Paper No 7th International Conference on Multiphase Flow

ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

Experimental validation of the model for calculating the drag reduction ratio during

gas/power-law fluid flow

Jing-yu Xu and Ying-xiang Wu

Key Laboratory for Hydrodynamics and Ocean Engineering, Institute of Mechanics, Chinese Academy of Sciences

Bei si huan xi road No15, beijing 100190, China

xujingyu@imech.ac.cn

Keywords: Drag reduction; gas-liquid flow; non-Newtonian fluids; horizontal pipes

Abstract

The drag reduction by gas injection for power-law fluid flow in stratified and slug flow regimes has been studied. The

methods for predicting of the maximum drag reduction ratio in stratified flow and slug flow regimes were presented. The

results show that the drag reduction should occur over the large range of the liquid holdup when the flow behaviour index

remains at the low value. Furthermore, for turbulent gas-laminar liquid stratified flow, the drag reduction by gas injection for

Newtonian fluid is more effective than the drag reduction of shear-shinning fluid when the dimensionless liquid height

remains in the area of high value. The pressure gradient model for a gas/Newtonian liquid slug flow is extended to liquids

possessing the Ostwald--de Waele power law model for calculating the drag reduction ratio. The proposed models were

validated against 340 experimental data point over a wide range of operating conditions, fluid characteristics and pipe

diameters. The drag reduction ratio predicted is well inside the 20% deviation region for 80% of the experimental data. These

results substantiate the general validity of the model presented for gas/non-Newtonian two-phase slug flows.

Symbols

Subscripts

Notation

A cross-sectional area

D pipe diameter

f friction factor

g acceleration of gravity

G the mass flux

h fluid level

AP pressure drop

11 liquid film zone of length

s1 liquid slug zone of length

1, slug unit of length

mi fluid consistency coefficient

nl flow behaviour index

Re Reynolds number

S pipe perimeter

u mean velocity

ud drift velocity

Greek letters

a liquid holdup

E absolute pipe roughness

/eff effitive viscosity

T shear stress

p density

FA drag reduction ratio

(12 dimensionless pressure drop

X2 Lockhart-Matinelli parameter

2

m

m/S2

kg/m2 sec

m

Pa/m

m

m

m

Pa sn

m

m/s

m/s

m

Pa s

Pa

kg/m3

gas phase

interface

liquid phase

two-phase

superficial liquid phase

superficial gas phase

liquid slug

slug unit

mixture velocities of the superficial gas

and liquid phases

Introduction

In the last decades some work has been carried out to study

on drag reduction in gas-liquid systems. The significant

achievement is that the injection of gas into non-Newtonian

liquids, especially for power-law (shear thinning) liquids, at

a given liquid flow rate will result in the reduction of

pressure drop. The earliest studies concerning this

phenomenon were carried out by Ward and Dallavalle

(1954), who injected air into clay suspensions flowing in

the laminar regime. The drag reduction ratio can be defined

as:

0 A- = 1-0AP

AP, (1)

where D A is the drag reduction ratio, D12 is the

dimensionless pressure drop, AP is the pressure drop and

the subscripts tp, and sl refer to the two-phase and the

Paper No

superficial liquid phase, respectively. Here (D>0 meant

that two-phase pressure drop is smaller than that of the

liquid phase flowing on its own at the same flow rate. Thus

the drag reduction occurs.

Most of models traditionally depended on flow pattern to

predict the drag reduction in horizontal pipes. For stratified

flow the Heywood and Charles (1979) extended the model

of Taitel and Dukler (1976) for gas/Newtonian liquid

stratified flow to liquids obeying the Ostwald-de Waele

power law model, and defined conditions for drag

reduction of the liquid flow by the presence of the gas.

They found that drag reduction occurred over the largest

ranges of liquid and gas flow rates at the lowest nl values

provided that liquid flow remains laminar. However,

Heywood-Charles model did not carry out experiments to

test their model.

Considering the slug flow regime, Farooqi et al. (1980)

described the theological behaviour of the suspensions as

the Bingham plastic model, and extended the Ducker and

Hubbard model (1975) to allow for non-Newtonian

behaviour of the suspensions for predicting the extent of

drag reduction in the slug flow regime. The results showed

that the drag reduction effect became progressively more

marked as both the yield stress and plastic viscosity

parameters increased with increasing suspension

concentration. By analyzing the experimental data of

Farooqi and Chhabra (1982b), Dziubinski (1995) presented

a general expression of drag ratio for two-phase pressure

drop of gas/non-Newtonian fluid based on the concept of

loss coefficient during the intermittent flow. Bishop and

Deshpande (1986) studied the power-law (shear thinning)

non-Newtonian liquid-gas uniform stratified flow. They

found that the Heywood-Charles model was valid for

predicting the pressure drop and liquid holdup for a

uniform stratified flow, and two-phase drag reduction,

which was predicted by the Heywood-Charles model, did

not occur because there was a transition to semi-slug flow

before the model criteria were reached. Ruiz-Viera, et al.

(2006) experimentally observed the drag reduction

phenomenon using different geometries with both smooth

and rough surfaces during slug flow of a lubricating

grease/air mixture. The experimental data showed that drag

reduction appeared to be dramatic by injecting relatively

low flow rates of air, even more as liquid flow rate

decreases, although it was dampened by increasing the

volumetric flow rate of air. In addiction to these, Xu J-y et

al. (2007) studied the co-current flow characteristics of air/

power-law fluid systems in inclined smooth pipes using

transparent tubes of 20, 40 and 60 mm in diameter. In their

works, the Heywood-Charles model (1979) was modified

for horizontal flow to accommodate stratified flow in

inclined pipes, taking into account the average void

fraction and pressure drop of the mixture flow of a

gas/non-Newtonian liquid. However they only presented

the criterion equation to determine whether drag reduction

existed in stratified gas/non-Newtonian liquid flow, the

drag reduction was not studied in detail using the equation

suggested.

Literature survey show that although some studies have

been done on the drag reduction for gas-liquid two-phase

7th International Conference on Multiphase Flow

ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

flow, few attempts have been made to study the drag

reduction characteristic in horizontal pipes under different

flow regimes. In the chemical process industries,

non-Newtonian liquids, especially pseudoplastic

(po\ic1-LiUv) liquids, are encountered frequently. Several

industrial applications utilize these liquid-gas mixtures

flowing through horizontal tubes. Therefore, there is a need

to understand in depth the hydrodynamics and transport

behavior of non-Newtonian liquid-gas systems. The

purpose of this work was to study the characteristic of drag

reduction in horizontal pipes, especially for flowing in a

commercial pipe. The proposed models of the drag

reduction ratio were tested extensively against a large set of

available experimental data for air/non-Newtonian fluid

systems flowing in smooth and commercial pipes in this

work and for others system reported in the literature.

Experimental Facility

The experiments reported below were carried out on the

multiphase flow facilities at Institute of Mechanics,

Chinese Academy of Sciences. The details of the flow-loop

can be found in the previous works (Xu et al. 2009). Air

came from a compressor pump via gas mass flow-meter.

Polymer solutions used as the liquid phases were conveyed

from liquid phase tank into the pipeline. Liquid phase and

gas phase were fed into the pipeline via a T-junction. The

volumetric flow rates of all phases could be regulated

independently and were measured by thermal mass flow

meter for air phase and electromagnetic flow-meter for

polymer solutions. The multiphase flow pipeline was

manufactured of perspex tubing with an internal diameter

of 50mm through which the flow could be observed. The

total length of this pipeline between the entrance and the

separation unit was approximately 30m. The pipeline

consists of two horizontal legs with a leg length of 10m and

14m, respectively, connected by a horizontal U-turn. The

sampling frequency of the pressure was 500 Hz. Flow

patterns were recorded using a high-speed video camera,

and the flow patterns for each test condition were recorded

and could be observed later in slow motion.

Four different concentrations CMC (carboxymethyl

cellulose) solutions used as non-Newtonian fluid. Solutions

were prepared by adding small quantities of dry polymer

powders accompanied by gentle stirring to prevent the

formation of lumps. The density of each solution was

measured using a constant volume density bottle. The CMC

rheology experiments are measured with a ThermoHaake

RS300 rheometer. A double gap cylinder sensor system

with an outside gap of 0.30 mm and an inside gap of 0.25

mm was used. As expected, CMC solutions in this study

were shear-thinning fluids whose rheology can be

described by Ostwald--de Waele power law model.

= m )nl (2)

Numerical Scheme

Stratified flow in horizontal pipes

Assuming a fully developed stratified flow, the integral

Paper No

forms of the momentum equations for the two fluids are

written for the liquid and gas phase as follows:

dp dh_, Ad(G,u,)_

-A(-L ), iS, + S, +A4pg- -A- =0

dx dx dx (3)

dp dh d(GgUg) )

-A,( ) -Sp zSg + +A g -A = =

dx dx dx (4)

Eliminating the pressure drop by combining equations (3)

and (4), and ignoring the acceleration terms, yields a

relation can be used to calculate the liquid holdup by

solving for the liquid height:

S SI 1 1 h,/D Ia

F= ,-- -+ fS (--+ -)- pgD-

SA A1 A1 A 8ac &x

7th International Conference on Multiphase Flow

ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

( ) -=2f pu -+ 4 ( S + S )

dxt D 1,r-D2 1 2 2 (10)

where the following relations have been used in a

commercial pipe (Taitel and Bamea, 1990):

S=0.001375[l+(2x104 o +- 1)]

D, Rek (11)

The dimensionless pressure drop can be expressed in a slug

flow:

o 2 f

where

By designating the dimensionless quantities by a tilde (~), a

general dimensionless expression given in the case of a

uniform film thickness for stratified flow:

x j, 2 f it2 2, SI2

X i- (q.-).-q.- (+)=0

A, i i -9 -, a A, A

2 f u2

(13)

n4 f lPg2 fp 2 2

2 2

2 f pPu,

D (14

Once a solution has been obtained for h, by equation (6),

the dimensionless pressure drop can be given respectively

as:

2 -+ S -- )

d o D' g X2 Dm

g (7)

where Os and Of are the dimensionless pressure drop in

the liquid slug and in the film zone respectively. Thus

the drag reduction ratio in slug flow can be expressed as:

qA =1-(qs+q )

Results and Discussion

Thus the drag reduction ratio can be expressed as:

A 1 =I-K'

where

K= S{1

.{i

[ +(1-q.- ) 1-q. +

A u A A

2.2 Slug flow in horizontal pipes

In the slug unit of length, l,, consists of two separate

sections: the liquid slug zone of length 1, and the film zone

of length l. Assuming that the film contains no entrained

gas bubbles and a uniform film along the film zones, the

average pressure gradient in a slug unit is obtained by

performing a momentum balance over a global control

volume of the slug unit:

The drag reduction ratio, ( A, as predicted from the

equation (8) is presented in Fig.1 for various ni values

corresponding to power-law flow behaviour in stratified

horizontal flow. It can be seen that over the range

(8) 0.1

0.1, but for a high value of a the reverse is true. The

drag reduction occurs over the greatest range of a at the

lowest n, values. However, Fig.1 also reveals the

interesting result that the maximum drag reduction ratio

occurs at the highest n, value plotted for a constant liquid

holdup, a namely that the drag reduction by gas injection

(9) for Newtonian fluid in a laminar flow is more effective

than the drag reduction of shear-shinning fluid when the

dimensionless liquid height remains in the area of high

value.

In this work, provided that q and n, are known, the effect of

variation in h on the drag reduction ratio can be

calculated using the equation (8). When the drag reduction

ratio reach the maximum value, h may be obtained by the

differentiation of equation as:

S=0

9h

(14)

Paper No

where ,A is only the function of h. Thus the maximum

drag reduction ratio can be obtained by the equation (16).

In order to validate the method of stratified flow presented

by this work, the experimental data of Bishop and

Deshpande (1986) were compared with the results

predicted from the equations (7) as shown in Figs.2. The

results of this comparison indicate good agreement for the

dimensionless pressure drop. In their work two-phase drag

reduction can not be achieved in stratified flow of

non-Newtonian liquid-gas mixtures. They hypothesized

that the drag reduction was restricted to those situations

where streamline flow patterns existed at the head of an

elongated bubble so that the drag reduction could not exist

in stratified liquid-gas flow. However, in the present work,

it can be seen in Fig. 1 that the drag reduction should occur

over the large range of the liquid holdup when ni remains at

the low value. Thus the reason that the drag reduction was

not observed may be due to the fact that the flow behavior

index of non-Newtonian material in their experiments is not

enough low so that The pressure drop was reduced below

the value for which the liquid flows alone at the same

liquid flowrate (n1 > 0.68 in Bishop and Deshpande' work,

1986)

For calculating the pressure drop of gas/Newtonian fluid in

a horizontal slug flow, we carried out a series of

experiments to study the drag reduction and further

modified the model suggested by Xu J-y et al. (2007, 2009)

to study the drag reduction ratio by considering the

Ostwald--de Waele power law model. In addition, we used

a large set of available experimental data over a wide range

of operating conditions and pipe diameters in the literature

to validate the developed model.

Fig.3 illustrates the effects of liquid flow rate on the drag

reduction ratio for air/CMC solution flow. At lower gas

flow rate within the range of 1.25 m3/h eQ, < 10.0 m3/h,

q, increases monotonically with the gas flow rate

increasing. However, the drag reduction ratio tends to

reach constant values when gas flow rate is further

increased. The reason can be explained by the fact that,

supposing the no slip velocity between the gas and liquid

phases and the homogeneous flow, the Reynolds number of

two-phase can be obtained via equation (11):

Du p.

Re, "

pl/ (17)

where D. =D 8 1N" IK(u, +u ) -1 (n1 1) is defined as the

"effective viscosity". It can be observed from equation (17)

that, for a fluid of given rheology (coefficient nl and mi),

increasing the superficial gas velocity will reduce the

effective viscosity so that the frictional pressure gradient is

decreased. However the gas will always disturb the flow

and there will be additional pressure losses in the mixture

of two phase flow so that two-phase pressure gradient is

augmented. Therefore, the drag reduction ratio, q), might

show different tendencies when the gas flow rate increasing,

as shown in Fig.3.

7th International Conference on Multiphase Flow

ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

To calculate exactly the drag reduction ratio, the pressure

gradient of two-phase flow calculated has to be validated

firstly. Fig.4 displays that the model predictions were tested

against the data of Farooqi and Richardson (1982b) for air

and kaolin suspensions flowing in a pipe of 0.0417 m in

diameter. A very good agreement was obtained between the

theoretical and experimental pressure gradients in the

superficial gas velocity range of 0-1.0 m/s. The data in the

high gas velocity range of 1.0-6.5 m/s were over-predicted

by the model presented in this work. However in the whole

range both the theoretical curves and the experimental data

for the two-phase pressure drop exhibit the same trend. At

low superficial gas velocities the pressure drop decreases as

Usg is increased. It reaches to a minimum value at the

critical velocity for the transition from laminar to turbulent

flow (Farooqi and Richardson, 1982b). Past this velocity,

the pressure gradient increases steadily. Furthermore,

increasing the superficial liquid velocity at any given usg

results in higher theoretical as well as experimental

pressure drop over the entire range of the tested data air

and kaolin suspensions flow. Fig.5 compares the predicted

pressure gradient with experimental data of Chhabra et al.

(1984) and the present work for air/CMC solutions flowing

in a pipe of 0.0417 m I.D. and of 0.05 m I.D. respectively.

An excellent agreement was obtained between theory and

data. The pressure gradient predicted by the model for

gas/power-law fluid slug flow, as well as the experimental

data, indicate that the drag reduction by gas injection is

more prominent with low superficial gas velocities, as

shown in Figures.

Finally, the proposed method for slug slow has been

checked by plotting the experimental values of the drag

reduction ratio vs. the predicted ones calculated from (15).

As Fig.6 shows, the use of equation (15) allows a good

prediction of the drag reduction ratio for the

gas/non-Newtonian power-law fluid mixture flow. eighty

percent of the experimental values are well inside the 20%

deviation region using 340 experimental data point

collected from different references (Chhabra et al. 1983;

Chhabra et al. 1984; Farooqi and Richardson 1982b;

Ruiz-Viera et al. 2006), including the smooth and rough

pipes.

Conclusions

An experimental and theoretical study of a

gas/non-Newtonian fluid flow through the horizontal pipe

has been conducted. Special attention was given to study

the drag reduction ratio by gas injection for power-law

fluid flow in stratified and slug flow regimes. The method

for predicting of the maximum drag reduction ratio in

stratified flow regime was presented by modifying the

model suggested by Xu et al. The results show that, for

turbulent gas-laminar liquid stratified flow, the drag

reduction by gas injection for Newtonian fluid is more

effective than the drag reduction of shear-shinning fluid

when the dimensionless liquid height remains in the area

of high value. Furthermore, the drag reduction should

occur over the large range of the liquid holdup when the

flow behaviour index remains at the low value. The

method for predicting the gas-liquid stratified was

Paper No

validated by the experimental data of Bishop and

Deshpande, and results of this comparison indicate good

agreement for the dimensionless pressure drop. The

pressure gradient model for a gas/Newtonian liquid slug

flow is extended to liquids possessing the Ostwald--de

Waele power law model for calculating the drag reduction

ratio. The proposed models were validated against a large

set of available experimental data over a wide range of

operating conditions, fluid characteristics and pipe

diameters. A very good agreement was obtained between

the predicted and experimental results. The drag reduction

ratio predicted is well inside the 20% deviation region for

80% of the experimental data. These results substantiate

the general validity of the model presented for

gas/non-Newtonian two-phase slug flow

Acknowledgements

The authors are grateful to the financial support provided

by the National Natural Science Foundation of China (No.

10902114)

References

Bendiksen, K. An experimental investigation of the motion

of long bubbles in inclined tubes. International Journal of

Multiphase Flow 10, 467-483, 1984.

Bishop, A.A., Deshpande,S.D. Non-Newtonian liquid-air

stratified flow through horizontal tubes-II. International

Journal of Multiphase Flow 12, 977-996, 1986.

Chhabra, R.P, Farooqi, S.I., Richardson, J.F. Isothermal

two-phase of air and aqueous polymer solutions in a

smooth horizontal pipe. Chemical Engineering Research

and Design 62, 22-31,1984.

Duker, A.E., Hubbard, M.G. A model for gas-liquid slug

flow in horizontal and near horizontal tubes, Ind. Eng.

Chem. Fundam. 14 337-34, 1976.

Dziubinski, M. A general correlation for the two-phase

pressure drop in intermittent flow of gas and

non-Newtonian liquid mixtures in a pipe. Chemical

Engineering Research and Design 73, 528-533, 1995.

Farooqi, S.I., Richardson, J.F. Horizontal flow of air and

liquid (Newtonian and non-Newtonian) in a smooth pipe.

Part II: Average pressure drop. Transactions of the Institute

of Chemical Engineers 60, 323-333, 1982b.

Farooqi, S.I., Heywood, N.I., Richardson, J.F. Drag

reduction by air injection for suspension flow in a

horizontal pipeline. Transactions of the Institute of

Chemical Engineers 58, 16-27, 1980.

Heywood, N., Charles, M.E. The stratified flow of gas and

non-Newtonian liquid in horizontal pipes. International

Journal of Multiphase Flow 5, 341-352, 1979.

Lockhart, R.W, Martinelli, R.C. Proposed correlation of

data for isothermal two-phase, two-component flow in

pipes. Chemical Engineering and Processing 45, 39-48,

7th International Conference on Multiphase Flow

ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

1949.

Ruiz-Viera, M.J., Delgado, M.A., France, J.M., Sanchez,

M.C., Gallegos, C. On the drag reduction for the two-phase

horizontal pipe flow of highly viscous non-Newtonian

liquid/air mixtures: Case of lubricating grease.

International Journal of Multiphase Flow 32, 232-247,

2006.

Taitel, Y., Barnea, D. A consistent approach for calculating

pressure drop in inclined slug flow. Chemical Engineering

Science 45, 1199-1206, 1990.

Tailer, Y., Dukler, A.E. A model for prediction flow regime

transition in horizontal and near horizontal gas-liquid.

A.I.C.H.E. Journal 22, 47-55, 1976.

Ward, H.C., Dallavalle, J.M. Co-current

turbulent-turbulent flow of air and water-clay suspensions

in horizontal pipes. Chemical Engineering Progress 10,

1-14, 1954.

Xu, J-y, Wu, Y-x, Shi, Z-h, Lao, L-y, Li, D-h. Studies on

two-phase co-current air/non-Newtonian shear-thinning

fluid flows in inclined smooth pipes. International Journal

of Multiphase flow 33: 948-969, 2007.

Xu, J.-y., Wu, Y.-x. Li, H., Guo, J. and Chang, Y. Study of

drag reduction by gas injection for power-law fluid flow in

horizontal stratified and slug flow regimes. Chemical

Engineering Journal 147, 235-244, 2009.

7th International Conference on Multiphase Flow

ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

Fig.1 the effect of the flow behavior index on the drag

reduction ratio, o2, in horizontal stratified flow

10-

1

0.1-

Fig.2 Comparison of the theoretical predictions obtained

for the dimensionless pressure drop with experimental data

in this work and those in Bishop and Deshpande' work in

horizontal stratified flow regime

air/CMC-4 flow in this work

L !l .... .... ( (m /h)

S.1 -

-i 1.25

S0 2.50

0o) A 3.75

o- Predicted V 5.00

d 7.50

0 5 10 15 20

Gas flowrate, Qg (m2/h)

Fig.3 Effects of fluid flow rate on the drag reduction ratio

for air/CMC slug flow.

Fig. 4 Comparison of the predicted pressure gradient with

the data of Farooqi and Richardson for air and kaolin

suspensions slug flowing in a pipe of 0.0417 m in diameter

(the flow behaviour index, nl=0.175)

101

10

Ug (m/s)

101

10

0 1 2 3 4

U (m/s)

sg

Paper No

0.5

0.0

-0.5

-1.0

Experimental data by Farooqi and Richardson 1982b

0 0.244

0 0.488

A 0.976

ug (m/s)

--- Predicted by the model (n =0.85)

* Experimental data, Bishop and Deshpande (1986)

n =0.952

g 0.765 0.595 0.535

-0- Predicted by the model, U =0.1769 m/s

Experimental data in this work

Sair/CMC-3 flow in this work

U1l (m/s)

O 0.1769

A 0.3539

A A <1 0.5308

A 0.7077

0 1.0616

0 -Predicted

I AZ

7th International Conference on Multiphase Flow

ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

Usg (m/s)

Fig. 5 Comparison of the predicted pressure gradient with

experimental data of Chhabra et al. and the present work

for air/CMC solutions flowing in a pipe of 0.0417 m I.D.

and of 0.05 m I.D. respectively (a the flow index, n=0.535;

b the flow index, n=0.595; c the flow index, n=0.58)

1.0 a +30

0.8 -20%

0.2 >

0.0

0.0 0.2 0.4 0.6 0.8 1.0

Experimental, *A

Fig. 6 Compared between experimental and theoretical

obtained values of the drag reduction ratio, for

gas/non-Newtonian fluid flow studied in this work and for

others systems reported in the literature.

Paper No

C Experimental data by Chhabra et al. 1984

CVCMC, conc 1.25%

SPredicted

'u"s (m/s)

5 0.244

-o E 0 0.490

A 0.732

0.976