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Momentum Balance for Two-Phase Horizontal Pipe Flow Part 2 Testing of Models.

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Dev. Chem. Eng. Mineral Process. 12(1/2), pp. 189-198, 2004.
Momentum Balance for Two-Phase
Horizontal Pipe Flow
Part 2: Testing of Models
P.L. Spedding", J.S. Cole and G.F. Donnelly
School of Aeronautical Engineering, The Queen 's University of Belfast,
Stranmillis Road, Belfast BT9 SAG, Northern Ireland, UK
Momentum balance models were tested against reliable data for both holdup and
pressure drop. The best prediction performance was achieved using a model that
considered the actual shape of the liquid phase in the pipe. In such circumstances the
momentum balance calculation tended to under predict both the holdup and pressure
drop for some of the annular and stratijied regimes. Suggestions are made for
improvements in the momentum balance approach.
Introduction
The one-dimensional momentum balance model for the prediction of holdup and
pressure drop in two-phase pipe flow requires the input of wall shear stresses for the
two phases and for the interface in order to achieve closure of the derived equations.
In this work an evaluation is conducted on the models, which employ the various
methods proposed to predict these shear stresses.
*Authorfor correspondence.
189
P.L. Spedding, J.S. Cole and G.F. Donnelly
Momentum Balance Models
Although all existing momentum balance models were tested against a wide spread of
data ranging from 0.0259 m to 0.0953 m in diameter [l-81, only the outcome of the
more successful models is be presented here. The general method of calculation is
given by Spedding and Hand [9].
Kowalski Model
Figure 1 tests the Kowalski [ 101 model against the data of Hand [5]. Along with other
data, the results highlight that the Kowalski model tended to over predict liquid
holdup, with deteriorating performance as the diameter was reduced and the gas rate
increased into the annular-type flows.
Generally the pressure loss was under
predicted, with performance improving as the diameter rose and the calculated data
being confined to a narrow range. This suggests that a modification of the method
could be advantageous.
Hand Model
Figure 2 details the results for the Hand [5] model tested against the data of Donnelly
[8]. The general result was that this model possessed an improvement in performance
over that of the Kowalski [ 101 model, but still had a wide scatter in the prediction of
liquid holdup that increased as the pipe diameter and gas rate were reduced. The
inadequacies of the Hand [ 5 ] model were in some ways attributable to the formulation
of T
~ but~ mainly
,
to
zi,where modelling solely in terms of Ysc invariably gave
poor scale-up characteristics. This was due primarily to initiation of two-dimensional
surface waves at much higher superficial gas rates in larger diameter pipes.
190
Momentum Balance for Two Phase Horizontal Pipe Flow: Testing of Models
0.0 1
0.1
1
ExperkntalHold up
10
100
lo00
Eprkntal phssure Loss (palm)
Figure 1. Holdup and pressure gradient prediction using Kowalski [IOJ fi-iction
factor expressions tested against 0.0935 m diameter data of Hand [5J.
191
P.L. Spedding, J.S. Cole and G.F. Donnelly
1
9
a
z
0.1
-
B
5
e
c
0.01
0.01
0.1
1
EiJperinrcntalHoldup
Figure 2. Holdup and pressure gradient prediction using Hand [S] friction factor
expressions tested against 0.0259 m diameter data of Donnelly [8].
I92
Momentum Balance for Two Phase Horizontal Pipe Flow: Testing of Models
Baker-Jardine Model
Of the commercial computer packages available only the Baker-Jardine [11J model
will be reported as it gave very similar results to the best of the codes. The
performance of the model was satisfactory for pressure drop in the mid diameter
range of 0.0508 m at the low to medium gas rate range as shown in Figure 3.
However, there was an observable deterioration in pressure gradient prediction at
higher and lower diameters. The model had difficulty in prediction of the liquid
holdup in the annular-type regimes as illustrated in Figure 3.
Andritsos-Hanratty Model
Application of the Andritsos and Hanratty [4, 121 model revealed that the method
predicted the pressure gradient reasonably well when compared to other models, as
shown in Figure 4. However, it showed a lack of rigour with the prediction of holdup.
Modified Apparent Rough Surface ( M A R S )Model
The MARS [7] model gave emphasis to the crescent shape of the gas liquid interface,
and suggested new fnction factor calculation procedures for both the interface and
liquid wall friction where the wetted wall fraction was involved. The model was
reported to be applicable to small pipe inclinations although the level of accuracy was
shown to be superior for slight downflow. Typical results presented in Figure 5 show
the technique gave the best performance overall. The model was designed to be
applicable within the range of
vsG from 1.8 to 40 m s-'
and liquid holdup not
exceeding 0.42. However, results show the level of confidence to diminish for
superficial gas velocities in excess of 22 m s-' and liquid holdup exceeding 0.38. A
degree of deterioration was exhibited for stratified and annular flows which
manifested as an over prediction for pipe diameters in excess of 0.05 m.
The
converse held for smaller diameters although sensitivity to scale-up was somewhat
less pronounced.
I93
P.L. Spedding, J.S. Cole and G.F. Donnelly
0.15
1p 0.12
U
a
5.-
0.09
G
;3
-u
P 0.06
3
6 0.03
0
0
0.03
0.06
0.09
0.12
0.15
Measund Liquid Hoki up
Figure 3. Holdup and pressure gradient prediction using the Baker-Jardine model
[I 1) tested against 0.0935 m diameter data of Hand [5J and the 0.0508 m
diameter data of Ferguson [6] respectively.
I94
Momentum Balance for Two Phase Horizontal Pipe Flow: Testing of Models
1
L
a
5?
p
0.1
B
AST+RW
0
mF+D
0.01
1
0.1
0.01
Epnimental Hold up
.-10,
T
,
*
.
, , , , ,,
100
loo0
...I
loo00
FaperimcntalRessm Loss (Palm)
Figure 4. Holdup and pressure gradient prediction using the Andritsos-Hanratty
model [I21 tested against 0.0454 m diameter data of Nguyen [2].
195
P.L. Spedding, J.S. Cole and G.F. Donnelly
0.01
0.1
Experimental Hold up
10
100
lo00
!3pnmxtalPressure Loss (Palm)
Figure 5. Holdup and pressure gradient prediction using the MARS model [7/ tested
against 0.0454 m diameter data of Nguyen [2].
I96
Momentum Balance for Two Phase Horizontal Pipe Flow: Testing of Models
Discussion
The momentum balance model shows promise in predicting two-phase parameters if
consideration is given to the shape of the liquid interface in the pipe and the resulting
wetted perimeter. Ignoring fluctuations, undoubtedly a balance of forces is established
with the fluids in the pipe cross-section between the actual liquid shape within the
pipe and the shear stresses due to fluid movement. Most models that assumed smooth
stratified liquid geometry have developed interfacial friction relations that encompass
not only the actual interfacial roughness but also inadvertently the associated
turbulence and the wetted surface. There has been an observed dependence of the
initiation of definite wave structure on diameter which complicates prediction scaleup. In addition, as evidenced in Figure 4, there exists a definite variation in the
pressure loss prediction pattern as droplet and annular-type patterns of flow were
initiated. Thus, a simple function used for prediction of, say, interfacial shear stress
cannot possibly correctly handle both surface effects and size of the interface. The
whole momentum balance would be made more reliable if some accurate method
could be employed to predict the actual liquid holdup and its cross-sectional shape.
This would allow a relatively simple correlation to be used in the closure of the
balance equations to handle interfacial shear stress.
Conclusions
Detailed experimental data have demonstrated that prediction methods used to
determine liquid phase and interfacial shear stresses in two-phase pipe flow often
result in a very wide scatter [13]. Despite the possible error in the value obtained
when the shear stresses were applied to the momentum balance calculation reasonable
results were often obtained, more so for the pressure drop estimates. However,
improved predictions were realised when consideration was given to the shape of the
liquid phase as with the use of the MARS model. Improvements are still required as
the MARS model tended to under predict both holdup and pressure loss for annular
and stratified-type flows. Better performance may be achieved if an independent but
197
P.L. Spedding, J.S.Cole and G.F. Donnelly
accurate method were used to predict liquid holdup, thus enabling the liquid interface
geometry and shear stress to be determined in a more simplified balance closure
calculation. It should be noted that the slughntennittent flow regime was not included
in any of these calculations
Nomenclature
A
Annular regime
St
BTS
D
F
Blow through slug regime
Droplet regime
V
Stratified regime
Velocity ( m s-’
T
Shear stress (kg m.’
IW
LRW
R-
R
RW
SA
Film regime
Interfacial wave regime
Long roll wave regime
Ripple regime
Holdup
)
Subscripts
G
Gas
i
Interfacial
L
Liquid
S
Superficial
W
Wall
Roll wave regime
Semi annular regime
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
1 1.
12.
13.
Andrews, D.E. 1996. The prediction of pressure loss during two phase horizontal flow in two-inch line
pipe. MSc. Thesis, Univ. Texas.
Nguyen, V.T.1975. Two phase gas-liquid co-current flow. An investigation of holdup, pressure drop
and flow pattern in a pipe at various inclinations. Ph.D. Thesis, Univ. Auckland.
Chen, J.J.J. 1979. Two phase gas liquid flow with particular emphasis on holdup measurements and
predictions. Ph.D. Thesis, Univ. Auckland.
Andritsos, N. 1986. Effects of pipe diameter and liquid viscosity on horizontal stratified flow. Ph.D.
Thesis, Univ. Illinois Urabana.
Hand, N.P. 1991. Gas liquid co-current flow in a horizontal pipeline. Ph.D. Thesis, The Queen’s Univ.
of Belfast.
Ferguson, M.E.G. 1993. An investigation of horizontal and inclined two phase pipe flow. Ph.D. Thesis,
The Queen’s Univ. of Belfast.
Grolrnan, E. 1994. Gas-liquid flow with low liquid landing in slightly inclined pipes. Ph.D. Thesis,
Univ. Amsterdam.
Donnelly, G.F. 1997. An analytical evaluation of horizontal multiphase flow. Ph.D. Thesis, The
Queen’s-Univ. of Belfast.
Spedding, P.L. and Hand, N.P. 1997. Prediction of stratified gas-liquid co-current flow in horizontal
1923-1935.
pipelines. Int. J. Heat Mass Transfer, 9,
Kowalski, J.E. 1987. Wall and interfacial shear stress in stratified flow in a horizontal pipe. AIChEJ,
21,274-28 I .
Baker, A. and Gravestock, N. 1987. New correlations for predicting pressure loss and holdup in gascondensate pipelines. Int. Conf. Multiphase Flow, 2,417435.
Andritsos, N. and Hanratty, T.J. 1987. Interfacial instabilities for horizontal gas-liquid flow in
pipelines. Int. J. Multiphase Flow, 583-603.
Spedding, P.L., Cole, J.S. and Donnelly, G.F. 2004. Momentum balance for two phase horizontal pipe
flow: 1. Friction factors. Dev. Chem. Eng. Min. Process., in this issue.
u,
Received: 16 July 2002; Accepted ajler revision: 1 May 2003.
198
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