Flow-pattern-prediction models used for gas-liquid two

Flow-pattern-prediction models used for gas-liquid two-phase flowWANG Haiyan1,*, WANG Chunsheng1, LI Yuxing2, CAI Xiaohua3

1.CNOOC Research Institute Co. Ltd.; 2. College of Pipeline and Civil Engineering, China University of Petroleum (East China); 3. PetroChina Tarim Oilfield Company

Keywords:

Gas-liquid two-phase flow

Flow-pattern-prediction models

Model verification

Model comparison

ARTICLE INFO ABSTRACT

In order to study the flow-pattern transition laws of gas-liquid two-phase flow and establish

the gas-liquid hydraulic calculation model with high precision, three flow-pattern-prediction

models, i.e. the general model, the modified Taitel-Dukler model and the slug characteristic

analysis model, were introduced, and their application effects to predict the flow pattern of gas-

liquid tow-phase flow were verified based on the experimental data from Shoham and Kokal.

Then, based on these three flow-pattern-prediction models, the flow pattern prediction maps

were plotted and compared with the experimental data. Finally, the characteristics of the three

models were summarized. It is shown that the unified flow-pattern-prediction model and the

model via slug characteristic analysis do better in the flow pattern prediction of gas-liquid two-

phase flow and the unified model is more applicable to different situations. The research results

provide the basis for selecting the flow pattern prediction algorithm used for the hydraulic

calculation of gas-liquid two-phase flow.

Gas-liquid two-phase flow is a common flow pattern in petroleum industry, and flow pattern judgment is very important for predicting the flow parameters of gas-liquid two-phase flow [1-2]. In the early stage, the judgment basis of two-phase flow pattern is based on the phenomena observed by experiments [3-4]. Later, a quantitative analysis method of flow pattern is proposed to study the influence of fluid physical parameters and flow parameters on the flow pattern. Based on this, theoretical and semi-theoretical flow-pattern-prediction models are proposed, such as Taitel-Dukler discriminant model [5] and software discriminant model [6].

The flow-pattern-prediction algorithm is a very important part of the gas-liquid hydraulic calculation model with high precision and is the foundation of hydraulic calculation [7]. Based on the flow mechanism of gas-liquid two-phase flow, a variety of flow-pattern-prediction methods have been proposed by predecessors [8-9]. The currentgeneral flow pattern prediction model, the modified Taitel-Dukler model and the slug characteristic analysis model [10-11]

are used to verify the prediction effect of flow pattern, and the characteristics of three flow-pattern-prediction models applied to the flow pattern prediction of the gas and liquid are obtained, and then the accuracy and applicable conditions of flow pattern prediction are evaluated.

1 Prediction criterion

1.1 The general flow pattern prediction modelZhang, et al [12] proposed a general flow-pattern-

prediction model based on slug flow in 2003. In the flow-pattern-prediction model, the flow type judgment algorithm is consistent with the flow parameter algorithm, and the boundary conditions of the transitions between flow patterns are calculated according to the momentum equation and continuity equation.

(1) Conversion from dispersed bubble flow to slug flow. When the gas phase apparent velocity wSG is greater than 0.1 m/s, the transition boundary of the dispersed bubble flow to the slug flow is predicted by the mechanism model

Received date: 23 Jul. 2017; Revised date: 23 May 2019*Corresponding author. E-mail: [email protected] item: Supported by the National Science and Technology Major Project during the 13th Five-Year-Plan (2017ZX05032-005)https://doi.org/10.6047/j.issn.1000-8241.2019.01.008Copyright © 2019, Journal of Oil & Gas Storage and Transportation Agency.

Journal of Oil & Gas Storage and Transportation, 2019, 1(1):55-60

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WANG Haiyan, et al.

established by Zhang [11]. The mechanism model considers that the dispersed bubble flow at the transition boundary will contain the largest amount of gas. When the gas phase apparent velocity is smaller, Barnea model [13] is used to predict the transition boundary.

(2) Conversion from slug flow to a stratified flow or an annular flow. When the slug flow is converted to the stratified flow or the annular flow, the membrane length lF of the slug flow membrane region becomes infinite, and the momentum exchange of the liquid film and the bubble in the membrane region is 0. The general model momentum equations for stratified flow and annular flow are:

－τFSF

HLFA＋

τC SC

(1－HLF)A＋τISI

1HLFA

＋1

(1－HLF)A－

(ρL－ρC)gsinθ＝0 (1)

－τFSF

HLFA＋τISI

1HLFA

＋1

(1－HLF)A－(ρL－ρC)gsinθ＝0 (2)

Where τF, τC, τI are respectively the liquid wallshear stress, the gas wallshear stress and the interphaseshear stress, Pa; SF, SC, SI are respectively the liquid wallwet perimeter, the gas wallwet perimeter and the interphase wet perimeter, m; A is the crosssectional area of the pipeline, m2; θ is the inclination angle of the pipeline, (°); g is the acceleration of gravity, m/s2; ρL, ρC are the density of liquid phase and gas core, kg/m3; HLF is the liquid holding rate of the liquid film part in liquid membrane area.

The parameters in the momentum equation are related to the apparent velocity of gas phase wSG, the apparent velocity of liquid phase wSL, physical parameters and fluid state parameters. The momentum equations of the stratified flow and annular flow are iteratively calculated respectively, thus the apparent velocity of the liquid phase during the transition of slug flow to stratified flow or annular flow at a given gas phase apparent velocity can be obtained.

(3) Conversion from stratified flow to annular flow. With the increase of gas velocity, the liquid membrane in the stratified flow will flow to both sides of the pipeline wall, the gas-liquid interface will become concave, the wet wall fraction θ will become larger and larger, and finally the stratified flow will become an annular flow. The Grolman equation [14] uses wet wall fraction to predict the transition boundary of stratified flow to annular flow. When θ>0.9, the flow pattern is annular flow; when θ<0.9, the flow pattern is stratified flow.1.2 The modified Taitel-Dukler model

The improved Taitel-Dukler flow-pattern-prediction model is based on the Taitel-Dukler flow-pattern-prediction model, which is improved by Barnea [15]. The flow-pattern-prediction model is widely used [16].

(1) Conversion from stratified flow to non-stratified flow. The simplified K-H prediction model is used to predict the

conversion from stratified flow to the non-stratified flow. This model does not consider the existence of droplets in the gas phase. The equations are as follows:

F 2

(1－h~

L)2

1A~

G

w2GdA

~

L /dh~

L≥1 (3)

dA~

L

dh~

L

＝[1－(2h~

L－1)2]0.5 (4)

F＝ ρL－ρG

ρG wSG

Dgcosθ (5)

Where F is the dimensionless number; wG is the gas phase velocity, m/s; A

~

L and A~

G are the dimensionless numbers of the crosssectional areas occupied by the liquid phase and the gas phase respectively; h

~

L is the dimensionless number of the liquid high level in the pipeline; D is pipeline diameter, m; wSG is the gas phase apparent velocity, m/s.

(2) Conversion from annular flow to slug flow. The conversion of annular flow to slug flow is determined by two mechanisms, which cause the liquid phase block the gas core and flow pattern changing to slug flow.

The first mechanism is that the liquid membrane is unstable due to the downward flow of liquid near the pipeline wall. The criterion of liquid membrane instability is obtained by simultaneously solving two dimensionless equations (6) and (7). The steady state solution of liquid holdup HL is obtained by equation (6), and the liquid holdup value under unstable condition of liquid membrane is obtained by equation (7), and the expressions are as follows:

Y＝(1－HL)2.5HL

1＋75HL－

H 3L

1X2 (6)

Y≥H 3

L (1－1.5HL)2－1.5HL X 2 (7)

X 2＝

D4C L

μL

ρLwSLD －n

2ρLw2

SL

D4CG

μG

ρGwSGD －m

2ρGw2

SG (8)

Y＝(ρL-ρG)g sinθ

D4CG

μG

ρGwSGD －m

2ρGw2

SG (9)

Where Y is dimensionless gravity parameter; X is Lockhart-Martinelli parameter; μL and μG are respectively the dynamic viscosity of liquid and gas phases, Pa·s. WSL is the apparent velocity of the liquid phase, m/s; CL, CG, n and m are constants, which are related to the flow pattern of the gas and liquid phase.

The second mechanism is that the growth of interfacial wave caused by the large liquid volume of liquid membrane. If there is enough liquid, the interface wave will grow and bridge the pipeline, thus the slug flow will occur. The


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WANG Haiyan, et al.

conditions for such a mechanism is as follows: HL≥0.24 (10)

When either of the above two mechanisms is satisfied, the conversion of the annular flow to the slug flow will occur.

(3) Conversion from slug flow to dispersed bubble flow. When the liquid velocity is high, the turbulent force overcomes the interfacial tension and diffuses the gas phase into small bubbles. The maximum bubble diameter under this mechanism is:

dmax＝ 4.15 wM

wSG0 .5

＋0.725 ρL

σ 0.6

D2fMw3

M－0.4

(11)

wM＝wSG＋wSL (12)Where wM is the mixing speed, m/s; σ is the surface tension of the liquid, N/m; fM is the mixed friction factor in the bubble flow, which is calculated according to the relevant equation of bubble flow.

Two critical bubble diameters need to be considered here. The first critical diameter is the diameter of the bubble deformation, and bubbles smaller than this diameter will not deform, thus avoiding the aggregation and coalescence. The expression of the critical diameter dCD is as follows:

dCD＝2 (ρL－ρG)g0 .4σ 0 .5

(13)

The other critical diameter is the bubble floating diameter, which is applied to the case of small fluctuation angle of the pipeline (|θ|≤10°). In this case, due to buoyancy, bubbles larger than this diameter will move toward the upper part of the pipeline and form stratification, thus converting to slug flow. the equation of the critical diameter dCB is:

dCB＝ 83

(ρL－ρG)gcosθρLfMw2

M (14)

When the maximum possible bubble diameter is less than dCD and dCB, the flow pattern will be converted to dispersed bubble flow.

It should be noted that the above discriminant for the conversion of slug flow to dispersed bubble flow is only valid when the volume gas holdup α≤0.52, which indicates the maximum possible number of bubbles in a cubic lattice shape [17]. When the void fraction is higher, bubbles will converge without being affected by turbulent flow, and slug flow pattern will be maintained.

1.3 The slug characteristic analysis modelThe slug flow characteristic analysis model is based on

the stability of slug flow structure, that is, the slug flow is assumed to exist firstly, and other slug flow characteristic parameters [17] are determined under this condition, and finally the flow pattern is determined.

HLU is the liquid holdup of the slug unit and HLS is the liquid holdup of the slug body. When HLS＜HLU, it indicates that the liquid holdup in the liquid membrane area is greater than that in the slug unit, and the result is not consistent with the actual model, indicating that the slug flow does not exist, and the flow pattern inside the pipeline is a dispersed bubble flow. Considering the bubble in the slug flow as a hexahedron of the same size, the maximum gas holdup is 0.74, and the minimum value of the liquid holdup is 0.26 [18]. If HLS＜0.26, the flow pattern is not a slug flow or a bubble flow, but an annular flow or a stratified flow. Based on this theory, the criteria for the slug characteristic analysis model can be obtained: when HLS＜0.26, it is a stratified flow or an annular flow; when 0.26≤HLS＜HLU, it is a dispersed bubble flow;when HLS≥0.26 and HLS≥HLU, it means that the flow pattern may be slug flow, and further flow pattern discrimination of flow pattern should be made according to the characteristic parameters of slug flow. The specific method is as follows: calculating the ratio of slug length lS to slug unit length lU according to the slug flow model [19]. If lS/lU＜0, it is stratified flow orannular flow. When 0≤

lS/lU≤1, it is a slug flow. When lS/lU＞1, it is dispersed bubble flow. The transition boundary between stratified flow and annular flow can be determined according to K-H instability criterion, as shown in equation (3).

2 Instance verification

Based on the above three flow pattern prediction models, the program is developed, and the flow pattern diagram with the apparent velocity of gas and liquid as the horizontal and vertical axisis calculated through the program, and comparing with the experimental data (Table 1) of Shoham [20] and Kokal et al [21], and the characteristics of each flow patternprediction modelare obtained.

Table 1. Experimental data obtained by Shoham and Kokal in the study of gas-liquid two-phase flow patterns

Experimenter Experimental medium

Pipeline diameter/mm

Pipelinelength/m

Density of the liquid phase/(kg·m－3)

Viscosityof the liquid phase/(Pa·s)

Viscosityof the gas phase/(Pa·s)

Inclinationangle/(°)

Shoham Air/Water 25.4/50.8 10 998.7 1.0×10－3 1.8×10－3 －5-＋5

Kokal Air/Light mechanical oil 25.8/51.2/76.3 25 860.0 6.5×10－3 1.8×10－3 －5-＋5

2.1 Comparison of experimental results and computational flow patterns obtained by Shoham

The flow pattern diagrams drawn by the above three calculation models are compared with the results of Shoham’s experiment, and the results of Shoham experiment

and flow pattern diagrams under different pipeline inclination angles are obtained (Fig. 1, the flow pattern identified in the Fig. is the flow pattern calculated by different flow pattern prediction models, and the boundary calculated by different discriminant methods is different; the points of different


58

shapes represent the Shoham experimental results of the flow patterns at the apparent gas velocity and liquid velocity), and the difference between experimental results and theoretical calculations is compared. The analysis shows that for the flow with air/water as the medium, the three flow pattern prediction models have their own characteristics under different pipeline inclination angles. Under each inclination angle, the error of flow pattern transition boundary between the general flow pattern prediction model and the modified Taitel-Dukler flow pattern prediction model is relatively small. When the slug flow characteristic analysis model is used to calculate this boundary, the calculated apparent flow velocity of the liquid phase is relatively small, and the slug flow is misjudged as the dispersed bubble flow. The general flow pattern prediction model and the slug flow characteristic analysis model have higher calculation accuracy in calculating the flow pattern transition boundary from the slug flow to the stratified flow or the annular flow, but as the

down inclination angle of the pipeline increases, the error of slug flow characteristic analysis method in calculating the transition boundary increases gradually. The modified Taitel-Dukler flow pattern prediction model has a large calculation error in calculating the transition boundary from the slug flow to the stratified flow in the upward-inclined-pipeline, and it is easy to mistake slug flow as stratified flow; for the transition boundary from the stratified flow to annular flow, the modefied Taitel-Dukler flow pattern prediction model and the slug flow characteristic analysis model adopt the KH instability criterion to discriminate the flow pattern transition of stratified flow and annular flow. The flow pattern diagrams of the two methods at the transition boundary are coincident. According to the comparison, their calculation results are better than the general flow pattern prediction model, but the three models all have large errors at the transition boundary, and it is easy to misjudge annular flow as the stratified flow.

Fig. 1. Shoham experiment results and flow pattern diagram calculation results at different pipeline inclination angles

(c) upward-inclined-pipeline with 5°(a) Horizontal Pipelines (b) upward-inclined-pipeline with 1°

(d) downward-inclined-pipeline with 1° (e) downward-inclined-pipeline with 5°

In conclusion, the following conclusions can be drawn from the flow pattern prediction of air/water pipeline flow:

(1) The general flow pattern prediction model is superior to the other two flow pattern prediction models, and its performance is relatively stable under all pipeline inclination angles. However, the calculation method of the transition boundary between the stratified flow and the annular flow needs to be improved, such as reducing the wet wall fraction at the transition boundary appropriately. (The wet wall fraction is 0.9 in the general flow pattern prediction model).

(2) The modified Taitel-Dukler flow pattern prediction model is more suitable for the flow pattern prediction of horizontal pipeline and downward-inclined pipeline, and the calculation error of the transition boundary between theslug flow and stratified flow of upward-inclined pipeline is relatively large.

(3) The calculation error of the slug flow characteristic analysis model is relatively small, but the calculation result at the transition boundary of the slug flow and the dispersed bubble flow is not good, and the calculation error of transition boundary between stratified flow and slug flow at

WANG Haiyan, et al. Journal of Oil & Gas Storage and Transportation, 2019, 1(1):55-60

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the down inclination angle is large, which tends to increase with the increase of thedown inclination angle.

(4) When predicting the conversion rules form annular flow to any other flow pattern in upward-inclined pipelines, the errors of the three prediction models are all large, and the annular flow is easy to be misjudged as a stratified flow under different inclination angles.2.2 Comparison of experimental results and computational flow patterns obtained by Kokal

The flow pattern diagrams drawn by the above three calculation models is compared with the results of Kokal’s experiment, and the results of Kokal experimental and flow pattern diagrams under different pipeline inclination angles are obtained (Fig. 2, the flow pattern identified in the Fig. is the flow pattern calculated by the above flow pattern prediction models, and the boundary calculated by different discriminant methods is different; the points of

different shapes represent the Kokal experimental results of the flow patterns at the apparent gas velocity and liquid velocity), and the difference between experimental results and theoretical calculations is compared. According to the analysis, for the flow of air/light mechanical oil asmedium, the three flow pattern discriminant methods have small error in calculating the transition boundary between slug flow and dispersed bubble flow. For the transition boundary from the slug flow to stratified flow or annular flow, the calculated results of the general flow pattern prediction model and the slug flow characteristic analysis model are close to the experimental results, and the error of the slug flow characteristic analysis model is smaller, and the results of the slug flow characteristic analysis model is similar to the experimental verification results under Shoham pipeline flow condition, although the improved Taitel-Duker flow pattern discriminant method can be used.

Fig. 2. Kokal experimentresults and flow pattern diagram calculation results at different pipeline inclination angles

(a)Horizontal Pipelines

(d)downward-inclined-pipeline with 1° (e)downward-inclined-pipeline with 5°

(c)upward-inclined-pipeline with 5°(b)upward-inclined-pipeline with 1°

Although the modified Taitel-Duker flow pattern prediction model can discriminate the decreases of the stratified flow in upward inclined pipelines, its prediction results still cannot reach the calculation level of the other two prediction models, and many slug flows measured under experimental conditions are misjudged as stratified flow. For the transition boundary between the stratified flow and the annular flow, the calculation results of the three flow pattern prediction models are similar, but there are also drawbacks in mistaking annular flow as stratified flow. It is worth noting that in thestratified flow has not been detected in the two groups experimental data, and only the general flow pattern prediction model can well predict this phenomenon.

In conclusion, the following conclusions can be drawn from the flow pattern prediction of air/light mechanical pipeline flow:

(1) Although the general flow pattern prediction model is not the model with the smallest calculation error at some flow pattern transition boundaries, the predicted flow pattern diagram is closer to the experimental results in the overall distribution, and the calculation results are stable under different inclination angles. Therefore, for flow media of air/light mechanical oil, it is recommended to use the general flow pattern prediction model.

(2) Similar to the verification results of Shoham experiment, the modified Taitel-Dukler flow pattern


60

prediction model is easy to misjudge the slug flow as the stratified flow in upward inclined pipelines, which is far inferior to the other two models in predicting the stratified flow in upward inclined pipelines.

(3) The slug flow characteristic analysis model has small calculation errors at multiple flow pattern transition boundaries, but for the upward inclined pipeline flow, the slug flow characteristic analysis model incorrectly misjudges the annular flow asthe stratified flow under some experimental conditions, which needs to be further improved in the identification of the annular flow/stratified flow, so this model is not recommended.

3 Conclusion

(1) It is recommended to use the general flow pattern prediction model to discriminate the gas-liquid two-phase flow pattern. The calculation results of this method are stable under different media and different inclination angles. Although it is not the optimal prediction model under each experimental condition, it has the strongest adaptability to different flow conditions.

(2) There is a serious defect in the modified Taitel-Dukler flow pattern prediction model, that is, the slug flow is easily misjudged as the stratified flow which is not easy to occur in upward inclined pipelines, and this problem needs to be improved urgently.

(3) The slug flow characteristic analysis model is close to the experimental results in the flow pattern discrimination, but its adaptability to different flow conditions is worse than that of the general flow pattern prediction model. For example, when using this model to discriminate the flow pattern of air/light mechanical oil in upwardinclined pipelines, it erroneously determined it as an annular flow.

(4) The transition boundary of annular flow/stratified flow and the influence on the inclination angles change of the pipeline are the points that need to be further improved in each flow pattern prediction model.

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Flow-pattern-prediction models used for gas-liquid two