## L Factor Robbins Correlation

Equation (8.13) states that pressure drop is the sum of two terms. The first term describes the friction loss through the packing, and is the only important term in the preloading regime and when Lf is below 20,000. Under these conditions, the pressure drop is proportional to the square of the gas rate. The second term describes the increase in the slope of the pressure drop with gas rate in the loading regime.

Equation (8.13) applies only for Lf <, 20,000. Figure 8.20 is a graph of the Robbins correlation that applies for values of L^both below and above 20,000. When Lf > 20,000, only Fig. 8.20 should be used, not Eq. (8.13) (89,90).

For some packings with dry-bed packing factors lower than 15, Eq. (8.15a) does not accurately represent the liquid rate dependence. Equation (8.156) gives a better preliminary estimate of Lf at these lower packing factors. Due to the approximation involved, Zy jumps up by a factor of about 1.5 when changes from 15 to 14.

The Robbins correlation applies at atmospheric pressure and under vacuum, but not at elevated pressures (90). Equation (8.146) includes a gas density correction term for a preliminary estimate at pressures exceeding atmospheric. Due to the approximation, Eq. (8.146) is unsuitable for design (90). Generally, the Robbins correlation is not recommended for superatmospheric pressures (90).

At very high liquid rates, pressure drop for nonaqueous systems can be considerably higher than with aqueous systems (60). In this veiy high liquid rate region (flow parameter > 0.3), Robbins's correlation was extensively tested only for aqueous systems. Caution is required.

For a dry packed bed (L - Lf= 0) at atmospheric pressure, Eq. (8.13) reduces to

Flgur* 8.20 The Robbins generalized pressure drop correlation. (From L. A Robbins, Chem. Eng. Progr., May 1991, p. 87. Reprinted courtesy of the American Institute of Chemical Engineers.)

Flgur* 8.20 The Robbins generalized pressure drop correlation. (From L. A Robbins, Chem. Eng. Progr., May 1991, p. 87. Reprinted courtesy of the American Institute of Chemical Engineers.)

Equation (8.16) permits estimating F^ for any packing from dry pressure drop measurements. Table 8.3 gives F^ for various commercial packings. A more comprehensive list is elsewhere (89). The dry packing factors in Table 8.3 are those to be used in Eqs. (8.14) and-XiL15k

Theoretical correlations. Two approaches have been used for theoretically modeling packed-tower pressure drop:

1. The channel model: This model attributes packed-column pressure drop to the resistance to flow in a multitude of parallel channels. The channels may have bends in them or may have contractions and enlargements. Liquid flows down the walls of the channel, thus consuming some of the available cross-section area. This in turn increases the pressure drop. The channel model has been applied both for random and structured packings (e.g., 3,62,736,78,91,92,92a). A popular application of this model is the Bravo et al. (91) correlation for structured-packing pressure drop:

table 8.3 Dry Bed Packing Factors (or the Robblns Pressure Drop Correlation (89)

Random Packings

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