Flow regime, estimation

The most reliable methods for fully developed gas/liquid flows use mechanistic models to predict flow pattern, and use different pressure drop and void fraction estimation procedures for each flow pattern. Such methods are too lengthy to include here, and are well suited to incorporation into computer programs commercial codes for gas/liquid pipeline flows are available. Some key references for mechanistic methods for flow pattern transitions and flow regime-specific pressure drop and void fraction methods include Taitel and Dukler (AIChEJ., 22,47-55 [1976]), Barnea, et al. (Int. J. Multiphase Flow, 6, 217-225 [1980]), Barnea (Int. J. Multiphase Flow, 12, 733-744 [1986]), Taitel, Barnea, and Dukler (AIChE J., 26, 345-354 [1980]), Wallis (One-dimensional Two-phase Flow, McGraw-Hill, New York, 1969), and Dukler and Hubbard (Ind. Eng. Chem. Fun-dam., 14, 337-347 [1975]). For preliminary or approximate calculations, flow pattern maps and flow regime-independent empirical correlations, are simpler and faster to use. Such methods for horizontal and vertical flows are provided in the following. 

Figure 12 shows the estimated liquid flow rate versus the actual liquid flow rate. The tests for Qa — 0.6 m3/h are of the stratified flow type. The tests of 1.8 < Qa < 7.5 m3/h are of the elongated bubble and slug flow type (Brennen, 2005 Govier and Aziz, 1972). In this study, the flow conditions are compared with the flow regime charts of Govier and Omer (1962 in Govier and Aziz, 1972) and Mendhane (1974 in Brennen, 2005). 

Taking the active pulse height as 0.05 m and the pulse velocity as 1 m/s, we derive for the mass transfer coefficient in the gas-continuous zone, 11, a value of 10 m/s and in the pulse proper, k, a value of 6 10 m/s. These values compare very well with those given in literature (5, 6) for both gas-continuous and dispersed bubble flow regimes. An estimate of k can also be made by means of the penetration theory, taking the respective liquid in and outside the pulse as the basic for the calculation of the con-... 

The mean free path is inversely proportional to the pressure and varies from 30-100 nm at 0.1 MPa to 0.3-1 nm at 10 MPa for normal gases. As previously described, the average size of the pores of commercial catalysts varies over a wide range (1- 200 nm). Therefore, typical values of the Knudsen number are lO-4 - 102. This rough estimate shows that different flow regimes of different complexity occur in practice. 

It is worth emphasizing that Eqs. (13-61) to (13-68) hold regardless of the models used to calculate the interphase transport rates and EJ. With a mechanistic model of sufficient complexity it is possible, at least in principle, to account for mass transfer from bubbles in the froth on a tray as well as to entrained droplets in a spray, as well as transport between the phases flowing over and through the elements of packing in a packed column. However, a completely comprehensive model for estimating mass-transfer rates in all the possible flow regimes does not exist at present, and simpler approaches are used. 

Recommendations The gas holdup in the bubble-flow regime can be estimated using either Cq. (7-13) or F.q. (7-14). For the estimation of liquid holdup in the bubble-flow regime, use of Eq. (7-9) is recommended. In the pulsed-flow regime, the data of PERC and Eq. (7-15) would be useful. More experimental work with the hydrocarbon systems is needed. 

Recommendations The best available correlations for fq nL, fcL, and aL are the energy correlations shown in Figs. 7-19, 7-18, and 7-17, respectively and, at least for large packing size, their use is recommended. For the estimations of fcLaL, the suggestions of Charpentier are possible alternatives. For shaped particles and in the bubble-flow regime, the correlations ofAlexander and Shah for fcLaL are recommended. Future work in this area should consider small particles and the hydrocarbon systems. 

Recommendations The information given in Chap. 6 can be used for an approximate estimation of the flow regime. The flooding conditions can be estimated from Fig. 8-1. 

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