'The number is followed by a suffix A; for instance, No. 1 means Cascade* MiniRing No. LA.

AP = (0.395 + , * (8.17, v ReG / \dngj( 1 - CgFr08)8

where

Values of 6, d^, e, and C6, where available, and the range of data used for deriving the correlation, are listed in Table 8.1. For the Sulzer BX* packing, data from several systems were used in the correlation deviation, but for corrugated-sheet packings, only air-water data were used.

2. The particle model: This model attributes pressure drop to friction losses due to drag of a particle. The presence of liquid reduces the void fraction of the bed and also increases the particle dimensions. Ergun (94) applied this model for single-phase flow (e.g., fixed and fluidized beds). Stichlmair et al. (95) successfully extended this model to correlate pressure drop and flood for both random and structured packings. Their correlation is complex and requires some additional validation, but is the most fundamental correlation available.

Which method to use? This question is addressed in the next section.

Interpolation of pressure drop data is more accurate and reliable than correlation prediction. However, it requires that an interpolation chart be available, and is difficult to computerize.

GPDC interpolation. Superimposing experimental data points (for a given packing) on the curves of generalized pressure drop correlation (GPDC) chart (Sec. 8.2.8) converts the GPDC chart into an interpolation chart (for the packing), e.g., Fig. 8.19d. Pressure drops are calculated by interpolating the plotted pressure drop data. The correlation curves help guide the interpolation. Chapter 10 contains the entire atlas of interpolation charts and an application procedure.

For random and grid packings (Fig. 8.19rf, and Charts 10.1002 to 10.3517 and 10.8005 to 10.8205 in Chap. 10), the curves on the interpolation charts are those of the Strigle version of the Eckert GPDC (Fig. 8.196). For structured packings (Charts 10.5001 to 10.6504),-tie curves on these interpolation charts are those of the Kister and Gill GPDC (SP) (Fig. 8.19c). For ali charts (random, structured or grid packings), the abscissa of the correlation is the flow parameter, given by

For all charts (random, structured, and grid packings), the ordinate of the correlation is the capacity parameter, given by

In Eq. (8.22), v is the kinematic viscosity of the liquid. [Note; The kinematic viscosity (centistokes) is obtained by dividing the dynamic viscosity (centipoises) by the specific gravity, not by the liquid density).] Cs is the C-factor, i.e., the superficial gas velocity corrected for vapor and liquid densities, given by

Fp is the packing factor, which is an empirical factor characteristic of the packing size and shape. The packing factor to be used is marked on each GPDC interpolation chart in Chap. 10. Table 10.1 lists the values and sources of these packing factors.

Flood and maximum operational capacity (MOC) data are also plotted on the GPDC interpolation charts, and the charts can be used for interpolating these. Where flood and MOC data Eire absent, Eqs. (8.1) and (8.10) can be used for inferring flood points and MOCs from pressure drop data on the charts.

The suitability of the GPDC interpolation charts as a basis for interpolation is not accidental. Packing pressure drops correlate extremely well with GPDC coordinates, i.e., the flow parameter and the capacity parameter. The dependence does not always follow the correlation contours, but always appears to exist. Further, the correlation coordinates are essentially a "performance diagram," i.e., a plot of a vapor load against liquid load, a tool commonly used for analyzing column performance.

The conversion of the GPDC into interpolation charts overcomes the multitude of correlation limitations (Sec. 8,2.8). The GPDC interpolation charts readily identify any regions where data veer off the corre-; lation curves and give reliable estimates (by data interpolation) in these regions. Packing factors, often criticized for being inaccurate and inconsistent (Sec. 8.2.10), cease to be critical variables. Inaccuracies in packing factors merely cause data to veer off the curves, and have no effect on the interpolation.

It may be argued that the interpolation procedure breaks down when data are absent. The counter argument is that the GPDC correlation curves are always there to fall back on and get a prediction, but now there is also a tool to warn that there are no data in this region and that uncertainty is involved.

One problem that the GPDC interpolation charts cannot solve is the

Capacity parameter = Cs .F® V05

inherent data limitations (Sec. 8.2.5). Even here these charts help. Table 10.1 lists the source of data and experimental conditions. This information is essential for evaluating and allowing for the uncertainty associated with the inherent data limitations.

A shortcoming of the GPDC interpolation data chart procedure is that it replaces a single correlation chart by an atlas. The interpolation charts consume more storage space in the design manual or on the computer and require a greater updating effort.

Robbins interpolation procedure (89,90). This procedure makes use of pressure drop versus gas rate plots at constant liquid rate for a reference system. For most packing, such plots are available in the manufacturer's literature (e.g., 8,10,12,13,22,24,31,82), usually with air-water as the reference system. Tlje plots look exactly like Fig. 8.15, but contain curves for many liquid rates.

The Robbins correlation {Eq. (8.13) or Fig. 8.20] expresses the pressure drop as a function of Gf and Lf alone. Applying Eq. (8.14a) for the reference system gives

A similar application of Eq. (8.15a) gives

Hfer

Equations (8.25) and (8.26) express the vapor and liquid rates for any system in terms of equivalent vapor and liquid loads of the reference system. These equivalent rates, i.e., and L^, are then used with the reference system plots to obtain the pressure drop. When the reference system is air-water, then pG rof = 0.075 lb/ft3, pi ref = 62.4 lb/ ft8, and p,L>rer = 1 cP.

The Robbins interpolation procedure overcomes many of his correlation limitations (Sec, 8.2.8). The packing factor is eliminated and so are any associated inaccuracies (Sec. 8.2.10). The inaccuracy of the liquid rate dependence for low dry packing factors CF^ < 15) is no longer a problem, because experimental data are directly interpolated to establish this dependence. Any inaccuracies in generalizing Fig. 8.20

have no effect on the interpolation procedure. If data are available for a nonaqueous reference system, the Robbins interpolation procedure is suitable also for predicting pressure drop for nonaqueous systems at very high liquid rates (flow parameter > 0.3).

One problem that the Robbins interpolation procedure cannot overcome is predicting pressure drop for elevated pressure systems. Another problem that the Robbins interpolation procedure cannot overcome is the inherent limitations of the pressure drop data (Sec. 8.2.5).

Which method to use. Section 8.2.8 draws attention to the systematic nature of the limitations of packed-tower pressure drop correlations. Due to this systematic nature, the author warns against basing packing pressure drop calculations on any correlations whose limitations are not well known. Section 8.2.8 presents three correlations and elaborates on their limitations and application boundaries. Within their boundaries, these correlations should give reliable predictions. Use of any other correlation is dangerous unless its limitations are explored.

Interpolation of packing pressure drop data is superior in accuracy and reliability, and should always be preferred to correlations. Section

8.2.9 presents two interpolation procedures: The GPDC interpolation charts, and the Robbins interpolation.

The Robbins interpolation procedure can rapidly convert typical manufacturer data into a powerful pressure drop predictor. It requires no special interpolation charts. It is ready for use with any new packing that may crop up. On the other hand, the GPDC interpolation charts bring together data from different sources, test systems, and operating conditions. The GPDC interpolation charts compare the data and check data validity. The author believes that the two interpolation procedures are complementary, and recommends both within their application changes.

Several of the predictive methods above use a "packing factor" to account for the type and size of packing. The packing factor was introduced by Lobo et al. (69) as an approximation for the Op/e3 term in tfan original Sherwood correlation. With the evolution of the general pressure drop correlation (GPDC), the packing factor shifted away from As ratio Op/e3 to become an empirical constant that must be experime»-tally determined for each packing (31). Packing factors are obtained

■ By backward calculation from the GPDC correlation, based on average performance of the packing at 0.5, 1.0, and 1.5 in of water pressure drop per foot of packed depth (1). This method proved on-

suitable for the larger second- and third-generation packings that flood at the above range of pressure drop.

■ By selecting a factor that gives the best fit of available experimental pressure drop data to the GPDC correlation curves (316,60). This method biases the packing factor toward the regions on the chart for which experimental data exist.

■ By inferring packing factors from dry pressure drop measurements, using Eq. (8.16). This method is only suitable for use with the Bobbins pressure drop correlation (Sec. 8.2.8). With the GPDC correlation, it biases the packing factor toward the low-liquid-rate region.

Limitations. Additional limitations to the packing factor concept find to its application for pressure drop and flood prediction are

■ The packing factor depends on the version of the correlation used. Any changes to correlation curves requires revisions to packing factors.

■ With many packings, the rate of change of pressure drop with either flow parameter or capacity factor or both is not adequately predicted by the GPDC correlation (60), For these packings, the packing factor may not give a good data fit.

■ Since packing factors are derived from experimental pressure drop data, they are affected by the inherent limitations of the experimental data (Sec. 8.2.5).

* There is confusion as to what are the best packing factors. For instance, Eckert (53,74) gives a packing factor of 20 for 2-in metal Pall® rings; Perry's Handbook (14) cites the same factor based on Eckert's work. This packing factor applies both for the early and latest versions of the GPDC correlation (Figs. 8.17 and 8.19a,6). Strigle (15) recently gave a factor of 27 for the same packing using the same correlation. Kister and Gill (60) show that a packing factor of 27 reflects published experimental data well, yet the packing factor of 20 was used by the industry for two decades. Robbins (89) reports that different manufacturers used different packing factors for the same packing.

Packing factors: to use or not to use? Due to the limitations of the Eckert GPDC (Sees. 8.2.6, 8.2.8) and the problems above, many manufacturers supply no packing factors for their products. This is especially true for structured packings, where the Eckert GPDC curves do not fit experimental data well (30,31,316,60a). Unfortunately, this creates a situation where packing capacities are described by a mul titude of correlations. Each correlation has its own pitfalls and limitations, and these are often unknown and seldom reported. A designer can at best gain limited experience with each correlation, and this experience becomes rapidly outdated. Keeping track of experiences gained with these correlations becomes a mammoth task. The designer loses feel for their reliability and limitations, and with it, the ability to apply them with confidence.

A major advantage of the "packing factor" approach is that the limitations of both the packing factors and correlations are well-recog-nized. Further, in distillation, where the liquid to vapor mass ratio is relatively close to unify, the effect of the packing factor limitations is considered relatively small (1,15).

The interpolation procedures in Sec. 8.2.9 completely overcome both the limitations-tracking problem and the packing factor limitations listed above. The Robbing interpolation technique uses no packing factors. Packing factors are used by the GPDC interpolation charts, but only as arbitrary parameters that shift experimental data up or down relative to the chart curves. Any inaccuracies in packing factors are reflected as data deviation from the curves and are accommodated for by the interpolation procedure.

Table 10.1 gives packing factors for use with charts in Chap. 10 and in Fig. 8.19 (i.e., Fig. 8.19a or 8.196 for random packing; Fig. 8.19c for structured packings). Whenever available, those were extracted from Strigle (15) or from the manufacturer's literature. Strigle (15) also has good packing factors for first-generation random packings. Packing factors for use with the Robbins correlation (Sec. 8.2.8) are listed in Table 8.3.

The point of transition from the preloading regime to the loading re-gime is termed the loading point (points B or B' on Fig. 8.15). Although early workers proposed that the loading point can be recognized by a sharp change of slope on Fig. 8.15, the present consensus is that the change of slope is gradual, and that no sharp loading point exists in most commercial applications (1,51,52,63,69,76).

The difficulty of defining the flood point (Sec. 8.2.3) extends to the load point. Billet (80) defines the load point where liquid holdup starts increasing with gas velocity. Kunesh (51) defines it as the point beyond which a very small increase in boilup results in a rapid deterioration in efficiency (i.e., point E on Fig. 8.16a). Strigle (15) gives two definitions—the lower loading point, which is the highest flow rate at which the pressure drop is proportional to the square of the gas flow rate, and the loading point, which is the flow rate at which the vapor phase begins to interact with the liquid phase to increase interfacial area in a packed bed, i.e., point B on Fig. 8.16a. Strigle'a and Billet's definitions are similar and are adopted here. Billet (80) shows that the loading point occurs at about 70 percent of the flood point.

Prediction. A rough rule of thumb by Fair et aL (14) suggests that for random packing, the loading point will occur at a packing pressure drop above 0.5 in of water per foot of bed. A correlation by Billet and Schultea (79) is presented below. Considering the uncertainty in defining the loading point, the need for an elaborate correlation may be questioned.

pL 0.3048a,

where

Lfor Fh 1.446J

Fiy, ReL, and GaL are given by Eqs. (8.3), (8.8), and (8.9), respectively; Op, €, CltLo. and are constants for each packing, and are tabulated in Table 8.2. The Reynolds number Re^ is based on the liquid velocity at the load point. The Billet and Schultes correlation predicted most of their load point data within about ± 10 percent (79). It applies for both random and structured packings.

Flood point Packed towers are usually designed to 70 to 80 percent of the flood point velocity (17,55,56,96). This practice provides sufficient margin to allow for uncertainties associated with the flood-point concept (Sec. 8.2.3) and prediction (Sec. 8.2.6) and to keep the design point away from the region at which efficiency rapidly diminishes (just below the flood point).

MOC. Strigle et al. (15,57,97) recommended designing packed towers with a 10 to 20 percent margin from the maximum operational capacity (MOC). Since the MOC is usually about 5 percent below the flood

Type of System |
Maximum pressure drop, inch water/ft packing |
Reference |

Atmospheric fractionator |

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