Two-phase pressure drop correlations

TABLE 17.22 Shellside Two-Phase Pressure Drop Correlations... 

Two-phase pressure drop correlation of Lockhart and Martinelli... 

The flow of a gas-liquid mixture in a pipeline is common. The flow patterns present should be recognized. For vertical piping, the pattern alone often determines the proper line size. Two-phase pressure drop correlations have a high uncertainty associated with them. Typically, the estimated pressure drop can be 40% of the true value. 

The two-phase pressure drop is obtained by multiplying either the liquid-phase drop by (t) or the gas-phase pressure drop by. Figure 7-23 gives the Lockhart-Martinelli correlation between X and ([t s... 

A computer program (TWOPHASE) was developed that uses the Lockliart-Matinelli correlation and determines the total pressure drop based on the vapor phase pressure drop. The total length of the unit depends on the nature of the Reynolds numher. The program also calculates the gas-liquid phase regime employing a modified Baker s map [33]. Table 7-13 gives the results of the two-phase pressure drop. 

Qu W, Mudawar I (2002) Prediction and measurement of incipient boiling heat flux in micro-channel heat sinks. Int J Heat Mass Transfer 45 3933-3945 Qu W, Mudawar I (2004) Measurement and correlation of critical heat flux in two-phase micro-channel heat sinks. Int J Heat Mass Transfer 47 2045-2059 Quiben JM, Thome JR (2007a) Flow pattern based two-phase pressure drop model for horizontal tubes. Part I. Diabatic and adiabatic experimental study. Int. J. Heat and Fluid Flow. 28(5) 1049-1059... 

Tran TN, Chyu M-C, Wambsganss MW, France DM (2000) Two-phase pressure drop of refrigerants during flow boiling in small channels an experimental investigation and correlation development. Int J Multiphase Flow 26 1739-1754... 

This matter was discussed in Sect. 5.8. For channeis of dh = 0.9-3.2 mm, the two-phase pressure drop can be caicuiated using the Lockhart-Martineiii modei with parameter C, ranging from 5 to 20. The parameter C decreases when the hydraulic diameter decreases (Zhao and Bi 2001). For channels of = 100 pm, (Kawahara et al. 2002) two-phase pressure drop can be correlated within an accuracy of 10% using the Lockhart-Martineiii model with C = 0.24. 

Baroczy, C. J., 1966, A Systematic Correlation for Two-Phase Pressure Drop, NAA-SR-Memo-11858, North American Aviation Co., Canoga Park, CA. (3)... 

Lockhart and Martinelli divided gas-liquid flows into four cases (1) laminar gas-laminar liquid (2) turbulent gas-laminar liquid (3) laminar gas-turbulent liquid and (4) turbulent gas-turbulent liquid. They measured two-phase pressure drops and correlated the value of 0g with parameter % for each case. The authors presented a plot of acceleration effects, incompressible flow (3) no interaction at the interface and (4) the pressure drop in the gas phase equals the pressure drop in the liquid phase. 

Baroczy, C. J., A systematic correlation for two-phase pressure drop. AIChE. reprint no. 37, paper presented at 8th National Heat Transfer Conference, Los Angeles, August 1965, Chemical Engineering Progress Symposium Series, 62, No. 64, pp. 232-49 (August 1965). 

IV. Correlating Methods for Two-Phase Pressure Drops and Void Fractions 220... 

Three major reviews exist which give detailed coverage of the literature available up to about 1955. In particular, the review by Gresham et al. (G7) may be consulted for empirical correlations limited to specific flow patterns, and the papers by Isbin et al. (II) and by Bennett (B9) are particularly valuable for aspects of two-phase flow related to steam-water systems. Bennett has also given useful tabulations of available correlations (up to 1957) for the estimation of two-phase pressure drops. 

The original correlation showed a scatter of nearly 50% in predicting two-phase pressure drops, and, in addition, a decided dependence on liquid rate (which the correlation averaged out). Much of this scatter seemed to be a systematic drift depending on total mass flow rate. This dependence on mass flow was pointed out by Gazley and Bergelin (L6) and by Isbin et al. (12). In the following summary, satisfactory predictions can be taken to mean prediction of pressure drops no worse than the above, and, in some cases, considerably better. 

In summary, the calculation of pressure drops by the Lockhart-Marti-nelli method appears to be reasonably useful only for the turbulent-turbulent regions. Although it can be applied to all flow patterns, accuracy of prediction will be poor for other cases. Perhaps it is best considered as a partial correlation which requires modification in individual cases to achieve good accuracy. Certainly there seems to be no clear reason why there should be a simple general relationship between the two-phase frictional pressure-drop and fictitious single-phase drops. As already pointed out, at the same value of X in the same system, it is possible to have two different flow patterns with two-phase pressure-drops which differ by over 100%. The Loekhart-Martinelli correlation is a rather gross smoothing of the actual relationships. 

Obviously, correlations of one of these friction factors with an analogous Reynolds number, or with two-phase pressure-drop, throws little light on the other variables concerned, and these quantities will appear as parameters in any proposed relationship. However, Govier and Omer point out that plots of such a form do give a systematic spread of data above the single phase lines and allow easy comparison of trends. 

In the original work on two-phase pressure-drops at the University of California (B13), tests were made in tubes inclined at 1 6, as well as in horizontal tubes. In general, these data for small inclinations also fitted the correlations proposed finally by Lockhart and Martinelli for horizontal tubes. 

The two-phase pressure drop term (APgl/Z) can be calculated using the correlation of Huntington (Ramachandran and Chaudhari, 1984) ... 

Pressure drop Using the Ergun equation, the liquid and die gas pressure drop are 0.726 and 2.12 kPa/m, respectively. Then, by using the correlation of Larkins et al., die two-phase pressure drop is equal to 10.8 kPa/m, ten times lower than in die pulsing-flow regime and low enough to assure diat the gas density is almost constant. Thus, die condition (e) is satisfied. 

Wammes et al. [33] also proposed a theoretical correlation to estimate the two-phase pressure drop. The following assumptions were made. 

Figure 5.2-21. Correlation of the two-phase pressure drop with its 50 % limits and 97.5 % confidence (after Larachi [36] and Larachi et al. [37]).

Other correlations for two-phase pressure drops in TBR have been summarized by different authors [40, 41, 51], the majority of them being mostly empirical and restricted to their specific narrow ranges of process conditions. 

At the present time, the best new correlation for two-phase pressure drop, both for low and high interaction regimes, is that proposed by Iliuta et al. [47], and derived using a neural... 

With the same approach as described for the two-phase pressure drop, Iliuta et al. [47] also proposed a new correlation for the total external liquid hold-up in the high interaction regime, with an average absolute relative error of 13.6 %. 

Figure 6.9. Pressure drop gradient and liquid holdup in liquid-gas concurrent flow in granular beds. [Sato, Hirose, Takahashi, and Toda, J. Chem. Eng. Jpn. 6, 147-152 (1973)]. (a) Correlation of the two phase pressure drop gradient A P/L, = 1.30 + 1.85Y-0 85. (b) Correlation of frictional holdup hL of liquid in the bed a, is the specific surface, 1/mm, d is particle diameter, and D is tube diameter, h, - 0.4a]/3Y 22.

Winkelmann et al. (54) have studied air-water flows in a corrugated heat exchanger. Flow visualization and two-phase pressure drop measurements have been performed. The flow visualizations have shown that the flow pattern is complex and that a wavy or a film flow occurs in most cases (Figure 29). The two-phase pressure drop depends on the total flow rate and vapor quality, and Chisholm-type correlation is proposed. More work is required to characterize the flow structure in compact heat exchangers and to develop predictive methods for the frictional pressure drop and the mean void fraction. 

The Lockhart and Martinelli [32] correlation is employed to estimate the two-phase pressure drop in the Kenics mixer. The pressure drop... 

There are a number of pressure drop correlations for two-phase flow in packed beds originating from the Lockhart-Martinelli correlation for two-phase flow in pipes. These correlate the two-phase pressure drop to the single-phase pressure drops of the gas and the liquid obtained from the Ergun equation. See, for instance, the Larkins correlation [Larkins, White, and Jeffrey, AIChE J. 7 231 (1967)]... 

Since some of the published pressure drop correlations can differ by an order of magnitude, it is best to verify the relationship with actual data before designing a reactor. Other approaches to two-phase pressure drop include the relative permeability method of Saez and Car-bonell [AIChE J. 31(1) 52-62 (1985)]. 

Correlations for the dynamic liquid holdup have also been developed as function of various dimensionless numbers including the liquid and gas Reynolds number, and the two-phase pressure drop [see, e.g., Ramachandran and Chaudhari, Three-Phase Catalytic Reactors, Gordon and Rreach, 1983 and Hofmann, Hydrodynamics and Hydrodynamic Models of Fixed Bed Pieactors, in Gianetto and Silveston (eds.), Multiphase Chemical Pieactors, Hemisphere 1986],... 

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