Number of stages/ bed (at 100% distribution quality) (b)
FIG. 14-64 Effect of irrigation quality on packing efficiency. (a) Case histories demonstrating efficiency enhancement with higher distribution quality rating. (b) Correlation of the effect of irrigation quality on packing efficiency. (From F. Moore and F. Rukovena, Chemical Plants and Processing, Europe edition, Aug. 1987; reprinted courtesy oof Chemical Plants and Processing.)
Billingham (Trans. IChemE. 80, Part A, p. 373, May 2002; Trans. IChemE. 81, Part A, p. 134, January 2003) modeled maldistribution as two parallel columns, one receiving more liquid (1 + f)L, the other receiving less (1 — f )L. The vapor was assumed equally split (Fig. 14-65)
without lateral mixing. Because of the different L/V ratios, the overall separation is less than is obtained at uniform distribution. A typical calculated result (Fig. 14-66) shows the effective number of stages from the combined two-column system decreasing as the maldistribution fractionf increases. Figure l4-66a shows that the decrease is minimal in short beds (e.g., 10 theoretical stages) or when the maldistribution fraction is small. Figure 14-66a shows that there is a limiting fraction fmax which characterizes the maximum maldistribution that still permits achieving the required separation. Physically, fmax represents the maldistribution fraction at which one of the two parallel columns in the model becomes pinched. Figure 14-66b highlights the steep drop in packing efficiency upon the onset of this pinch. Billingham and Lockett derived the following equation for fmax in a binary system:
f _ yN+1 — yN + X1— Xo yN — yo xn+1— xo yN+1 - yN Vn — yo
This equation can be used to calculate fmax directly without the need for a parallel column model. Billingham and Lockett show that the various terms in Eq. (14-162) can be readily calculated from the output of a steady-state computer simulation. Multicomponent systems are represented as binary mixtures, either by lumping components together to form a binary mixture of pseudolight and pseudoheavy components, or by normalizing the mole fractions of the two key components. Oncefmax is calculated, Billingham and Lockett propose the following guidelines:
• fmax <0.05, extremely sensitive to maldistribution. The required separation will probably not be achieved.
• 0.05 < fmax <0.10, sensitive to maldistribution, but separation can probably be achieved.
• 0.10 <fmax <0.20, not particularly sensitive to maldistribution.
• fmD >0.20 insensitive to maldistribution.
Figure 14-66b shows that shortening the bed can increase fmax. Relative volatility and L/V ratio also affect fmax. The bed length and L/V ratio can often be adjusted to render the bed less sensitive to maldistribution.
Implications of Maldistribution to Packing Design Practice
These are discussed at length with extensive literature citation in Kister's book Distillation Operation, McGraw-Hill, New York, 1990. Below are the highlights:
0.02 0.04 0.06 0.08 Maldistribution fraction f
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