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03.2011
UDC 622.691.12; 622.279.8
New Mechanistic Model for Gas Flow
with Small Liquid Rates in Pipelines
V.A.Suleymanov, O.A.Bychkova
(Gazprom VNIIGAZ)
Summarizing of results of theoretical and experimental researches allow to create the method of
determination of basic parameters of gas flow with low quantity of liquid in offshore pipelines is
presented. This method is based on improved method of Taital and Duckler and taking into account the
interface friction factor. Besides, criterions for determination of flow pattern change from stratified to
homogeneous and slug flow are presented. The method was tested on the design of the transportation
system from the Shtokman gas condensate field to shore..
Key word: gas-liquid flow, multiphase flows, criterions of flow pattern change, low loads of liquid in
gas, mechanistic model, interface friction factor, offshore pipelines
Адрес связи: [email protected]
DOI: 10.5510/OGP20110300083
Simultaneous liquid and gas flow in pipelines needs to
be controlled, monitored, analyzed and managed.
In the oil and gas industry transport of gas with low
liquid yield is normally carried out in infield and trunk
pipelines.
For proper design and modeling of these pipelines
it is necessary to provide accurate prediction of flow
pattern, liquid hold-up and pressure drop which is
consistent with thermo- and hydrodynamic properties of
the gas-liquid mixture.
Many theoretical models and experimental
correlations for prediction of pressure drop and liquid
hold-up in pipelines were developed during the last
70 years. However no single one works for all flow
regimes in multiphase gas-liquid flow. Further, gasliquid flows with low liquid content are less investigated
and information about them is limited.
The purpose of this research is the quantification of
the influence of liquid yields to parameters of wet gas
patterns in pipelines. The following tasks were carried
out for achieving this purpose:
1) analyse existing approaches to determination of
patterns of wet gas flow with low liquid loading;
2) work out the algorithm for calculation of liquid film
level in wet gas flow with low liquid loading; and
4) test this algorithm at modelling of Stockman
trunk line.
Comparison of field data and calculated
data for pressure drop in wet gas pipelines
One of the most significant and consistent assessments
of the concurrent flow of gas and low loads of liquid was
done by Hope et al (1977) [8]. They compared three well
known single phase gas equations (AGA, ColebrookWhite and Pranhandle) with three two-phase models
(Baker et al, 1954; Dukler, 1964 and Beggs&Brill, 1973).
They predicted the pressure drop of a North sea pipeline
transporting approximately 25.5 MSm3/d of gas with a
liquid load of 28 sm3/m3. The single phase models gave
better predictions than the two-phase models and the
AGA correlation was by far the best single phase model.
Ullah (1987) [13] performed a similar analysis with
wet gas system (liquid load in gas is 5.6 sm3/m3) off
the coast of the West Indies and came up with similar
findings.
Asante and et al (2000) provided the similar
investigation for three existing wet gas pipelines: Frigg,
Viking и Yacheng [4]. The results indicated that the
difference between field and calculated data using AGA
correlation was minimum for wet gas with low load of
liquid (less than 45 sm3/m3). The Beggs&Brill and the
Dukler correlations showed bigger errors of pressure
drop prediction (for different production rates).
Gould and Ramsey (1975) [6] looked at an 16 inch
pipeline transporting gas with a liquid loading of 56-112
sm3/m3 and concluded that the Beggs&Brill correlation
gave better predictions than the single phase Pranhandle
model.
Besides, there is a challenge to measure void
fraction and hold-up in the two-phase gas-liquid
flows. In literature different types of techniques were
implemented to measure the void fraction in the twophase, gas-liquid closed flows: Microwave Flow Sensor,
Optical probe, Gamma-ray densitometers, Capacitance
sensor, Quick-closing-valves. In addition, synchrotron
X-rays, pulsed neutron technique, conductance probe,
ultrasonic technique, and ring impedance probe have
been used successfully to measure the void fraction in
two-phase flow systems [10]. But all these techniques
are limited by the amount of liquid they are able to
measure. For example, the total uncertainty, based on
root-sum square combination of precision (random) and
systematic (bias) components at 95% confidence (± 2σ ),
was determined for each type of gamma densitometer
system (GDS) measurement. The wide beam edge
measurement was averaged for a total uncertainty of ±
0.017 in void fraction [12].
The results indicates that up-to-date methods and
correlations for predicting of the parameters of twophase flow with low loads of liquid (including simulators
PipePhase, PipeSim, OLGA etc) can lead to significant
errors.
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At the interface of gas and liquid phases
there is a shear stress which mostly depends
on the liquid level. It also depends on density,
velocity and viscosity of gas. The shear stress
causes deceleration of gas phase and speed-up
of liquid film.
Geometry of liquid layer is considered as a
symmetric annular segment at the bottom of
the pipeline (Fig.1, b).
As it seen from above, suggested mechanistic
model is based on the basic principles of fluid
mechanics and assumption about the interface
behavior. Verification of the model should be
based on stable solution of set of equations
and physical considerations.
The model allows to:
• calculate the liquid level at the pipeline
cross section;
• calculate the hold-up;
• calculate the pressure drop;
• determine the borders of stratifiedwavy flow regime.
Fig.1. Dominated flow patterns in long distance wet gas
Our mechanistic model is based on Taitel &
pipelines: а) dispersed flow; b) dispersed-stratified
Dukler approach [5] which includes solution of
flow with segment (up) and lunar (down) interfaces
momentum conservation equations separately
for gas and liquid phases in condition of
Flow patterns in long wet gas pipelines
stratified flow regime.
The fact that the single phase models gives better
The stratified regime is a basic in Taitel & Dukler
predictions of pressure drop than the two-phase models approach (Fig.2); change of flow regime occurs when
can be explained by domination of dispersed-stratified flow special parameters reach their critical values (these
regime in long distance wet gas pipelines [2,3] (Fig. 1).
values are determined by experiments).
These flow regimes (for wet gas with load loan of
In our developed mechanistic model (in contradiction
liquid) are characterised by friction factor values close to to Taitel&Dukler model) the interfacial friction factor
dry gas.
and friction factor at gas-wall interface are not equal.
The interfacial friction factor depends on liquid level.
Mechanistic model of wet gas flow in pipeline
As calculations show this approach allows to get stable
A mechanistic model for calculation of main solutions for stratified-wavy flow in wider intervals of
parameters of gas flow in pipeline with low loads of production rates and inclination angles of terrain than
liquid is based on the following statements:
in Taitel & Dukler approach.
Wet gas flow regime is stratified. All liquid in wet
Momentum conservation equations for both gas and
gas flow is transferred as a film at the bottom of the liquid phases of two phase stratified flow are [5]:
pipeline. Dispersed liquid in gas flow is not considered
 dP 
(entrainment of liquid drop from gas-liquid interface
(1)
− AL 
0
 − τ WLSL + τ iSi + ρ L AL sin α =
 dx 
were analyzed by authors in [9]).
Stratified transfer of gas and liquid phases is
 dP 
described by their own momentum conservation
(2)
− AG 
0
 − τ WGSG − τ iSi + ρG AG sin α =
 dx 
equation.
The mass conservation equation including
phase transition in transported fluid is:
Fig.2. Main characteristics of stratified flow in pipeline
56
ϕρLuL + (1-ϕ)ρGuG = const
For reduction of equations (1) and (2) to
dimensionless form we did the following:
• sum-up the equations (1) and (2) to
exclude pressure drop;
• calculate shear stress by traditional
formulas;
• calculate friction factors by dimension
formulas which are based on Nikuradze`s
hypothesis about the dimensional behaviour
of axial velocity profile in turbulent flow [14];
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Borders of stratified-wavy flow
• use different correlations for the interfacial friction
factor and friction factor at gas-wall interface.
As a result the dimensionless balance equation takes a
form:


− n u 2 SL  −  u D
− m u 2 ×
X 2  u L D
L
L G
G
G
AL  

 S
S
S  
0
×  G + χ iG i + χ iG i   − 4Y =
A

A
A
L
G 
 G

According to up-to-date hydrodynamic approach, the
regime of wet gas flow with low loads of liquid is dispersed
when liquid hold-up ϕ is equal or less than 0.005÷0.006
[4]. It should be noted that these values of ϕ are based
on very poor experimental investigations and very thin
liquid films were not considered because of measurement
challenges described above. The threshold of dispersed
and stratified regimes is specified in this article.
As a criterion of changing regimes (stratified to
where:
dispersed) the authors suggest to use the ratio of interface
(dP / dx) L
friction factor to friction factor at gas-wall surface χiG. If
X2 =
χiG > 1 then flow regime is stratified, and model works
(dP / dx)G
properly. If χiG < 1 then flow regime is dispersed, and
the suggested mechanistic model cannot be used for
( ρ L − ρG ) g sin α
Y=
calculation of two-phase flow parameters (the model
(dP / dx)G
works only for stratified flow).
Although the accuracy of χiG criterion depends on used
π − cos −1 (2h L =
− 1), SG cos −1 (2 h L − 1),
S L =
equation (13), the authors think that this accuracy is good
enough for engineering evaluation of changing the regime
Si = 1 − (2 h L − 1)2
from dispersed to stratified. It is important to keep in mind
that actual threshold of dispersed and stratified regimes is
unknown for PVT parameters in pipelines which transport
−
1
2
=
A
0.25 π − cos (2 h L − 1) + (2 h L − 1) 1 − (2 h L − 1)
L
gas flow with low liquid loads.
The Kelvin-Helmholtz criterion which was modified by
=
A
0.25 cos −1 (2 h L − 1) − (2 h L − 1) 1 − (2 h L − 1)2
Taitel & Dukler [5] is used for determination of the border
G
between stratified and annular or slug regimes:
A
A
u L =
,
FrM ≤ Frrev,
u G =
A
AG
L
where:
4 AL
4 AG
ρG
uGS
DL =
,
DG =
Fr
=
M
S
+
S
SG + Si
L
i
ρ L − ρG Dg cos α
(
(
)
(
)
(
χ iG =
)
)
λi
λG
For transformation of all variables to dimensionless
form it is necessary to:
• variables, measured in [m], divide by D;
• variables, measured in [m2], divide by D2;
• variables, measured in [m/s], divide by uSL and
uSG,
where uSL and uSG – superficial liquid and gas velocities
in case when liquid and gas respectively alone in the
pipeline with perimeter S.
All dimensionless variables mark by tilde (~).
Let us remember that Taitel & Dukler solved equation
(4) providing that χiG = 1.
Taking into consideration Hamersma & Hart
experimental results, interfacial friction factor is obtained
from Eck (1973) [7]:
λi =
0.25

 15

+ 0.619 h L  
 Log 

 ReG


2
Gas phase friction factor λG is obtained from well
known Coalbrook & White correlation.
Liquid holdup is obtained from classic formula:
A
ϕ = L
AL + AG
C
Frrev =
uG
1 − (2 h L − 1)2
A
G
C= 1 − h L
If the inequality (15) is right then flow regime is
stratified-wavy.
The following notations are used in equations (1) – (18):
АL and АG – flow cross-sectional area occupied by
liquid and gas respectively;
SL, SG and Si – perimeter area occupied by liquid, gas
and interfacial border respectively;
τWL, τWG and τi – share stress between pipe wall
and liquid, between pipe wall and gas and interfacial
respectively;
ρL and ρG – density of liquid and gas phases respectively;
α – angle between the pipe axis and the horizontal,
positive for downward flow;
fL, fG and fi – friction factors: for liquid phase, for gas
phase and interfacial respectively;
uL and uG – velocity of liquid and gas phases respectively;
νL and νG – velocity normal to the x direction of liquid
and gas phases respectively;
DL and DG – hydraulic diameter occupied by liquid and
gas respectively;
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СL and СG – parametric coefficients;
ĎL and ĎG – dimensionless hydraulic diameter referred
to inlet pipeline diameter D occupied by liquid and gas
respectively;
n, m – exponents (n=0.25 and m=0.1);
ŠL, ŠG and Ši – dimensionless perimeter area occupied
by liquid, gas and interface respectively;
ũL and ũG – dimensionless velocity of liquid and gas
phases respectively;
X – Martinelli parameter;
Y – dimensionless inclination parameter;
(dP/dX)L and (dP/dX)G – pressure drop of one liquid or
gas phases respectively flowing alone in the pipeline.
During derivation of the equation (4) it was taken into
consideration that fi ≈ fG and uL << uG.
All variables in balance equation (4), except parameters
X and Y, depend on dimensionless liquid level ĥL = hL/D,
were hL- geometric level of liquid film in the pipeline.
Equation (3) is solved by enumeration of variable ĥL
until the value of left hand side of equation (4) is less than
a predetermined small value.
Calculation of parameters of wet gas flow
with low loads of liquid by the example
of Stockman trunk line
The suggested modified Taitel – Dukler model was
used for calculation of liquid film level, hold-up and
determination of flow regime. The data obtained data are
compared with results of simulation in OLGA software
which was used for hydraulic calculations in FEED project.
The Stockman trunkline consist of two 36 inch lines.
Production rate of one line is 35.2 MMSCM/d.
Results of liquid film level calculations (for some parts
of trunkline), using considered modified Taitel – Dukler
model, are presented in the following table (Table 1).
The results show that liquid film level in Stockman
trunkline is from 3 to 10 mm. Comparison of the calculation
results of hold-up using modified Taitel – Dukler model
and OLGA software for different production levels are
presented in the following tables 2-5.
Comparison of calculated results shows that OLGA
provides conservative evaluation of hold-up along
all trunkline. According to OLGA calculation at 80%
production capacity slugs come up at the end of trunkline
Table 1
Results of liquid film level calculation for different
parts of Stockman trunkline depending on different
production capacity (%)
58
Liquid film thickness, mm
Table 2
Results of hold-up calculation for different parts of
Stockman trunkline at 100% production capacity
Hold up, fraction unit
Distance from
the beginning
of pipeline, km
OLGA
Modified
Taitel – Dukler
model
1
0.00041
0.00046
100
0.00190
0.00078
200
0.00238
0.00111
300
0.00294
0.00139
400
0.00363
0.00164
500
0.00361
0.00180
573
0.00343
0.00235
Table 3
Results of hold-up calculation for different parts of
Stockman trunkline at 80% production capacity
Hold up, fraction unit
Distance from
the beginning
of pipeline, km
OLGA
Modified
Taitel – Dukler
model
1
0.00063
0.00051
100
0.00341
0.00123
200
0.00341
0.00144
300
0.00352
0.00164
400
0.00403
0.00176
500
0.00390
0.00184
573
0.00231
0.00187
Table 4
Results of hold-up calculation for different parts of
Stockman trunkline at 60% production capacity
Hold up, fraction unit
Distance from
the beginning
of pipeline, km
OLGA
Modified
Taitel – Dukler
model
1
0.00038
0.00080
Distance from t
he beginning
of pipeline, km
100%
80%
60%
40%
1
3.2
3.7
4.1
4.9
100
0.53565
0.00093
100
4.8
6.5
5.9
5.4
200
0.38676
0.00116
200
6.1
7.2
6.2
6.4
300
0.00252
0.00139
300
7.0
7.8
7.8
7.0
400
0.00413
0.00144
400
7.8
8.2
8.3
7.2
500
0.00348
0.00203
500
8.3
8.4
8.6
8.9
550
0.00416
0.00201
573
8.3
8.5
9.4
9.0
573
0.00146
0.00208
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Table 5
Results of hold-up calculation for different parts of
Stockman trunkline at 40% production capacity
Hold up, fraction unit
Table 7
Regime determination criterion values
for different parts of Stockman trunkline
at 80% production capacity
Distance from
the beginning
of pipeline, km
OLGA
Modified
Taitel – Dukler
model
Distance from
the beginning
of pipeline, km
FrM
Frrev
χiG
1
0.00063
0.00060
1
0.55
2.34
3.72
100
0.00293
0.00111
100
0.51
2.00
4.55
200
0.00405
0.00114
200
0.53
1.94
4.73
300
0.00333
0.00166
300
0.55
1.89
4.89
400
0.00407
0.00179
400
0.59
1.87
4.98
500
0.00387
0.00191
500
0.64
1.85
5.04
573
0.15596
0.00222
573
0.70
1.85
5.07
and at lower capacity slug flow occurs along all trunkline.
Modified Taitel – Dukler model identifies slug regime
at 60% production capacity and even at 40% production
capacity slugs occur only at the end of trunkline where
terrain profile is strongly upward. This analyse allows to
make a conclusion that ramp-up level 80% of production
capacity, which was provided in FEED, should be
considered to decrease.
Criterion χiG (12) and the Kelvin-Helmholtz criterion
(15) are used for determination of flow regime at different
parts of Stockman trunkline. The results for different
production capacities are presented in tables 6-9.
Regime determination criteria show that almost along
all Stockman trunkline stratified flow is determined with
liquid level from 3 to 10 mm. Only at the end of trunkline
where the terrain profile has a big inclination to horizontal
(5÷7°) there are conditions for slugging up to 60% of
production capacity.
This conclusion was confirmed by investigation results
which were presented by Stockman Development AG
at workshop "Integrated development of the Stockman
gas-condensate field – Phase 1" in Gazprom VNIIGAZ
(02/12/2009). Pressure drop and hold-up were calculated
in different versions of OLGA and results were compared
(Fig.3). The calculation results in new generation software
Horizon were also presented. Horizon is based on
Table 6
Regime determination criterion values
for different parts of Stockman trunkline
at 100% production capacity
advanced mechanistic model designed for large diameter
pipelines and high pressure conditions.
Comparison shows that Horizon, in contrast to OLGA,
indicates start of intensive liquid accumulation when
production rate decreases to 20 MMSCM/d which is
approximately equal to 60% of production capacity.
Table 8
Regime determination criterion values
for different parts of Stockman trunkline
at 60% production capacity
Distance from
the beginning
of pipeline, km
FrM
Frrev
χiG
1
0.40
2.28
100
0.38
2.04
200
0.39
2.03
300
0.41
1.89
400
0.43
1.86
500
0.48
1.84
573
0.53
1.79
3.83
4.41
4.45
4.87
4.97
5.06
5.26
Table 9
Regime determination criterion values
for different parts of Stockman trunkline
at 40% production capacity
Distance from
the beginning
of pipeline, km
FrM
Frrev
χiG
Distance from
the beginning
of pipeline, km
FrM
Frrev
χiG
1
0.64
2.43
3.57
1
0.23
2.16
4.03
100
0.60
2.17
4.01
100
0.23
2.10
4.17
200
0.62
2.04
4.45
200
0.24
2.02
4.40
300
0.65
1.95
4.71
300
0.25
1.95
4.61
400
0.70
1.89
4.91
400
0.27
1.94
4.66
500
0.78
1.86
5.02
500
0.31
1.82
5.09
573
0.87
1.77
5.05
573
0.35
1.81
5.13
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200
190
180
170
160
150
140
130
120
110
100
3000
90
2000
80
70
1000
60
0
10
15
20
25
30
35
50
40
Flowrate, MSm3/sd
Fig.3. OLGA versions sensitivity to pressure drop and hold-up
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TRANSPORTATION, STORAGE OF OIL AND GAS
Inlet pressure, bar
Liquid holdup, m3
OLGA 5.3.2 Stratified and slugflow
OLGA 5.3.2 Stratified flow
OLGA 6.1 - OVIP
Horizon 2
OLGA 6.1
OLGA 5.3.2 Stratified and slugflow
OLGA 5.3.2 Stratified flow
OLGA 6.1 - OVIP
Horizon 2
NOSLIP
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Новая механистическая модель течения сырого газа
с малым содержанием жидкости в трубопроводах
В.А.Сулейманов, О.A.Бычкова
(Газпром ВНИИГаз)
Реферат
На основе обобщения результатов теоретических и экспериментальных исследований режимов течения сырого газа с малым содержанием жидкости в протяженных морских трубопроводах разработана методика определения основных параметров его течения. Данная методика
основана на усовершенствовании методики Тайтела-Даклера и учете в ней коэффициента
гидравлического сопротивления на поверхности раздела фаз. Кроме того, для рассматриваемых
двухфазных систем разработаны критерии для определения границ перехода расслоено-волнового режима в дисперсный и пробковый режимы. Представленная методика апробирована на
примере проектируемого газопровода Штокмановское ГКМ – берег.
Boru kəmərlərində az maye tərkibli xam qazın
axınının yeni mexanistik modeli
V.Ə.Süleymanov, O.A.Bıçkova
(Qazprom VNİİQAZ)
Xülasə
Uzaq məsafəli dəniz boru kəmərlərində, az maye tərkibli xam qazın axını rejimlərinin nəzəri və
təcrübi tədqiqatların nəticələrinin ümumiləşdirilməsi əsasında, axının əsas parametrlərinin təyin
ediməsi metodikası işlənmişdir. Verilmiş metodika, Taytel – Dakler metodikasının təkmilləşdirilməsi
və ondakı fazalar bölməsi səthində hidravlik müqavimət əmsalının nəzərə alınmasına əsaslanmışdır.
Bundan başqa, nəzərdən keçirilən ikifazalı sistemlər üçün təbəqələnmiş dalğa rejiminin dispers və tıxac
rejimlərinə keçid sərhədlərinin təyin edilməsi üçün kriteriyalar işlənmişdir. Təqdim edilən metodika
layihələndirilən Ştokmanov QKY – sahil qaz boru kəməri nümunəsində təsdiq edilmişdir.
TRANSPORTATION, STORAGE OF OIL AND GAS
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