Minimum Vapor Rate

When vapor velocity through a packed bed is eimessivefy low, the following adverse effects may be encmmtered. 

Vapor maldistributum - Packing pressure drop plac a resistance in the vapor path that he spread the vapor radially. If pressure drop is too low, vapor will tend to channel thnnigdi the bed, leading 

Laminar vapor flow This wU] tend to reduce mass transfer. 

For these reasons, it is a common practice (15,52,63) to demgn random packed beds for a pressure drop not smaller than 0.1 in of water per foot of packing. In practice, there are many columns that operate efficiently at a lower pressure drop. 

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The multicomponent form of the Underwood equation can be used to calculate the vapor flow at minimum reflux in each column of the sequence. The minimum vapor rate in a single column is obtained by alternate use of two equations ... 

Turndown ratio is the ratio of the maximum allowable vapor rale at or near flooding conditions (rates) to the minimum vapor rate when weeping or liquid leakage becomes significant it may be termed the minimum allowable vapor velocity [193, 199, 200]. 

These trays will dump liquid excessively through the perforations giving exceeding low efficiencies [47] unless a minimum vapor rate is maintained for a given liquid capacity. The smaller the holes the lower the dump point (vapor velocity). 

Comment 2 Suppose that our feed composition had been a little higher, say xp. No matter how many steps we took, we could never get a liquid composition higher than that at the intersection of the operating and equilibrium curves. In that case, any solution for the specified L/V ratio is impossible. Instead the L/V ratio would have to be decreased, which will rotate the operating line clockwise about the specified point. This will raise the liquid composition at the intersection point and make the separation possible. It turns out there exists maximum L/V, or a minimum vapor rate V which allows a particular bottoms composition xp to be produced from a given feed composition xp and liquid flowrate L. This minimum V/L is called the minimum boil-up ratio. 

The minimum vapor rate may be estimated by use of Fig. 12-14. To use this graph, the following quantity must be evaluated... 

In an overall process of absorption and stripping, the cost of steam is often a major expense, and the process is designed to use as little steam as possible. The stripping column is operated at close to the minimum vapor rate, and some solute is left in the stripped solution, rather than trying for complete recovery. When the equilibrium line is curved upward, as in Fig. 22.17, the minimum steam rate becomes much higher as Xj, approaches zero. 

As shown in Fig. 2.4, a minimum vapor rate exists below which liquid may weep or dump through tray perforations or risers instead of flowing completely across the active area and into the downcomer to the tray below. Below this minimum, the degree of contacting of liquid with vapor is reduced, causing tray efficiency to decline. The ratio of the vapor rate at flooding to the minimum vapor rate is the turndown ratio, which is approximately 10 for bubble cap and valve trays but only about 3 for sieve trays. 

If the chemical plant must operate over a wide range of throughputs, the distillation columns in the plant must be able to turn down to low throughputs. Hydrauhc limitations will be unavoidably encountered, so the control structure must be able to avoid these limitations. In this chapter, we assume that the minimum vapor rate is the limitation. 

In all cases the equilibrium curve is above the operating line except at a 0.925. Thus the minimum reflux ratio for tower 1 is determined by a pinched-in condition at a 0.925. The minimum vapor corresponding to this condition is 832 mols which is greater than the 760 mols calculated for tower 2. This larger value will be taken as the minimum vapor rate for the system. Thus,... 

Porter and Momoh have suggested an approximate but simple method of calculating the total vapor rate for a sequence of simple columns. Start by rewriting Eq. (5.3) with the reflux ratio R defined as a proportion relative to the minimum reflux ratio iimin (typically R/ min = 1-D- Defining Rp to be the ratio Eq. (5.3) becomes... 

ADM = Minimum downcomer area, fT ATM = Minimum column cross-sectional area, fr CAF = Vapor capacity factor CAFo = Flood capacity factor at zero liquid load CFS = Vapor rate, actual ftVsec DT = Tower diameter, ft DTA = Approximate tower diameter, ft FF == Flood factor or design percent of flood, fractional FPL = Tray flow path length, in. 

The design vapor rate is, or is very close to, the minimum rate. 

Reduction in efficiency can be tolerated if vapor rate falls to weep point minimum or below. 

Select a design hole vapor rate, v , of 1.25 to 1.5 times the minimum values of the plate activation point, or about 25% below the hole velocity at flood conditions. 

Note that Figure 8-147 indicates the operating liquid minimum range is quite stable in the region of design for these trays. The vapor rate must never fall below the above values or instability will immediately set in and dumping will result. 

The mass vaporization rate at XeC c is at a minimum relative to the incongruent mass vaporization rates that occur at compositions greater and less than XeCwC- When VmC is calculated for XeC diT), we call it the mass congruent vaporization rate. 

Produce a shortlist of candidates by ranking the alternatives following the total vapor rate. A minimum reflux calculation design based on Fenske-Underwood-Gilliland method should be sufficiently accurate. 

To minimize vapor channeling, valve trays are designed to exceed a minimum unit reference (50). A unit reference is the ratio of the vapor rate to the vapor rate at which all the valves are open (Sec. 6.3.2). A minimum unit reference of 40, 60, and 80 percent is recommended for one-, two-, and four-pass trays, respectively (50). If the unit reference falls below the minimum, selected valves can be blanked, valve density can be reduced, or the ratio of light to heavy valves can be varied (7,50). 

Valve tray turndown is normally about 4 to 5 1. The minimum operating rate in valve trays is usually restricted by excessive weeping, but it may also be restricted by the onset of vapor channeling (Sec. 6.2,13). 

Table 13-6 shows subsequent calculations using the Underwood minimum reflux equations. The a and Xo values in Table 13-6 are those from the Fenske total reflux calculation. As noted earlier, the % values should be those at minimum reflux. This inconsistency may reduce the accuracy of the Underwood method but to be useful, a shortcut method must be fast, and it has not been shown that a more rigorous estimation of x values results in an overall improvement in accuracy. The calculated firnin is 0.9426. The actual reflux assumed is obtained from the specified maximum top vapor rate of 0.022 kg- mol/s [ 175 lb-(mol/h)] and the calculated D of 49.2 (from the Fenske equation). 

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