Pressure drop vapor-flow

We have yet to discuss the most important factor in determining the height of liquid in the downcomer. This is the pressure drop of the vapor flowing through the tray deck. Typically, 50 percent of the level in the downcomer is due to the flow of vapor through the trays. 

When vapor flows through a tray deck, the vapor velocity increases as the vapor flows through the small openings provided by the valve cajjs, or sieve holes. The energy to increase the vapor velocity comes 

The height of water needed to exert a liquid head pressure of 1 psi is equal to 28 inches, of water. If we were working with gasoline, which has a specific gravity of 0.70, then the height of gasoline needed to exert a liquid head pressure of 1 psi would be 28 inches/0.70 = 40 inches of clear liquid. 

To summarize, the total height of clear liquid in the downcomer is the sum of four factors  

Unfortunately, we do not have clear liquid, either in the downcomer, on the tray itself, or overflowing the weir. We actually have a froth or foam called aerated liquid. While the effect of this aeration on the specific gravity of the liquid is largely unknown and is a function of many complex factors (surface tension, dirt, tray design, etc.), an aeration factor of 50 percent is often used for many hydrocarbon services. 

When vapor flows through a tray deck, the vapor velocity increases as the vapor flows through the small openings provided by the valve caps, or sieve holes. The energy to increase the vapor velocity comes from the pressure of the flowing vapor. A common example of this is the pressure drop we measure across an orifice plate. If we have a pipeline velocity of 2 ft/s and an orifice plate hole velocity of 40 ft/s, then the energy needed to accelerate the vapor as it flows through the orifice plate comes from the pressure drop of the vapor itself. 

This means that if we calculated a clear liquid level of 12 in in our downcomer, then we would actually have a foam level in the downcomer of 12 in/0.50 = 24 in of foam. 

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Whereas liquid flow is caused by gravity in vapor-liquid countercurrent columns, a pressure gradient is necessary to induce vapor flow. Pressure drops exist from tray to tray, so the lower trays must be maintained at a higher pressure than the upper trays. One consideration in tray design is to attempt to keep the pressure drop at a minimum. 

Vapor Flows. Pressures and pressure drops in the various sections of the steady model can be specified, and no valves are required between the fictitious vessels. However,... 

A simultaneous flow of a gas and a liquid, a gas and a solid, two different liquids, or a liquid and a solid is described as a two-phase flow. Among these types of two-phase flow, gas-liquid flow is the most complex flow due to the deformability and the compressibility of the phases. The analysis of the two-phase flow is very important for liquid-cooled reactors. Two-phase flow occurs in the BWR core and in the steam generator of the PWRs. In order to analyze reactor systems with liquid-vapor mixtures, it is necessary to predict liquid-vapor density, pressure drop across a given channel length, flow stability, maximum flow rates, and heat transfer rates. As the liquid is vaporized, the mixture of vapor and liquid flow gives rise to interesting flow and heat transfer challenges. 

In the situation where heat is not added (adiabatic), or is not added quickly enough (rapid gaseous withdrawal) to compensate for the heat of vaporization, the pressure drop can eventually result in a pressure of 14.7 lbf/in (abs) (101.3 kPa, abs) in the cylinder that can result in a cessation of flow since there would no longer be a pressure differential. This... 

DP is uncorrected vapor line pressure drop, in psi DPx is corrected vapor line pressure drop, in psi AC is acceleration factor, dimensionless G is mass flux, in lb/sec- 12 v is line velocity, in fl/sec A is line inside cross sectional area, in fl2 w is vapor weight flow, in Ib/sec PI is line inlet pressure, in p a F2 is line outlet pressure, in psia Pavg is average line pressure, see Eq. (4d), in psia. 

The upward flow of gas and Hquid in a pipe is subject to an interesting and potentially important instabiHty. As gas flow increases, Hquid holdup decreases and frictional losses rise. At low gas velocity the decrease in Hquid holdup and gravity head more than compensates for the increase in frictional losses. Thus an increase in gas velocity is accompanied by a decrease in pressure drop along the pipe, a potentially unstable situation if the flows of gas and Hquid are sensitive to the pressure drop in the pipe. Such a situation can arise in a thermosyphon reboiler, which depends on the difference in density between the Hquid and a Hquid—vapor mixture to produce circulation. The instabiHty is manifested as cycHc surging of the Hquid flow entering the boiler and of the vapor flow leaving it. 

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