Lagrangian slug ﬂow modeling and sensitivity on hydrodynamic slug initiation methods in a severe slugging case

8/13/2019 Lagrangian slug flow modeling and sensitivity on hydrodynamic slug initiation methods in a severe slugging case

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Lagrangian slug flow modeling and sensitivity on hydrodynamic slug initiation

methods in a severe slugging case

T.K. Kjeldby a,⇑, R.A.W.M. Henkes b, O.J. Nydal a

a Norwegian University of Science and Technology, Department of Energy and Process Engineering, Kolbjørn Hejes vei 1B, 7491 Trondheim, Norwayb Delft University of Technology, Laboratory for Aero and Hydrodynamics, Leeghwaterstraat 21, 2628 CA Delft, The Netherlands

a r t i c l e i n f o

Article history:

Received 12 July 2012

Received in revised form 11 January 2013

Accepted 15 January 2013

Available online 8 February 2013

Keywords:

Two-phase flow

Severe slugging

Slug tracking

Two-fluid model

Slug capturing

Slug flow

a b s t r a c t

Severe slugging is a dynamic two-phase flow phenomenon with regular liquid accumulation and blow-

out in flow-line riser geometries. This paper discusses the applicability of a slug tracking model on a case

wherehydrodynamic slug initiation in a horizontal part of the pipeline upstream the riser base affects the

severe slugging cycle period. The given experimental case is from the Shell laboratories in Amsterdam:

air–water flow in a 100 m long pipe (65 m horizontal and 35 m 2.54 downwards) followed by a

15 m long vertical riser.

A Lagrangian slug and bubble tracking model is described. A two-fluid model is applied in the bubble

region and the slug region is treated as incompressible flow, with an integral momentum equation. Slug

initiation from unstable stratified flow can be captured directly by solving the two-fluid model on a fine

grid (a hybrid capturing and tracking scheme). Alternatively, slug initiation can be made from sub grid

models, allowing for larger grid sizes. The sub grid models are based on the two established flow regime

transition criteria derived from the stability of stratified flow and from the limiting solution of the unit

cell slug flow model.

Sensitivity studies on hydrodynamic slug initiation models on the severe slugging characteristics are

presented. No hydrodynamic slug initiation (e.g. large grid size in the capturing scheme) overestimates

the severe slug period compared with the experiments. Slug capturing and sub grid initiation modelsboth give good predictions for small grid sizes (provided the detailed inlet configuration is included in

the capturing case). Good predictions are also shown for larger grid sizes (factor of 50) and sub grid ini-

tiation models.

The numerical tests show that correct prediction of the severe slugging cycle is sensitive to the initia-

tion of upstream hydrodynamic slugs, but less sensitiveto the local structure of the slug flow (frequencies

and lengths) in the upstream region.

2013 Elsevier Ltd. All rights reserved.

1. Introduction

The slug flow regime occurs in a wide range of industrial mul-

tiphase pipe flow applications. Slug flow represents a particular

challenge in the oil and gas industry where large scale flow insta-bilities may occur in pipeline-riser systems.

The modeling of slug flow may be approached on different time

and length scales. A common procedure is to solve the two-fluid

equations (mass and momentum conservation equations for each

phase) on an Eulerian grid. This is a procedure typically used by

nuclear safety codes like CATHARE and RELAP (Bestion, 1990;

Umminger et al., 2002), as well as by oil and gas pipeline simula-

tors like OLGA (Bendiksen et al., 1991).

Small scale slug flow is then treated as an averaged flow

whereas the large scale severe slug flow phenomenon is captured

by the two-fluid model. This gives a computationally efficient

model, but requires implementation of averaged hydrodynamic

slug flow models and criteria for flow regime transitions fromstratified flow.

Some studies have demonstrated the capability of the two-fluid

model to also resolve small scale slug flow, without the need for

transition models (Issa and Kempf, 2003; Bonizzi et al., 2009).

These slug capturing methods rely on a fine grid spacing to resolve

the sharp discontinuities in holdup at bubble noses and slug fronts.

One way of reducing the need for a fine grid spacing when a sta-

tionary grid is utilized is to apply higher order mass-and momen-

tum flux functions (see Flåtten, 2003; Wangensteen, 2010; Loilier

et al., 2005).

Another approach is to formulate a Lagrangian model. This al-

lows for tracking of fronts with a moving grid and elimination of

0301-9322/$ - see front matter 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.ijmultiphaseflow.2013.01.002

⇑ Corresponding author. Tel.: +47 98646395.

E-mail address: [email protected] (T.K. Kjeldby).

International Journal of Multiphase Flow 53 (2013) 29–39

Contents lists available at SciVerse ScienceDirect

International Journal of Multiphase Flow

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numerical diffusion at discontinuities. Such concepts have been

tested with different discretization and solution procedures (Nydal

and Banerjee, 1996; Leebeeck and Nydal, 2010; Renault, 2007;

Kjølås, 2007).

The slug tracking model version by Kjølås (2007) is extended

here, and applied as a computational framework to investigate

the coupling of the initiation of hydrodynamic slugs and severe

slugging cycles as observed experimentally.

2. The model

The discretization of the governing conservation equations is

implemented in terms of a hybrid two-fluid and slug tracking mod-

el formulation. The object oriented design is illustrated in Fig. 1,

where the computational objects are referred to as borders, sec-

tions and units. A section can either be a bubble or a slug, while

a unit consists of a list of sections of equal type. Two sections are

always separated by a border, which can either be stationary or

moving. The computational grid is shown in Fig. 2.

In bubble sections the full two-fluid model is solved. A slug unit

is assumed to be incompressible, which allows for the application

of a single momentum balance over each slug unit.

The mass balance for phase k is obtained by integration over the

section control volume:

d

dt

Z V k; J

qkdV þ

Z L J

@ qkðuk ubÞ

@ x Akdx ¼ _M sk; J ð1Þ

Here, q denotes density, u velocity, A cross section area and V vol-

ume. The term _M sk is a possible mass source. The border velocity

is denoted as ub. Mass balances are solved for all sections in the

pipe. The mass balances are discretized by the upwind donor cell

principle and they are integrated implicitly in time.

The pressure equation is written as:

@ p J @ t X

k

@ qk; J

@ p

V k; J qk; J !þ

@ V J @ t

þXk

1

qk; J Z L J @ qkðuk ubÞ

@ x Akdx ! ¼ X

k

_M sk; J qk; J !

ð2Þ

This equation is obtained by adding the mass conservation equa-

tions for each phase and by expanding the time derivative term

by the product rule together with the introduction of an equation

of state for the gas. The pressure equation is solved for all bubble

sections. The pressure in a slug section is not a computational var-

iable, but it follows from the computed frictional and gravitational

contributions along the slug unit.

The momentum equation for phase k is obtained by integration

of the momentum balance over the momentum control volume j:

d

dt Z V k; j qk

ukdV

þZ L j

@ qkukðuk ubÞ

@ x A

kdx

¼

Z V k; j

@ p

@ xdV

Z V k; j

qk g cos h@ hk@ x

dV

Z V k; j

skS k Ak

dV

Z V k; j

siS i Ak

dV

Z V k; j

qk g sin hdV ð3Þ

The pipe inclination is given by h and the height of the liquid film is

given by hl. The gravitational acceleration is denoted by g . This

momentum control volume is staggered relative to the mass bal-

ance and pressure control volume J .

The shear stress between phase k and the pipe wall is denoted

as sk while the interface shear stress is denoted as s i. The friction

factor between the wall and phase k is obtained from the Blasius

model:

kk ¼ 0:316Re0:25k ð4Þ

Here, Rek is the Reynolds number of phase k. There are numerous

empirical expressions for the interface friction in the literature.

For test purposes, we determine ki as the product of an Interface

Friction Multiplier (IFM) and the gas friction factor, as shown in

Eq. (5). IFM = 1 often leads to acceptable holdup predictions for

smooth stratified flows:

ki ¼ IFM k g ð5Þ

The momentumequations are solved at bubble–bubble borders and

in slug units. The single momentum balance applied for each slug

unit in combination with zero gas fraction in slugs implies that

the liquid phase velocity ul is the same within all sections in a slug

unit, given that the pipe diameter is constant.

An important closure model is the one for the bubble nose

velocity ub:

ub; j ¼ C 0; jul; j þ U 0; j ð6Þ

Fig. 1. Units, sections and borders.

Fig. 2. Computational grid.

30 T.K. Kjeldby et al. / International Journal of Multiphase Flow 53 (2013) 29–39



Several experimental investigations have been made to establish

empirical correlations for the distribution coefficient C 0 and for

the drift velocity U 0, where Dumitrescu (1943) and Davies and Tay-

lor (1950) were some of the earlier ones. The coefficients by Bendik-

sen (1984) apply for all pipe angles:

C 01 ¼ 1:05 þ 0:15sin2h

C 02 ¼ 1:2

U 0v ¼ 0:35 ffiffiffiffiffiffi gD

p sin h

U 0h ¼ 0:54

ffiffiffiffiffiffi gD

p cos h

ð7Þ

C 0 ¼ C 01 U 0 ¼ U 0v þ U 0h if jumj 6 ulim

C 0 ¼ C 02 U 0 ¼ U 0v if jumj > ulim

ð8Þ

ulim ¼ U 0hC 02 C 01

ð9Þ

A transition to laminar flow needs to be included for more viscous

systems. To allow the model to decide whether a bubble–slug dis-

continuity is a slug front or a bubble nose, a bubble turning criterion

is needed. The criterion used in the model is that a bubble nose al-

ways travel in the direction of lower pressure. A gradual transition

relation has also been included in the model to avoid discontinuities

at the point of bubble turning.

If a slug–bubble border is not a bubble nose, it is treated as a

slug front. The velocity of the slug front border is determined froma liquid mass balance across the front as given by Eq. (10). The spa-

tial indexes are defined in Fig. 3. From the mass balance Eq. (10) a

corresponding set of slug front velocity coefficients is obtained

similar to the bubble nose coefficients given by Eq. (8):

ub; j ¼ Al; J 1ul; j1 Al; J ul; J

Al; J 1 Al; J

ð10Þ

3. Experiments and simulation setup

Four experimental cases from a severe slugging experimental

facility described in Seim et al. (2011), have been compared with

simulations. The combinations of gas and liquid mass flow rates

and the corresponding superficial velocities are given in Table 1.The pipeline geometry is shown in Fig. 5 which is a screenshot

from the dynamic animation of the simulation results. Thebdimen-

sions of the setup are given in Table 2. The simulation geometry

closely resembles the experimental geometry. The large diameter

pipe in the leftmost part of the configuration has been included

to simulate a 250 l air buffer tank at the inlet. This tank provides

the upstream compressibility which is needed for the severe slug-

ging cycle to occur.

The option to define a curved pipe geometry with a bend has

been implemented in the model. This enables a continuous change

in the gravity term as slugs and bubbles pass the bend. This has

proved to be particularly useful for a numerically well behaved

bubble turning process. The curved pipe geometrical definitions

used in Table 2 are illustrated in Fig. 4.

A closed inlet and an open outlet at fixed atmospheric pressureis applied. A fully open valve is connected to the end of the riser

(PIPE 10 in Table 2). Air is supplied to the system by a gas mass

source at the inlet, while liquid enters from a liquid mass source

slightly downstream from the inlet (PIPE 2 in Table 2).

The experimental time series shown in Fig. 6a and b are the

pressure at the riser base for Case 1 and 3, respectively. Case 1

shows large variations in the pressure. There is a well defined per-

iod of severe slugging, with liquid accumulation in the riser. Case 3

shows only very small pressure variations which represent stable

flow.

The experimental pipeline is constructed from steel, which

makes visual inspection of the flow difficult. The shape of the time

series shown in Fig. 6a, however, and in particular the quick pres-

sure recovery at the location denoted (4), indicates the generationof hydrodynamic slugs upstream of the riser base during the blow-

out. Liquid is accumulating in the horizontal part of the pipeline

(PIPE 4 in Table 2) during the severe slug build-up (1) and this li-

quid is transported to the bend during the blowout (3).

A fairly close agreement between experiment and simulation

was obtained without inclusion of the valve for Case 1. For the sta-

ble Case 3 inclusion of the valve in the model was needed in order

to obtain stable flow. Both a stratified and a mixed flow valve for-

mulation were tested.

The stratified valve model was implemented by using equiva-

lent friction factors for both phases based on a provided valve coef-

ficient of C v = 12[gal min1 psi1/2]. This was observed to give a too

low friction for the gas phase in the two fluid region, resulting in

too high gas flow through the valve and severe slugging behaviorin Case 3 where stable flow was expected.

Fig. 3. Slug front.

Table 1

Experimental cases.

Case U sl (m/s) U sg (m/s) _ml ðkg=sÞ _m g ðkg=sÞ Type

1 0.20 1.80 0.399225 0.004438 Severe slugging

2 0.11 0.90 0.218253 0.002216 Severe slugging

3 0.40 3.60 0.806991 0.008881 Stable flow

4 0.24 0.90 0.483247 0.002216 Severe slugging

Table 2

Simulation geometry with pipes numbered from 1 at the inlet to 10 at the outlet.

Pipe L (m) D (m) h () hin () hout () R(m)

1 7.958 0.2000 45.00

2 2.100 0.0508 45.00

3 0.157 0.0508 45.00 0.00 0.2

4 65.000 0.0508 0.00

5 35.000 0.0508 2.54

6 0.323 0.0508 2.54 90.00 0.27 2.500 0.0508 90.00

8 13.000 0.0450 90.00

9 0.314 0.0450 90.00 0.00 0.2

10 6.000 0.0450 0.00

Fig. 4. Curved pipe geometrical definitions.

T.K. Kjeldby et al. / International Journal of Multiphase Flow 53 (2013) 29–39 31



A mixed flow valve model based on no slip with the provided

valve C v was observed to perform better, i.e. giving a reduced

amplitude in the pressure oscillations. Tuning of the valve coeffi-

cient, however, was found necessary to obtain stable flow as in

the experiments. A valve model based on the non-dimensional

pressure loss coefficient K for mixture flow assumption has been

applied. The pressure drop across the valve is then written as:

D pm ¼ K qmu

2m

2 ð11Þ

where qm and um are defined as:

qm ¼ qlal þ q g a g ð12Þ

um ¼ ulal þ u g a g ð13Þ

Fig. 5. Simulation geometry. Diameter to length ratio is exaggerated.

800 850 900 950 10001

1.5

2

2.5

3x 10

5

1

2

3

4

(a) Pressure recordings for severe slugging - Case 1

800 850 900 950 10001

1.5

2

2.5

3

x 105

(b) Pressure recordings for stable flow - Case 3

Fig. 6. Experimental pressure time series at the riser base from Seim et al. (2011).

(a) 1 - Liquid column in riser is growing and pressure at riser base increases

(b) 2 - Liquid column accelerates up the riser. This gives a sudden upstream pressure drop and an increase in gas velocity

(c) 3 - The increase in gas velocity gives hydrodynamic slug initiation in the upstream horizontal pipe

(d) 4 - Rapid pressure recovery at riser base due to arrival of hydrodynamic slugs which increase hydrostatic pressure as

they propagate into the vertical riser

Fig. 7. Severe slugging inducing hydrodynamic slug initiation. Diameter to length ratio is exaggerated.




The volume fraction of phase k is here given as ak. This pressure

drop is set equal to the pressure drop of each phase k in the two-

fluid model:

D pk ¼ qkkku

2kS k

8 Ak

D x ð14Þ

Here, Ak is the cross section area and S k the wetted perimeter of

phase k. Eqs. (11) and (14) then gives the friction factor for a pipesection of length D x to which the valve is connected:

kk ¼ qmu

2m4 AkK

qku2kS kD x

ð15Þ

To approach no-slip conditions in a pipe segment with a valve, the

interface friction factor is set to a high value:

ki ¼ 1000 k g ð16Þ

A pressure loss coefficient K = 136 was found to givegood results for

both Case 1 and Case 3, see Fig. 9 and Fig. 13. Fig. 7 contains a set of

screenshots from the Case 1 simulation showing the different stages

of the severe slugging cycle. The numbers given in the figure cap-

tions are comparable with the numbers shown in Fig. 6a.

4. Slug initiation models

The capability of slug capturing models to initiate hydrody-

namic slugs directly from the two-fluid model has been demon-

strated by Issa and Kempf (2003) and Bonizzi et al. (2009) as

well as by others. This approach requires the application of a very

fine grid. If a coarse grid is applied, these small scale flow dynamics

are not resolved and sub-grid slug initiation models must be ap-

plied. Two such slug initiation models are tested in this study:

One is based on the instability of stratified flow and the other on

the existence of slug flow.

The initial length of a slug created by one of the models is de-

noted as Linit , while the minimum slug length needed to survive

during a simulation is set to 1D. Slugs shorter than this length

are removed and their liquid is redistributed across neighboring

bubble sections.

4.1. Hydrodynamic slug initiation at the stratified flow stability limit

The Stratified Stability criterion, from now on indicated as SS, is

derived from a stability analysis of the two-fluid model (see among

others Barnea and Taitel (1993)), and it is given by Eq. (17):

ðql q g Þ g cos h Al

ql@ Al@ hl

þ A g

q g @ A g @ h g

0@

1A ðu g ulÞ

2> 0 ð17Þ

Utilizing

@ A g

@ h g ¼

@ Al

@ hl ;

@ Al

@ al ¼ A and

@ hl

@ al ¼

@ hl

@ bl

@ bl

@ al together with a relation forwetted angle bl derived by Biberg (2005)

bl ¼ pal þ 3p2

1=3

1 2al þ a1=3

l a1=3

g

ð18Þ

and the definition of stratified liquid height hl

hl ¼ D

2ð1 cosblÞ ð19Þ

gives the slug initiation criterion depending on the wetted angle.

ðql q g Þ g cos h al

ql

þ a g q g

!@ hl

@ bl

@ bl

@ al

> ðu g ulÞ2

ð20Þ

A hydrodynamic slug is created when this relation is satisfied. Thegeometrical relations are shown in Fig. 8.

4.2. Hydrodynamic slug initiation at the slug existence limit

Another model used to predict the transition from stratified to

hydrodynamic slug flow is the Slug Existence criterion, from now

on termed SE. This criterion was derived by Bendiksen and Espedal

(1992) and is equivalent to the limiting solution of the unit-cell

slug flow model, when the slug fraction is zero. In our case of no

gas entrainment into the liquid slug, a hydrodynamic slug is cre-

ated when the following is satisfied:

u g > ub ð21Þ

Here, um is the local mixture velocity, ub is the slug bubble velocity

and u g the stratified flow gas velocity.

ub ¼ C oum þ U o ð22Þ

5. Selected time series

Experimental and simulated time series for Case 1, 2, 3 and 4

are presented in Figs. 9–13. The base case simulation parameters

are:

Hydrodynamic slug initiation from SE (Slug Existence criterion)

activated in the horizontal part of the pipeline (PIPE 4 in

Table 2), Linit = 2D.

Interface friction multiplier, IFM = 3.

Valve coefficient, K = 136.

Inclination of inlet region (PIPE 2 in Table 2), h2 = 45.

Inclination of horizontal part of the pipeline (PIPE 4 in Table 2),

h4 = 0.

Comparison between the D x = 21D and 81D time series from

Case 1 reveals small differences in shape as well as in the slugging

period. The amplitude of the local oscillations at the instant of the

pressure recovery, corresponding to (4) in Fig. 6a, however, is

slightly higher when a coarse grid is applied.

A good agreement between experiments and simulations for

the slugging cycle period, minimum pressure and maximum pres-

sure is found for both Case 1 and 2. Some larger deviation for the

slugging cycle period is observed in Case 4.

A close agreement between experiment and simulation for Case

3 was obtained by tuning of the valve coefficient K . The animation

in Fig. 14 shows the presence of short hydrodynamic slugs in the

horizontal part of the pipeline which die as they propagate intothe declining part of the pipeline.

Fig. 8. Stratified flow geometry.




6. Sensitivity analysis for Case 1 and Case 3

Sensitivity simulations were carried out to assess the effects of

slug initiation methods, interface friction, pipe angles and gridspacing.

Some of the simulations for Case 1 give time series with a non-

constant oscillation period as shown in Fig. 15, while other simula-

tions develop into stable flow as shown in Fig. 6b. Simulations

where these characteristics are observed have been used to definethe outer limits of the range over which the sensitivity to a variable

0 100 200 300 400 5001

1.5

2

2.5

3 x 10

5

Fig. 9. Pressure at the riser base for Case 1, D x = 21D.

0 100 200 300 400 5001

1.5

2

2.5

3

x 105


0 100 200 300 400 5001

1.5

2

2.5

3 x 10

5


0 100 200 300 400 5001

1.5

2

2.5

3 x 10

5


0 100 200 300 400 5001

1.5

2

2.5

3x 10

5





is checked. Consequently, only simulations with constant ampli-

tude as shown in Fig. 16 have been presented in Figs. 18 and 20.

The standard simulation settings listed in Section 5 are applied.The parameter to which sensitivity is checked is stated explicitly

in each sub-section.

The flow regime within PIPE 2 is not known from the experi-

ments. Only stratified flow has been found in PIPE 2 in the captur-

ing simulations.

6.1. Sensitivity to slug initiation model and bubble section grid spacing

– Case 1

Hydrodynamic slugs can be formed in the horizontal pipe dur-

ing blowout of a severe slug. When a slug accelerates up into the

vertical riser, then the gas velocity increases, and hydrodynamic

slugs can be generated upstream. When a hydrodynamic slug is

formed it accelerates downstream and flushes liquid towards theriser base. The location and time of slug initiation might thus influ-

ence on how much liquid is removed from the horizontal pipe dur-

ing each slugging cycle. This influences the slugging cycle period.

Fig. 17 shows liquid holdup profiles for the hydrodynamic slug

generation for D x = 4.5, 21 and 161D. Each sequence of pictures

shows a staged process where the liquid level close to the inlet

of the horizontal part of the pipeline grows from low to high. Ulti-

mately a hydrodynamic slug is formed. For small D x a distinct

hydraulic jump can be seen prior to slug initiation. At D x = 4.5D

slug initiation is obtained directly from the two-fluid model. At

D x = 21 and 161D the grid is too large for slug capturing and slugs

are generated based on predictions made by the SS initiation

criterion.

The slug lengths grow when the grid spacing of the bubble sec-tion is increased. This effect is due to the fact that only one slug can

be initiated in a bubble section at the time. Consequently, when a

fine grid spacing is utilized, hydrodynamic slug initiation can be

predicted by the slug initiation model in a high number of bubblesections in the horizontal region at the same time. A similar mass

and momentum transfer in the horizontal part of the system can

however be obtained by a lower number of longer slugs. This is

why the resulting period of the severe slugging cycle, however,

hardly depends on the bubble section grid spacing, even if the

hydrodynamic slug frequency will be grid dependent.

The results presented in Fig. 18 show severe slugging cycle peri-

ods resulting fromsimulations where hydrodynamic slug initiation

from the SE criterion, from the SS criterion and from the two-fluid

model (by slug capturing) have been compared. Hydrodynamic

slug generation directly from the two-fluid model (by slug captur-

ing) is captured for a grid size D x < = 8.5D when holdup waves

bridge the pipe. The predicted slugging period approaches the

experimental value when the grid spacing is reduced. For a gridspacing above D x = 8.5D hydrodynamic slug initiation is not cap-

tured by the two-fluid model and the period becomes approxi-

mately 50% higher.

The two slug initiation criteria SS and SE give quite similar re-

sults for the slugging period. Both show only a minor grid depen-

dency. Based on the results given in Fig. 18, the SE model has

been chosen as the standard simulation setting.

6.2. Sensitivity to inclination of the inlet – Case 1

A picture of the experimental inlet configuration is shown in

Fig. 19. Air arrives at the mixing point through a large diameter

pipe which is connected to the buffer tank, whereas water enters

via a smaller diameter pipe at an angle to the air pipe. When wateris pumped into the system at an angle it carries momentum. In the

Fig. 14. Case 3 animation. Diameter to length ratio is exaggerated.

500 600 700 800 900 1000 1100 1200 1300 1400 15001

1.5

2

2.5

3x 10

5

Fig. 15. Case 1 with non-constant period during sensitivity tests.

500 600 700 800 900 1000 1100 1200 1300 1400 15001

1.5

2

2.5

3x 10

5

Fig. 16. Case 1 with constant period during sensitivity tests.




simulations, momentum contributions from the sources have not

been included.

The influence of gravity and of gas drag on the water accelerates

the water to enter the horizontal part of the pipeline with a posi-

tive velocity. Simulations show that this gives a hydraulic jump

at the inlet of the horizontal pipe, as can be seen in Fig. 17. Thevelocity at which water enters the horizontal pipe influences the

precise location where the hydraulic jump occurs. Fig. 20a shows

a sensitivity analysis of how the angle of the inlet, denoted as h2,

influences the slugging period.

Simulations performed at D x = 161D appear to be more sensi-

tive to h2. At this grid spacing stable flow is found when h > 25.

For simulations with the slug capturing approach it turned out

the liquid source had to be included in the declining inlet (PIPE 2 in

Table 2). An attempt was made to position the liquid source at the

inlet of the horizontal pipe (PIPE 4 in Table 2), but this resulted in

rapid filling of the nearby short sections, slug formation and severeslugging simulations with non-constant period as shown in Fig. 15.

Fig. 17. Examples of slug initiation sequences in the horizontal part of the pipeline (PIPE 4 in Table 2). Diameter to length ratio is exaggerated.

Fig. 18. Case 1 grid dependency of the slugging period.

Fig. 19. Experimental inlet configuration from Seim et al. (2011).




Fig. 20. Case 1 sensitivity analysis results. SE denotes slug initiation from the slug existence model while SS denotes initiation at the stratified stability limit.




This illustrates the dependency of the slug capturing approach on

an accurate simulation setup.

6.3. Sensitivity to inclination of the pipe downstream of the inlet –

Case 1

A sensitivity analysis of the angle of the pipe downstream of the

inlet (the horizontal PIPE 4 in Table 2), denoted as h4, has been per-formed to investigate the effect on the hydrodynamic slug genera-

tion and on the overall slugging cycle period. The results are

presented in Fig. 20b. For small negative angles hydrodynamic

slugs are generated, similarly to how they are generated when

the pipe is horizontal. When the angle is decreased further, hydro-

dynamic slugs are no longer formed, and liquid flows as a stratified

layer towards the riser base, where severe slugging without hydro-

dynamic slug initiation is obtained for D x = 21D. In the absence of

hydrodynamic slugs, the slugging period of the severe slugging cy-

cle has doubled. However, for a too coarse grid spacing with

D x = 161D stable flow is found.

At small positive angles hydrodynamic slugs are formed similar

to the configuration with the horizontal pipe. When the angle is in-

creased further, liquid fallback contributes to the formation of hydrodynamic slugs. Now such slugs are no longer generated

exclusively by the hydrodynamic mechanism and irregular slug-

ging cycle periods are obtained. This trend is observed for both

D x = 21D and D x = 161D.

6.4. Sensitivity on Linit – Case 1

Slugs that are created based on one of the hydrodynamic initi-

ation criteria are set up with an initial length Linit . The results from

the sensitivity analysis of this variable obtained with the SE

and the SS slug initiation models are shown in Fig. 20c and in

20d, respectively. The severe slugging frequencies are similar for

Linit < 6D.

6.5. Sensitivity on interface friction factor – Case 1

The sensitivity on the interface friction is checked through var-

iation of the variable IFM (Interface Friction Multiplier). The results

are presented in Fig. 20e. A relatively small influence on the results

is observed for both D x = 21D and D x = 161D.

6.6. Sensitivity to hydrodynamic slug initiation model and bubble

section grid spacing – Case 3

The sensitivity on the grid spacing of the bubble section and on

the hydrodynamic slug initiation model is checked for Case 3 andpresented in Fig. 21. The three methods give similar results for

small grid sizes. Capturing and the SS initiation methods fail for

larger grid sizes.

The results obtained with the SS model show the characteristic

large pressure oscillations similarly to what is observed in the se-

vere slugging Case 1. SE provides an earlier hydrodynamic slug ini-

tiation than SS and slug flow upstream the riser base stabilizes the

severe slugging.

7. Conclusion

Pipeline-riser flow loop experiments for severe slugging dem-

onstrate the coupling between hydrodynamic slug initiation and

the severe slugging frequency. Liquid accumulation in a horizontalpipe segment upstream the riser base is propagated towards the

bend during the severe slug blowout, and affects the initiation of

the next severe slug at the riser base. The case has been computa-

tionally explored with a dynamic slug tracking model with three

slug initiation methods: slug initiation from a two fluid model

(slug capturing on a fine grid), from a stratified flow stability crite-

rion and from a slug existence criterion (sub grid initiation mod-

els). The different initiation models give good correspondence

with the experimental results for small grid sizes. The slug captur-

ing method naturally has to fail for increasing grid sizes whereas

the sub grid initiation models give quite similar results also at lar-

ger grid sizes. Sensitivity tests on pipe inclinations shows that for

the capturing simulations it is also important to include a detailed

representation of the inlet geometries at the point of the mixingsection.

Acknowledgements

Thanks to O. Novak (NTNU), who has made improvements to

the animation tool that helped the interpretation of the predictions

by the slugging models.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, in

the online version, at http://dx.doi.org/10.1016/j.ijmultiphaseflow.

2013.01.002.

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Lagrangian slug ﬂow modeling and sensitivity on hydrodynamic slug initiation methods in a severe slugging case