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and, by Eq. (16-23), hp - JfciFJ + k%V* + hùL + 0.12 (16-35)

The term (h'9 - h°L - 0.12 ^ is equal to HVt/N)2 + k2(VT/N)*

and will be termed the velocity head for uniform vapor distribution, hy. It is equal to the pressure drop due to the vapor flow in the riser, cap, and slots for a plate operating with a uniform velocity distribution.

For a plate with the inlet row of caps just inactive, 2hv is equal to (M h°L) and Eq. (16-34) reduces to the previous criterion. When

(M h°L) is small in comparison to 2hv, the equation gives V0 =

i.e., the vapor distribution is uniform. To use these equations, h'p is calculated using V equal to (Vr/N) and hL = h°L, and V0 is obtained from Eq. (16-34). The pressure drop for the plate is then calculated by Eq. (16-35).

The distribution of the vapor among the caps is important, and an approximation can be obtained by the following relation:

where Vn = vapor rate through inflow cap.

In order to obtain a velocity through the first row of caps equal to one-half that through the last row would require that 2hv be twice the hydraulic gradient, and this would appear to be about the minimum ratio of velocities that should be considered for design purposes.

Plate Dumping. This condition can occur in extreme cases. When the upstream row of caps becomes inactive owing to an increase in the hydraulic gradient, the liquid level in the caps will be depressed below the top of the slots by an amount equal to the surface tension effect. If the gradient is increased further, the liquid level under the inactive caps rises and the pressure drop for the same rate of vapor flow increases. Eventually a condition is reached where the liquid level under some of the inactive caps reaches the top of the riser and liquid spills to the plate below. In extreme cases, essentially all of the liquid flowing to a plate will dump down through,the risers of the first few rows of caps, and very little will flow across the plate. Under these conditions, there is frequently an abrupt drop in liquid level on the plate between the section of inactive and active caps. The momentum of the vapor issuing from the active caps acts as dam for the liquid giving a " Red Sea " effect. Plate dumping is undesirable because with the usual column, with liquid flowing in opposite directions on successive plates, the liquid that spills through the risers by-passes the vapor on two plates.

Equations for the condition of plate dumping, similar to those for inactive caps, can be derived but, because it is an undesirable condition, it is better to control conditions such that all the caps are active. This will ensure against plate dumping. Plate dumping conditions in a large commercial tower have been described by Harrington et al. (Ref. 15).

General Design Considerations. It is usually desirable to have a bubble plate that gives (1) a low pressure drop and (2) a reasonably uniform vapor distribution. These two conditions are partly incompatible because a high pressure drop usually gives more uniform vapor distribution.

The vapor distribution relation of Eq. (16-36) indicates that the two main factors involved in obtaining a low variation in (V/V0) across the plate are (1) low value of the hydraulic gradient and (2) a high value of hv. Equation (16-16) shows that a low liquid gradient will be obtained for a given liquid flow rate by increasing h0, or decreasing N.

Increasing the liquid depth should be very effective in lowering the gradient due to the increase in n and the decrease in V/. A deep liquid level above the top of the caps is not desirable because it allows surges and wave action to occur. Raising the caps to allow liquid flow below the skirts is probably one of the most effective ways of reducing the hydraulic gradient. It does introduce the possibility that part of the liquid will cross the plate without intimate contact with the vapor. This condition would be most serious when the column is operating at reduced capacity. This method has the advantage that it reduces the gradient without increasing the pressure drop.

The space above the caps should be as unobstructed as possible to allow free passage of the liquid. Hold-down bars for the caps or other mechanical devices should be arranged in the direction of liquid flow.

Decreasing the value of N is a common method of improving vapor distribution, and this result is obtained by the use of split plates or multiple downspouts. This shortened path may be accomplished by having the inlet downspout on one plate in the center and the exit downspouts placed uniformly around the circumference (Fig. 16-4(7). Thus, the liquid flows out radially and crosses only half of the plate. On the next plate below, the liquid would flow radially into the center. Other designs bring the liquid in at opposite sides and flow across half the tower to central weirs that extend across the tower perpendicular to the direction of flow (Fig. 16-4F). On the plate below, the liquid flow is outward. This latter method can be arranged to give any fractional distance across to plate desired, such as or }{.

These arrangements tend to decrease the hydraulic gradient, but they may lower the plate efficiency by reducing the cross flow effect, and they offer difficulties in properly proportioning the overflow

I------------flow weir. If the segments are nar row and the weirs are all adjusted Fig, 16-8. Cascade plate. to tbe proper height, the level at the caps can be kept uniform. The plate also has the advantage of complete cross flow. The main difficulty is the constructional complexity.

Increasing the value of hv by increasing the pressure drop will be effective in improving vapor distribution. The use of excessive pressure drops to obtain this result is not desirable, although it may be the simplest method of correcting a column that has already been built. In this latter case, some of the caps can be removed, or constrictions can be placed in the risers to increase the pressure drop. This increase in pressure drop increases the possibility of flooding the column by liquid backing up the down pipes. Good original design should give low pressure drop and good vapor distribution.

Entrainment. Entrainment is the carrying of the liquid from one plate to the plate above by the flow of the vapor. It is usually defined between the different sections.

Another arrangement that attempts to obtain complete cross flow, but reduced hydraulic gradient, is the staggered plate illustrated in Fig. 16-8. In this case; the plate is broken up into narrow segments, each with its own over-

as the weight of liquid entrained per weight of vapor. Entrainment is undesirable, since it reduces plate efficiency by tending to destroy the countercurrent action of the tower, and it also may affect the distillate adversely from the standpoint of color or oth¡er nonvolatile impurities.

The entrainment of the liquid is due to two main causes: (1) the carrying of liquid droplets due to the mass velocity of the gas and (2) the splashing of the liquid on the plate. These depend on the slot-vapor velocity, the superficial column velocity, and the plate spacing.

Several investigators have published quantitative data on the amount of entrainment in bubble-plate columns. Most of their investigations have been on systems involving air and water.

The data of Volante (Ref. 36) are given in Fig. 16-9 where the entrainment, expressed as pounds of liquid per pound of vapor, is plotted as a function of the superficial velocity, VC} in feet per second, multiplied by the square root of the vapor density in pounds per cubic foot. The entrainment increases rapidly with the vapor throughput and with a decrease in plate spacing. An entrainment of 0.01 lb of liquid per pound of vapor does not seriously lower the plate efficiency (see page 454), although it may give contamination. The superficial vapor velocity for these data is lower than commercial practice, and values of the abscissa of 0.3 and 0.7 would be more comparable. Other data are given in Fig. 16-10. The curves labeled A are based on the data of Peavy and Baker (Ref. 26) for the entrainment in an 18-in.-diameter column with ten 3-in.-diameter caps per plate. They investigated the entrainment when distilling an alcohol-water mixture for plate spacings of 12 and 18 in.

Curves B are based on the air-water results of Sherwood and Jenny (Ref. 31). The tower contained two plates and was 18 in. in diameter. Four-inch caps were employed having 33 notched-type slots. The slots were % in. high and tapered from %e ^ the bottom to % in. at the top.

Holbrook and Baker (Ref. 16) studied entrainment in an 8-in. bubble-plate column using steam and water. Curves C are based on a portion of their data. They conclude that the plate spacing and vapor velocity were the main factors in determining the amount of entrainment and that the amount of liquid flow and slot-vapor velocity were of less importance.

Curve E is based on the data of Ashraf, Cubbage, and Huntington (Ref. 1) for the entrainment in a 7- by 30-ft. commercial absorber. The tower contained 10 trays, 22 in. apart. The tower was operating on ft gas oil-natural gas system at 45p.s.i.a. The investigators obtained a maximum entrainment of 0.0017 at a mass velocity of 23.4 lb. per min. per sq. ft.

Fig. 16-9. Entrainment of water by air. %

Entrainment separators and baffles have been suggested, and tests of various arrangements have shown that they are effective in reducing the amount of liquid carried by the vapor, but they have not been used to any extent in industrial rectifying towers.

Plate Spacing. Rectifying columns are built with the plates spaced as close as 6 in. to as much as 4 to 6 ft. There are a numbersr of facto