Sherwood-Eckert generalized pressure drop correlation (GPDC). For several decades, the Sherwood-Eckert GPDC chart has been the standard of the industry for predicting flood points and pressure drops. This chart was initially developed by Sherwood et al. (68). Sherwood's chart, later modified by Lobo et al. (69), contained only a single curve that predicted packing flood points. Leva (70) retained the flood-point curve and added a new family of curves onto the chart to predict packing pressure drop. Copigneaux (71) and Eckert (53,72) proposed further modifications. In a later version, Eckert (74) omitted the flood curve from the chart, retained only the pressure drop curves, and performed other minor modifications. Finally, Strigle (15) changed the scales of Eckert's later version from log-log to semilog to make interpolation between adjacent pressure drop curves easier. McNulty and Hsieh (31) detailed the history of modifications to the correlation.
L = liquid rale, Ib/s, ft2 M - viscosity of liquid, centipoise (cP)
G = gasratejb/s, ft2 y _ ratio Density ot water pL liquid density, lb/It3 ' Density of liquid pG = gas density. lb/It3 & = gravitational constanl = 32.2
F = packing factor \
Figure 8.17 The Eckert 1970 version of the GPDC correlation. (From J. S. Eckert, Ckem. Eng. Progr., 66(3), March 1970, p. 39. Reproduced courtesy of the American Institute of Chemical Engineers. >
was the industry's standard for flood-point prediction for random packings (e.g., 14,41,55,58-60).
The GPDC chart ordinate describes the balance between the vapor momentum force, that acts to entrain swarms of liquid droplets, and the gravity force, that resists the upward entrainment. This closely resembles the force balance used by Souders and Brown for entrainment flooding in tray columns (Sec. 6.2.4). A comparison of Eq. (8.22) (whici describes the GPDC chart ordinate per a recent version) and Eq. (6.10) depicts the close resemblance. The relevance of this force balance la packed tower flooding was demonstrated recently by the success of the Higee technique (centrifugal distillation) to largely increase columm capacity by enhancing the gravity force that resists droplet entrainment.
The GPDC chart abcissa is the flow parameter [Eq. (8.21)], the ratio of liquid kinetic energy to vapor kinetic energy. This parametw has been applied to tray columns (Sec. 6.2.3), but is far more suitahfc for describing the influence of liquid rate in a true counter-current contactor like a packed tower.
Silvey and Keller (75) compared predictions from the Eckert correlation to experimental data for ceramic Raschig rings. Agreement was good for rings 1.5 in and smaller, but for 3-in rings the correlation predictions were optimistic.
Bolles and Fair (55) compared flood-point predictions from the Eckert correlation to published experimental data for random packings. Their massive data bank consisted mainly of data for first-generation packings, but also included some data for second-generation packings. For the data compared, Bolles and Fair showed that Eckert's correlation gave reasonable flood-point prediction. Statistically, they showed that if a safety factor of 1.3 was applied to the correlation flood-point predictions, the designer will have 95 percent confidence that the column will not flood.
MacDougall (58) compared flood-point data to predictions from the Eckert correlation for first- and second-generation packings. His study came up with an identical conclusion and an identical safety factor to those derived by Bolles and fair.
Kister and Gill (60) compared flood-point predictions from the Eckert correlation to published experimental data for random packings. Their massive data bank consisted solely of second- and third-generation packings, 1 in and larger in nominal size. They showed that the Eckert correlation gave grossly optimistic predictions for all but the smaller modern packings. For most larger modern packings, the flood point coincided with the curves for pressure drops of 0.5 to 1.5 in/ft of packing (see Fig. 8.17) rather than with the flood curve. Kister and Gill concluded that the Eckert correlation gives good flood-point predictions only for lower-capacity random packings (packing factors, Fp > 60). A corollary is that the Eckert correlation works well for most first-generation packings, for which it was developed, but not for most modern high-capacity packings.
Based on the above reliability studies, the author recommends the Eckert flood correlation (the flood curve on Fig. 8.17) only for random packings whose packing factors Fp exceed 60.
The Kister and Gill correlation. Zenz (76) discovered that packing pressure drop at the flood point decreases as the packing capacity increases. A similar observation was reported by Strigle and Rukovena (15,77) and Madkowiak (736). Kister and Gill (60) applied this principle to derive a simple flood point correlation
Equation (8.1) expresses the pressure drop at the flood point as a func tion of the packing factor alone. Once this pressure drop is known, the flood velocity can be calculated using one of the standard pressure drop prediction methods (Sees. 8.2.8 and 8.2.9).
Kister and Gill compared flood-point predictions from Eq. (8.1) to their massive data banks for second- and third-generation random packings (60) and for structured packing (60a). Pressure drops were calculated using the Kister and Gill GPDC interpolation charts (Sec. 8.2.9). They showed that Eq. (8.1) predicted all the flood points in their data bank to within ±15 percent and most to within ±10 percent.
The flood velocity calculated by the Kister and Gill correlation is tolerant to inaccuracies in flood pressure drop predictions. For instance, an error of 20 percent in the flood pressure drop calculated by Eq. (8.1), at a flood pressure drop of 1 in of water per foot of packing, will only introduce an error of 4 to 8 percent in the flood velocity calculation. This is because of the convergence (or "bunching") of the pressure drop curves for pressure drops in the range of 0.5 to 1.5 in of water per foot of packing (Fig. 8.17). Further, the effect of packing factor on the flood pressure drop acts in an opposite direction to the effect of packing factor on the flood velocity. This makes the flood velocity also insensitive to inaccuracies in the packing factors.
A weak link in the correlation is the packing pressure drop prediction. Inaccurate pressure drop prediction procedures will lead to inaccurate flood-point predictions using this correlation. For best results, the author recommends applying Eq. (8.1) together with pressure drop predictions by interpolation (Sec. 8.2.9).
For high packing factors (Fp > 60), Eq. (8.1) predicts flood pressure drops greater than 2 in of water per foot of packings. In this situation, Eq. (8.1) will give similar predictions to those obtained from the flood curve on the Eckert correlation (Fig. 8.17).
For high-capacity structured packings of unique geometry, such as the Norton Intalox® 2T and the Jaeger MaxPac®, Eq. (8.1) consistently predicts flood points that are 5 to 10 percent low (316,60a). Although this is well within the correlation accuracy, it suggests that Eq. (8.1) does not distinguish the unique "high capacity" features of these two structured packings.
Flood prediction by the Billet and Schultes correlation. Billet and Schultes (79,80) modified the GPDC to take liquid holdup into recount. The important parameter was left out of earlier versions of the correlation. Its inclusion improves the theoretical validity of the correlation at the expense of greater complexity. Billet and Schultes derived their flood-point correlation from their liquid holdup equation by postulating that at the flood point, a small increase in vapor or liq uid velocity effects a near-inifinite change in holdup. The Billet and Schultes (79) correlation is
Fw is the flow parameter given by
C, Fj and npi are given by
ap, e, C1F1 and C2>fi are constants obtained from Table 8.2. ap is the specific surface area and e is the void fraction of the packing. AL F1 is the fractional liquid holdup (ft3 liquid/ft3 of bed) at the flood point, calculated from hln(3hLjn-e) = (8.6)
This gives a fourth-order equation in hun. The equation has only one solution of physical significance, given by
The Reynolds number used in Eq. (8.6) is based on the liquid velocity at the flood point. The Reynolds and Galileo numbers ReL and Ga£ are given by
The Billet and Schultes correlation applies both to random and structured packings, has a good theoretical basis, and was demonstrated (79) to predict a large number of flood data to within ± 10 percent. On
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