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THE FOREGOING fundamental considerations lead directly to procedures for sizing a mesh or vane mist eliminator in terms of cross-sectional area, to handle the throughput for a particular application.
The key variable is gas velocity. In a given application, a mist eliminator has a definite operating range, indicated by the lighter background color in Figure 16. At velocities above this range, performance is impaired by re-entrainment, accompanied by flooding for all but the lightest mist loads. As velocity decreases within the operating range, droplet capture efficiency declines—more steeply for smaller droplets than for larger ones. At some point, the efficiency for droplets at the lower end of the size range has fallen to an unacceptable level. This is the bottom of the operating velocity range. For the typical case in Figure 16, it is roughly 3 ft/sec. Dividing that into the re-entrainment limit of about 11 ft/sec yields an approximate turndown ratio of nearly four to one for the operating range.
It is generally recommended that the nominal operating velocity be established toward the top of the range—about 10 feet per second for an air-water application such as this. Capture efficiency is higher there than farther down in the range, and performance is satisfactory at velocities from about 30% to 110% of that value.
A certain formula is widely used in sizing a mesh or vane mist eliminator for a given throughput. It generalizes the characteristics reflected in Figure 16 (notably excepting the low end of the operating range) from the base case of air and water to other gases and liquids. Called the Souders-Brown equation, it has long been the customary tool for predicting the maximum allowable vapor velocity in a trayed vapor-liquid contactor column. (M. Souders and G. G. Brown, “Design of fractionating Columns. I. Entrainment and Capacity,” Industrial & Engineering Chemistry, Volume 26 [1934], Pages 98-103.) The equation is similar in form to Newton’s Law for the terminal velocity of falling spheres.
The version of the Souders-Brown equation commonly used for mist eliminators establishes a variable K called the vapor load factor—also known as the system load factor, Souders-Brown velocity, or K factor—as follows:
The K factor can be considered an effective gas velocity for the purpose of expressing the throughput capacity limit, adjusted for the effects of liquid and gas density. This parameter allows data gathered for a given mist eliminator and gas-liquid system—typically air and water—to be used in sizing mist eliminators of the same type for different gases and liquids.
For example, Figure 18 shows the graphs of Figure 16, with the X axis converted from velocity to vapor load factor. The conversion factor is 28.8, calculated as shown in the figure. The effect is to shift the graphs of Figure 16 toward the left by that amount. The recommended design velocity of 10 feet per second for this mesh pad in this horizontal configuration corresponds to a load factor of about 0.35 ft/sec. The top of the operating range, in turn (11 ft/sec in Figure 16), lies at a load factor of about 0.38. Amistco publishes graphs such as this as design aids for a number of its products. (See appendix.)
The point is that re-entrainment, flooding, and loglog pressure-drop plots (although not capture efficiency) all correlate well with vapor load factor for different liquids and gases having various densities. The correlation generally holds at pressures from atmospheric up to about 7 atmospheres (100 psia) for gases and liquids whose surface tension and viscosity vary roughly alike with density. This includes most light hydrocarbons, for instance.
As an example, consider a TM-1109 mist eliminator in the top of a distillation column or knockout drum as shown in Figure 19. In this particular case, the squareroot divisor in Equation 1 is 11.7. The design velocity (corresponding to a K-factor of 0.35 ft/sec) is 4.10 ft/sec which is 41% of the value for air and water in Figure 16. The pressure-drop curves and re-entrainment and flooding points will likewise be shifted to about 41% of their positions in Figure 16.
Figure 19 also shows how the Souders-Brown equation is typically used in sizing a vessel with a mist eliminator of this type for flow area to achieve the design velocity (K = 0.35) with a given design vapor flow rate.
Capture efficiency is an entirely separate matter from sizing. As explained earlier, the inertial capture efficiency for a given velocity, wire diameter, and droplet size is enhanced by higher liquid density and lower gas density.
Such density changes result in a higher square-root divisor in the Souders-Brown equation. In the example case in Figure 19, however, the divisor (11.7) is lower than for air and water (28.5). Therefore the efficiency of this pad in this application at any given velocity will be lower than for air and water. To achieve minimal acceptable efficiency, the low end of the operating velocity range will be higher than the typical 30% of design velocity.
Table 2 shows generally recommended design values of K for various typical cases. Note that the values for vane units are higher than for mesh pads. This is because vanes are less susceptible to re-entrainment and flooding (discussed later).
Furthermore, for both mesh and vanes (except double-pocket vanes), design K-factors are higher for horizontal flow through vertical units than for vertical flow through horizontal units. This is because with horizontal flow, draining of captured liquid is not retarded by gas flowing in the opposite direction.
In all cases listed in Table 2, performance is typically acceptable over the same range of velocities discussed for vertical flow in a horizontal mesh pad—from about 30% to 110% of the design value. However, as explained before, the low end of the operating range varies in the opposite direction from the design velocity; the lower the design velocity, the narrower the acceptable range.
Similarly, as mentioned earlier, this correlation breaks down at pressures outside the range of 1 to 7 atmospheres. For higher or lower pressures, the design K-factor will be as low as 60% of the tabulated value for each configuration in Table 2.
Finally, the design K-factors for both horizontal and vertical mesh pads are applicable only for low to moderate mist loads—up to about 0.1% liquid by volume. For a velocity of 10 feet per second, this corresponds to about 0.5 gallons of liquid captured per minute per square foot. For higher mist loads, the design K should be derated. Vane units are not so sensitive to the effects of mist load on capacity.
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