Slug Frequency in Horizontal Gas-liquid Slug Flow A correlation for slug frequency in horizontal gas-liquid slug flow involving the use of the input liquid quality and mixture Froude number is presented. It is based on both prior literature data and recent data collected by the authors and has been effectively used in pressure drop calculations.
C o c u r r e n t flow of gas and liquid in horizontal pipes is a topic of considerable current interest, owing to the increasing importance of two-phase flow in process equipment, in nuclear reactors, and in long distance pipelines. Of all the twophase flow applications, the latter (involving mainly crude oil and natural gas systems) requires special attention regarding accurate calculation of pressure drop. When ecoiioniic considerations are taken into account, the overwhelming nmjority of long-distance lines operate in the slug flow regime. Due to the unsteady-state nature of this regime, pressure drop predictions based on generalized correlations such as those of Lockhart and Martinelli (1949), Bertueei et al. (1956), and Cheiiowet,h and Martin (1955), can deviate widely from experimental data for fully developed slug flow. T o predict more accurately pressure drop in the slug flow regime, a number of physical models for this regime has been proposed. These models not only incorporate specific f l o ~ phenomena but also energy Considerations applicable t'o only the slug flow regime. Published studies covering model developnieiit for slug flow include those of Kordyban (1961), Hubbard (1965), and Hubbard and Dukler (1968). The Hubbard-Dukler model is the most up-to-date and has been shown by Greskovich aiid Shrier (1971) to be useful and accurate for slug flow pressure drop calculations. I n this model, the pressure drop is directly proportional to the slug frequency. Therefore, deviations ill frequency predict'ions are directly reflected in pressure drop calculations. The utility of the mixture Froude number and input liquid quality as two-phase flow correlation parameters has been previously discussed by Greskovich et al. (1969) for in situ holdup and flow regime transitions. Similarly, the correlation of slug frequeiicy data presented in Figure 1 has been used and is discussed in detail, along with the Hubbard-Dukler
k----'-
0
8
16
24
32
40
model, for pressure drop calculations by Greskovich and Shrier (1971). The correlation is based on air-water data collected in our laboratory with a 1.5-iii. pipe, aiid literature data from Hubbard (1965) for a 1.5-in. pipe and from Kordybail arid Ranov (1963) for a 1.25-in. pipe. To test the effect of pipe: diameter on the correlation, some data for established slug flow in a 6-in. pipe aiid for 0.10 < X < 0.20 were collected and plotted. For the limited range of input liquid qualities evaluated, the results indicated relatively little diameter effect. In addition, the effect of system properties 011 the slug frequency correlation was tested by using a kerosenenitrogen system in the 1 . 5 4 pipe. ~ These results also indicated little effect, if any, of system properties on the correlation. I n a recent publication by Gregory aiid Scott (1969), the authors conclude that slug frequency is dependent 011 pipe diameter. This coiiclusioii was based 011 a comparison of their data collected from a 0.75-in. tube using the air-water system with data from Hubbard (1965) for a 1.50-in. pipe. The proposed correlation was given as
The quantities in Equation 1 are expressed in meters and seconds. The equation yielded a standard deviation of 15.8% a,nd from our estimation [based on Figure 5 in Gregory aiid Scott (1969)l the arithmetic deviations were as great as 30 to 50%. I3y rearranging terms in Equation 1, it is fourid that the two parameters, X and .VF~,previously used by Greskovich aiid Shrier (1971) to correlate effectively the slug frequency appear along with the pipe diameter as follows: v S = 0.0226
[ ('F+ -YF.)]'" X
---
46
56
64
72
80
86
96
104
112
120
128
MIXTURE FROUDE NUMBER, NFr
Figure 1. Slug frequency correlation Ind. Eng. Chem. Process Des. Develop., Vol. 1 1 , No. 2, 1972
317
Since the data collected by Gregory and Scott and by Hubbard appear to be for fully developed slug flow, a diameter effect based on Equation 2 evidently does exist for small pipes (0.75 in. to 1.50 in.). However, we would question the applicability of Equation 1 to larger pipe sizes. Slug frequency data from a 6-in. pipe a t our facility indicate that the magnitude of the diameter effect expressed by Equations 1 and 2 is too great for larger diameter pipes. Apparently, the effect of pipe diameter on slug frequency diminishes for larger pipe diameters more strongly than indicated by Equation 2. In conclusion, we are recommending the use of Figure 1 for slug frequency rather than the Gregory-Scott equations for large pipe sizes.
Literature Cited
Bertuzzi, A. F., Tek, M. R., Poettmann, F. H., J . Petrol. Technol., 8, (January 17, 1956). Chenoweth, J. M., Alartin, AI. W., Petrol. Rejner., 10, 151 (1955). Gregory, G. A., Scott, D. S., AIChE J., 15, 933 (1969). Greskovich. E. J.. Shrier. A. L.. Bonnecaze. R. H.. Ind. Eno. Chem. Fdndam.,'8, 591 11969).' Greskovich, E. J., Shrier, A. L., AIChE J., 17, 1214 (1971). Hubbard, M. G., PhD thesis, University of Houston, Houston, T X (1965). Hubbard, 11. G., Dukler, A. E., presented at AIChE National Meeting, Tampa, FL (May 1968). Kordyban, E. S.,Trans. A S M E Ser. D,613 (December 1961). Kordyban, E. S., Ranov, T., blultiphase Flow Symp. Winter Annual Meeting of ASNE, Phila., PA., November 17-22 I1 \ , -96.1 -~ ,. Lockhart, R. W., lIartinelli, R.C., Chem. Eng. Progr., 45 (l), 39 (1949). EUGEKE J. GRESKOVICH' ADAM L. SHRIER
Nomenclature
d
pipe diam, m gravitational constant, m/ sec2 LVF~ ,VsG)z/dg = mixture Froude number, dimensionless V,,, V S G= superficial velocity of the liquid and gas, respectively, m/sec = V.L V,C = no-slip velocity, m:sec V77S = V q L , ' ( V s L VqG)= input liquid quality, volume x fraction VS = slug frequency, sec-' = = =
9
(vsL+
+
+
Department of Chemical Engineering Bucknell Universitu Lewisburg, P A Esso Research. and Enaineerina Co. Florham Park, N J RCEIVED for review May 27, 1971 Accepted Kovember 5, 1971 1
To whom correspondence should be addressed.
Bed Porosities in Gas-liquid Fluidization Bed porosity data of gas-liquid fluidization for different beds in circular as well as annular channels, operating under different ranges of both liquid and gas velocities, have been determined and the data could b e satisfactorily correlated by the equation proposed by Dakshinarnurty et al. ( 1 971).
I n the present work, a n attempt has been made to predict the bed porosity data of gas-liquid fluidization for beds of different geometries, containing glass balls and beads and rockwool shot and lead shot by the equation proposed by Dakshinamurty et al. (1971). The importance of the gas-liquid fluidization in general and bed porosity data in particular has been emphasized earlier [Dakshinamurty et al. (1971)l. gstergaard (1965) ~~
~
has proposed a semiempirical method involving trial and error procedure for the prediction of bed porosity data in gasliquid fluidized beds. Also, Dakshinamurty e t al. (1971) have proposed the following equation: t
=
2.65 ( u ~ / u ~ ) ~ . ~ for( ~~ V ~ > ~R500 ~ /~ u ~) ~(1) . ~ ~
for the prediction of the same, covering wider ranges of gas and liquid velocities and particle sizes. I n the present work, a n
~~
Table 1. Systems Studied Along With Specifications of Particle Size, Density, Terminal Velocity, and Range of Gas and liquid Velocities
Electrolyte density = 1.021 g/cc; viscosity = 0.0086 poise
System
1. Lead shot-air-water 2. Glass balls (A)-air-water 3. Glass balls (B)-air-water 4. Glass beads-Kitrogen-Electrolyte 5. Glass balls (B)-Nitrogen-Electrolyte 6. Glass balls (A)-Nitrogen-Electrolyte 7. Glass beads (A)-Kitrogen-Electrolyte 8. Rockwool shot-Yitrogen-Electrolyte 9. Glass balls (A)-Nitrogen-Electrolyte
3 18
Particle Size, cm
0.213 0.418 0.602 0.684 0.603 0.418 0.335 0.130 0.418
Ind. Eng. Chem. Process Des. Develop., Vol. 1 1, No. 2, 1 9 7 2
Particle density, g/cc
11.175 2.448 2.448 2.470 2.448 2.448 2.420 2.700 2.448
u L, crn/sec
78 44 52 50 52 44 35 24 44
Ul,
crn/sec
11-16 7-12 8-1 3 9-16 7-16 7-14 5-10 4-8 7-14
Range of ug, cmfsec
4-19 4-18 4-17 0.5-15.0 1.0-20.0 0.5-25.0 1.0-16.0 1.0-13.0 0.5-25.0
Diam of the channel,
De, cm
5.6 5.6 5.6 3.2 3.2 3.2 3.2 3.2 3.5
