal dimensions. They used the same simulation settings as Ghaffarkhah et al. (2018), but tested two additional turbulence models, Komega and Reynolds stress. When comparing against experimental data, they concluded that Kepsilon provided a better agreement.
Description of numerical simulations
Geometry
Settings of CFD simulations
Oil and gas properties for multiphase simulation
Parameters  Values 

ρ_{o} (kg/m^{3})  814 
μ_{o} (Pa s)  0.0095 
ρ_{g} (kg/m^{3})  128 
μ_{g} (Pa s)  1.6E−5 
The following boundary conditions were used for the simulations (locations are indicated in Fig. 2): mixture velocity uniform over the crosssectional area, gas volume fraction (GVF) at the inlet, and average static pressure at the gas and liquid outlets. This combination of boundary conditions was chosen because it resembled more closely the real physical system, where outlet pressures can be controlled by adjusting components (e.g., valves) in the downstream lines of liquid and gas. The wall roughness of the pipe is set to smooth with a noslip boundary condition. The effect of wall roughness on simulation results has not been evaluated in the present work.
CFD model

Liquid continuous–gas continuous phases and homogeneous mixture: This model employs mixture momentum equations with average properties that depend on the volume fraction. It is usually suitable for stratified gravity flow where the interface is clear and in cases where the interface momentum transfer is large.

Liquid continuous–gas continuous phases, homogeneous mixture and free surface: This model is similar to the previous one, but in addition considers the curvature of the interface using the surface tension and uses it to allocate volume fractions of mesh cells.

Liquid continuous–gas dispersed phases and inhomogeneous mixture: This model employs separate momentum equations for each phase (i.e., accounts for slip), which makes it more computationally expensive. Interfacial forces considered were: buoyancy, drag, lift, wall lubrication, and turbulent dispersion.

Liquid continuous–gas continuous phases and inhomogeneous mixture: This model employs separate momentum equations for each phase. Interfacial forces considered were: buoyancy and drag.
The momentum interphase term for gas is the same as for oil, but with opposite sign.
The interfacial length \(d_{\text{og}}\) is given as an input (in this work, it was assumed \(d_{\text{og}}\) = 1 mm). The drag coefficient is, assuming fully turbulent flow, \(C_{\text{D}}\) = 0.44.
The mixture density is \(\rho_{\text{m}} = \alpha_{\text{o}} \cdot \rho_{\text{o}} + \alpha_{\text{g}} \cdot \rho_{\text{g}}\). The mixture viscosity (\(\mu_{\text{m}}\)) is written in a similar fashion.
The software employs an elementbased finite volume method to solve the conservation equations. Control volumes are constructed around each mesh node. The value of variables and gradients of variables of the element are approximated with a finiteelement shape function (that depends on the type of element) that makes a weighted sum of all nodes within an element. The conservation equations are integrated over each control volume, and Gauss’ divergence theorem is used to convert integrals of volume to surface integrals. In this work, the advection terms were modeled with highresolution scheme, which uses a blend factor to combine upwind and secondorder differencing schemes. The blend factor is estimated at each node trying for it to be as close to 1 based on the principles discussed by Barth and Jesperson (1989). The transient term was discretized with a secondorder backward Euler stencil.
Mesh validation
Main properties and characteristics of the meshes employed
Mesh Nr.  Nr. nodes (k)  Maximum aspect ratio  Maximum ortho skew (Fluent)  Equiangle skew (Fluent) factor range (%)  

0–0.25  0.25–0.5  0.5–0.75  0.75–1  
1  375  75  0.86  39  60  1  0 
2  558  59  0.84  39  59  2  0 
3  1226  49  0.80  40  59  1  0 
4  1824  49  0.82  41  58  1  0 

Mass flow through both outlets

Area average pressure in 13 crosssectional planes along the geometry

Pressure difference, delta P, between the inlet and the two outlets

Velocity magnitude in 6 points. The points were located in the pipe center at the following locations: (1) inlet pipe just before the first branch, (2) elbow at exit of the first branch, (3) and (4) inlet and outlet of the third branch, and (5) and (6) inlet and outlet of the sixth branch.
The CFD model employed uses wall functions to handle the near wall region (i.e., imposing a velocity profile depending on the turbulence model chosen). Therefore, to obtain accurate results, usually the centroid of the mesh cell adjacent to the wall should be located in the log region of the boundary layer. To verify this criterion quantitatively, turbulence models often provide a suggested y^{+} range (y^{+} is the dimensionless distance of the first node to the wall, defined by Eq. 1). For the turbulence model used in this work, Kepsilon, the recommended y^{+} range is y^{+} < 300.
Description of CFD simulations performed

Inlet mixture velocity, \(U_{\text{inlet}}^{\text{mix}} = 2\,{\text{m}}/{\text{s}}\).

Outlet liquid (OL) average static pressure, P_{OL} = 85 bara
Simulation plan for performance evaluation
Case  Inlet GVF  \(\varvec{P}_{{{\mathbf{OG}}}}\) (bara) 

Case 1  
Case 1.1  0.3  84.90 
Case 1.2  84.91  
Case 1.3  84.92  
Case 1.4  84.93  
Case 1.5  84.94  
Case 1.6  84.95  
Case 1.7  84.96  
Case 1.8  84.97  
Case 1.9  84.99  
Case 2  
Case 2.1  0.5  84.95 
Case 2.2  0.7 
Case 2 is a sensitivity study varying the inlet gas volume fraction. The effect of three different volume fractions is studied (0.3, 0.5, 0.7).
In Case 3, a study on the ability of the separator to handle upstream slug flow conditions of various periods was conducted. Slug flow at the inlet was modeled by alternating with time the GVF at the inlet between primarily liquid with gas entrained (GVF = 0.1) and primarily gas with liquid entrained (0.9). Constant boundary conditions are an inlet velocity of 2 m/s, outlet gas pressure sets to 84.95 bara, and outlet liquid pressure sets to 85 bara.
Simulation plan for evaluation of slug handling
Case  Inlet GVF  Slug period (s) 

Case 3  
Case 3.1  0.1/0.9  2 
Case 3.2  8 
The total simulation time for these simulations was set to 10 times the longest residence time of the two fluids inside the separator. Approximate residence times are found by dividing the distance travelled by the velocity.

Root mean square (RMS) residuals below a value of 5E−5

Maximum (MAX) residuals below a value of 1E−3

Imbalances below 1%
Results
Effect of the outlet pressure on separation performance
The gas outlet (OG) pressure has a significant effect on the flow distributions in the branches (vertical pipes). For an OG pressure between 84.93 bara and 84.95 bara, all gas flows up the first branch, while the oil flows in the lower part of the separator as shown in Fig. 6. Lower OG pressures cause some oil to flow with the gas up the first branch and flow down some of the next branches. For example, for \(P_{\text{OG}}\) = 84.92 bara (Fig. 6b) the liquid flows up in the first branch and flows down in branches 2, 3, and 4. For \(P_{\text{OG}}\) = 84.90 bara (Fig. 6a), the liquid flows up in the first branch and flows down in branches 2, 3, 4, 5, and 6. In these cases, most of the downward flow of liquid occurs through the last branch.
An increase in OG pressure above 84.95 bara (Fig. 6d) leads to gas flowing upwards through other branches (2–6). Gas recirculation is seen for these cases, where the gas flows back down through the branches to the left of the branch that has upward flow. Thus, \(P_{\text{OG}}\) = 84.96 bara results in upward flow through branch 3 and downward flow through branches 1 and 2, and \(P_{\text{OG}}\) = 84.97 bara (Fig. 6e) causes upward flow through branch 5 and downward flow through branches 1–4 while upward flow through the last branch and downward flow through branches 1–5 are detected for \(P_{\text{OG}}\) = 84.99 bara (Fig. 6f).
The increased GCU for OG pressures below 84.92 bara is due to the change in the flow distribution. The oil moves up with the gas through the first branch and down the last two vertical pipes for these pressures. This results in gas being carried with the oil down the last branches and out of the liquid outlet.
A decreased separation performance is seen for OG pressures above 84.96 bara, in which \(P_{\text{OG}}\) = 84.97 bara results in a GCU of 1.27%, while \(P_{\text{OG}}\) = 84.99 bara results in a GCU of 67.39%. This is because the gas starts to flow together with the oil in the oilcollecting pipe at the bottom, as shown in (Fig. 6e) and (Fig. 6f), respectively. No significant effect is observed on the LCO. In general, values of ∆P_{outlets} (\(P_{\text{OL}}\)\(P_{\text{OL}}\)) between 0.03 and 0.09 bar result in acceptable gas and oil separation performances.
Impact of the inlet GVF on separation performance
CFD simulations for evaluation of slug handling
An inlet condition with 2mlong liquid slugs (2s slug period) creates a cyclic oscillation of the liquid level in the vertical branches. The number of branches filled with gas changes in time from 1 (when an oil slug enters the separator) to 3 (when a gas pocket enters the separator).
The inlet pressure fluctuates in time but stays between 84.95 and 85 bara. Keeping the pressure constant at the outlets results in back flow at the liquid outlet for the low liquid level during gasdominated feeds. It also results in back flow at the gas outlet for the high liquid level during oil slugs. No back flow is allowed through the outlets, which is why a wall is placed automatically at the crosssectional area by the simulation program. This did not happen in the case with shorter (2m) slugs.
Conclusions and recommendations

An inhomogeneous model with continuous–continuous phases considering buoyancy and drag showed acceptable convergence and physically logic results of oil–gas segregation inside the multibranch pipe separator.

For operating conditions that had high separation efficiency, gas–liquid separation occurs only through some of the vertical branches closer to the inlet while a static liquid level is established in the branches closer to the outlet. This static liquid level is depended on the outlet pressure set at the gas and oil outlet.

If the pressure difference between the liquid and gas outlets is changed to values below 0.03 bar, there will be significant gas carry under. If the pressure difference between the liquid and gas outlets is changed to values above 0.09 bar, there will be a significant liquid carryover and gas carry under. Translating these pressure differences to liquid heights, this means that the separation efficiency is optimal when the liquid level in the separator is in the range 18–56% of the total length of the last vertical branch.

The liquid level in the separator was not affected significantly by the value of the inlet volume fractions in the range 0.3–0.7 when using a constant inlet flow velocity.

The multibranch separator showed well slughandling abilities and high separation performances for the studied slug flow conditions. The liquid level of the static branches oscillated to compensate for the variations in the inlet oil and gas rates. For long liquid slugs, it is necessary to install check valves at the outlets of the separator to avoid back flow.
Notes
Acknowledgements
This work was carried out as a part of SUBPRO, a Researchbased Innovation Centre within Subsea Production and Processing. The authors gratefully acknowledge the financial support from SUBPRO, which is financed by the Research Council of Norway, major industry partners, and NTNU.
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