Vertical, Upward Gas-Liquid Flow

Many of the salient features of multiphase flow can be illustrated by considering the simultaneous gas-liquid flow up a vertical pipe with the apparatus sketched in Fig. 14.1. Assume that at first only water flows then from Bernoulli s equation 

For zero flow rate we can calculate - P2 = pg = 8.7 psi. = 60 kPa. As we start the flow rate of water only, Pj - P will increase, because of the increase in with increasing velocity. j 

Now let us hold the water flow rate constant at some modest average velocity, such as 2ft/s, and slowly increase the air velocity from zero to some large value. This will cause to increase, since the j overall linear velocity is increased. However, now there will be bubbles of gas in the pipe the density in Eq. 14.1 is no longer the density of water but is the average density of the gas-liquid mixture in the vertical pipe. At low flow rates the density goes down much faster than goes up, so Pj — P decreases steadily as we increase the gas flow rate. Finally, a point is reached where further increase in the gas velocity causes to increase faster than p decreases Pj Pj will increase with an increasing gas flow rate. A typical plot of experimental data for such a system is shown in Fig. 14.2. j 

Typical experimental results for vertical, upward air-water flow in the apparatus shown in Fig. 14.1, with constant liquid flow rate. Here is Q,IA. [From G. W. Govier, B. A. Radford, and J. S. C. Dunn, The upward vertical flow of air-water mixtures, Can. J. Chem. Eng. 35 58-70 (1957). Reproduced by permission of the publisher.] 

Two-phase flow patterns in vertical tubes. The liquid flow rate is upward at a small, constant velocity. The gas flow rate upward increases steadily from left to right. The annular pattern shown is often referred to as climbing film flow. [From D. J. Nicklin and J. F. Davidson, The onset of instability in two-phase slug flow, in Symposium in Two-Phase Flow, Institution of Mechanical Engineers, London, 1962. Reproduced by permission j of the publisher.] 

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In a vertical upward gas-liquid flow, a continuous swarm of bubbles flows upward with the liquid stream due to a buoyancy effect, and the gas slips past the liquid with a relative velocity U0 (rise velocity) ... 

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