Re-entrainment correlations for demisting

cyclones acting at elevated pressures on a

range of fluids

Trond Austrheim and Lars H. Gjertsen

Statoil ASA

7005 Trondheim, Norway

and

Alex C. Ho!mann

Dept. of Physics and Technology, University of Bergen

Allegt. 55, 5007 Bergen, Norway

May 21, 2007

Key words: Gas scrubber; axial-flow cyclone; high pressure; re-entrainment;

hydrocarbon fluids;

Abstract

In this paper separation e!ciency results for three di"erent demisters

acting on three di"erent fluid systems: Exxsol D60/nitrogen, a syn-

1

thetic natural gas and a real natural gas at a range of pressures up

to 114 bara are brought together using two dimensionless parameters:

1) a re-entrainment parameter and 2) the Weber number. The fact

that this can be achieved shows that demisting cyclones limited by

re-entrainment can be modeled by adapting re-entrainment concepts

derived for liquid films in a gravity film.

1 Introduction

Much research literature has been dedicated over the years to predict the

performance of cyclone dedusters and demisters acting on particles/droplets

close to their cut size. Both analytical models and CFD models have been

presented. While the former are still often superior in predicting the separa-

tion performance of a given cyclone, the latter can be valuable in revealing

details of the flow pattern in the separator that would otherwise not be rec-

ognized. In CFD, a very exiting development is that of large eddy turbulence

modelling (LES), which is very computationally intensive, but avoids much

of the empiricism in other types of turbulence models (see e.g. the recent

articles by Derksen et al. [1, 2]). However, CFD remains mainly useful for

studying the flow of pure gas or for low solids or liquid loadings; for high

loadings, with siginificant two-way coupling, CFD simulations becomes in-

creasingly unreliable and inaccurate.

However, in reality, for a separator acting at high liquid loading, the separa-

tion performance may well be dominated by re-entrainment of liquid rather

than penetration of liquid droplets under the separator’s cut size.

2

In particular in a commonly used gas scrubber configuration the last sep-

aration step, after an inlet vane and a mist mat, is a bank of axial-flow

cyclones and re-entrainment from the cyclones may well limit the separation

performance.

Only little research literature on high liquid loading in, and re-entrainment

from, demisting cyclones has been published. Ng et al. [3] studied flood-

ing and re-entrainment phenomena in once-through swirl tubes with upflow.

They installed and tested design improvements to the swirl vanes, using vanes

with peripheral rather than axial inflow, to delay the onset of flooding and

entrainment.

This paper describes how re-entrainment from a cyclone bank, acting as

the final separation internal in natural gas scrubbers, influences separation

e"ciency.

2 Re-entrainment mechanisms and two exist-

ing models

In this section an outline of the two dominating re-entrainment mechanisms

is given.

2.1 Mechanisms

Di!erent mechanisms of entrainment are dominant in di!erent flow regimes.

Ishii and Grolmes [4] summarize four basic mechanisms for entrainment from

3

a liquid film into a gas flowing co-currently above it. Two of these are relevant

for this work, they are shown in Fig. 1.

Gas flow

Gas flow

a FdFσ

λ

Figure 1: Two mechanisms [4] for entrainment from a liquid film into a gas

flowing over it. Top: entrainment by droplets being sheared from the surface

of a roll wave, which is dominant at higher film Reynolds numbers. Bottom:

entrainment by the gas undercutting a wave crest, which dominates at low

film Reynolds numbers

Which entrainment mechanism is active depends on the film Reynolds num-

ber:

Rel !!lul"

µl=

!l#

µl(1)

where " is the thickness of the film, ul its mean velocity and !l and µl

the density and viscosity of the liquid, respectively. # is the liquid flow in

the film per unit wetted perimeter, Pw. # is sometimes called the “liquid

loading”, but we reserve that term for the volumetric liquid concentration in

the droplet-laden gas flow. We have defined Rel as Verlaan [5] did, this is

four times lower than that used by Ishii and Grolmes [4].

4

The paper of Ishii and Grolmes [4] states that there exists a lower limit of Rel,

whereunder roll-wave entrainment will not take place no matter how high the

gas velocity over the film. In the other extreme, at high Rel, where the film

is fully turbulent, the gas velocity necessary for the inception of entrainment

becomes independent of Rel. The two limits are not firmly quantified, but

the lower limit may be from 2 to 160 dependent on whether the flow is upward

or downward in the gravity field, and the upper limit may be in the range

1500–1750.

2.2 Higher liquid film Reynolds numbers, roll-wave en-

trainment

Ishii and Grolmes derived a criterion for the onset of roll-wave entrainment

by considering a force balance between the drag force Fd , from the gas acting

on a wave crest on the film, and the retaining force of the surface tension F!

as indicated in Fig. 1. They assumed that roll wave entrainment was possible

when the drag forces exceeded the retaining force of the surface tension #:

Fd " F!. (2)

They derived as criterion for the inception of entrainment:

µlug

#

!!g

!l" 11.78N0.8

µ Re!1/3l for Nµ #

1

15

µlug

#

!!g

!l" 1.35Re!1/3

l for Nµ "1

15

. (3)

In these equations, ug is the superficial gas velocity, µl and !l the liquid

viscosity and density, respectively, and !g the gas density.

5

Nµ is a ’viscosity number’, which originally was used by Hinze [6] to analyze

the problem of droplet disintegration in a gas flow. This number compares

the viscous force induced by an internal flow to the surface tension force,

and, when used for droplet entrainment, is defined as:

Nµ !µl!

!l#"

!g!"

, (4)

where $! is the di!erence between the liquid and gas densities.

The expression"

!g!" has the dimension of length and is proportional to the

critical wavelength of a Taylor instability. The dependence on the accelera-

tion of gravity, g, is explained by the stabilising e!ect of the gravity force on

the wavy interface.

2.3 Low film Reynolds numbers, undercut entrainment

When Rel becomes very low, the evidence is that the roll-wave entrainment

no longer occurs. However, entrainment is still possible at high gas velocities,

as found by van Rossum [7], through the undercut mechanism shown in the

lower figure in Fig. 1.

Van Rossum carried out entrainment experiments for nine di!erent fluids

with interfacial tension ranging from 30 to 78 mN/m. In his study, van

Rossum analyzed the onset of entrainment in terms of two dimensionless

numbers, the film Weber number, We, with the liquid film thickness as

length scale, and a ‘correlation parameter’, S:

We !!gv2

g"

#S ! ugµl

#. (5)

6

For velocities higher than 25 m/s he found that the critical Weber number for

inception of entrainment was practically independent of S for S > 5, while

it became dependent on S for lower S-values.

3 Experimental facilities

We are in this paper analyzing the results from three di!erent experimental

rigs. The rigs and the results have been described in three other articles [8–

10].

Each of the rigs have specific advantages and limitations. They are:

– A low-pressure rig. This rig could operate up to 7 bara, and two fluid

systems were used: air/water and air/Exxsol D60.

– A high-pressure rig, capable of operating up to 100 bara. Two fluid

systems were used: nitrogen/Exxsol D60 and a live natural gas synthe-

sized from methane, ethane and N-pentane.

– A large-scale test installation at an on-shore gas processing facility.

This rig could operate at pressures up to 150 bara. A real, live nat-

ural gas, obtained by recombining dry natural gas with natural gas

condensates, was used as fluid system.

The range of physical fluid properties are given in Table 1. Note that in

the “live” natural gas systems in the high-pressure and large-scale rigs the

physical properties of the liquid phase change so drastically with pressure

due to their changing composition, governed by the phase equilibria at the

7

given pressures. The interfacial tensions were calculated using the simple

method that Weinaug and Katz [11] used for methane-propane mixtures.

Fig. 2 shows a 3-D diagram of the test scrubber in the large-scale rig. The

configuration of the other two test scrubbers are similar, except that the

cross-sectional areas—and therefore the number of cyclones in the cyclone

banks—are di!erent. There are 7 cyclones in the scrubber in the low-pressure

rig, 2 in the high-pressure rig and 31 in the large-scale rig.

Figure 2: The test scrubber configuration in the large-scale rig. Lowest is

the inlet vane, in the middle the mist-mat and on top is the cyclone deck

The drainpipes and manifolds under the cyclones were arranged such that

they did not block the cyclones significantly. In the high-pressure and low-

pressure rigs, where there were only a few cyclones in the decks, the drain-

pipes were positioned at the side of the deck and did not interfere with the

cyclones at all. The arrangement in the large-scale rig is shown in Fig. 3.

Although the pipes can be seen to block part of the cross-sectional area, they

8

Table 1: Overview of the physical fluid properties, where relevant the pres-

sures in bara are given in parentheses

Density

(kg m!3)

Viscosity

(kg m!1 s!1)

Interfacial

tension

(mN m!1)

Low-pressure rig

Air 1.19 1.84$ 10!5

Exxsol D60 785 1.4$ 10!3 24.3

Water 1000 0.89$ 10!3 72.8

High-pressure rig, N2/Exxsol D60

Gas 1.14 (1)

113.7 (100)

1.78$ 10!5 (1)

2.03$ 10!5 (100)

Liquid % 788 % 1.58$ 10!3 22.7 (1)

16.0 (100)

High-pressure rig, synthetic natural gas

Gas 17.2 (20.1)

97.0 (92)

1.1$ 10!5 (20.1)

1.5$ 10!5 (92)

Liquid 602.2 (20.1)

496.5 (92)

2.07$ 10!3 (20.1)

0.96$ 10!3 (92)

11.4 (20.1)

2.2 (92)

Large-scale rig

Gas 22.0 (28)

104.0 (113)

1.2$ 10!5 (28)

1.6$ 10!5 (113)

Liquid 704 (28)

640 (113)

4.5$ 10!3 (28)

2.6$ 10!3 (113)

14.5 (28)

5.0 (113)

9

are reasonably far below the cyclone deck, such that the flow to some extent

redistributes over the cross-section above the pipes before reaching the deck.

The liquid flowrate to the deck was measured as the sum of the overhead and

captured liquid fractions.

Figure 3: The drainage arrangement under the cyclone deck in the large-

scale rig

The intention of the inlet vane is to distribute the mist-laden gas evenly over

the scrubber cross-section, and separate bulk liquid. The mist-mat separates

more droplets, or, when the scrubber is operated such that the mist-mat is

flooded, may act as a coalescer for the cyclone bank. The final separation

step is the cyclone bank, where a number of cylindrical axial flow cyclones

with swirl vanes generating the swirling flow, work in parallel.

The axial flow cyclones are the most important in this present context, and

a diagram is shown in Fig. 4. This is the type and size of cyclone used in the

cyclone banks of all three rigs.

Table 2 gives an overview of the experimental facilities and the operating

10

4 cm

25 cm

5 cm

Vortexfinder

Secondaryoutlet

Figure 4: A diagram of an axial flow cyclone constructed in accordance

with the cyclones used by Verlaan [5]. The cyclone is equipped with vertical

drainage slits as shown, and, in contrast to that of Verlaan, with a vortex

finder to reduce re-entrainment

11

conditions used for generating the results analyzed in this article. Figure 5

shows scaled drawings of the three test scrubbers used with the distances

between the internals.

Table 2: Overview of the experimental facilities, operating conditions and

approximate fluid rates used

Low-press.

rig

High-press.

rig

Large-scale

rig

Scrubber diameter [m] 0.384 0.15 0.84

Cyclones in deck 7 2 31

Pressures [bara] 2–5 20, 50 and 92 56 and 114

Temperature Ambient 30" 30"

Fluid systems Air/Exxsol

D60

N2/Exxsol

D60

Synthetic live

natural gas

Live natural

gas

Superficial gas velocity

in cyclones [m/s]

7–30 1–6 9 and 5.4

Liquid loadings [vol % ] 0.002–0.09 0.05–0.7 0.07–0.95

12

800

350 410

790

740

710

Low-pressure rig High-pressure rig Large-scale rig

Figure 5: Scaled drawings of the three test scrubbers used for generating the

results analyzed in this article. The distances in mm between the internals:

lowest the vaned inlet, then the mist mat and highest the cyclone bank are

given

4 Re-entrainment from cyclones in gas scrub-

bers and its modeling

4.1 Basic assumptions

Some results obtained in the high-pressure test rig are shown in Fig. 6.

Clearly the e"ciency drops with increasing gas velocity through the cyclones.

In general the results from the cyclone experiments in this rig show [9] that

the e"ciency drops o! with increasing gas velocity and liquid load. They also

13

70

75

80

85

90

95

100

0 1 2 3 4 5 6 7

Superficial gas velocity [m/s]

Sepa

ratio

n ef

ficie

ncy

[%]

20 bar50 bar92 bar

20 bar50 bar92 bar

N2/Exxsol

Natural gas

Figure 6: Cyclone e!ciency in the high-pressure rig with a constant liquid

flowrate to the cyclones of 45 l/hr per cyclone

show that the liquid carry-over is much larger when the pressure is increased

and a natural gas fluid is used instead of a N2/Exxsol D60 fluid. Table 1

show the density and viscosity of the liquid and gas phases to be somewhat

similar for the two systems, but calcuations [12] showed, as indicated in the

last column of Table 1 that the interfacial tension is much the lower in the

natural gas system, perhaps explaining most of the di!erence in behaviour

between the two fluid systems. Further on in this paper, we bring the results

from the two systems onto one curve taking into account the di!erences in

physical properties between them.

All cyclone models, including the one we derived for axial flow cyclones in [8],

predict that if the droplets are so small that the cyclone separation e"ciency

is determined by the droplet size, the e"ciency should increase with increas-

ing volumetric gas flow and probably with increasing liquid loading (the latter

due to coalescence e!ects).

14

However, if re-entrainment is the determining factor, the e"ciency would

be expected to drop o! with higher volumetric gas flow and liquid loadings.

Since this is the case in the results from the three rigs, we assume that the

liquid carry-over from the cyclones is dominated by re-entrainment of liquid

that has already settled on the cyclone wall.

We now attempt to derive a parameter that will unify the results on the basis

of Ishii and Grolmes’ [4] work. While they were only focusing on the inception

of re-entrainment, this study also focuses on the the rate of re-entrainment.

Near the point of inception of droplet entrainment, the entrainment rate

increases quite slowly with increasing gas velocity, but at relatively high

entrainment fraction the entrainment rate increases faster and appears to

be linearly correlated with the superficial gas velocity. Since the droplets

that are re-entrained inside a cyclone are exposed to a centrifugal force one

can think of liquid carry-over as a dynamic equilibrium between capture and

re-entrainment at the inner wall or the outlet of the cyclone.

We propose that this dynamic equilibrium can be described as a function of

the ratio of the two forces used by Ishii and Grolmes, the drag force and the

retaining force:

$cycl = f

#Fd

F!

$when re-entrainment dominates. (6)

We are aware that re-entrainment may well take place to a large extent

from edges in the separator. For instance, Verlaan [5] states that rivulets

formed at the edges of the slits in his separators, and that this limited the

separation e"ciency. However, he used liquids with higher interfacial tension,

and generally lower liquid loading, which will give rise to di!erent creep flows

15

than we are likely to encounter in our systems. We assume, moreover, that

re-entrainment from edges in the equipment will be governed by the same

physical parameters as from liquid films.

We need, however, to adapt this theory to the present situation: a film

moving on the wall of a cyclone in a strongly swirling flow.

4.2 Adaptation of the theory

The first task is to determine Rel, the liquid film Reynolds number in Eq. (1).

Under the influence of the upward swirling gas flow, the film moves upward

on the cyclone wall at an an angle, %, to the horizontal. We can therefore take

the wetted perimeter as Pw = &D/ cos %, if we define the wetted perimeter as

the width of the film measured normal to the direction of flow (a consequence

is that the wetted area cannot be calculated as PwH, with H the cyclone

height). The gas moves at an angle ' to the horizontal, where ' is the exit

angle from the swirl vanes, and as an approximation we assume that the

liquid moves at the same angle, i.e. % = '.

If we further assume that the captured fraction $ of the total liquid flow to

the cyclone Q̇ moves in the liquid film, i.e. that most of the droplets entering

the cyclone are so large that they are slung to the wall almost immediately,

we obtain for Rel:

Rel =Q̇l$!l

Pwµl. (7)

Ishii and Grolmes found that the transition from low Reynolds number

entrainment to transition regime entrainment occurred at approximately

16

Rel = 160 (their definition) for horizontal flow or vertical up-flow and Rel = 2

for vertical down-flow. The transition to a rough turbulent regime occurred

when Rel exceeded 1500–1750. When Rel is calculated for the experiments

in the high-pressure rig, most of the N2/Exxsol D60 results are found to be in

the low Reynolds number regime, while most of the natural gas experiments

are found to be within the transition regime. If transition regime theory is

used for experiments that are calculated to be within low Reynolds number

regime, the results will become increasingly inaccurate as the velocity is de-

creased. However, on balance it was thought best to use the same theory

for all the results avoiding an anomalous jump in prediction when changing

from one theory to the other. All the results from the high-pressure rig are

therefore treated as if they were within the transition regime in this analysis.

The theory of Ishii and Grolmes is based on two fundamental assumptions:

1. The initiation of roll-wave entrainment depends on a balance between

the gas drag force and the surface tension retaining force acting on the

liquid in a wavelet.

2. To calculate the amplitude, a, of a wavelet, it was assumed that the

flow in the wavelet is simple shear flow, while flow in the film as such

may be turbulent, and that the shear stresses above and below the wave

are the same as those for the rest of the film (the shear stress acting

on the film from the gas and that acting on the wall from the film have

to be equal, since the film is not accelerating).

This paper is not discussing the merits of these assumptions but adapting

this model, that has stood the test of time, to our system, which di!ers from

17

theirs in that it involves a centrifugal field rather than the gravitational one.

We also note here that Verlaan [5] handles two criteria for re-entrainment

to take place: that droplets are created by shear, and that these droplets

are transported in the surrounding gas flow. Consistent with the work of

Ishii and Grolmes, we focus on the creation of droplets here, but, as stated

above, consider that a model must describe the dynamic equilibrium between

re-entrainment and capture at the cyclone wall.

The length scale chosen for Nµ,"

!g!" is the critical wavelength of a Taylor

instability, and therefore characteristic for the length of waves on the film.

This length scale involves the gravitational constant, g. We replace this

by the centrifugal force acting on the liquid film, u2l,#/R, where ul,# is the

tangential component of the liquid velocity, and R the cyclone radius.

This makes it necessary to find ul,# = ul cos %, which we do in a way similar

to Ishii and Grolmes, as follows.

If we call the tangential components of the shear stresses acting on the film

due to the gas and on the wall due to the film (i,# and (w,#, respectively, we

can say:

(i,# = fg,i

!gu2r,#

2% fg,i

!gu2g,#

2(w,# = fl,w

!lu2l,#

2= (i,#, (8)

where ur is the relative velocity between the liquid and the gas, assumed to

be approximately equal to the gas velocity, since ug & ul.

Solving these two equations for ul,# gives:

ul,# =

%fg,i!gu2

g,#

fl,w!l(9)

18

We need the friction factor for the gas flow over the liquid film, fg,i. Wallis [13]

proposed for the rough wavy regime in a tube of diameter D:

fg,i = 0.005

#1 + 300

"

D

$.

For the present case of flow swirling with an angle of about 45", we propose

to replace D by R, the radius of the cyclone:

fg,i = 0.005

#1 + 300

"

R

$.

The liquid friction factor, fl,w, can, following Ishii and Grolmes, be obtained

from the empirical correlation for a liquid film given by Hughmark [14]

&fl,w = K · Rem

l where:

'(

)K = 3.73; m = '0.47 for 2 < Rel < 100

K = 1.96; m = '1/3 for 100 < Rel < 1000

The gas friction factor requires information about the liquid film thickness.

Obviously:

" =Q̇l

Pwul=

Q̇l cos %

Pwul,#=

Q̇l cos2 %

&Dul,#(10)

We now have two expressions for the two unknown variables " and ul,#.

ug,# is the last parameter we need to find ul,# from Eq. (9) in order to evaluate

the “centrifugal force” acting on the rotating liquid film. Clearly:

ug,# =uz

tan %.

Measurements [15] have shown that the mean axial velocity in the cyclone

(uz) is approximately 0.8 times that at the wall, and that the axial flowpat-

tern is fairly uniform throughout the cyclone, so that:

ug,# =(uz)

0.8 tan %(11)

19

4.3 The re-entrainment number

Based on the calculated Rel for the experiments in the high-pressure rig,

most experiments seem to be within the transition regime, where entrainment

depends on Rel as explained above. For all experiments in that rig, Nµ <

1/15.

Assuming that transition regime is the dominant liquid film regime on the

inner cyclone wall, the top criterion in Eq. (3) can be used in the force ratio

in Eq. (6) and, hence, we get the re-entrainment number:

Rent(a) =

µlug

!

""g

"l

NaµRe!1/3

l

(12)

where, as discussed above, g is replaced by u2l,#/R in Eq. (4) for the evaluation

of Nµ. The argument a signifies that the power of the viscosity number is

as yet undetermined. We can thus say that the cyclone e"ciency, $cycl is a

function of Rent(a):

$cycl (Rent(a)) = f

*

+µlug

!

""g

"l

NaµRe!1/3

l

,

- . (13)

Ishii and Grolmes adjusted the power, a, of the viscosity number, Nµ, to fit

their data for the inception of the entrainment. The power should there-

fore be adjusted to the cyclone experiments. The power of Nµ is important

when experiments with di!erent physical fluid properties like natural gas and

N2/Exxsol are scaled.

The re-entrainment number for all experiments that have been carried out in

the high-pressure rig have been calculated in accordance with Eq. (13) and

20

are plotted in Fig. 7. Since many of the experiments with low liquid loading

showed increasing e"ciency with increasing gas flow, it was assumed that

droplet size played an essential role for the e"ciency at these low loadings.

Therefore only experiments were the liquid load exceeded 9 l/hr have been

included in the plot.

0 0.5 1 1.5 2 2.5 3

Reentrainment Number [-]

Sepa

ratio

n ef

ficie

ncy

[%]

20 bar50 bar92 bar

20 bar50 bar92 bar

N2/Exxsol Natural gas

70

75

80

85

90

95

100

Figure 7: The cyclone e!ciency in the high-pressure rig as function of the

re-entrainment number ([µlug/!]["g/"l]0.5)/(N0.4µ Re!1/3

l ). The plot includes

superficial gas velocities of 1–6 m/s, and liquid loads of 0.0009–0.007 vol%

Although these results and the ones shown in the following figure cover a

wide range of operating conditions and also di!erent fluid systems, they are

all obtained in one type of cyclone and may well be geometry dependent.

However, the general mechanisms governing reentrainment in other types of

cyclones are likely to be the same.

The power a = 0.4 gives a good fit between the natural gas and Exxsol

D60 data as seen in the figure. However, the pressure scaling, although

good, could be even better. One may therefore think that the gas and liquid

21

densities could be accounted for more precisely. For this reason the power of

the gas to liquid density ratio was subjected to regression and a good scaling

was found with a power of 0.8, as seen in Fig. 8.

0 0.5 1 1.5 2 2.5 3

Reentrainment Number [-]

Sepa

ratio

n ef

ficie

ncy

[%]

20 bar50 bar92 bar

20 bar50 bar92 bar

N2/Exxsol Natural gas

70

75

80

85

90

95

100

Figure 8: The data from Fig. 7 plotted against the modified re-entrainment

number ([µlug/!]["g/"l]0.8)/(N0.4µ Re!1/3

l )

The excellent correlation between the cyclone e"ciency and the re-entrainment

number confirms that the cyclone e"ciency is dominated by liquid film re-

entrainment rather than the penetration of fine droplets. The plot in Fig. 8

can be regarded as the maximum achievable e"ciency due to limitations

caused by re-entrainment for this particular geometry. However, if a signifi-

cant amount of droplets comparable to the cut size of the cyclone are present

in the inlet liquid loading, an extra contribution will be added to the liquid

carry-over of the cyclone. Experiments with such contributions will have

lower e"ciency than predicted by the re-entrainment number solely.

There is still some scatter in the results in Fig. 8, but with all the simplifi-

22

cations done and the complex process of gas-liquid interactions involved, the

correlation is still remarkably good. Some of the scatter might also be caused

by liquid carry-over due to the presence of small droplets, especially for the

high-pressure natural gas case. Some of the most important simplifications

are:

– Gradual drainage of liquid film through the slits in the cyclone wall has

not been accounted for

– The film is assumed to be evenly distributed on the wall

– Transition regime entrainment is assumed even though some of the

experiments appear to have a liquid Reynolds number smaller than the

limit given by Ishii and Grolmes

Finally, it is possible that wavelet behaviour in a centrifugal field, where the

centripetal acceleration varies with the radius, is somewhat di!erent from

that in a gravity field.

4.4 Re-entrainment at low pressures, the Weber num-

ber

As in the high-pressure rig, the cyclone e"ciency from the low-pressure rig

shows a general tendency of decreasing e"ciency with increasing gas and

liquid flow, consistent with re-entrainment limitation. Figure 9 shows sep-

aration e"ciency data from the low-pressure rig plotted against superficial

velocity in the cyclones. The physical properties of the fluids are given in

23

Table 1. The pressure was not varied independently in this rig, but was

always in the range 2–7 bara.

Superficial gas velocity [m/s]

Effic

ienc

y [%

]

70

75

80

85

90

95

100

6 8 10 12 14 16 18 20 22 24 26 28 30

0.068-0.094 Vol%0.02-0.024 Vol% 0.002-0.003 Vol%

0.02-0.06 Vol%0.028-0.036 Vol%0.0018-0.0026 Vol%

Exxsol: Water:

Figure 9: Separation e!ciency in the low-pressure rig plotted against the

superficial velocity in the cyclones. The liquid loadings are given in the legends

However, at low pressure the calculated values for Rel indicate that the

liquid film is below the regime where roll-wave entrainment is possible. If

these results are plotted against the re-entrainment number the decrease in

performance is much faster than in the high-pressure rig, as seen in Fig. 10.

However, the re-entrainment number appears to bring also the low-pressure

rig results, which were obtained [8] under a wide range of gas and liquid

flows, and with two di!erent fluid systems, onto one curve.

Since the velocity is considerably higher in the low-pressure rig, re-entrainment

is still possible by the undercut mechanism. However, as we also mentioned

above, at these low values of Rel, the film Weber number can better be used

24

0 0.5 1 1.5 2 2.5 3

Reentrainment Number [-]

Sepa

ratio

n ef

ficie

ncy

[%]

20 bar50 bar92 bar

20 bar50 bar92 bar

N2/Exxsol Natural gas

70

75

80

85

90

95

100

Results from low-pressure rig with Exxsol D60

Figure 10: A comparison between the cyclone e!ciency in the high-pressure

and the low-pressure rigs in terms of the modified re-entrainment number

([µlug/!]["g/"l]0.8)/(N0.4µ Re!1/3

l ). The data from the low-pressure rig include

cyclone superficial gas velocities in the range 6–30 m/s and liquid loads in the

range 0.002–0.09 vol%

25

for correlating the results [7].

$ = f (Wel) = f

#!gu2

g,s"

#

$. (14)

Figure 11 a) shows the low-pressure results plotted against Wel, where we

have used Eq. (10) to calculate the film thickness, ". Clearly the results

are brought onto one curve. We note that since the liquid density and the

interfacial tension are approximately constant in the low-pressure rig, the

variation in the liquid film Weber number is near identical to the gas dynamic

pressure times the liquid rate.

When the results from the high-pressure rig are plotted onto the same coor-

dinates, as in Fig. 11 b), they can be seen to globally form a cloud of points in

the same area as the low-pressure results. This shows that Wel does account

for important parameters governing re-entrainment. On the other hand, a

closer inspection of the figure shows that Wel does not account su"ciently

well for di!erences in the fluid properties with pressure. We have included

this plot to show that Wel actually is able to bring results from the two rigs

closer together, something that the re-entrainment number did not do.

In experiments with kerosine, a liquid that is comparable to Exxsol D60,

van Rossum [7] found that a Weber number of around 6 is a lower limit

for the onset of re-entrainment. This result is in agreement with the plot

in Fig. 11 a) where re-entrainment appears to become significant around

Wel = 6. Once again, this criterion was originally used to determine the

onset of entrainment, and not the entrained fraction.

26

Wel [-]0 2 4 6 8 10 12 14 16

Sepa

ratio

n ef

ficie

ncy

[%]

20 bar50 bar92 bar

N2/Exxsol

Low-pressure rig results

20 bar50 bar92 bar

Natural gas

b)0 5 10 15 20 25 30 35 40

Sepa

ratio

n ef

ficie

ncy

[%]

a)

70

75

80

85

90

95

100

70

75

80

85

90

95

100

Wel [-]

Figure 11: a) The results from the low-pressure rig plotted against the

liquid film Weber number, Wel. b) The results from the low-pressure and

high-pressure rigs plotted against Wel

27

4.5 The influence of scale

The e"ciency in the high-pressure rig is totally dominated by re-entrainment,

at least for liquid flows per cyclone above 9 l/hr. However, in the experiments

at K-lab it was seen that outer cyclones in the cyclone deck handled up to 2.5

times the amount of liquid that the inner cyclones handled [10], due to cross-

sectionally uneven liquid distribution. Since the cyclone e"ciency generally

drops o! with increasing liquid load the outer cyclones might su!er from

poorer e"ciency. If, in addition, some of the cyclones in the middle of the

cyclone deck receive a small amount of liquid but distributed as a fine mist,

this might also have a negative impact on the e"ciency. Based on earlier

experience [16] we believe that the uneven distribution to some extent is due

to the vaned inlet not distributing the liquid and gas ideally over the column

cross-section.

In the small scale high-pressure rig only two cyclones where installed and

obviously, little liquid mal-distribution could have occurred. Therefore, the

e"ciency in the this rig can be regarded as the maximum e"ciency when the

e"ciency is limited by re-entrainment.

In Figure 12 the measured cyclone e"ciency at the large scale rig is compared

to the maximum e"ciency found in the high-pressure rig. The results are

plotted as function of the re-entrainment number and the average liquid load

per cyclone has been used as input in the calculations.

The figure shows that the cyclone deck in the K-lab tests is very influenced

by the poor liquid distribution. In fact, in one case the e"ciency drops from

an expected maximum e"ciency of more than 80% down to approximately

28

Sepa

rarti

on e

ffici

ency

[%]

3035404550556065707580859095

100

0 0.5 1 1.5 2 2.5 3

55 barg113 barg

Maximum efficiency due to reentrainment

Reentrainment Number [-]

20 bar50 bar92 bar

20 bar50 bar92 bar

N2/Exxsol Natural gasHigh-pressure rig

K-lab

Figure 12: The cyclones in the large scale rig su"er from reduced e!ciency

compared to the results from the high-pressure rig. The maximum e!ciency

found in the high-pressure rig is indicated and extrapolated. The large-scale

rig results include cyclone superficial gas velocities of 9 m/s and 4.3–5.4 m/s

(at 56 and 114 bara, respectively) and liquid loadings in the approximate range

0.06–0.095 vol%

29

40%.

This e!ect of severely reduced e"ciency at larger scale has, to the authors’

knowledge, never before been documented. The result is very important,

since it demonstrates how much the e"ciency of a large scale scrubber can

deviate from the e"ciency found in a small scale lab—even when the gas

velocity, the liquid concentration and the fluid properties are identical. The

re-entrainment number o!ers an analysis tool to quantify the impact of liquid

mal-distribution.

5 Concluding Remarks

– A first step in the direction of modelling and scaling cyclone e"ciency

when this is limited by re-entrainment rather than by separation e"-

ciency for small droplets has been outlined

– Results with di!erent fluid systems and spanning wide ranges of pres-

sures, gas flowrates and liquid loadings have been brought to collapse on

one curve by plotting them against a modified re-entrainment number

derived on basis of the theory for the onset of roll-wave re-entrainment

of Ishii and Grolmes [4]. All the results were obtained under conditions

such that the Reynolds number of the liquid film on the cyclone wall,

Rel was moderate or high.

– Results generated at lower pressures, where Rel is lower, but also for

two di!erent fluid systems, and at a wide range of gas and liquid flows,

were brought to collapse on one curve when plotted against the liq-

30

uid film Weber number, agreeing with the work on the onset of re-

entrainment at low Rel of van Rossum [7].

– An important e!ect of scale in reducing the e"ciency of cyclone banks,

probably due to mal-distribution of liquid between the cyclones, has

been documented.

– For further understanding of the phenomena taking place, measure-

ments of the droplet sizes throughout the equipment are desirable, and

achieving this will have a high priority in the future.

Acknowledgment

Financial support from the Research Council of Norway through the HiPGaS

programme, and the industrial sponsors Statoil AS, ConocoPhillips, Norsk

Hydro AS, Vetco, FMC Kongsberg Subsea and Aker-Kværner is highly ap-

preciated.

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33