Phase inversion and associated phenomena in oil-water vertical pipeline flow.
Hu, Bin ; Angeli, Panagiota
Phase inversion and its associated phenomena are experimentally
investigated in co-current upward and downward oil-water flow in a
vertical stainless steel test section (38 mm I.D.). Oil ([rho].sub.o]=
828 kg/m3, [[micro].sub.o]= 5.5 mPa s) and tap water are used as test
fluids. Two inversion routes (w/o to o/w and o/w to w/o) are followed in
experiments where either the mixture velocity is kept constant and the
dispersed phase fraction is increased (type I experiments), or the
continuous phase low rate is kept constant and that of the dispersed
phase is increased (type II experiments). By monitoring phase continuity
at the pipe centre and at the wall it was found that phase inversion
does not happen simultaneously at all locations in the pipe
cross-section. In type I experiments, the velocity ratios
([U.sub.o]/[U.sub.w]) where complete inversion appeared acquired the
same constant value in both low directions, although the phase inversion
points, based on input phase fractions, were different. In contrast to
previous results in horizontal lows, frictional pressure gradient was
found to be minimum at the phase inversion point. The interfacial
energies of the two dispersions before and after phase inversion,
calculated from the measured drop sizes, were found to be different in
contrast to the previously suggested criterion of equal energies for the
appearance of the phenomenon. In type II experiments the phase inversion
point was found to depend on mixture velocity for low and medium
velocities but not for high ones. In all cases studied an ambivalent region, commonly reported for inversion in stirred vessels, was not
observed.
L'inversion de phase et ses phenomenes associes sont etudies
experimentalement dans un ecoulement huile-eau dans une section
d'essai en acier inoxydable verticale (38 mm de diametre
interieur). De l'huile ([rho].sub.o]= 828 kg/m3, [[micro].sub.o]=
5,5 mPa s) et de l'eau du robinet sont utilisees comme guides
d'essai. Deux voies d'inversion (de w/o a o/w et de o/w a w/o)
sont etudiees dans les experiences, dans lesquelles soit la vitesse de
melange est gardee constante et la fraction de phase dispersee est
augmentee (experiences de type I), ou soit le debit de phase continue
est garde constant et la phase dispersee est augmentee (experiences de
type II). En surveillant la continuite des phases au centre de la
conduite et a la paroi, on a trouve que l'inversion de phase
n'arrive pas simultanement a tous les endroits de section
transversale de la conduite. Dans les experiences de type I, les
rapports de vitesse ([U.sub.o]/[U.sub.w]) ou apparait l'inversion
complete, acquierent la meme valeur constante dans les deux directions
de l'ecoulement, meme si les points d'inversion de phase,
bases sur les fractions de phase d'entree, sont differents.
Contrairement aux resultats anterieurs dans les ecoulements horizontaux,
on a trouve que le gradient de pression frictionnel etait minimum au
point d'inversion de phase. Les energies interfaciales des deux
dispersions avant et apres l'inversion de phase, calculees
d'apres les tailles de gouttes mesurees, s'averent differentes
que dans le cas du critere anterieurement suggere pour l'apparition
des phenomenes. Dans les experiences de type II le point
d'inversion de phase s'avere dependre de la vitesse du melange
pour des vitesses faibles et moyennes mais non pour des vitesses
elevees. Dans tous les cas etudies, on n'a pas observe la region
ambivalente couramment signalee pour l'inversion en reservoir
agite.
Keywords: phase inversion, vertical flow, two-phase flow,
liquid-liquid flow, ambivalent region, pressure gradient
Immiscible liquid-liquid dispersions, where usually one phase is
aqueous (e.g. water) and the other is organic (e.g. oil), are very
common in a number of applications such as crude oil transportation and
production of food and pharmaceuticals. Generally, for dispersions
formed by two immiscible liquids one phase acts as the continuous medium
entrapping the other phase in the form of drops. Phase inversion is then
defined as a phenomenon of phase interchange, whereby the continuous
phase changes to become dispersed and the dispersed phase becomes
continuous. This phenomenon often occurs spontaneously at some critical
operational condition, for example volumetric phase fraction or power
input (e.g. velocity for pipeline systems or agitation speed for stirred
vessels). Knowing when phase inversion appears is important for
industries as the change in phase continuity will lead to a system with
different properties (i.e., rheology). In many cases phase inversion is
part of the process (e.g. production of margarine or polymerisation). Of
significance to transportation of dispersions is the observed increase
in pressure gradient accompanying phase inversion. In the petroleum
industry, for example, where crude oil and water need to be transferred
from seabed to offshore to plant, failure to predict this phenomenon can
result in substantial decrease of oil productivity and pipeline
capacity.
A large number of previous studies on phase inversion have been
carried out in dispersions generated by mechanical agitation in batch or
semi-batch systems (for a review see Yeo et al., 2000). The results
clearly indicated that the critical volume fraction of dispersed (or
organic) phase where inversion appears (phase inversion point) varies
with system and is affected by a number of physical and operational
parameters, such as liquids' properties, container geometry and
initial conditions. In contrast to stirred vessels significantly less
work has been carried out on phase inversion during pipeline flows.
A number of researchers have investigated experimentally the
occurrence of phase inversion and its associated phenomena in oil-water
horizontal pipe flow (Arirachakaran et al., 1989; Pal, 1993; Nadler and
Mewes, 1997; Soleimani, 1999; Ioannou et al., 2004, 2005). The main
aspects of these studies are summarized in Table 1. Generally, it is
found that the phase inversion point is dependent on many system
parameters, e.g. viscosity ratio, velocity, pipe diameter and material.
Previous experiments suggested that the more viscous oil tends to form
the dispersed phase while the less viscous water is likely to be
continuous. The critical input water fraction required for inverting a
water-in-oil dispersion decreased as the oil viscosity increased. For
oil-water dispersed flow, the pressure drop in the pipeline could differ
greatly between an oil-in-water and a water-in-oil system. Pal (1993)
observed an abrupt increase of the mixture viscosity at phase inversion
from experimental data in laminar pipeline flow. In turbulent dispersed
flow, a large pressure drop during phase inversion has also been widely
reported, which suggests a dramatic increase in mixture viscosity
(Arirachakaran et al., 1989; Angeli and Hewitt, 1998; Soleimani, 1999;
Ioannou et al., 2005). Based on the experimental data obtained from
horizontal pipe flow, Arirachakaran et al. (1989) reported that the
mixture velocity has little effect on the inversion point as long as
there is no transition in the flow regime. Furthermore, Ioannou et al.
(2005) investigated the effect of pipe diameter and wettability on phase
inversion by using different sizes of stainless steel and acrylic pipes.
Their experiments clearly showed an ambivalent range (within which
either phase can be dispersed) in the large diameter (60 mm I.D.)
stainless steel and acrylic pipes, which however, was not observed in
the small acrylic pipe (32 mm I.D.). In addition, the pressure gradient
peak at conditions where phase inversion occurs was much sharper and
larger in the acrylic than in the steel pipe.
Compared to investigations of phase inversion in horizontal flows,
only limited work has been reported for vertical pipe flows (Luo et al.,
1997; Liu et al., 2004; Liu, 2005). Luo et al. (1997) experimentally
studied the oil-water upward flows in a stainless steel pipe of 44 mm
I.D., using oil with viscosity 452.6 mPa s. From the measured frictional
pressure drops, they obtained the effective emulsion viscosity at pre-
and post-inversion and correlated it to water fraction, temperature and
pressure. They found that phase inversion is affected by the mixture
velocity while the emulsion becomes unstable probably due to phase
inversion when the mixture velocity exceeds 0.8 m/s. The phase inversion
point was not measured directly but calculated from a correlation by Yeh
et al. (1964) while it was also associated to the pressure drop change
observed. Recently, Liu et al. (2004) used a laser-induced fluorescence (LIF) technique to directly visualize the dynamic evolution of the
dispersion and the internal flow structure in concentrated liquid-liquid
downward flows. It was found that there is an unstable region between
the two possible dispersions (o/w and w/o), wherein complex flow
structures (i.e., multiple dispersions) are often observed. Phase
inversion for a given well-established dispersion is suggested as a
transitional process of crossing this unstable region.
Information on phase distribution in a horizontal pipe
cross-section by gamma densitometry (Soleimani, 1999; Hussain, 2004) and
high frequency impedance probe (Angeli and Hewitt, 2000; Ioannou et al.,
2004) indicated mixture inhomogeneity and suggested that phase inversion
could occur at different cross-sectional locations even in fully
dispersed flow. For example, the inversion of a water-in-oil dispersion
could take place first at the bottom part of the pipe, where water tends
to accumulate. Local rather than global appearance of phase inversion
was also found by Liu et al. (2005) in agitated systems using the LIF
technique.
Apart from the above studies of unstable dispersions (no added
surfactants) in pipeline flow, Pal et al. (1986) and Pal (1993) also
investigated phase inversion during stable emulsion pipe flow where
non-ionic surfactants have been added. The viscosity of the emulsion
(measured by a coaxial cylinder viscometer) was found to increase as the
dispersed phase concentration increased and, similarly to unstable
dispersions, there was a sudden increase in the viscosity when inversion
occurred. Furthermore, secondary and multiple emulsions (continuous
phase is entrapped in dispersed drops) were widely observed in the
water-in-oil emulsion before inversion. Due to the large number of
secondary continuous phase drops a dramatic increase in the dispersed
phase drop size was also observed before inversion, which has not been
reported for pipe flow of unstable dispersions.
A number of mechanisms for phase inversion have been suggested in
the literature such as minimum system energy or equal surface energy of
the two possible dispersions (oil-in-water and water-in-oil) at phase
inversion (Tidhar et al., 1986; Brauner and Ullmann, 2002), the inverse of mixture relative viscosity minus 1 tending to 0 (Pal et al., 1986)
and zero interfacial shear stress (Yeh et al., 1964; Nadler and Mewes,
1997). Nevertheless, there are large discrepancies among the predictions
of these models.
Despite the amount of work on phase inversion, mainly experimental
but also theoretical, the underlying mechanism of this phenomenon is
still not well understood. The segregation of the phases and the
resulting inhomogeneity in horizontal systems add an extra complication to the study of phase inversion in dispersed pipeline flows. In this
paper, phase inversion and a number of associated phenomena (e.g.
pressure drop, in situ hold-up and drop size distribution) are again
addressed and further investigated in both upward and downward vertical
pipeline flows where mixture spatial inhomogeneities are reduced.
EXPERIMENTAL
The experimental work is carried out in the WOLF (Water-Oil Liquid
Flow) system in the Department of Chemical Engineering at University
College London. Tap water and EXXSOL Oil D140, whose properties are
given in Table 2, are used as test liquids. Oil and water are stored
separately in 0.88 [m.sup.3] capacity tanks made of glass reinforced
plastic and are pumped out by two 7.5 KW centrifugal pumps
(Ingersoll-Dresser, 40-25CPX200) respectively, with 240 l/min (3.5 m/s
superficial velocity) maximum output capacity for each liquid. Figures
1a and 1b illustrate the experimental rigs for upward and downward flow
respectively used in this study. After leaving their respective storage
tank and pump, the oil and water phases join together right before the
entrance of the vertical test section. Following a 90[degrees] elbow,
the oil-water mixture passes through a coarse mixer (see Figure 2),
which is located just after the elbow. The purpose of the inlet mixer is
to premix the fluids and shorten the flow developing length so that
fully dispersed flow can be obtained at the downstream measuring point.
The oil-water mixture after exiting from the test section is delivered
into a 0.8 [m.sup.3] separator unit (containing a KnitMesh DC
9201/SS/PPL coalescer inside). The separator together with the
liquids' storage tanks provide sufficiently long residence time (at
least 10 min for the highest mixture velocities used) that allows
efficient separation of the small droplets expected at the highest
mixture velocities in this study (2.5 m/s). Separated oil and water are
then transported back to their respective storage tanks to assure the
flow is running continuously. Two armoured variable area flow meters
(ABB, 10A5400) one for each phase are mounted at the beginning of the
flow loop and the recorded flow rates are logged into a PC for analysis.
Each test section has 38 mm I.D. (D) and is made of stainless steel
except for a transparent part located at the end, designed for
visualization and hold-up measurements. The vertical test sections for
upward and downward flow measurements have a total length of 3.2 m and
2.3 m respectively. A heat exchanger immersed in the oil tank is used to
remove excess heat from the oil. In this work the temperature of the
oil-water mixture was kept at about 25[degrees]C.
[FIGURES 1-2 OMITTED]
Pressure gradient is measured with a differential pressure
transducer connected to the test section between 42D and 81D from the
inlet for upward flow and between 16D and 55D for downward flow. The
type of dispersion (o/w or w/o) in the test section and the phase
inversion point, where phase continuity changes, are identified by three
different techniques, namely conductivity probe, glue-on hot-film probe
and visual observation. The conductivity probe consists of two wire
sensors 10 mm apart, with each sensor exposed by 10 mm in the axial direction into the flow. The probe is located at the pipe centreline at
a distance from the inlet 81D for upward flow and 58D for downward flow.
The data from the conductivity probe are logged into a PC at a sampling
rate of 10 Hz; each measurement lasts 1 min, which, from comparison with
longer sampling times, was found to be sufficient for obtaining
representative time averaged values. To obtain the dispersion type near
the pipe wall a glue-on hot-film anemometry (HFA) probe (Dantec Ltd.,
55R47) is employed and linked to a computer controlled hot-film
anemometer (Dantec Ltd., HFA 90P10/C10). The glue-on hot-film probe is
flush mounted onto the inner wall and is positioned at the same distance
from the inlet as the conductivity probe. The hot film sensor is very
sensitive to the cooling effect of the ambient liquid that depends on
its nature, and thus the HFA system can produce a fast and precise
indication of the continuous phase that covers it. For example, for
fully dispersed oil-in-water flows where water wets the wall surface and
the probe, a high voltage signal is expected due to the fast cooling
effect of the water phase. Alternatively, in a water-in-oil dispersion
the HFA system gives a low voltage output as oil has reduced cooling
effect. Because of its location, however, it can only detect the
continuous phase in the vicinity of the wall. Although to the
authors' knowledge this technique has not been used before to
identify phase inversion, the results from the present study show a good
stability and accuracy of this instrument. Apart from the above
techniques, the phase inversion point can also be identified by
observing the dispersion through the transparent test sections using a
Kodak digital camera. Water-in-oil dispersions appear more opaque than
oil-in-water ones while there is also a major visual difference between
water and oil drops.
The drop velocity profile and drop size distribution are measured
by a dual impedance probe. The detailed description of this instrument
and signal processing technique can be found elsewhere (Lovick and
Angeli, 2004; Hu et al., 2006). In total, 11 different radial locations
in the pipe cross-section are sampled. During drop size measurements the
test section of the glue-on hot-film probe is replaced with that of the
impedance probe. The average in situ hold-up of each phase is also
measured by simultaneously shutting two quick-closing valves, installed
at each end of the transparent acrylic pipe sections (see Figures 1a and
1b).
In the present studies, two types of experiments were carried out
to observe phase inversion and its associated phenomena. In the first
one (type I), phase inversion is achieved by varying the input
superficial velocities of both oil and water phases, while keeping the
total mixture velocity constant at each run (e.g. 1.5, 2.0 and 2.5 m/s).
The velocity of the initial continuous phase is reduced while that of
the dispersed phase is increased until phase inversion is achieved and
beyond it. Within type I experiments more detailed studies on pressure
drop, in situ hold-up and drop size are carried out. In the second type
(type II) of experiments phase inversion is obtained by increasing the
input superficial velocity of the initial dispersed phase, either oil or
water, while maintaining that of the other, continuous, phase unchanged
until phase inversion occurs and beyond it.
During both types I and II of experiments, phase inversion has been
approached from two different routes, from oil to water continuous
(denoted by w/o [right arrow] o/w) and from water to oil continuous
(denoted by o/w [right arrow] w/o) dispersions, respectively. In the o/w
[right arrow] w/o experiments, for example, the test section is filled
initially with either pure water or oil-in-water dispersion such that
the inner wall is wetted only by water phase.
RESULTS AND DISCUSSION
Type I Experiments
Phase Inversion Point
Figure 3 illustrates the average dimensionless conductivity value
of the mixture (normalized to the single-phase water value) at the pipe
centre obtained by the conductivity probe in upward vertical flows at
2.0 and 2.5 m/s mixture velocity. The conductivity values are plotted as
a function of input oil volume fraction and are compared for the two
different routes used to approach phase inversion, namely o/w [right
arrow] w/o and w/o [right arrow]o/w, respectively. Here, the input oil
fraction is defined as [[epsilon].sub.o]=[Q.sub.o]/([Q.sub.o]+[Q.sub.w])
where [Q.sub.o] and [Q.sub.w] are the volumetric flow rates of oil and
water phases respectively. It can be seen that for both inversion routes
there is a high conductivity value for water-continuous dispersions
until a critical input oil fraction [epsilon].sub.1.sub.0], while there
is a low conductivity value for oil-continuous dispersions beyond a
second critical input oil fraction [[epsilon].sup.2.sub.0]. The
conductivity value in the water continuous dispersion decreases with
increasing dispersed phase fraction as more and larger drops pass
through the two probe needles and bridge them. The results indicate that
between the two types of dispersions there exists a transitional region
since the two critical oil fractions are not the same, i.e.
][epsilon].sup.1.sub.0]. =74% and [[epsilon].sup.2.sub.0] =84% for 2.5
m/s (Figure 3b). In this transitional region the two phases seem to
compete to become continuous. This is similar to the transitional region
between the two types of dispersions observed visually by Liu et al.
(2004) and Liu (2005) with the LIF technique. Their work indicated that
within the transitional region (also called unstable region) the flow
structure is very complex, where secondary and multiple dispersions are
frequently seen, and both o/w and w/o dispersions can co-exist in the
pipe. The unstable characteristics of the transitional region can also
be seen from the time history plot of the conductivity signals for
volume fractions before and after phase inversion, as illustrated in
Figures 4a to f for 2.5 m/s mixture velocity. High values can be seen
for 70% and 74% oil fraction indicating a water continuous phase
interrupted by the many oil drops at these dense dispersions, while low
values are seen for an oil continuous dispersion at 84% oil fraction. In
the intermediate volume fractions the signals are shifting in between
these two limits reflecting that the dispersion is neither clearly
water-continuous nor clearly oil-continuous but complex structures may
exist.
[FIGURES 3-4 OMITTED]
The phase continuity was also identified with the glue-on hot-film
probe and the results are illustrated in Figure 5 for all cases studied
in this work, both upward and downward flows at 1.5, 2.0 and 2.5 m/s
mixture velocities. High values indicate that water is in contact with
the probe and the pipe wall while low values indicate that oil is now in
contact with the wall. Since visual observations showed that the flow
regime was fully dispersed, it can be assumed that the phase in contact
with the wall is the continuous phase of the dispersion. As can be seen
from Figure 5, the HFA output illustrates a clear and abrupt transition
between o/w and w/o dispersions in between the two critical oil
fractions given by the conductivity probe. A possible explanation for
this difference is that even when the flow at the centre of the pipe has
started to invert and create complex structures, as indicated by the
changing conductivity values, the region close to the wall will preserve
the continuous phase until phase inversion is complete and the new
continuous phase establishes everywhere in the pipe and at the wall,
which is the point detected by the HFA probe. Therefore, the phase
inversion detected by the glue-on HFA probe is the complete phase
inversion in pipeline flows. These complete phase inversion points are
further found to match those identified visually from the difference in
the optical characteristics of the two types of dispersions.
[FIGURE 5 OMITTED]
Both measurements of phase inversion in the middle of the pipe and
at the wall showed very few differences between the o/w [right arrow]
w/o and w/o [right arrow] o/w inversion routes (Figures 3 and 5),
suggesting that there is no hysterisis effect (or ambivalent range) in
the current pipeline system. This observation agrees with the
experimental data obtained by Ioannou et al. (2005) in horizontal
acrylic pipes with 32 mm I.D., where the phase inversion point was found
to be the same for inversions from o/w [right arrow] w/o and from w/o
[right arrow] o/w. In that work, however, ambivalent range was seen in
the large diameter pipes (60 mm I.D.) used for the same range of flow
rates, with width about 6% input oil fraction. This difference was
attributed to flow pattern transitions in the large pipes where higher
flow rates would have been required to get fully dispersed flow than in
the small pipe. It should be noted here that in all the other works
reported in Table 1 the existence of ambivalent range between the
inversion points from oil continuous and from water continuous
dispersions was not addressed.
From Figure 3 and Figure 5 it can also be seen that the critical
input oil fraction [[epsilon].sub.o] for complete phase inversion, found
by the HFA probe, is close to the upper oil fraction limit
[[epsilon].sup.2.sub.0],of the transitional region, indicated by the
conductivity probe, for both inversion routes. This could be due to the
different coalescing characteristics of o/w and w/o dispersions
(Chesters, 1991). Water drops coalesce more promptly and perhaps once
some inversion has been initiated it spreads to the whole pipe
cross-section with very little further increase in the dispersed phase
volume fraction. On the other hand oil drops in water have low
coalescence rate, perhaps because of the electric double-layer effect
that repels drops from each other (Kumar, 1996), and they remain
dispersed even when some initial inversion appears until the volume
fraction of the oil increases significantly more.
Additional phenomenological investigations around the complete
phase inversion point (which is abbreviated in the following to phase
inversion point) were carried out in type I experiments.
Frictional Pressure Drop
Equation (1) is used to calculate the frictional pressure gradient
in the vertical pipeline flows:
[(dp/dx).sub.f] = [(dp/dx).sub.g] [+ or -] [[rho].sub.w] -
[[rho].sub.o]) [[phi].sub.0]g (1)
where (dp/dx)f is the frictional pressure gradient, [(dp/dx).sub.m]
is the pressure gradient measured by the pressure transducer,
[[rho].sub.w] and [[rho].sub.o] are the densities of water and oil
phase, [[phi].sub.o] is the average in situ hold-up of the oil phase
that is obtained by the quick-closing valves, g is the gravitational
acceleration and the '[+ or -]' sign corresponds to upward or
downward flow, respectively. In the current experiments, the maximum and
average errors in obtaining the frictional pressure gradient are 6.0%
and 4.6%, respectively.
In horizontal pipeline flow phase inversion is often accompanied by
a peak in pressure drop, which suggests a maximum of the dispersion
viscosity (Arirachakaran et al., 1989; Angeli and Hewitt, 1998;
Soleimani, 1999; Ioannou et al., 2005). This increase in pressure drop
is more noticeable at high mixture velocities. The frictional pressure
gradients measured in the current work are shown in Figures 6a-c for
vertical upward flow and in Figures 6d-f for downward flow.
Interestingly, there is no peak in the pressure gradient data during
phase inversion. In contrast, comparisons with the change in phase
continuity shown in Figure 5 indicate that at the phase inversion point
pressure gradient seems to have its lowest value. For both routes of
approaching phase inversion starting from a high water fraction,
pressure gradient decreases slightly with increasing oil fraction. At
higher oil fractions, and especially in upward flow, pressure gradient
seems to increase and then to sharply decrease before phase inversion.
After the inversion point it increases again with further increase in
the oil volume fraction towards the single-phase oil value. The region
of sharp decrease and increase in pressure drop is within the
transitional region given by the conductivity probe (see Figure 3) while
the minimum in this region matches exactly the boundary identified by
the glue-on hot-film probe (see Figure 5).
[FIGURE 6 OMITTED]
The reduction in pressure gradient from the single phase oil or
water values with the addition of dispersed water or oil, respectively,
is attributed to the drag reduction phenomenon. This is in agreement
with previous findings (Pal, 1993; Nadler and Mewes, 1997; Angeli and
Hewitt, 1998). Drag reduction has been found to be stronger in oil than
in water continuous dispersions and to increase with dispersed phase
fraction. Pal (1993) reported that the drag reduction behaviour can only
be observed during the flow of unstable dispersions but not of stable
emulsions with added surfactant. He further attributed the appearance of
drag reduction to the turbulence modification of the continuous phase in
the presence of dynamic drop breakage and coalescence processes, which
would explain its absence in stable emulsions.
In addition, it has been suggested that drop size can also affect
the pressure gradient of dispersions. Pal (1993) found experimentally
that the effective viscosity of liquid-liquid mixtures was strongly
dependent on the size of the dispersed phase. By comparing stable (with
surfactant) and unstable (without surfactant) emulsions, he observed
that there is a dramatic rise of the relative viscosity with volume
fraction of dispersed phase in stable emulsions that have small
droplets, but not in unstable emulsions that have large droplets in both
laminar and turbulent flows. It was further suggested that for a given
volume fraction the larger the drops are, the easier their deformation during flow and therefore the lower the viscosity of the mixture will
be. As the mixture approaches phase inversion the drops will tend to
grow even larger (which is more significant at low velocities) and,
based on the above, cause a reduction on mixture viscosity and pressure
gradient.
A combination of the drag reduction phenomenon and the effect of
drop size (see Figure 12) on pressure gradient could explain the
pressure drop behaviour found in the current work. Starting from pure
oil the addition of the dispersed water would decrease pressure gradient
because of drag reduction. As the mixture enters the transitional region
and the drops grow larger they start deforming and further reduction in
pressure gradient occurs. At the point of complete phase inversion a new
continuous (water) phase establishes. With further decrease of the
dispersed oil fraction, the oil drops decrease in size as well and the
pressure gradient increases again until it reaches either a peak or a
plateau at the limit of the transitional region. After the transitional
region the dispersed drops are becoming small and less easy to deform.
Combined with the reduced effect of drag reduction in water continuous
dispersions the pressure gradient is much closer to the single phase
water value and approaches it as the dispersed phase oil fraction
further decreases. A lower drag reduction is observed in the water than
in the oil continuous dispersions perhaps due to the reduced
deformability of the more viscous oil drops.
A lack of pressure gradient maximum during phase inversion, in
contrast to what has been observed before from experiments carried out
in horizontal flows, could be attributed to the large drop sizes
encountered in the current work. Because of the orientation of the flow
gravity does not promote phase separation in a pipe cross-section and
dispersed flow can easily be achieved at low mixture velocities, such as
1.5 m/s, for which the flow would not be fully dispersed in the
respective horizontal system. As a result larger drops form in our
vertical pipe, compared to those formed at fully dispersed flows in
horizontal systems. The large drops will also deform more easily.
Perhaps a further increase in the mixture velocity, accompanied by a
decrease in drop size, would also result in a peak in pressure gradient
in the current system during phase inversion. In fact there are some
small peaks close to the phase inversion point in upward flows (see
Figure 6). It should also be pointed out that in the previous
investigations, where changes in phase continuity were related to
pressure gradient changes (Pal, 1993; Nadler and Mewes, 1995, 1997;
Ioannou et al., 2005), phase inversion was identified at only one
location in the pipe and the increase in pressure gradient was not
matched with the change in phase continuity at different locations in
the pipe cross-section. In other studies the peak in pressure drop was
used as an indication of phase inversion but was not related to phase
continuity changes. It is possible, therefore, that a maximum in
pressure gradient appears not at the exact point of complete phase
inversion but close to it, as the location of the small peaks in upward
flow seems to suggest.
In Situ Hold-Up and Velocity Ratio
The average in situ hold-up of the dispersion is obtained from the
quick-closing valves with [+ or -]3% manual operating error. In
agreement with the previous results on phase continuity and pressure
gradient it was found that the route of approaching phase inversion
(from oil or from water continuous dispersion) also had little effect on
the hold-up data, provided that a long enough experimental running time
is allowed (to assure the previously stagnant liquids remaining in the
test section after shutting off the quick-closing valves are removed
before a new measurement is taken). The in situ hold-up results in
upward and downward flows averaged over the two inversion routes are
shown in Figures 7a and 7b respectively. It can be seen that in both
flow directions the dispersed phase travels faster than the continuous
phase for oil-in-water dispersions when [[epsilon].sub.o] <70% and
for water-in-oil dispersions when [[epsilon].sub.o] >85%. Also, the
difference between continuous and dispersed phase velocities gradually
decreases as the flow approaches phase inversion. Figure 8 presents the
average in situ oil to water velocity ratio (S=[U.sub.o]/[U.sub.w])
calculated by Equation (2) at immediately before and after the phase
inversion point:
S = [[epsilon].sub.o][[phi].sub.w]/[[epsilon].sub.w][[phi].sub.o]
(2)
where [[epsilon].sub.w] and [[epsilon].sub.o] are the input
fractions of water and oil respectively and [[phi].sub.w] and
[[phi].sub.o] are the measured average in situ hold-up of water and oil
respectively. As can be seen, complete phase inversion is not
accompanied by equal in situ average velocities (S=1) between the two
phases. To further investigate this behaviour, the in situ oil hold-up
and velocity ratio at the complete phase inversion points (according to Figure 5) are plotted in Figures 9 and 10 respectively at various
mixture velocities.
[FIGURES 7-10 OMITTED]
It can be seen that the critical velocity ratio where inversion
occurs is similar for the two flow directions and tends to a constant
value, S [approximately equal to] 0.77. Discrepancies appear at the
lower velocity 1.5 m/s for downward flow, where the visual observation
showed that at high oil fractions very large oil drops (similar to
plugs) appeared in the middle of the pipe.
Detailed measurements of the in situ hold-up profile in a pipe
cross-section were also obtained with one of the sensors of the
impedance probe. The results for 2 m/s mixture velocity are shown in
Figure 11 for different input oil fractions ([[epsilon].sub.0]), for
upward and downward flows, where R is the pipe radius. Most are for
oil-in-water dispersions apart from [[epsilon].sub.o]=86% in upward flow
and [[epsilon].sub.o]=76% and 80% in downward flow that are for
water-in-oil dispersions (indicated with dotted lines and full marks).
As can be seen, the profiles of o/w dispersions in both flow directions
exhibit a centre peak as the oil fraction increases up to 50%, which is
consistent with the findings by Farrar and Bruun (1996) in upward
kerosene-water flows. With further increase of the dispersed phase input
fraction the profiles become gradually flatter while approaching phase
inversion and the two phases are more evenly distributed over the pipe
cross-section. This phase distribution profile seems to build up the
preparation for the occurrence of complete phase inversion in the whole
pipe cross-section. It is interesting that although there are
differences in the local hold-up between upward and downward flows for a
given [[epsilon].sub.o], as illustrated in Figure 11, which would
explain the differences in the complete phase inversion points between
the two directions, phase inversion does happen at both directions at
the same velocity ratio, especially at the higher velocities (see Figure
10).
[FIGURE 11 OMITTED]
Chord Length and Drop Size Distribution
By cross-correlating the signals of the two sensors of the dual
impedance probe the velocity of the dispersed phase drops can be found.
This velocity can then be combined with the time duration of the
interactions between the dispersed phase and either of the two probe
sensors to provide a distribution of the drop chord lengths that have
been intersected by the sensor. If a Sauter mean chord length is defined
as [L.sub.32]=[[sigma][P(L)[L.sup.3]]/[sigma][P(L)[L.sup.2]] where P(L)
is the number density of chord length L, Figures 12a and 12b show the
radial profile of L32 measured at 2 m/s mixture velocity in upward and
downward flows respectively for different input oil fractions before and
after phase inversion, following the w/o [right arrow] o/w inversion
route.
[FIGURE 12 OMITTED]
As can be seen from Figure 12b for downward flows, in the o/w
dispersions (denoted by empty marks) with increasing oil fraction the
dispersed phase size at the wall is not significantly affected, but it
increases a lot at the pipe centre particularly for fractions between
[[epsilon].sub.o]=0.3 and [[epsilon].sub.o]=0.4. At oil fractions 40%
and above the L32 profile has a peak at the pipe centre and shows a
significant decrease at one radial position; this characteristic
position moves towards the wall with increasing oil fraction (i.e. from
0.3R at [[epsilon].sub.o]=0.4 to 0.78R at [[epsilon].sub.o]=0.64). The
downward o/w flow at high oil concentrations, therefore, seems to
consist of two different regions, a core region with large oil drops and
a wall-annulus region with small oil drops. Once this pattern is
established (at about [[epsilon].sub.o]=0.4) any further increase in the
oil fraction extends the size of the region towards the wall but affects
less the size of the drops. This may be because there exists a maximum
drop size in the core region under a given mixture velocity (or
turbulence level) and any further increase in the dispersed phase
fraction cannot increase the drop size in the centre any more but can
affect (increase) the size of the smaller drops closer to the wall,
extending the core region. After the o/w dispersion completely inverts
to w/o (full marks) smaller water drops are formed due to dilution as
shown in Figure 12b.
Chord lengths [L.sub.32] in upward flows of o/w dispersions (see
Figure 12a) have large values in the pipe centre similarly to downward
flows, which also reduce to low values after inversion to w/o mixtures
(water drops). However, the [L.sub.32] profiles in o/w dispersions at
the highest oil fractions ([[epsilon].sub.o]=0.74 and 0.8) seem to be
almost uniform across the pipe or slightly increase closer to the wall.
In addition, the differences in drop size between the pipe centre and
wall regions are not as great as in downward flow even for the lower oil
fractions.
This disagreement between upward and downward flow dispersed phase
size and distribution (also reflected in the hold-up profiles, see
Figure 11) suggests that the structure of the two-phase mixture in the
two flow directions while approaching phase inversion is different. It
is interesting, however, that despite these differences phase inversion
appears at the same velocity ratio in both directions. Perhaps a
mechanism based on the momentum of the two phases during inversion is
more relevant to phase inversion in pipeline flow. This would agree with
the theory proposed by Yeh et al. (1964) and Nadler and Mewes (1995) of
zero interfacial shear stresses during inversion.
From the local measurements of chord length the area-weighted
integrated distributions of chord length (L) over the pipe cross-section
can be obtained and are shown in Figures 13a-f for different input oil
fractions ([[epsilon].sub.o]) at 2.0 m/s downward flow. In o/w flows
(see Figures 13a-d) as the dispersions become denser the likelihood of
the probe intersecting large chords rises. This is understandable since
the coalescence rate of oil drops will increase with oil concentration,
which will result in many large drops in the flow. Particularly for
[[epsilon].sub.o]=64% before the phase inversion point (74%) intersected
chords as long as 19 mm (=D/2) can frequently be seen. Visual
observations (see for example Figure 17) showed that drops were still
spherical at this fraction but it is expected that as the oil fraction
further increases such large chord lengths may also originate from
smaller deformed drops. The distributions after phase inversion to w/o
(Figures 13e and 13f) confirm the presence of many small water drops.
[FIGURE 13 OMITTED]
One of the criteria suggested for phase inversion is that at the
inversion point the system surface energies of the two possible
dispersions, oil-in-water and water-in-oil are equal (Tidhar et al.,
1986; Brauner and Ullmann, 2002). The system free surface energy
consists of the liquid-liquid interfacial energy and the liquid-solid
wall surface energy. The latter is found to be much smaller in the
current experimental system than the former, which can be calculated
from the dispersed phase size. To estimate the interfacial energy the
chord length distribution is converted to a drop size distribution based
on the algorithm developed by Hu et al. (2006). From these distributions
the Sauter mean diameter ([D.sub.32]) is found,
[D.sub.32]=[sigma][P(D)[D.sup.3]]/[sigma][P(D)[D.sup.2]] where P(D) is
the number density of drops with diameter D. The interfacial energy
([E.sub.S]) is then equal to [E.sub.S]=6[[phi].sub.d][phi]/[D.sub.32]
where [phi].sub.d] is the in situ dispersed phase hold-up and [sigma] is
the interfacial tension. The variation of interfacial energy
([E.sub.s]/[sigma]) with input oil fraction for mixture velocities of
1.5 and 2.0 m/s is presented in Figure 14. Points very close to phase
inversion in the water continuous mixtures cannot be obtained as at
these high oil fractions drops are no longer spherical and drop
diameters cannot be calculated from the measured chord lengths. However,
the trends in the curves show that in both upward and downward flows
there is a difference in the interfacial energies of the two dispersions
before and after phase inversion, which is greater for downward flows,
and suggest that the criterion of equal surface energy at phase
inversion point may not always hold. This interfacial area difference at
phase inversion was also observed by Luhning and Sawistowski (1971) in
dispersions formed in stirred vessels. Hence, other factors may also be
important to phase inversion such as drop coalescence and break up
rates.
[FIGURE 14 OMITTED]
Type II Experiments
In the experiments of type II, the appearance of phase inversion is
observed by keeping constant the flow rate of the initial continuous
phase and increasing that of the initial dispersed phase until inversion
is observed and beyond. Figure 15 illustrates the critical input oil
fractions in both upward and downward flows that lead to the occurrence
of complete phase inversion for the two different approaching routes,
o/w [right arrow] w/o and w/o [right arrow] o/w. It can be seen that in
vertical downward flow the amount of input oil required for inversion
increases as the mixture velocity increases until it reaches an almost
constant value. It is understandable that at low mixture velocities
buoyancy would have a greater effect on the in situ hold-up and the
amount of in situ oil is expected to be higher than the input one. As a
result phase inversion will appear at lower input oil fraction. While,
for upward flow the critical oil fraction is found to decrease with the
mixture velocity. The opposite will happen in the upward flow where
buoyancy will now favour lower in situ oil hold-up than the input one.
As shown in Figure 15, when the mixture velocity increases above 3.5 m/s
the buoyancy effect seems to be negligible and the critical input oil
fraction for inversion becomes independent of mixture velocity. This is
more obvious for downward than for upward flow, perhaps because the
dispersed drops close to inversion have smaller size in downward than in
upward flow and therefore are less affected by buoyancy.
[FIGURE 15 OMITTED]
No obvious ambivalent region is found in type II experiments, which
is consistent with the previously described results of type I
experiments. Interestingly, during type II experiments, it was also
observed that a particular dispersion, for example water-in-oil formed
by increasing the oil flow rate up to the inversion point could be
readily inverted back to the oil-in-water dispersion by slightly
reducing the oil flow rate. This characteristic may further prove the
absence of clear ambivalent region in pipeline systems, although it has
been reported extensively for mechanically agitated vessels. Some small
discrepancies of the complete phase inversion points between repeated
experiments, as seen in Figure 15, are attributed to the differences
that can experimentally exist in the system set-up and operating
conditions as well as contamination and temperature variation.
Previous works have indicated that phase inversion is independent
of mixture velocity (Arirachakaran et al., 1989; Soleimani, 1999;
Ioannou et al., 2004), which would agree with the current findings for
the higher mixture velocities used.
PHASE INVERSION PROCESS
On the basis of the visual observations in this work, supported by
the experimental work by Liu (2005), a sequence of flow configurations
before and after phase inversion is proposed, which is schematically shown in Figure 16 for an o/w to w/o transition. In the o/w dispersion
at low oil fractions, oil is entrapped into the water continuum in the
form of spherical drops (graph A). As the input oil fraction increases a
relatively dense dispersion with larger drops is formed due to drop
coalescence (graph B). If more oil is fed into the pipe the drops will
be more closely packed and the dispersion will become more concentrated.
Although the close packing would occasionally force the drops,
especially the larger ones to deform into various shapes (e.g. ellipsoid
and strangely elongated shapes in graph C), the majority of the
dispersed drops would still be spherical. At this stage drops can stay
together exhibiting negligible coalescence even for systems with no
added surfactants, as shown by Figure 17. The formation of such
concentrated o/w dispersions is attributed to the electrical
double-layer effect around the oil drops because of preferential adsorption of ions from the continuous water phase, which was found to
significantly suppress coalescence in both less dense (<10%, Collins
and Knudsen, 1970) and dense dispersions (< 45%, Pal, 1993).
[FIGURES 16-17 OMITTED]
With further increase of the dispersed oil fraction, much closer to
complete phase inversion point and within the transitional region, the
flow pattern can change from dispersed-dominant flow to the
complex-structure-dominant flow where complex multiple dispersions and
large elongated drops are present. The dispersion could have either
water at the wall (and considered as water continuous, as depicted by
graph D in Figure 16) or oil at the wall (oil continuous, graph E), as
clearly visualized by Liu (2005), with the complete phase inversion
point located in between these two cases. The oil at the wall case seems
to exist for only a narrow range of oil fractions. Because of the
structures formed at the transitional region the conductivity of the
mixture at a point inside the pipe would fluctuate between oil and water
continuous values as the probes are alternatively wetted by the oil and
water continuous complex structures. Once the oil fraction is beyond the
critical value for complete phase inversion, a water-in-oil dispersion
is formed (graph F in Figure 16). The transitional region is found in
this study to be over 4-6% input oil fraction and is expected to narrow
down with an increase in the mixture velocity.
The above process would also describe the w/o to o/w inversion. In
this case, however, the continuous oil phase is non-polar and there is a
higher possibility of water drops to coalesce due to the absence of the
double-layer effect. This would justify the lower dispersed water
fraction required to invert an oil continuous dispersion, compared to
the dispersed oil fraction required to invert a water continuous
dispersion as well as the shorter range of the oil continuous
transitional region.
CONCLUSIONS
Phase inversion in co-current oil-water vertical flows at both
upward and downward directions is experimentally investigated in this
study. Two inversion routes (w/o to o/w and o/w to w/o, respectively)
are followed to study the behaviour of phase inversion and associated
phenomena. Experiments are carried either by keeping the mixture
velocity constant and increasing the dispersed phase fraction (type I
experiments) or by keeping the continuous phase superficial velocity
constant and increasing the dispersed phase superficial velocity (type
II experiments). A conductivity probe at the pipe centre and a glue-on
HFA probe at the pipe wall indicate that phase inversion does not happen
simultaneously at all locations in the pipe cross-section. The input oil
fraction at which inversion is detected at the wall signifies that the
new continuous phase has spread into the whole pipe cross-section and is
defined as the complete phase inversion point.
Based on the above experimental investigations around the complete
phase inversion point, the following conclusions can be drawn:
* The results from type I experiments in both upward and downward
flows indicate that frictional pressure gradient reaches a minimum at
the complete phase inversion point. Drag reduction as well as the effect
of drop size on mixture viscosity are suggested as possible reasons for
this behaviour;
* No obvious ambivalent region is found in type I and type II
experiments at both flow directions. There is however, a narrow range of
input phase fractions ([DELTA][[epsilon].sub.o]<4-6%) where complex
structures may form;
* The phase inversion point is found by the type II experiments to
depend on mixture velocity for low and medium mixture velocities;
* In type I experiments the phase inversion points were found to be
different for the two flow directions. However, the velocity ratios
where complete inversion appeared, acquired the same constant value in
both flow directions apart from the lowest velocity investigated;
* In contrast to the previously postulated phase inversion
mechanisms, it was found, based on drop size measurements, that the
interfacial energies of the dispersions before and after phase inversion
are not equal. Other phenomena, such as increased coalescence rate
before inversion, supported by the large drops observed, could also be
responsible for the appearance of the phenomenon.
A number of issues would still need to be resolved in order to
establish a mechanism of phase inversion, such as turbulence
modification as the system approaches phase inversion and during the
phenomenon and the existence (or absence) of ambivalent range. More work
is also necessary to relate the velocity and momentum of each phase to
the complex structures and multiple dispersions formed close to
inversion.
ACKNOWLEDGEMENTS
The authors would like to acknowledge the financial support from
the Engineering and Physical Sciences Research Council (EPSRC, grant
number GR/R56044/01). B. Hu is also grateful to EPSRC and Overseas
Research Students Awards Scheme (Universities U.K.) for providing
financial support for the studentship.
Manuscript received June 21, 2005; revised manuscript received
November 1, 2005; accepted for publication November 7, 2005.
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Bin Hu (1,2) and Panagiota Angeli (1 *)
(1.) Department of Chemical Engineering, University College London,
Torrington Place, London, WC1E 7JE, U.K.
(2.) Department of Chemical Engineering, Imperial College London,
Prince Consort Road, London, SW7 2BY, U.K.
* Author to whom correspondence may be addressed.
E-mail address: p.angeli@ucl.ac.uk
Table 1. Experimental studies of phase inversion in liquid-liquid
pipeline flows
Author (year) Main aspects of the work
Tidhar et al. (1986) 1. Surface energy
Arirachakaran et al. (1989) 1. Pressure drop;
2. Phase inversion point;
3. Pipe diameter;
4. Temperature;
5. Viscosity
Pal (1993) 1. Surfactants;
2. Drag Reduction.
Luo et al. (1997) 1. Mixture velocity;
2. Temperature;
3. Pressure;
4. Dispersion viscosity;
5. Pressure drop
Nadler and Mewes (1997) 1. Oil viscosity;
2. Temperature;
3. Pressure drop
Angeli and Hewitt (1998, 2000) 1. Wettability;
2. Mixture velocity;
3. Pressure gradient
Soleimani (1999) 1. Pressure drop;
2. Flow pattern
Gillies et al. (2000) 1. Surfactants;
2. Intensity and nature of shear
process;
3. Solids content of oil
Ioannou et al. (2004, 2005) 1. Wettability;
2. Pipe diameter and material;
3. Pressure drop;
4. Phase distribution
Liu et al. (2004); Liu (2005) 1. Flow structure;
2. Drop size;
3. Phase inversion point
Table 2. Properties of the test liquids at 25[degrees]C
Liquid Exxsol oil D140 Water
Density (Kg/[m.sup.3]) 828 998
Viscosity (mPa s) 5.5 0.993
Surface tension (mN/[m.sup.2]) 20 72
Interfacial tension (mN/m) 36.6 [+ or -] 0.3
