Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Effect of pipe diameter on pressure drop in vertical twophase flow
V. HernandezPerez, M. Zangana, R. Kaji and B.J. Azzopardi
Process and Environmental Engineering Research Division, Faculty of Engineering, University of Nottingham,
University Park, Nottingham, NG7 2RD, United Kingdom
Email: enxvh @nottingham.ac.uk
Keywords: pipe diameter, pressure drop, vertical
Abstract
Accurate prediction of the pressure drop in a pipe is of paramount importance for the design of a multiphase system. A wide
range of pipe diameters are used in different applications. In this work, data for twophase pressure drop on different vertical
pipe diameters are presented, and the effect of the pipe diameter has been analysed. In all cases the twophase flow was
airwater. Different twophase flow facilities located at Nottingham were employed to fit the pipes of diameters 19 mm, 38
mm, 67 mm and 127 mm in vertical airwater flow. In each pipe diameter, a differential pressure cell was employed in order to
measure the pressure drop, using similar flow conditions.
As expected, it was found that the pressure drop decreases as a function of the pipe diameter. This is particularly true for gas
superficial velocities higher than 2 m/s, as in this case the pressure drop is dominated by the frictional component. Based on
this data, an evaluation of different models and correlations available in the literature is carried out. The standard deviation in
its relative form was calculated, taking into account the size of the fluctuations with respect to the mean value. It was found
that this parameter is increasing when the pipe diameter is increased
Introduction
One of the main thermalhydraulics parameters in flow
recirculation systems is the pressure drop. It represents the
energy required for operating a pumping system, as pump
capacity must be matched properly with the system
requirements. Therefore it is important to know as exactly
as possible the amount of pressure drop. A considerable part
of this pressure drop occurs along vertical pipes, and it
becomes particularly important when the pipes are long.
Along a vertical pipe, the pressure drop is associated with
gravitational body force, acceleration forces and frictional
shear stress, meaning that pressure drop depends on many
parameters, such as flow conditions, fluid properties, and
pipe diameter.
Several studies on twophase flow pressure drop have been
reported in the literature. The early work of Baker (1954),
Griffith and Wallis (1961), Bonnecaze et al. (1971),
Grescovich and Shrier (1971), Chen and Speding (1981),
Jepson and Taylor (1993) provided data for the design of
equipment on twophase flow. However, knowledge of the
pressure drop at different conditions is often required, and
different methods have are usually employed for these
predictions. This includes the homogenous flow model, the
separated flow approach, direct empirical correlations and
flow pattern specific models. The first prediction approach
used was direct empirical correlations. These only apply for
flow conditions similar to those used in their development,
for instance, the Beggs and Brill (1973) correlation allows
liquid holdup and pressure drop computation for all
inclination angles, including in downward direction. In the
homogenous flow model the twophase mixture is treated as
a single fluid with mixture properties. It is usually applied
for bubbly flow. On the other hand, in the twophase flow
multiplier model the twophase pressure drop is calculated
from the single phase pressure drop by multiplying by a
twophase multiplier. A large number of correlations are
available for twophase multiplier; however, uncertainty
remains high due to large scatter among data. In an effort
to overcome the restrictions of empirical correlations,
researchers have moved towards the prediction of pressure
drop using a mechanistic flow approach. The unified
mechanistic models of Gomez et al. (2000) and Kaya et al.
(2001) are based on the principle that different flow
interaction mechanisms apply in different flow patterns. In
order to apply the comprehensive unified model for
twophase flow, first it is necessary to determine the flow
pattern and then for each predicted flow pattern, a separate
hydrodynamic mechanistic model to calculate the pressure
drop is applied.
One of the main factors influencing the pressure drop is
indeed the pipe diameter, due to the wide range of pipe
diameters used in different applications such as in chemical,
power, oil/gas production and oil refining plants. In fact,
Singh and Griffith (1970) reported that different pipe
diameters might have different effect on the pressure drop.
It is therefore important to study the flow behaviour in more
than one pipe diameter. However in the literature there is a
Paper No
lack of data on the effect of pipe diameter on pressure drop
in vertical flow.
In this work, the effect of pipe diameter on pressure drop in
twophase vertical flow is addressed by using the data of the
measurements carried out in four different pipe diameters,
and the effect of the pipe diameter is analysed.
Experimental arrangements
Four different pipe diameters have been employed, two of
them on the same facility as described below. The pipe
diameters are: 19 mm, 38 mm, 67 mm and 127 mm. In order
to perform a systematic comparison of the data, similar flow
conditions of liquid superficial velocities have been
reproduced in all of the facilities. In all cases the twophase
flow was airwater. All pressure drops were measured with
differential pressure cells (DP cell) coupled to Labview
software (National Instruments). The DP cells were
equipped with purging systems to ensure a line continuous
full of liquid from the pressure tappings to the DP cell. The
calibration curve of the DP cell followed a linear behaviour,
as stated by the manufacturer. Table 1 summarises the
relevant features of the sources of pressure drop data.
Table 1 Sources of data presented in this work
Pipe diameter Pipe length (m) Distance
(mm) between
DP cell taps
19 6 1.5
38 6 0.76
67 6 0.85
127 10 1.65
The 19 mm diameter pipe facility consists of a closed loop,
which has also been employed by Kaji et al. (2007). Figure
1 shows a schematic diagram of this facility. Both the 38
and 67 mm pipes were mounted in an inclinable steel frame
set to vertical, one at a time, as described in Hernandez
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Perez et al. (2007). Figure 2 shows a schematic diagram of
this facility. The data presented here was taken with the
test pipe mounted vertically. A closed loop facility was
used in the case of the 127 mm pipe, described in detail by
van der Meulen et al. (2009). Figure 3 shows a schematic
diagram of this facility.
Figure 1: Schematic diagram of the 19 mm rig
Test section
Figure 2: Schematic diagram of the 38 mm and 67mm rig.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Figure 3: Schematic diagram of the 127 mm rig
Results
In this work, time series of pressure gradient were obtained
directly from the DP cell. Compensation was made for
tapping lines of different heights which were full of liquid.
In general, it has been found that the time series for pressure
drop in the different pipes are similar. For the particular
situation illustrated in Figure 4, it can be observed that the
fluctuations in the pressure gradient are comparable but the
average value is higher for the 67 mm pipe. Due to the
separation distance between the two pressure tapings (which
means that the pressure gradient is averaged over this
distance) fluctuations produced by the liquid slugs are not
clearly observed, the shape of the PDF consists of one single
peak and the PSD frequency does not match the frequency
value from the liquid holdup, which has been reported in
HernandezPerez (2007). This is probably due to the
liquid hold up value being a local value and the pressure
drop being essentially an integral value over the pipe lengths
as given in Table 1.
10 10
ft o o
0 20 40
Time (s)
0 5 10
Pressure gradient (kPa/m)
x 107
0
0 1 2 3
Frequency (Hz)
38mm
20 40 60
Time (s)
0 5 10
Pressure gradient (kPa/m)
x 107
10
0123
0 1 2 3
Frequency (Hz)
The pressure drop in twophase flow can depend on a
significant number of variables, among them the conduit
diameter is of paramount importance. Figures 5 and 6 show
the effect of the pipe diameter on the average total pressure
drop for a liquid superficial velocity of 0.2 m/s and 0.7 m/s
respectively. At low gas superficial velocities, the pressure
drop decreases dramatically when the gas superficial
velocity increases, with the effect of pipe diameter being
very small.
At higher gas superficial velocities, the effect of the pipe
diameter is more remarkable. As expected, it was found that
the pressure drop decreases as a function of the pipe
diameter. This is particularly true for gas superficial
velocities higher than 2 m/s, as in this case the pressure drop
is dominated by the frictional component, which increases
dramatically as the diameter decreases. This might become
a very important issue in applications where even smaller
diameters are used, such as in refrigeration and air
conditioning systems. Baker (1954), states that the pressure
loss of a fluid flowing through a pipe is inversely
proportional to the fifth power of the pipe diameter.
a
0.8
06
404
I
0
' 0.2
C o
67mm
Figure 4: Comparison of time series, Probability density
Function and Power Spectral Density obtained from the
pressure gradient for 38 and 67 mm diameter pipes
respectively. Superficial velocities (m/s); liquid=0.7 and
gas=2.9.
Gas superficial velocity (n s)
Figure 5: Pressure gradient, liquid superficial velocity = 0.2
m/s and several pipe diameters
Paper No
19mm
0 A 38 mm
A 0 67 mm
1 127mm
A AA
Paper No
1 10
Gas superficial velocity (m/s)
Figure 6: Pressure gradient, liquid superficial velocity = 0.7
m/s and different pipe diameters
Discussion
Pressure drop correlations find extensive application in the
design of systems and components in industry. There has
been little work reported in which twophase pressure drop
is treated as a topic unique in itself, Spedding et al. (1982) is
perhaps the most extensive. Most models found today are
applicable, if not actually derived for, a specific flow pattern
or regime, for instance Hasan and Kabir (1988). One of the
most widely used correlations for prediction of pressure
drop is that of Beggs and Brill (1973). A comparison of the
present data with the Beggs and Brill's correlation is
presented in Figure 7. It can be deduced that this correlation
performs better for the 38 and 67 mm pipe diameters. This is
not surprising; due to the fact that they developed their
correlation based on the data they gathered using pipe
diameters of 25 and 38 mm. For the case of 19 and 127 mm
the correlation under predicts the experimental data,
particularly for the case of 19 mm, at the lowest and highest
pressure drops.
Measured pressure drop (kPalm)
Measured pressure drop (kPalm)
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Application of the homogeneous approximation to the
prediction of pressure drop for the experimental conditions
employed in this work gives the result shown in Figure 8. In
this case method performs better for the case of 38 mm
diameter.
*19 mm
A 38 mm
067mm
A 127 mm
"U,
1 I i i i i I i 1 i l I [U
67 mm
10
5 / +
6
0
0 5 10 15
Measured pressure drop (kPalm)
15
38 mm
10
5
0 5 10 15
Measured pressure drop (kPalm)
15
127 mm
10
5 .
0 5 10 15
Measured pressure drop (kPalm)
Figure 8: Comparison between the experimental data and
the homogeneous model, liquid superficial velocity: *
0.2m/s; 0 0.7 m/s
The separated flow approach using a twophase flow
multiplier based on the liquid phase has commonly been
adopted to calculate pressure drop. The literature contains
an innumerable number of relationships and models for
calculating the twophase multiplier. Using the Chisholm
(1967) algebraic correlations for twophase flow multiplier
and slip ratio, a comparison of the separated model
approach against the present data is performed in Figure 9.
It can be observed that in this case the best agreement is
obtained for the 67 mm diameter pipe.
15
19 mm
10
5
0
0 5 10 15
Measured pressure drop (kPa/m)
E 15
S10 38 mm
. 10
m 0
U 0 5 10 15
Measured pressure drop (kPalm)
0e
0 5 10
Measured pressure drop (kPalm)
Figure 7: Comparison between the experimental data and
the Beggs and Brill's correlation. Liquid superficial
velocity: 0.2m/s; 0 0.7 m/s
S0 0 '
0 5 10 15 0 5 10 15
Measured pressure drop (kPa/m) Measured pressure drop (kPa/m)
Figure 9: Comparison between the experimental data and
the separated flow model. Liquid superficial velocity: *
0.2m/s; 0 0.7 m/s
15
 19mm
0
10
100 U 0 5 10 15
Measured pressure drop (kPalm)
0 5 10
Measured pressure drop (kPalm)
Paper No
Another way of calculating the twophase flow multiplier is
used in the Friedel (1979) correlation. Figure 10 shows the
corresponding comparison between the pressure drop
database reported in this work and the Friedel correlation.
The result is very similar
Chisholm method.
19 nmn
0 5 10 15
Measured pressure drop (kPalm)
0 5 10 15
Measured pressure drop (kPalm)
to that obtained using the
S15
38 mrn
10
5
0 1
0
S 0 5 10 15
Measured pressure drop (kPalm)
0 5 10 15
Measured pressure drop (kPalm)
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
observed that this parameter usually gets higher when the
pipe diameter is increased. However, it takes higher gas
superficial velocity. This can be associated with the fact that
a flow pattern transition to intermittent flow takes place at
lower gas superficial velocities in smaller diameter pipes.
For instance, it has been reported that for 127 mm, slug flow
does not occur, OmebereIyari et al. (2008).
0 4 8 12 16 20
Gas superficial velocity (m/s)
Figure 10: Comparison between the experimental data and
the Friedel (1979) correlation. Liquid superficial velocity:
* 0.2m/s; 0 0.7 m/s
For the 19 mm pipe diameter, with both the Chisholm and
Friedel multipliers, the separated flow model is observed to
be poor. Particularly at low (0.2 m/s) liquid superficial
velocity, where the pressure drop also happens to be the
lowest. The reason for this to happen could be attributed to
the fact that in this situation the model seems to be more
sensitive to small changes in some of the parameters
involved in the overall calculation. For instance, in this case
the LockartMartinelli parameter becomes very small and
the twophase multiplier increases, which gives as a result a
higher predicted pressure drop. The way the friction factor is
calculated can also have an effect.
Based on the comparisons presented in figures 7 to 10, it
can be concluded that these methods should be used with
caution, as they are not very accurate to predict the pressure
drop in some cases.
Due to the fluctuating nature of the pressure drop signals
obtained, we need to be aware that the average value
presented in the previous section should not be taken as the
design pressure drop, as the critical pressure drop can get
bigger than that. One way of analysing this behaviour is
by means of the standard deviation. Although the standard
deviation is a good measure of the precision of a given set
of data, it can be difficult to compare the standard deviation
from two different measurements directly. Another way of
looking at the standard deviation is in relative form. This
takes into account the size of the fluctuations with respect to
the mean value. From Figures 11 a, b and c, it can be
E 0.4
0.3
 0.2
0.1
C 0
5 0.5
I 0.4
 0.3
.
o 0.2
0.1
I a
0 4 8 12 16 20
Gas superficial velocity (m/s)
+40.2 m/s
40.7 m/s
0 4 8 12 16 20
Gas superficial velocity (m/s)
Figure 11: Relative standard deviation of the pressure
drop. Diameters : a) 38 mm, b) 67 mm and c) 127 mm.
Paper No
A more complex approach is the mechanistic modelling.
The first stage of this method is the prediction of the flow
pattern. Therefore, the success of a comprehensive unified
mechanistic approach depends upon the accurate prediction
of the specific flow pattern. In addition, improvement might
be required in the closing relationships in order to get a fully
accurate prediction.
The comparisons reported above have been against what are
usually termed engineering methods. However, it can be
seen that there is a very useful data base available. The
next stage will be to test it against mechanistic models.
Conclusions
In this work a study of the effect of pipe diameter on the
pressure drop in vertical twophase flow has been carried
out. The following conclusions can be drawn:
The pressure drop decreases as a function of the pipe
diameter. This is particularly true for gas superficial
velocities higher than 2 m/s, as in this case the pressure drop
is dominated by the frictional component.
Based on this data, an evaluation of different models and
correlations available in the literature was carried out. It can
be concluded that methods for pressure drop calculation
should be used with caution, as they are not very accurate to
predict the pressure drop in some cases.
Acknowledgements
This work has been undertaken within the Joint Project on
Transient Multiphase Flows and Flow Assurance. The
Authors wish to acknowledge the contributions made to this
project by the UK Engineering and Physical Sciences
Research Council (EPSRC) and the following: Advantica;
BP Exploration; CDadapco; Chevron; ConocoPhillips;
ENI; ExxonMobil; FEESA; IFP; Institutt for Energiteknikk;
Norsk Hydro; PDVSA (INTERVEP); Petrobras;
PETRONAS; Scandpower PT; Shell; SINTEF; Statoil and
TOTAL. The Authors wish to express their sincere gratitude
for this support.
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7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
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