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
Threedimensional simulation of a multiphase flow is performed using the Eulerianhydrocyclones. The solution is developed using a mass conservationbased 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; EulerianEulerian 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 oilwater
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 oilwater
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 oilcontaminated 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 35mm 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 oilwater
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 particleparticle
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 10mm 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 5mm 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 EulerianEulerian
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 ensembleaveraging of NavierStokes
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 eddydiffusivity
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 LaunderReeceRodi (RSMLRR)
(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 pressurestrain
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 nonuniform 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 RhieChow (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 103 to 5×105
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 104 for continuity and 105
The under relaxation factors are assumed as 0.20.4 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 interphase 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 streamwise 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
EulerianEulerian 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.
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