Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Phase Distribution Characteristics of OilWater Dispersed Flow in Vertical Pipe
Liejin Guo, Dongjian Zhao, Xiaowei Hu and Ximin Zhang
State Key Laboratory of Multiphase Flow in Power Engineering, Energy and Power Engineering, Xi'an Jiaotong University
Xianning West Road 28#, Xi'an, 710049, China
ljguo~,mail.xjtu.edu.cn
Keywords: Skewness coefficient, Kurtosis coefficient, phase distribution, oilwater
Abstract
Based on the concept of Skewness and Kurtosis, a new description method for local phase distribution in dispersed oilwater
twophase flow was introduced in this paper against the limitation of description discontinuity in traditional method. This
description method for local phase distribution was verified according to the experimental data, and the variation
characteristics of Skewness and Kurtosis were obtained. The results show that the Skewness and Kurtosis both increase firstly,
and then decrease gradually with the increase of oil flow rates, which dynamically reflects the variation process of local oil
fraction from core peak to wall peak distribution. Finally, the prediction formulas of Skewness and Kurtosis for local oil
fraction distribution were set up according to the flow conditions.
Introduction
Phase fraction is a basic parameter for describing
macrocharacteristics and interfacial geometric structure
characteristics in twophase flow: which reflects the
heterogeneity of twophase flow both in time and space
scale. Compared to the average phase fraction, local phase
fraction includes more information on heterogeneous and
transition phenomena in multiphase flow. So the research on
local phase fraction in dispersed twophase flow has been
carried out widely both by numerical methods and
experiments ( Antal & Lahey et al. 1991: Hibiki & Ishii
1999; Takamasa & Goto et al. 2003). Take gasliquid
twophase flow for example, in order to understand and
describe the phase distribution characteristics more
comprehensively, based on the analysis of experimental
results by different researchers about local void fraction
distribution under different methods for bubble generation
in vertical upward twophase flow with pipe inner diameters
ranged from 2086.4mm, Serizawa & Kataoka (1988)
believed the local void fraction distributions included four
different patterns: wall peak, core peak, intermediate peak
and transition distribution, and presented the distribution
pattern map for local void fraction in fully developed
vertical upward gasliquid twophase flow. And then,
researchers investigated the local void fraction distributions
by different measurement methods under different ways for
bubble generation, pipe diameters and inlet void fractions.
And the typical core peak and wall peak distributions of
local void fraction were both observed in almost results
(Zun 1988: Reyankar & Ishii 1992: Hibiki & Ishii 1999).
According to the above analysis, we can understand that the
dividing of local void fraction distribution in gasliquid
twophase flow is actually a qualitative method, which leads
to discontinuity among different distribution types. Recently,
Shen & Mishima et al. (2005) analyzed the local void
fraction distribution of gasliquid twophase upward flow in
vertical pipe with diameter of 100mm quantitatively by
introducing the concept of Skewness in statistics. But
during the calculation of Skewness, the weighted average of
cross area of experimental section was used. And the
distribution of wall peak predicted by the calculation of
Skewness did not appear in experiment. So the method
based on Skewness concept should be still improved further
more.
Though the research on local void fraction distribution of
fully developed gasliquid twophase flow has been carried
out frequently in the past years, for liquidliquid twophase
flow with the same deformable interface, such as oilwater
twophase flow: the attention for local phase fraction has
been paid much less to. Almost research about oilwater
twophase flow has been mainly focused on the prediction
of flow patterns and pressure loss due to the industrial
demand. The relevant research on distribution
characteristics of local oil fraction is limited. For example,
Vigneaux & Chenais (1988) and Farrar (1996) measured the
local oil fraction of upward oilwater twophase flow in
vertical pipe by highefficiency probe and hotfilm
technique and observed the wall peak distribution of local
oil fraction and homogeneous distribution respectively,
which rarely appeared in gasliquid twophase flow. As we
know: the flow patterns in oilwater twophase flow include
oilinwater and waterinoil two types, which lead to
different interphase movements (Flores 1997) So the local
oil fraction distribution shows great difference
correspondingly. On the other hand, the special
phenomenon of phase inversion in oilwater twophase flow,
the prediction of local oil fraction is much more
complicated.
In order to investigate the phase distribution characteristics,
1~~ ' ' '
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Paper No
based on the measurement results of local phase parameter
of upward dispersed oilwater twophase flow in vertical
pipe, the distribution characteristics of local oil fraction is
analyzed quantitatively by the concept of Skewness and
Kurtosis in statistics in this paper. And the characteristics of
Skewness and Kurtosis with the flow conditions are also
obtained.
Nomenclature
Figure 2: Schematic diagram of doublesensor conductivity
probe
B
KU Kurtosis coefficient
SK Skewness coefficient
VFD W/O
O/W CF
o
*
*
Greek letters
a phase fraction
Subsripts
o oil phase
w water phase
D O/W
* ee ee*
VFD O
"o0.1
Experimental System and Measurement Method
O O O
0.01 L
0.1
J, /m s"'
Figure 3: Flow conditions based on the oilwater flow
regime map given by Flores & Sarica et al. (1998)
Results and Discussion
Distribution characteristics of local oil fraction
*core peak *transition VFD ON
wall peak v no peak
. .ONVCF
VFD WIO
0 11 0 1
Jo [m/s]
Figure 4: The distribution pattern map for oil phase fraction
of dispersed oilwater upward twophase flow in vertical
According to the measurement by doublesensor probe, the
distribution pattern map of oil phase fraction under
experimental conditions, as shown in Fig.4. Similar to the
analyzing method for local void fraction distribution, the
distribution patterns of local oil fraction include core peak,
wall peak, no peak and transition distribution in the
experiment.
Figure 1: Schematic diagram of experimental loop: (1)
separator; (2) water tank: (3) oil tank: (4) water pump; (5)
oil pump; (6) filter: (7) mass flow meter: (8) magnetic flow
meter: (9) mixing chamber: (10) mechanical traverser of
probe: (11) test section: (12) differential pressure transducer:
(13) digital highspeed camera; (14) light compensation
box: (15) light source and reflection board; (16)
measurement circuit of probe: (17) PC with highspeed
acquisition board inside.
The experiment in upward dispersed oilwater twophase
flow was carried out on oilwater twophase flow
experimental system in State Key Laborery of Multiphase
Flow of Xi'an Jiaotong University, as shown in Fig.1i. The
measurement for local phase fraction in dispersed twophase
flow was based on doublesensor conductivity probe, as
discussed by Zhao & Guo (2005) and Zhao & Guo (2006)
and shown in Fig. 2, which was proposed firstly for
measuring local phase fraction in twophase flow by Neal &
Bankofff (1963). The flow conditions in this paper based on
the oilwater flow pattern map given by Flores & Sarica et
al. (1998) are shown in Fig. 3, which indicates that the flow
conditions are almost in the regime of dispersion oil in
water (D O/W), partly in the transition regime between oil
in water chumn flow (O/W CF) and very fine dispersion oil
in water (VFD O/W), which are the right conditions for
doublesensor conductivity probe measurement application.
From the figure, we can understand that the distribution
characteristics of local oil fraction in upward dispersed
oilwater twophase flow have greatly changed with the
increase of oil phase superficial velocity when the
superficial velocity of water phase is less than 0.8m/s. When
the oil velocity is low, the oil drops distribute around the
core region of the pipe section, leading to a core peak
distribution of local oil fraction. With the increase of the oil
velocity: due to the effects of transverse force, such as lift
force, the oil drops transfer to the wall gradually, causing a
transition peak between the core region and wall region.
And the transition peak distribution of local oil fraction
transforms to wall peak distribution with the further increase
of oil velocity. And we can understand from Fig.4 that the
flow conditions arrange for wall peak distribution of local
oil fraction is very extensive. When the superficial velocity
of water phase is beyond 0.8m/s, the turbulence effects of
continues phase is strong enough to make the oil drops
break up into smaller ones, and the mixing between the
water phase and oil phase becomes more homogeneous.
With the increase of oil velocity, the peak of oil fraction
distribution around the wall gradually reduces, and the
width of the peak gradually extends towards the core region
of pipe section until the peak disappears. And a more
homogeneous distribution of oil phase appears on the pipe
section.
The distribution pattern map for local oil fraction in
oilwater twophase flow is greatly different from that for
local void fraction in gasliquid flow. Under the
experimental conditions in this paper, the intermediate peak
distribution observed in gasliquid flow with higher
superficial velocity of liquid phase did not appeared. With
the increase of superficial velocity of water, a homogeneous
distribution of oil fraction was observed on the pipe section.
Moreover, core peak and transition peak appeared when
superficial velocities of dispersed phase and continuous
phase were both lower. While in the pattern map of local
void fraction distribution by Serizawa & Kataokao (1988),
the core peak was only observed in the transition regime
between bubbly flow and slug flow.
Quantitative description for local oil fraction
From the above analysis, it is known that the phase fraction
distribution is qualitatively divided into some patterns based
on the experimental results when investigating the
distribution characteristics of local phase fraction in
twophase flow in early years, which leading to
discontinuity during the description obviously. In order to
overcome this limitation, we used the concept of Skewness
and Kurtosis in statistics and analyzed the distribution
characteristics of local oil fraction in dispersed oilwater
twophase flow quantitatively in this paper.
Figure 5: The principle of Skewness describing the
asymmetry degree of a distribution
Skewness is the measurement of deflection direction and
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
degree for a given distribution. Shen & Mishima et al. (2005)
introduced the concept of Skewness in order to analyze the
distribution characteristics of local oil fraction on pipe
section with large pipe diameter in vertical upward
gasliquid twophase flow. When the local phase fraction on
the section radial direction is symmetrical with the center
between the wall and core of the section, the Skewness is 0.
When the local phase fraction distribution is deflected to the
left direction, meaning a typical core peak distribution, the
Skewness is negative. When the local phase fraction
distribution is deflected to the right direction, which means
a typical wall peak distribution, the Skewness is positive.
And a larger of absolute value of Skewness indicates a
larger deflection degree for the distribution, as shown in
Fig.5. The Skewness is calculated by
.SK r=~ (1)
and B is the central moment of the distribution. Shen &
Mishima et al. (2005) used weighted average of section area
when analyzing the phase fraction of gasliquid twophase
flow to calculate B, which increases the contribution of
local phase fraction around wall in some degree. In order to
reduce the influence, a weighted average of radial position
was used to calculate in this paper. So the B, can be written
B,= R l (2)
a71 is crossav'erage oil raction.
Fig. 6 shows the Skewness comparisons between local oil
fraction distributions in upward dispersed oilwater
twophase flow in vertical pipe calculated by the model in
this paper and by the model of Shen & Mishima et al.
(2005). In the figure, variation tendencies for Skewness of
oil fraction distributions obtained by the two models are
almost the same except some differences in numerical value.
Except the conditions under the lower superficial water
velocity: the Skewness values of local oil fraction
distribution by the model in this paper are all larger than
that by model of Shen & Mishima et al. (2005). When the
water superficial velocity is 0.445m/s and oil superficial
velocity is 0.2m/s, as shown in Fig. 7 in detail, though no
obvious wall peak distribution appeared, the value of local
oil fraction around wall is a little higher than that of core
region. Take this distribution for example: the Skewness
value obtained in this paper is 0.0249. But the Skewness
value is 0.092 by model of Shen & Mishima et al. (2005),
which means a deflection direction of left for the
distribution of local oil fraction. And this is inconsistent
with experimental result. When the oil superficial velocity is
0.023m/s, the local oil fraction distribution is transition
distribution, also shown in Fig.7, a higher value of oil
fraction appeared around the core region. For this
distribution, a Skewness value of 0.478 was obtained by
the model in this paper, while 0.071 by the model of Shen &
Mishima et al. (2005), which is also inconsistent with
experimental result.
When measuring the local oil fraction by doublesensor
probe on the radial direction of section with equivalent
distance, annular area near the wall is larger than that near
the core. The method with weighted average of section area
Paper No
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
B:
B, is still calculated by equation (2).
will increase the weighted average value near the wall. In
other words, the equivalent distance distribution along the
radial direction will be stretched near the wall and will be
contracted near the core, which will make the peak of the
local oil fraction distribution migrate to the left direction
(core region). So the method to calculate Skewness with
weighted average of radial position is more reasonable than
that of section area.
Present work
Shen et al.
4 df0.445m/s
0.00 0.07 0.14 0.21
a, [ms]
Figure 6: Skewness comparisons between the local oil
fraction distributions calculated in this paper and in model
of Shen & Mishima et al. (2005)
Figure 8: The principle of Kurtosis describing the degree
for peak concentration of a distribution
In the following, the Skewness and Kurtosis will be applied
to describe the distribution characteristics of local phase
fraction. Fig. 9 shows the Skewness for local oil fraction
distribution of upward dispersed oilwater twophase flow
in vertical pipe against the superficial velocity of oil phase.
From the figure, it is obvious that the Skewness arranged
from 0.654.07 increases firstly and then decreases with the
increase of oil phase velocity. The Skewness is slightly less
than 0 under lower oil velocity, which reflects a core peak
distribution of local oil fraction or a transformation region
from core peak to wall peak. With the increase of oil phase
superficial velocity, the Skewness of oil fraction distribution
is larger than 0 obviously, indicating a typical wall peak
distribution. And the Skewness begins to decrease and is
close to 0 with the further increase of oil phase velocity,
which indicates the wall peak distribution of oil fraction
gradually disappeared. That is consistent with Fig. 7.
J =0.224m/s
J 0.335m/s
4 A J =0.444m/s
0. O 0.07 0.14 0.21
o, [mis]
Figure 9: Skewness distribution of local oil fraction
against the superficial velocity of oil phase
VI I I I I I
0.0 0.2 0.4 0.6 0.8 1.0
Figure 7: Distribution charac eitics of local oil fraction
with superficial water velocity of 0.445m/s
Similar to Skewness, the Kurtosis for local oil fraction
distribution of upward dispersed oilwater twophase flow in
vertical pipe is also investigated in this paper. Kurtosis is the
measurement for concentrative degree of some distribution
compared to normal school peak, as shown in Fig. 8. Due to
the Kurtosis for normal school is 3, when the Kurtosis for
local oil fraction distribution of dispersed oilwater
twophase flow is larger than 3, the local oil fraction
distribution should have an abrupt peak; when the Kurtosis
is small than 3, the local oil fraction distribution should have
a flat peak. The Kurtosis is calculated as
Paper No
K KU <
^ "
J,=0.445m/s
. Jo=0.023m/s
* Jo=0.067m/s
o,=0.11Omis
' o=0.200m/s
r
.* .. .. *. *
* * . . .
I
ti0.3.
10.1 .
0.
=Jo=0.011m/s
Jo=0.067m/s
4  Jo=0.112m/s
Jo=0.156m/s
2
C.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
J[m/s]
Figure 10: Skewness distribution of local oil fraction
against the superficial velocity of water phase
Fig. 10 shows the Skewness for local oil fraction
distribution of upward dispersed oilwater twophase flow in
vertical pipe against the superficial velocity of water phase.
We can understand that the Skewness does not vary
obviously except for the low water superficial velocity with
oil velocity of 0.067m/s and 0.112m/s. the Skewness of
local oil fraction distribution is negative with oil superficial
velocity of 0.011m/s, indicating a core peak distribution or a
transition distribution. The Skewness of local oil fraction
distribution is much higher than 0 with oil velocity of
0.067m/s, 0.112m/s and 0.156m/s, meaning typical wall
peak distributions of oil fraction.
Fig. 11 shows the Kurtosis of local oil fraction distribution
of upward dispersed oilwater twophase flow in vertical
pipe against the superficial velocity of oil phase. In the
figure, the Kurtosis arranges from 1.98 to 19.52. And the
Kurtosis increases firstly and then decreases with the
increase of oil phase velocity. With the lower oil phase
velocity, the Kurtosis is obviously less than 3, indicating a
flat peak distribution of oil fraction and a concentrating
degree weaker than normal school. And with the increase of
oil phase velocity, Kurtosis increases obviously and reaches
the maximum. In other words, the distribution peak is ver
abrupt when the oil fraction distribution is a wall peak
distribution. With the further increase of oil velocity, the
distribution of oil fraction transforms to homogeneous
distribution or core peak distribution with a Kurtosis value
less than 3.
Figure 12 shows the Kurtosis for local oil fraction
distribution of upward dispersed oilwater twophase flow in
vertical pipe against the superficial velocity of water phase.
From the figure, we can understand that the Kurtosis is less
than or closed to 3, not obviously varied with the increase of
water phase superficial velocity under the conditions for oil
velocity of 0.011m/s and 0.156m/s, which indicates a flat
peak distribution of local oil fraction. That is because the
distribution of local oil fraction is flat core peak distribution
or homogeneous distribution, not an abrupt wall peak
distribution under the above conditions. When the oil
velocity is less than 0.067m/s, the Kurtosis decreases with
the increase of water phase velocity. That is because the
local oil fraction distribution transforms from an abrupt wall
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
peak distribution to a flat core peak distribution or
homogeneous distribution.
24. aJ =0.224m/s
21~ w=0.335m/s
A J =0.444m/s
S18.
15. .
0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21
Jolm/s]
Figure 11: Kurtosis distributions for local oil fraction
against the superficial velocity of oil phase
24. _ d=0.011m/s
21. Jo=0.067m/s
J = 0. 112mis
Jo=0.156m/s
0. 04 06 .
12"/s
9.ue1:Kroi itiutosfrlclolfato
6.is h ueriilvlctyo ae hs
,codngt h anayi bvw a nesadta
Figre12 Kurtosi sdtrbios for local oil fraction itbuo acrn o
lagist thuae suerfcalh lciyofwtr hs
Acorin to te analyss aboee anunestndtht h
Skens an Kurosi fo oa olfatonhv h
33.Re.235 Re 300004579 4.
KU = 0.00122 +1.839
Re 4
(5)
and the Reynolds number for oil phase and water phase are:
Reo ii (6)
Re, =Li (7)
Paper No
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
appeared in local oil fraction distributions. And the flow
conditions for core peak and wall peak in oilwater
twophase flow are also different from that in gasliquid
twophase flow.
In order to overcome the discontinuity introduced in
distribution pattern map for local phase fraction, the
Skewness and Kurtosis in statistics were used to describe
the characteristics of local phase fraction. And according to
the experimental data, the method of quantitative
description for local oil fraction distribution was verified
and the variation characteristics for Skewness and Kurtosis
with the flow conditions were also obtained. The Skewness
and Kurtosis both increased firstly and then decreased with
the increase of superficial velocity of oil phase, which
dynamically described the processes of local oil fraction
distribution transforming from core peak to wall peak and
then transforming from wall peak to core peak.
Finally: according to the flow conditions in oilwater
twophase flow: the prediction model for Skewness and
Kurtosis of local oil fraction distributions was set up.
However, due to the limitation of single peak assumption
for Skewness and Kurtosis, some differences exist between
prediction model and experimental results, which should be
improved in the future.
Acknowledgements
We gratefully acknowledge the National Science
Foundation of China (No. 50536020) and Research Program
for Excellent State Key Laboratory (No.50823002).
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15.[
Fiur 1: omarsos f uross etee pedc*o
results~~~~~ a eprmna sut
Fi.10 i.1 r tecmaioso peito eu
and* *xeimna rsl o kwe a Ktsi r c
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