Previous Page 5.6 TRANSFER UNITS Computationally, distillation columns are treated as staged devices, even though in some designs they function as countercurrent contactors such as packed columns. Accordingly, stage concepts as detailed in Section 5.3 may be applied to packed columns as long as the physical contacting mechanisms are not under study. This approach has led to the concept of the "height equivalent to a theoretical plate/' discussed later in Section 5.10. When it is desirable to consider the true countercurrent contacting mode, the concept of the transfer unit should be used. Consider a differential height of a packed distillation column of unit cross section as shown in Fig. 5.6-1. For component /, (5.6-1) For equimolar counterdiffusion (approximately the case for distillation), dv - dl, and for net transfer of i from bulk vapor to the liquid interface, (5.6-2) (5.6-3) Note that this expression applies to the vapor phase only (transfer to the interface from the bulk vapor). For overall transfer from the bulk vapor to the bulk liquid, (5.6-4) where H v is defined as the height of a vapor-phase transfer unit and H ov is defined as the height of an overall vapor-phase transfer unit, using vapor-phase concentration units. (Similar expressions may be derived for heights of liquid-phase transfer units, but they are not often used in distillation calculations.) It should be noted that in Eq. (5.6-3), the term y im is the vapor mole fraction at the interface, whereas in Eq. (5.6-4), yf is the vapor mole fraction that would be in equilibrium with the bulk liquid mole fraction. Integration of Eqs. (5.6-3) and (5.6-4) gives (5.6-5) (5.6-6) The right sides of Eqs. (5.6-5) and (5.6-6) define the number of vapor-phase transfer units and the number of overall vapor-phase transfer units (vapor concentration basis), respectively. Thus, the required height FIGURE 5.6-1 Flows in a differential section of a countercurrent contactor.
of packing in a column is obtained from (5.6-7) where (5.6-8) and (5.6-9) evaluated under conditions such that the terms can be brought outside the integral signs of Eq. (5.6-5) and (5.6-6). For a binary distillation system of components A and B, N KA» N y # and N OVA = N OVB. For multicomponent systems, it is possible for each component to have a different value of the transfer unit. For a discussion of the multicomponent problem, see Krishnamuithy and Taylor. 1 The usual practice is to deal with the multicomponent mixture as if a staged column were to be used and then convert from theoretical stages to transfer units by the relationships (5.6-10) where N, = the computed number of theoretical stages X s= the ratio of slopes of the equilibrium and operating lines Equation (5.6-10) will be discussed in more detail in Section 5.10. 5.7 TRAY-TYPE DISTILLATION COLUMNS 5.7-1 General Description and Types The typical distillation column has dimensions sufficient for handling the required flows of vapor and liquid and for making the desired separation. The vessel contains internal devices that are designed to promote intimate contacting of the vapor and liquid. The amounts and properties of the streams usually follow from the equilibrium stage or transfer unit calculations (Sections 5.3 and 5.6). The internal devices may be grouped into two general categories: tray-type and packing-type. The former provides a stagewise contacting mode whereas the latter provides a countercurrent mode. In the present section the tray-type devices will be considered. An enormous amount of work has gone into the study of contacting devices, and the literature on their performance characteristics is extensive. Most of the work dealing with larger equipment has been based on plant observations, but a significant portion of it has been based on controlled experiments in commercialscale equipment by Fractionation Research, Inc. (FRI). The methods for analysis and design of distillation columns, presented in this section, are based on a combination of fundamental research papers, results released by FRI, and many reported plant tests. General types of tray columns are shown in Fig. 5.7-1. The crossflow tray column is the most prominent in industry, with the trays containing vapor dispersers in the form of bubble caps, liftable valves, or simple round perforations. Liquid flows down the column, from tray to tray, via connecting downcomer channels and thus intermittently comes in contact with the upflowing vapor. The counterflow tray ("dualflow tray") column has no downcomers; liquid and vapor use the same openings, which normally are round perforations but which in some cases are in the form of slots. Clearly, for such a device to operate stably, the hydrodynamics must be controlled carefully. The baffle tray column contains simple baffles, or shower decks, over which the liquid flows in a turbulent fashion, contacting the vapor during the fall from one baffle to the next. Views of typical tray-type devices are shown in Fig. 5.7-2. When one recognizes that in addition to trays, a number of different packing materials may be used for contacting devices, the problem of the selection of the optimum device becomes apparent. Table 5.7-1 presents several criteria that should be considered both for new designs and for the analysis of existing equipment. The listings are generally self-explanatory, but special mention should be made of the "design background*' criterion. The engineer must have reasonable confidence that the selected device will behave in the manner expected; this gives some advantage to the better-known devices but may exclude newer as yet untested devices that could have strong potential for cost savings. Such devices are often of a proprietary nature, with the owners persuading the users on the basis of undocumented experience in ill-defined installations. Designers must be wary of claims not based on hard results in known services.
Baffle Single crossflow Double crossflow D ua If low FIGURE 5.7-1 Types of tray columns. The contacting devices, or internals, of the distillation column may be classified as shown in Table 5.7-2. The categories represent convenient bases for presentation of design methods and as such are followed in this chapter of the handbook. For many years the crossflow tray dominated the chemical and petroleum processing industries, with the other devices being used only for special services. In recent years the packings have become prominent and today tend to be dominant both for new designs and for the retrofitting of existing columns to improve their efficiency and capacity. 5.7-2 Properties of Tray Froths and Sprays The sieve tray will be selected as the most common crossflow device, and detailed attention to its performance characteristics will be given. The other crossflow devices will then be considered as modifications of the sieve tray. A schematic diagram of this basic sieve, or perforated, tray is shown in Fig. 5.7-3. Allocations of cross-sectional area are shown in Fig. 5.7-4. Liquid enters from the downcomer at the left, flows through the zone aerated by the upflowing vapor, and departs into the downcomer at the right. A two-phase mixture exists on the tray and it may be either liquid-continuous (a bubbly froth) or vapor-continuous (a spray), or some combination of the two. The objective of the designer is to determine the mass transfer efficiency and pressure drop brought about by this contacting action; resultant typical performance profiles are shown in Fig. 5.7-5. It is convenient to define a contacting unit as the space between trays, including the downcomer(s) associated with one of the trays (Fig. 5.7-6). Within the unit three zones can be defined. Zone A is immediately above the perforations and is liquid continuous. Zone C is in the downcomer and is both liquid- and vapor-continuous. Zone B is at the vapor outlet end of the unit and is vapor-continuous. The locations of the boundaries shown in Fig. 5.7-6 are intended to be illustrative only; even if clear demarcation between zones were possible, the boundaries would change with many design and operating parameters. For a so-called "well-behaved" sieve tray, Zone A comprises a froth (bubbly, or aerated, mixture of vapor and liquid) with observable height. Liquid droplets are projected or carried into Zone B, and some of them may be entrained from that zone to the tray above. There is also droplet movement into Zone C, in addition to normal movement of froth over the outlet weir. For many designs an attempt is made to have Zone A predominate in the mass transfer process; the well-behaved sieve tray operates in the froth contacting mode if at all possible. Under some circumstances, usually at high volumetric ratios of vapor to liquid flow (as in vacuum fractionation), Zone A inverts to a vapor-continuous spray, with Zone B representing an extension of the
Dualflow tray (Fractionation Research, Inc.). Typical valve tray (Koch Engineering Co.). FIGURE 5.7-2 Typical tray-type devices. Cross!low sieve tray (Fractionation Research. Inc.). spray but with a higher fraction of vapor than for Zone A. When this happens, the liquid tends to move into the tray as a turbulent cloud of spray droplets. The region of inversion from froth to spray (and vice versa) can be predicted and this will be discussed later. FROTH CONTACTING When Zone A is expected to be largely froth, contacting efficiency can be predicted through the use of the following equations. The volume of the froth zone may be defined as and the average porosity of the froth is (5.7-1) (5.7-2) The average density of the froth is (5.7-3) The relative froth density (dimensionless) is (5.7-4)
TABLE 5.7-1 Criteria for the Selection of Distillation Column Contacting Devices Vapor-handling capacity Liquid-handling capacity Flexibility Pressure drop Cost Design background General The device must permit reasonable volumetric flow of vapor without excessive entrainment of liquid or, at the maximum vapor rate, flooding. There must be channels for liquid flow that will be nonconstrictive, otherwise the column will flood due to excessive liquid backup. The device should allow for variations in vapor and liquid flow, to accommodate those periods when demand for production fluctuates. For situations when pressure drop can be costly, for example, in vacuum distillations of heat-sensitive materials, the device should maximize the ratio of efficiency to pressure drop. The device should not be excessively complex, and therefore costly to manufacture. However, one must consider the total cost of the system; an expensive device might permit a smaller column, lower cost auxiliary equipment, and so on. The designer should work with a device in which he or she has confidence and an understanding of the physical principles by which the device will operate. Special 1. Possible fouling should be considered; some devices resist fouling better than others. 2. Potential corrosion problems place limitations of the type of material and the techniques for fabricating the device to be used. 3. If foaming is expected, some devices can provide a built-in foam-breaking capability. TABLE 5.7-2 Classification of Contacting Devices Crossflow trays Counterflow trays Baffle trays Random packings Ordered packings Bubble-cap trays Sieve (perforated) trays Valve trays Slotted sieve trays Round openings ("Dualflow") Rectangular openings ("Turbogrid") Segmental baffles Disk-and-donut baffles Shower decks with perforations Raschig rings, plain and slotted, metal and ceramic Other ring-type packings Berl saddles Intalox saddles, ceramic and metal Other saddle-type packings Specialty random packings Corrugated metal and plastic gauze Corrugated sheet metal Mesh-structured Grid-arranged
Tray above Clear; liquid Froth Active length "Froth" (foam) Downcomer apron Tray below FIGURE 5.7-3 Schematic diagram of sieve (perforated) tray. When (5.7-5) An average residence time of vapor flowing through the froth may be estimated as (5.7-6) In a similar fashion, average liquid residence time may be estimated: (5.7-7) Equations (5.7-6) and (5.7-7) involve froth height Zj. Estimation of this height may be made by the use of Fig. 5.7-7, which is adapted from work sponsored by the American Institute of Chemical Engineers (AIChE).' The more recently published approach of Bennett et al. 2 permits avoidance of this parameter by use of Eqs, (5.7-8) and (5.7-9): (5.7-8) (5.7-9) which imply that
Downcomer baffle Active area Downcomer baffle Downcomer area Active (bubbling) area Downcomer area FIGURE 5.7-4 Allocations of cross-sectional area, crossflow tray: A N = net area = A A + A D = active area + one downcomer area; A 7 = total tower cross-sectional area = A A + 2A D. (5.7-10) Values of the terms in Eqs. (5.7-8M5.7-10) may be obtained from Eqs. (5.7-25)-(5.7-28), presented later in the discussion of pressure drop through sieve trays. SPRAY CONTACTING As mentioned, under certain high ratios of the flow rates of vapor and liquid, a vapor-continuous region can exist in the contacting zone. While there is not a great deal of information on the characteristics of the resulting spray, at least with the implications regarding mass transfer, there are methods for predicting whether a froth is likely not to exist. One method, published by Hofhuis and Zuiderweg, 3 will be shown in connection with the prediction of flooding (Fig. 5.7-10). Another useful method for predicting whether a froth might exist is given by Loon et al. 4 and is shown graphically in Fig. 5.7-8. This chart indicates that the following conditions favor the spray regime: High vapor rate Low liquid rate Low hole area (i.e., high hole velocity) Large hole size 5.7-3 Vapor Capacity The usual approach for a new design is first to determine on a tentative basis the required diameter of the column. This diameter often is controlled by the amount of vapor to be handled, although in some cases it may be more a function of liquid flow. After the tentative diameter is calculated, based on an assumed
Sieve-valve plate E, Efficiency Sieve plate Pressure drop (mm H2O) Sieve plate Sieve-valve plate Vapor capacity factor FIGURE 5.7-5 Typical performance profiles for a sieve tray and a combination sieve and valve tray: ethylbenzene-styrene system at 0.13 atm (Ref. 19). Zone B Spray Zone A Froth Zone C Froth and spray FIGURE 5.7-6 Zones of a contacting unit (tray n).
FRACTIONAL APPROACH TO FLOOD FIGURE 5.7-7 Chart for estimating height of froth on sieve trays. Free area (%) FIGURE 5.7-8 Chart for estimating whether froth contacting can be expected. When operating point falls below the appropriate curve, the froth regime prevails (Ref. 4). : j in. (0.635 cm) holes; : j in. (1.27 cm) holes; : in. (1.91 cm) holes. Values on curves are liquid loadings in (m 3 /h)/m weir.
geometry of the contacting device, the capacity for liquid is checked and any needed adjustments are then made. Thus, initial attention is given to vapor capacity. 5.7-4 Maximum Vapor Flow It is clear that if the vapor rate through the tray is excessively high, liquid droplets ("liquid entrainment") will be carried to the tray above, either passing through its perforations or coalescing into larger drops that can fall downward. Also, the very high vapor rate is accompanied by a high pressure drop. It has been observed that when the flood point is approached, operation of the tray becomes unstable, mass transfer efficiency drops to a very low value (see Fig. 5.7-5), liquid builds up in the downcomers, and the maximum vapor loading has been reached. This flood point thus represents an upper operating limit and it is convenient for the designer to locate it in context with the other operating parameters (see Fig. 5.7-9). If a droplet of liquid is considered suspended above the two-phase mixture, with the drag force of the vapor being exactly counterbalanced by the force of gravity, the vapor velocity for suspension may be determined from the equation (5.7-11) where U N = velocity of approach to the tray (based on net area A N in Fig. 5.7-4) D d = diameter of the droplet C d = drag coefficient (dimensionless) PK, PL ~ vapor and liquid densities, respectively The first term on the right-hand side of Eq. (5.7-11) has a range of values depending on the droplet size distribution above the two-phase mixture. For practical design purposes it is termed the capacity parameter C SB» after the work of Souders and Brown. 5 For a condition of maximum vapor capacity ("entrainment flood capacity"), (5.7-12) Equation (5.7-12) is the basis for most correlations used to predict maximum allowable vapor velocity. The correlations are based on observed flood conditions in operating columns as evidenced by a sharp drop in efficiency (Fig. 5.7-5), a sharp rise in pressure drop, or a liquid loading condition giving difficulty in maintaining operating stability. A discussion of entrainment flood measurement has been given by Silvey and Keller. 6 Of the correlations for C SB/, the one that has best stood the test of time is shown in Fig. 5.7-10. 7 The abscissa term, a flow parameter, represents a ratio of liquid to vapor kinetic energies. It also indicates Blowing Flooding Vapor velocity Dumping Satisfactory operation Weeping Phase maldistribution Liquid gradient Flow parameter FIGURE 5.7-9 Generalized performance diagram, crossflow trays.
Spray zone Tray Spacing, mm Mixed froth Emulsion flow FIGURE 5.7-10 FLOW PARAMETER - L/G ip\^p\) ' S Flooding correlation forcrossflow trays (sieve, valve, and bubble-cap trays). zones where spray or froth might predominate. 3 For flow parameter values higher than about 0.1, a froth (two-phase bubbly mixture) is usually dominant. Figure 5.7-10 may be used for design purposes, for sieve, bubble-cap, or valve trays, to obtain the maximum velocity: (5.7-13) with the following restrictions: 1. Low-foaming to nonfoaming system. 2. Weir height less than 15% of tray spacing. 3. Hole diameter 12.7 mm (0.5 in.) or less (sieve trays) 4. Hole or riser area 10% or more of the active, or bubbling, area (Fig. 5.7-4). Smaller hole areas tend to produce jetting because of the high hole velocities 8 and require correction: AiJA 0 V Nf IU Nf from Chart 0.10 1.00 0.08 0.90 0.06 0.80 Figure 5.7-10 has been found to represent flood data for all crossflow trays. Since the correlation first appeared in 1961, a significant number of large-scale flood tests have been reported, many of them in the 1.2 m column of FRI. Analysis has shown that the correlation is conservative, 9 and one can use 90% of the predicted flood values as suitable operating levels for design. 5.7-5 Liquid Entrainment Reference has been made to liquid entrainment that occurs in increasing amounts as the flood point is approached. The entrained liquid is recycled back to the tray above, negating the effect of countercurrent contacting and decreasing tray efficiency. The recirculation due to entrainment is shown in Fig. 5.7-11. The deentraining device of Fig. 5.7-11 may not be needed if the "contaminated*' overhead vapor meets distillate specifications. Entrainment data for sieve and bubble-cap trays have been correlated by Fair and coworkers l0 as shown in Fig. 5.7-12. The sieve tray data are for trays with small (less than 1 mm) diameter. Visual data of FRI, released as a movie, 11 show that under distillation conditions 3 mm holes entrain significantly less than 12.7 mm holes, with hole areas and gross vapor rates being equal.
L MD GMD De-entrainer Trays L MD 6 MD FIGURE 5.7-11 a dry basis. Entrainment recirculation in column. L MD and G MD are liquid and vapor molar flows on FRACTIONAL ENTRAINMENT, ^ MOLES/MOLE GROSS DOWNFLOW %0f Flood Perforated Plates Bubble Cap Plates %0f Flood FIGURE 5.7-12 Chart for estimating effect of liquid entrainment on crossflow tray efficiency.
The parameter in the chart is the ratio of entrained liquid to gross downflow: (5.7-14) The terms are clear from Fig. 5.7-11. The $ parameter represents a fraction of the total liquid entering that is entrained upward. It may be used to correct a "dry" efficiency as follows: (5.7-15) where E mv is the dry Murphree tray efficiency, to be discussed in Section 5.9. Equation (5.7-15) is based on the early work of Colburn. 12 Figure 5.7-12 appears to be useful for estimating valve tray entrainment, although the available data are scarce. 9 Absolute values of entrainment obtained from the figure may not be very accurate, but the predicted effect of the entrainment on efficiency appears quite reliable. EXAMPLE 5.7-1 A distillation column is separating a methanol-water mixture and produces a 98.0 mol % distillate product. The reflux ratio is 1.0, the top of the column operates at 1.0 atm, and the condensing temperature of the overhead product liquid is 65 C (149 F). For the top condition, the vapor density is 1.22 kg/m 3, the liquid density is 751 kg/m 5, and the surface tension is 20 mn/m (dynes/cm). The net distillate rate is 13,500 kg/ h (29,768 lb m /h). The column dimensions are as follows: Tray Type: Sieve, Single Crossflow, Segmental Downcomers Column diameter 1.98 m 6.5 ft Tray spacing 0.61 m 24 in. Weir height 50 mm 2 in. Weir length 1.43 m 4.7 ft Hole diameter 6 mm in. Downcomer clearance 25 mm 1 in. Cross-sectional area 3.08 m 2 33.2 ft 2 Downcomer area 0.31m 2 3.32 ft 2 Net area 2.77 m 2 29.9 ft 2 Active area 2.46 m 2 26.6 ft 2 Hole area (12% open) 0.295 m 2 3.18ft 2 Tray metal thickness 2.6 mm 0.10 in. Calculate the following: (a) approach to flooding and (b) efficiency discount due to entrainment, based on a dry Murphree efficiency of 0.75 (75%). The calculations are to be based on the top plate conditions. Solution (a) Vapor mass rate = distillate + reflux = 13,500 4-13,500 = 27,000 kg/h Vapor volumetric rate = Net area vapor velocity Souders-Brown coefficient = Flow parameter = From Fig. 5.7-12, at 610 mm tray spacing, C SB/ = 0.12 m/s
(b) For 75% flood and a flow parameter of 0.020, Fig. 5.7-12 gives \f/ - 0.018. From Eq. (5.7-15) and for E mv «0.75 (dry basis), Thus, the dry efficiency is discounted by about 86%, to a value of E a «0.859(0.75) = 0.644, or 64%. 5.7-6 Weeping Whereas bubble-cap trays have a built-in seal against liquid draining through the tray during operation, this is not the case for sieve trays and valve trays. The sieve tray is especially prone to this drainage, which in relatively small amounts is called weeping and in large amounts, dumping. Liquid draining through the holes causes some short-circuiting, but at the same time provides surface for mass transfer; small amounts of weeping appear not to be detrimental to the operation and performance of a tray. Thus, it is the dumping that is normally to be avoided. Reference to Fig. 5.7-5 shows that at low vapor rates there is a decline in efficiency, and this must be taken into account in determining the "turndown ratio" (ratio of maximum allowable rate to minimum allowable rate) of the tray device. It has been found that a reasonable prediction of the minimum rate can be made with the use of Fig. 5.7-13. This chart was developed earlier by Fair 13 on the basis of visual tests and was later confirmed by Zanelli and Del Bianco. 14 In practice, it predicts the "point of minimum turndown" as denoted by Fig. 5.7-5. The pressure loss in forming a gas bubble may be estimated from the dimensional relationship (5.7-16) 5.7-7 Pressure Drop The pressure loss experienced by the vapor in flowing through a tray is that which might be measured by a manometer as shown in Fig. 5.7-3. It may be assumed that this is the sum of contributions by the dispersers (holes, caps, valves) and by the head of two-phase mixture: (5.7-17) The term h' L is treated as a residual and is not necessarily equal to the equivalent head of liquid h L on the tray. It also takes into account the fact that the orifice (disperser) has changed characteristics when it is wetted. Hole size mm liquid on tray Mayfield Mayfield Hutchison -3- in. 16 Hoie area Active area liquid on tray FIGURE 5.7-13 Chart for estimating the weep point of a sieve tray. {Note: If operating point lies above the appropriate curve, weeping is not expected.)
DISCHARGE COEFFICIENT HOLE AREA ACTIVE AREA ^h_ A A FIGURE 5.7-14 Discharge coefficient for sieve trays. For sieve trays, the simplified orifice equation is used to estimate the pressure loss for flow through the holes: (5.7-18) This is the so-called "dry drop." The discharge coefficient C v is obtained from Fig. 5.7-14, from the work of Leibson et al. 15 The plot was developed originally for small-hole sieve trays (7 mm diameter and less). It includes the corrections for velocity of approach and for sharpness of the orifice. For pressure loss through the two-phase mixture, the residual term is estimated from the relationship (5.7-19) where /8 is an aeration factor, originally utilized by Hutchinson et al. 16 for sieve tray experiments. This factor has been correlated as shown in Fig. 5.7-15 917 and leads to the final equation for estimating pressure loss across a sieve tray: (5.7-20) The curves of Fig. 5.7-15 may be represented by the equation (5.7-21) where L w = qll w in m 3 /s-m. The value of the weir crest h ow in Eqs. (5.7-19) and (5.7-20) is calculated by the classical Francis weir equation: (5.7-22) even though the two-phase mixture actually flows over the weir (unless "calming zones" (unperforated sections) are used upstream of the weir. If one wishes to consider that froth actually flows over the weir, (5.7-23) or (5.7-24) In the two foregoing equations, <f> f is a relative froth density, p f lp L.
Aeration factor, gal/min liquid in. weir Hole F factor, FIGURE 5.7-15 Aeration factor for sieve trays. (Note: ft/s (lbjft 3 ) 1 ' 2 x 1/22 - m/s (kg/m 3 ) 1/2 and [(gal/ min)/in. weir] X 0.00249 = (m 3 /s)/m weir. A more exact analysis of the hydraulic parameters is possible, and for this the paper by Bennett et al.' should be consulted. In that work, an effective froth density is defined as follows: (5.7-25) where Q 8 = C SB (A N /A a ) is a capacity parameter based on the active area instead of the net area. Liquid head above the perforations is given by (5.7-26) with the correction factor C obtained from Finally, the residual drop is obtained from Eqs. (5.7-16) and (5.7-27): (5.7-27) (5.7-28) and this is added to the dry tray drop to obtain the total tray pressure drop. The model of Bennett and coworkers correlates a large bank of data with an average error of -0.8% and a mean absolute error of 6.0%. The reliability of the aeration factor approach is about 10% mean absolute error. It should be noted that Bennett and coworkers suggest the use of the Leibson plot (Fig. 5.7-14) to obtain dry tray pressure loss. For valve trays, design manuals of the vendors should be used; these manuals are readily available. The approach used is the same as the aeration factor approach described above, except that constant values of this factor are used. For bubble-cap trays, the "dry drop*' is more complex because of the unique geometry and mode of flow. For example, the total dry drop can be the sum of losses for flow through the riser, through the annulus, and through the slots. The 1963 work by Bolles 18 is undoubtedly the best currently available method for determining the hydraulics of bubble-cap trays. Since these trays are rarely used for new designs, and since no advances in the technology have been made since 1963, the Bolles
paper should be consulted when it is necessary to analyze the performance of existing bubble-cap installations. 5.7-8 Liquid Handling Capacity The downflowing liquid is transported from a tray to the tray below by means of conduits called downcomers, and it is evident that if the downcomer is not sufficiently large to handle the required liquid load, the pressure drop associated with liquid flow will serve as a constriction and a point of flow rate limitation. In fact, downcomers usually serve to bottleneck operations of high-pressure fractionators and absorbers. They must be sized such that they do not fill completely under the highest flow rates expected for the column. As will be shown, the vapor flow rate contributes toward the liquid capacity limitation. Figure 5.7-16 shows a diagram of three trays with downcomers, on which is superimposed the liquid backup in one of the downcomers. This backup may be calculated from a pressure balance: (5.7-29) The segments of the buildup are (a) the equivalent clear liquid head on the tray h' Lt (b) any hydraulic gradient A caused by resistance to liquid flow across the tray, which usually is not significant for sieve trays, (c) liquid head equivalent to pressure loss due to flow under the downcomer apron, H 60, and (d) total pressure loss across the tray above, necessarily included to maintain the dynamic pressure balance between point A (just above the floor of tray 3) and point B in the vapor space above tray 2. Segments a and b are covered by the tray pressure drop calculations discussed in Section 5.7-6. For segment b, only bubble-cap trays require an evaluation, and methods for this are detailed in Ref. 18. For segment c, the head loss for flow under the downcomer may be estimated from the following empirical expression: (5.7-30) where Uda is in m/s and h^ is in mm of liquid. Equation (5.7-30) applies to flow under a simple downcomer apron, with no recessed discharge area or tray inlet weir (see Fig. 5.7-17 for liquid inflow arrangements). If an inlet weir is used, the value of H^ from Eq. (5.7-30) should be doubled. This so-called "clearance under the downcomer," represented by the area A (see Fig. 5.7-4), bears special mention, since improperly fitted tray sections can lead to inadequate clearance at one or more points in the column. Thus, the clearance is a dimension that should be checked very carefully during tray installation. Tray 1 Tray 2 Froth Tray 3 Froth (gradient) FIGURE 5.7-16 Components of downcomer backup.
(a) (b) (c) (d) FIGURE 5.7-17 Possible downcomer arrangements: (a) vertical baffle, no recess, no inlet weir (this type is quite common); (b) vertical baffle, no recess, inlet weir; (c) vertical baffle, recess, no inlet weir; (d) sloped baffle, no recess, no inlet weir; and (e) double crossflow, vertical baffles, no recesses, inlet weirs. (e) Returning to Fig. 5.7-16, we see that the backup relationship [Eq. (5.7-29)] is based on clear liquid heads. Actually, the fluid in the downcomer contains a large amount of entrapped vapor and can be represented as a froth with an average density of 4> dc. Accordingly, the actual downcomer backup is (5.7-31) The value of "$ dc in Eq. (5.7-31) is obtained as follows. If the flow into the downcomer is a tray froth of density <f> f, then <f> f = <f> dc, and if the flow out of the downcomer is clear liquid (4> dc ~ 1.0), then the average value is some mean of these two froth densities. If there is very rapid disengagement of vapor from liquid in the downcomer, the average may be as high as 0.8 or 0.9. On the other hand, for slow disengagement, as in fractionators operating near the critical point of the tray mixture, the poor buoyancy of vapor bubbles can lead to an average downcomer froth density of as low as 0.2 or 0.3. Designers often use an average value of <f> dc = 0.5, but this value should be considered carefully on the basis of the system as well as the geometry of the downcomer. It is possible for vapor to be entrained downward with the liquid, and this "reverse entrainment" has been studied by Hoek and Zuiderweg, 20 using Fractionation Research, Inc. data taken at pressures of 20 and 27 atm and a system operating close to its critical point. The downward entrainment was found to affect significantly the overall efficiency of the column. A maximum superficial velocity in the downcomer should be about 0.12 m/s, based on clear liquid and the smallest cross section of the downcomer. The above discussion of downcomer sizing has dealt with flow rates to minimize downward entrainment. From another point of view, the downcomer must have enough volume to allow collapse of any stable
TABLE 5.7-3 Downflow Capacity Discount Factors, Foaming Systems Nonfoaming systems 1.00 Moderate foaming, as in oil absorbers and amine and glycol regenerators 0.85 Heavy foaming, as in amine and glycol absorbers 0.73 Severe foaming, as in methyl ethyl ketone units 0.60 Foam-stable systems, as in caustic regenerators 0.15 foam that might develop from the tray aeration. This is handled by "system discount factors," developed empirically over the years for mixtures known to exhibit foaming tendencies. Typical factors are shown in Table 5.7-3. 21 The discount factor should be multiplied by the maximum allowable velocity of 0.12 m/s, mentioned above. In summary, the downcomer can limit column capacity when liquid flow rates are high, as in absorbers and pressure fractionators. Two viewpoints are used (and these are not necessarily independent of each other): height of froth buildup in the downcomer, obtained from a pressure balance, and residence time in the downcomer, obtained from an entrainment velocity limitation. When the downcomer backs up liquid, the vapor entrains more liquid, and a flooding condition can be approached. 5.7-9 Miscellaneous Comments The foregoing material relates directly to a "standard" single crossflow tray with vertical downcomer baffles as shown in Fig. 5.7-3. Departures from this design can be handled as follows: 1. For multiple crossflow trays, divide the liquid flow according to the number of liquid streams (e.g., two streams for a double crossflow tray), and then use the various hydraulic equations as given. Note that for a double crossflow tray the center weir is approximately equal to the column diameter, and for side-tocenter liquid movement there is diverging flow with the possibility of stagnant zones if the column size is quite large (4 m or larger). For center-to-side flow, stagnation is less likely. 2. For sloped downcomers, the critical liquid velocity is at the bottom, insofar as final disengagement of vapor is concerned. The total volume of the filled portion of the downcomer can be used in estimating residence time. For downcomers with bottom recesses, where the liquid must make an extra turn before entering the tray, the pressure loss under the downcomer may be estimated as twice that calculated from Eq. (5.7-30). This rule of thumb applies also to the case where an inlet weir is used to distribute the liquid after it has flowed under the downcomer baffle. 3. When it is necessary to decrease the hole area of an existing sieve tray, small blanking strips can be used; these are metal pieces that can be fastened directly to the plate and that block the vapor flow through the holes that are covered by the strips. Care should be taken to distribute these strips throughout the tray. 4. Because of changing vapor and liquid flows throughout the column, it may be desirable to vary the parameters such as hole area and downcomer area. For the former, a fixed design plus variable blanking strip arrangements is often feasible. Variations in downcomer area usually are limited to cases with very wide-ranging liquid flow rates. 5. For columns with wide variations in total pressure (vacuum columns where the bottom pressure may be twice or more the pressure at the top of the column), it may be desirable to vary the tray spacing, progressing from a larger value at the top to a smaller value at the bottom. Economics usually mitigate against this. 6. The various hydraulic parameters should be checked at various locations in the column. As a minimum this should be done at four points for a simple, single-feed column: top tray, tray above the feed tray, tray below the feed tray, and bottom tray. 7. Care should be taken in feeding mixed vapor-liquid streams to the column. The reboiler return is of this character, and its flow should be directed away from the bottom seal pan so as not to hinder liquid flow from that pan (see Fig. 5.7-17). Various baffling arrangements are possible for separating the liquid and vapor for a mixed-phase feed stream. EXAMPLE 5.7-2 For the problem of Example 5.7-1, calculate the following: (a) pressure drop across the top tray, (b) turndown ratio, and (c) downcomer backup for the tray below the top tray. Solution, (a) Vapor flow F-factor is obtained as follows: Based on active area
Based on hole area The discharge coefficient (Fig. 5.7-14), for a tray thickness/hole diameter of 2.6/6 = 0.43 and A h /A a = 0.295/2.46 = 0.12, is C v = 0.75. The weir rate is The aeration factor [Eq. (5.7-21)] is For the weir crest [Eq. (5.7-22)] mm liquid For the dry tray drop [Eq. (5.7-18)] mm liquid The total tray pressure drop [Eq. (5.7-20)] is given by mm liquid (b) Estimation of the turndown ratio utilizes Fig. 5.7-13 and a trial-and-error procedure. The pressure loss for bubble formation [Eq. (5.7-16)] is given by 1.73 mm liquid If we assume 50% of design vapor and liquid rates, Then, Dry drop = 63.7(0.25) = 15.9 mm liquid Weir crest = 9.62 mm liquid mm liquid mm liquid These values are on the curve of Fig. 5.7-13. Thus, our assumption is correct; (c) For this part, *,. 100 ^ Turndown ratio = - = 2 Downcomer discharge area = 0.025(1.43) = 0.0358 m 2 0.0050 Velocity under downcomer = U da = T - TTT^ = 0.140 m/s 0.0358 The pressure loss for flow under downcomer [Eq. (5.7-30) is Backup = = 165.2(0.14O) 2 = 3.24 mm liquid
Based on tray spacing. Fractional backup = j- = 0.189 610 (18.9% of tray spacing) 5.8 PACKED-TYPE DISTILLATION COLUMNS 5.8-1 Types of Packing Materials Packings for distillation columns come in many types, shapes, and sizes. Many of them are nonproprietary and are provided by more than one supplier, but most of the newer and more important devices are proprietary, patent-protected, and obtained from a single source. As noted in Table 5.7-2, the packing elements may be placed in the column in a random fashion, as by dumping. Alternatively, they may be stacked as individual elements or they may be fashioned as rigid meshes, grids, or multiple plates and inserted carefully into the column. This latter type of column internal is known as structured packing; the former type is known as random packing. A diagram of a *'composite*' packed column, taken from the paper by Chen, 1 is shown in Fig. 5.8-1. RANDOM PACKINGS Traditionally, packed columns have contained random packings. Descriptions of packings in 1934 ranged from jackchain and ceramic rings to carpet tacks and birdshot. Through the years various handy materials were used to provide contact surface for vapor and liquid. Emerging from early experimentation were the fairly standard Raschig rings and Berl saddles in the 1930s and 1940s. In more recent years, two particular random packings have been quite popular the slotted ring (Pall ring, Flexiring, Ballast ring) and the modified saddle (Intalox saddle, Flexisaddle). These packings have become available in ceramic, plastic, or metal materials. For convenience in the present work, these packings will be called Pall rings and Intalox saddles. Newer random packings include the Metal Intalox saddle (Norton Company), called IMTP, the Nutter ring (Nutter Engineering Co.), and the Cascade Miniring (Glitsch, Inc.), called CMR. The IMTP and Nutter packings are available only in metal, whereas the CMR is available in both metal and plastic. These newer packings have received extensive field and laboratory testing, and the vendors should be consulted for a review of such testing. Views of various random packings, useful particularly for distillation service, are shown in Fig. 5.8-2. Properties of several of these packings are shown in Table 5.8-1. It is important to note that the listed specific surface area of the packing (the amount of surface of a single element times the number of elements that can be packed in a given volume) is not necessarily indicative of the mass transfer capability of the packing. The packings in Fig. 5.8-2 may be separated into two types according to their resistance to the flows of liquid and vapor. The older packings require that the fluids flow around them, thus causing pressure loss both by form drag and by skin friction. The Raschig ring, the Berl saddle, and the ceramic Intalox saddle arerepresentative of this type. The newer packings permit fluids to flow through them, with greatly reduced form drag. The distinction between these types is significant, the *'through-flow" concept having led to the so-called "high efficiency packings" that produce increased mass transfer while minimizing pressure drop. STRUCTURED PACKINGS An early form of structured packing was introduced by Stedman 2 who cut pieces of metal gauze and placed them horizontally in small-scale laboratory and pilot plant columns. This packing was found to be quite efficient for mass transfer 34 but was regarded as practical only for small columns. In later times, expanded metal was used to fabricate structured elements for larger columns, 5 and knitted wire mesh was developed as a high-efficiency packing, 6 but this too was considered impractical and uneconomical for larger columns. It was not until the 1960s that a structured packing was developed that could be considered a proven and practical material for commercial distillation columns; this was the packing known as Sulzer BX (Sulzer Brothers, Winterthur, Switzerland) and was fabricated from metal gauze. The first test data of significance were published by Billet in 1969, 7 following the granting of a United States patent to Huber. 8 Representative data of Billet, for the ethylbenzene-styrene system, are compared against sieve trays and Pall rings (from Ref. 9) in Fig. 5.8-3. It is clear that the Sulzer BX packing gives a superior combination of high mass transfer efficiency and low pressure drop. A disadvantage of the Sulzer packing was its high cost of fabrication; in time more economical methods of manufacture plus the substitution of sheet metal for gauze led to a new group of structured packings: Mellapak (Sulzer Brothers), Flexipac (Koch Engineering), Gempak (Glitsch, Inc.), and Montz B (Julius
Vapor outlet to condenser Manway Liquid distributor Hold-down grid Structured packing Support grid Liquid collector Ringed channel Liquid distributor, redistributor Hold-down grid Random packing Support plate Rings or saddles Manway Manway Liquid distributor Structured grid Skirt Circulation pipe to reboiler Bottom product FIGURE 5.8-1 Composite packed column (Ref. 1).
Raschig Ring BerISaddle INTALOX Saddle PALL Ring INTALOX Saddle (Metal) (Ceramic) (Ceramic) (Meta!) (Metal) FIGURE 5.8-2 Representative random packings. Montz). These structured packings come in various dimensions and are available in a number of materials of construction (typically plastic as well as metals of various types). Views of several different structured packings are shown in Fig. 5.8-4; careful inspection will show that the packing elements are made from sheets of corrugated sheet metal or gauze and that the sheets are perforated. Furthermore, the sheet metal has been given a special surface treatment to aid in the spreading of the liquid film and thus to emulate the gauze surface, which by capillary action promotes liquid spreading. The elements of structured packing are installed in layers in the column, with care being taken that the adjoining elements of adjacent layers are oriented such that the liquid flow direction is reversed and that gas is redistributed. For the simple pilot plant element shown in Fig. 5.8-4, adjacent layers are usually rotated by 90. Properties of representative packings are shown in Table 5.8-2. More details on typical geometries will be given when the topics of pressure drop and mass transfer efficiency are addressed. 5.8-2 Packed Column Hydraulics LIQUID DISTRIBUTION It has always been recognized that for a packed bed to exhibit good performance it must be fed with a uniform and well-distributed liquid flow. The early work of Baker et al. 10 led to the conclusion that for randomly packed beds, unless the column diameter is at least eight times the nominal diameter of the packing pieces, there will be excessive liquid flow along the walls, with resulting loss of efficiency due to channeling. Through the years this limitation has been a guideline and has hampered "scaledown" studies in pilot plant equipment, it being necessary to use at least a 10 cm (4 in.) diameter pilot column if data on minimum size packings (12 mm) were to be scaled up to some commercial size. Fortunately for the designers, the traditional "bluff body" packings such as Raschig rings and Berl saddles have had some capability to correct any maldistribution of liquid in the center portions of the bed, especially when the column diameter to packing element diameter was very large. Silvey and Keller" reported on tests with 3.8 cm (1.5 in.) ceramic Raschig rings in a 1.2 m (4 ft) column and showed how the distribution of the liquid improved as it moved down the packed bed. Albright 12 has provided a method for estimating the "characteristic distribution" of liquid in randomly packed beds, based on a theoretical model involving the diversion of flow by the packing pieces. A number of researchers have found that for bluff packings an initial liquid distribution of at least 40 pour points per square meter of column cross section (4 points/ft 2 ) is generally satisfactory. For the higher efficiency packings, those having the "through-flow" characteristic mentioned earlier, the packed bed appears to offer little correction of a poor initial liquid distribution. This matter is discussed by Chen, 1 who also provides an excellent coverage of packed column internals in general, and by Kunesh et al. 13, who report on studies at Fractionation Research, Inc. The consensus of designers and researchers is that for the high-efficiency packings there should be at least 100 pour points per square meter (about 10 points/ft 2 ). Types of liquid distributors are shown in Fig. 5.8-5. The orifice/riser device can be developed in a variety of forms, and the risers are often of a rectangular cross section. The orifices must be distributed properly over the cross section and must offer enough resistance to liquid flow that an adequate head of liquid can be maintained over them. This can lead to difficulties: small holes can be easily plugged, and out-of-levelness of the distributor can lead to dry sections, especially when liquid rate is considerably below the design value. For orifice-type distributors, the head of liquid required to produce a given flow through the orifice can be calculated from a dimensional form of the orifice equation: (5.8-1) where /i dis( is in millimeters of liquid and U h is the velocity of liquid through the hole in meters per second. The perforated pipe distributor (Fig. 5.8-5) is capable of providing many pour points and can be
TABLE 5.8-1 Properties of Random Packings Packing Type Nominal Size (mm) Elements (per m 3 ) Bed Weight (kg/m 3 ) Surface Area (m 2 /m 3 ) evoid Fraction F p Packing Factor (m" 1 ) Vendors" Intalox saddles (ceramic) 13 25 38 50 75 730,000 84,000 25,000 9,400 1,870 720 705 670 670 590 625 255 195 118 92 0.78 0.77 0.80 0.79 0.80 660 320 170 130 70 402 190 108 81 45 Norton, Koch, Glitsch Intalox saddles (metal) 25 40 50 70 168,400 50,100 14,700 4,630 350 230 181 149 n.a. n.a. n.a. 0.97 0.97 0.98 0.98 135 82 52 43 127 77 50 41 Norton Pall rings (Ballast rings, Flexirings) (metal) 16 25 38 50 90 49,600 13,000 6,040 1,170 480 415 385 270 205 130 115 92 0.92 0.94 0.95 0.96 0.97 230 157 92 66 53 195 139 93 61 50 Norton, Glitsch, Koch Raschig rings (ceramic) 13 25 38 50 75 378,000 47,700 13,500 5,800 1,700 880 670 740 660 590 370 190 120 92 62 0.64 0.74 0.68 0.74 0.75 2000 510 310 215 120 819 279 143 118 68 Norton, Glitsch, Koch, others Berl saddles (ceramic) 13 25 38 50 590,000 77,000 22,800 8,800 865 720 640 625 465 250 150 105 0.62 0.68 0.71 0.72 790 360 215 150 304 166 108 78 Koch, others Intalox saddles (plastic) 25 50 75 55,800 7,760 1,520 76 64 60 206 108 88 0.91 0.93 0.94 105 69 50 87 60 44 Norton, Glitsch, Koch Pall rings (plastic) 16 25 50 213,700 50,150 6,360 116 88 72 341 207 100 0.87 0.90 0.92 310 170 82 325 138 69 Norton, Glitsch, Koch "Identification of vendors: Norton Company, Akron, OH; Glitsch, Inc., Dallas, TX; Koch Engineering Co., Wichita, KS. b n.a. not available.
Pressure drop/theoretica! stage, mm H2O EB/SM, 100 mm Hg Sieve tray 50 mm Pali rings Gauze Vapor flow factor, U o p l y, (m/s) (kg/m 3 ) 1/2 FIGURE 5.8-3 Pressure drop/efficiency comparisons, trays and packings: ethylbenzene-styrene system at 100 nm Hg pressure (Refs. 8 and 9). equipped with a central reservoir to allow variations in liquid head as flow rates change (and as the holes become partly fouled), and it also has the advantage of offering very little resistance to the flow of vapor. However, the need for resistance to liquid flow limits the total hole area (as in the case of the orifice/riser unit) that can be used. Also, for complex lateral piping (containing the holes), careful fluid flow calculations must be made to ensure that all holes discharge equally. For each hole, Eq. (5.8-1) may be applied. The trough-type distributor can accommodate to wide swings in liquid rate, since the V-notch orifices can function at various heads. A disadvantage is that a uniform and extensive distribution of pour points may be difficult to achieve. Also, the streams from the V-notch weirs tend to be coarse and with attendant splashing, and the troughs offer some resistance to vapor flow. However, the trough distributor is more resistant to fouling and indeed can collect significant amounts of solids before losing its ability to distribute the liquid. Thus, troughs are often used when distribution is not overly critical and when dirty liquids are used. If the trough openings are in the form of V-notches, the following equation is suitable for estimating flow as a function of liquid head over the bottom of the notch: (5.8-2) where B is the notch angle and q is in m 2 /s-notch. The effect of distributor type on packing mass transfer efficiency is shown in Fig. 5.8-6, taken from the presentation by Kunesh et al. 13 The "tubed drip pan" is an orifice riser distributor with tubes extending toward the packing from each orifice. The system studied was cyclohexane-w-heptane. The term HETP, to be discussed in Section 5.10, refers to "height equivalent to a theoretical plate" and is a measure of reciprocal efficiency of the packed bed. The tubed drip pan shows a 50% higher mass transfer efficiency than the notched trough unit when a through-flow packing such as slotted Raschig rings is used. Sprays also may be used for liquid distribution. When more than one nozzle is needed, overlapping (or underlapping) of spray patterns is inevitable. Care must be taken to select a full cone spray nozzle that does not have too fine a mean drop size (to prevent entrainment of liquid by the rising vapor) and which has a good pattern of spray over the needed cross section. Nozzles are available for handling liquids containing suspended solids, and thus spray distribution is a possible solution to the need to distribute a dirty liquid. LIQUID REDISTRIBUTION As shown in Fig. 5.8-1, when a stream is added or withdrawn from the side of the column, it is necessary to collect the liquid from the bed above and redistribute to the next bed below. Considering the bed from which the liquid is to be collected, a support plate (see below) is used for the packing support, and liquid flowing from this plate is collected in a device that resembles the orifice/riser distributor, except that instead of the orifices a sump or weir box is used to channel the liquid to a distributor serving the bed below. In the instance of a liquid feed being admitted between these beds, the liquid is fed to the lower distributor and mixed with the liquid from the collector above. This arrangement is diagrammed in Fig. 5.8-7. For a vapor feed, or a feed that is a mixture of vapor and liquid, a special baffling arrangement can be used to separate the two phases. Another aspect of liquid redistribution involves the handling of liquid that has migrated to the walls
(a) (b) FIGURE 5.8-4 Structured packing (Flexipac) of the sheetmetal type: (a) fabricated to fit a pilot-scale column and (b) arranged to fit through the manways of a larger-diameter column (Koch Engineering Co.). within the packed bed itself. This can be handled with wall wiping devices, if the bed contains random packing; such devices are simple ring-type affairs that slope downward (Fig. 5.8-8) and that must be placed in the bed during the packing process. Wall wipers are generally not needed if the column diameter is more than 10 times the packing piece diameter. SiIvey and Keller 11 found that for Raschig rings and a troughtype distributor, no redistribution was needed for bed heights up to about 10 m (33 ft). A good general rule is to limit the height of randomly packed beds to about 7 m (23 ft). VAPOR DISTRIBUTION While it is apparent that vapor (or gas) should be distributed uniformly to the packing at the bed support, there is usually the assumption that if the initial distribution is not good, pressure drop in the bed will make the necessary correction. While this assumption is valid for the traditional bluff body packings, it does not apply to the high-efficiency through-flow random packings or to the modern structured packings. The inherent low pressure drop of such packings may not be sufficient to correct vapor maldistribution. There are no quantitative guidelines for determining how "good" the distribution should be. The bed support may offer little help in ironing out maldistribution. Reasonable care should be used to disperse
TALE 5.8-2 Properties of Structured Packings Name Material Nominal Size Surface Area (m 2 /m 3 ) Void Fraction Packing Factor (m" 1 ) Vendor Flexipac Metal 1 2 3 4 558 250 135 69 0.91 0.93 0.96 0.98 108 72 52 30 (D Gempak Metal 4a 4a 2a Ia 525 394 262 131 (2) Sulzer Metal gauze CY BX AX 700 500 250 0.85 0.90 0.95 (3) Kerapak Ceramic BX 450 0.75 (3) Munters Plastic 6,560 12,060 17,060 25,060 400 220 148 98 193 89 56 33 (4) Rombopak Metal 755 (5) Montz Goodloe Metal Metal knit (6) (2) Vendors: (1) Koch Engineering Co., Wichita, KS. (2) Glitsch, Inc., Dallas, TX. (3) Sulzer Brothers Ltd., Winterthur, Switzerland. (4) Munters Corp., Fort Myers, FL. (5) Kuhni, Ltd., Basle, Switzerland. (6) Julius Montz Co., Hilden, West Germany. side-entering vapor (e.g., the vapor-liquid return from a reboiler) across the column cross section. For critical cases, one or two crossflow trays may be used to improve the distribution, if the pressure drop they consume can be tolerated. LIQUID HOLDUP The void space in a packed bed is occupied by vapor and liquid during operation. As might be expected for countercurrent flow, higher vapor rates restrict liquid downflow and increase liquid holdup. In the extreme case, a sufficient amount of holdup can represent an incipient flooding condition. Figure 5.8-9 shows typical holdup and interfacial areas for 1 in. ceramic Raschig rings. At low liquid rates there is little influence of vapor rate on holdup or interfacial area, the latter approximating the specific surface area of the packing itself. At higher rates of liquid and vapor flows, there is clear interaction between the streams and a buildup of liquid takes place. This happens in the so-called "loading zone." The holdup shown in Fig. 5.8-9 is given as a fraction of the total bed volume. It is a dynamic, or total holdup, and is given the notation H 1. If the vapor and liquid flows were to be stopped, and the bed then allowed to drain, a certain amount of liquid would be retained in the interstices of the bed; this is the static holdup, H s. The difference between these holdup values is the operating holdup, H 0. Thus, The effective void fraction under operating conditions is For random packings, Shulman et al. 14 proposed the following relationship for the static holdup: (5.8-3) (5.8-4) (5.8-5)
(a) (b) FIGURE 5.8-5 nozzle. (c) Types of liquid distributors: (a) orifice/riser; (b) perforated pipe; (c) trough; and (d) spray (d) Notched trough HETP Ratio Tubed drip pan SI conversion kpa = psi x 6.89 Percentage of useable capacity FIGURE 5.8-6 Effect of liquid distributor type on packing efficiency (Ref. 13) for 1 in. Pall rings, 24 psia, cyclohexane-/i-heptane.
Upper bed Upper bed support Collector tray Feed liquid Downcomer Distributor tray Lower bed hold-down screen ("limiter") Lower bed FIGURE 5.8-7 Collection and redistribution at a packed-column feed tray. FIGURE 5.8-8 Wall-wiper liquid redistributor.
H,, Liquid holdup, ft 3 liquid/ft 3 packing 1.0 in. Raschig rings Loading point 2 3 a, Effective interfacial area, ft /ft packing 1.0 in. Raschig rings Loading point G, Gas rate, lb m /h ft 2 G, Gas rate lb m /h ft 2 FIGURE 5.8-9 Liquid holdup and interfacial area, 1 in. ceramicrings (Ref. 14). Values of the constants in Eq. (5.8-5) are as follows: C 1 C 2 C 3 25 mm carbon Raschig rings 0.086 0.02 0.23 25 mm ceramic Raschig rings 0.00092 0.02 0.99 25 mm ceramic Berl saddles 0.0055 0.04 0.55 The packings tested by Shulman and coworkers are of the traditional bluff body type. One would expect holdup values to be lower for the through-flow type packings. Vendors usually have available holdup values based on air-water tests. Operating holdup may be estimated from the dimensionless equation of Buchanan: 15 (5.8-6) The first group on the right is a film number and the second is the Froude number. More will be said about these dimensionless parameters when structured packings are discussed. Representative operating holdup data for a structured packing material are given in Fig. 5.8-10. LOADING/FLOODING As mentioned above, when the vapor rate is very high, downflowing liquid tends to be held up by the drag of the vapor. This reduces the net available cross section for vapor flow and causes the pressure drop to increase. If vapor rate continues to increase, liquid will be carried overhead and the column will reach a state of incipient flooding. The same situation can arise if there is a large increase in liquid rate, when vapor rate is kept constant, and excessive rates of liquid also can lead to a state of incipient flooding. These effects of liquid and vapor flow rates are exhibited in Fig. 5.8-11, based on the studies of Sarchet. 17 At low liquid rates, there is essentially vapor flow through a dry bed; that is, liquid occupies a relatively small portion of the available cross section for vapor flow. The effect on pressure drop of higher liquid rates is evident; the pressure drop curves bend upward, as a result of the greatly increased liquid holdup. At the very high rates of vapor and liquid flows, flooding occurs, and this represents a maximum possible operating condition. As for tray-type devices, it is convenient to relate certain aspects of packed bed operation to this maximum condition, even though it does not represent a practical operating condition. A discussion of the techniques for measuring the flood condition has been given by SiIvey and Keller; 18 as one considers making such a measurement he or she soon realizes that the flood point determination is influenced by the measurement approach and that it is really not a "point" but a fairly narrow range of values. Even so, methods for making an estimate of the flood point are useful and are outlined in the following section dealing with pressure drop.
in. H2O/ft 2 O O -n > Volume holdup, % Volume holdup % L = Water rate, lb m /h ft 2 x = Point where water begins to build up over Gas rate, lb m /h ft 2 FIGURE 5.8-11 Pressure drop for flow through 1-in. ceramic Raschig rings, air-water system (Ref. 17).
I NTERFACIAL AREA The amount of interfacial area that is available in the packed column is of vital importance in determining the mass transfer efficiency of the packed column. However, it is rarely known with any degree of accuracy. It bears some relation to the specific area of the packing, that is, the amount of dry packing surface provided by the packing elements. But even this parameter is not really known with accuracy in the case of the random packings, since an exact count of elements contained in the column is not feasible for commercial scale columns, and even for controlled pilot-scale units the elements may nest or otherwise block out area that can then serve no purpose for mass transfer. Figure 5.8-9 shows effective interfacial areas that were deduced by Shulman et al. 14 from experiments on the sublimation of naphthalene Raschig rings. Many other studies have been made in an attempt to relate effective area to specific packing surface, as a function of liquid and vapor flow rates. Generally, it is thought that the effective area reaches the specific area near the onset of flooding, but Fig. 5.8-9 shows that this may not be the case. It also should be noted that the total area available for mass transfer includes film surface ripples, entrained liquid within the bed, and vapor bubbling through pockets of liquid held up in the bed. Another important point: relative specific surface of different packings might indicate relative mass transfer efficiencies, but this is often not the case. In the present state of development, at least for the random packings, it is prudent to deal with an "effective mass transfer surface", as used by Bravo and Fair, 16 that can be deduced by semiempirical means, or simply to couple the area term with the mass transfer coefficient to form a volumetric-type coefficient. Pressure Drop RANDOM PACKINGS It is clear from experimental data such as those shown in Fig. 5.8-11 that the loss of pressure experienced by the vapor as it flows through the packing is a function of flow rates, system properties, and packing characteristics. The resistance offered by the bed is a combination of form drag and skin friction, and thus the shape of the packing elements must be considered. While some efforts have been made to correlate pressure drop in randomly packed beds by means of a dry bed friction factor that is modified according to vapor flow, the efforts have not been successful for handling the many different possible packing shapes and sizes. (Such an approach has been more successful for the structured packings and will be described in the next subsection.) As a result, it has been necessary to use empirical approaches for estimating pressure drop in beds containing the random packings. These approaches are based on the observation that at flooding, or incipient flooding, most beds exhibit a pressure drop of about 20 mbar/m of packed height (2.5 in. water/ft). In working with a modification of an early flooding correlation of Sherwood et al., 19 Eckert 20 developed a graphical method for pressure drop estimation, shown in Fig. 5.8-12. The Eckert diagram originally was designed to provide both flooding and pressure drop information. The effects of packing type and size are forced to merge through the use of a packing factor that is presumed to be a constant for a given packing type and size. Representative values of the factor are given in Table 5.8-1, and vendors of packings not listed can supply values of the packing factor for their products. This approach to the estimation of pressure drop is quite simple and rapid. It gives approximate values and is recommended for applications when the pressure drop estimation is not of critical importance. A more fundamental approach to pressure drop prediction is being pursued by current researchers. The usual first step is to consider the dry pressure drop only, utilizing a conventional Fanning or Darcy type relationship: pressure drop height of bed K ' ' ' Any consistent set of units may be used. After dry pressure drop is determined, the influence of irrigation liquid is introduced: (5.8-8) In this equation A' is a constant, characteristic of packing type and size. Pressure drops through beds of random packings have been correlated by these equations, 21 " but it is not yet possible to point toward a particular piece of work that gives reliable results for the full range of possible packings. An adaptation of the basic theory has been presented by Billet and Mackowiak 23 and is stated to be valid for loadings up to about 65% of the flood point. Liquid holdup is obtained from (5.8-9)
Parameter Of Curves Is Pressure Drop, mm Hg/meter Of Packed Height L = Liquid rate, kg/s m 2 G = Gas rate, kg/s r>2 Pj_ = Liquid density, kg/m3 Pg = Gas density, kg/m3 Fp = Packing factor, m"1 ^L - Viscosity of liquid, mpa s * = Ratio, (density of water)/(density of liquid) g = Gravitational constant, 9.81 m/s 2 FIGURE 5.8-12 Eckert method for estimating packed column flooding and pressure drop (Ref. 20). {Note: mm Hg/m x 0.163 = in. H 2 O/ft.) where Froude n u m b e r ( 5. 8-1 0 ) dry bed drop= (5.8-11) In this expression d p is the effective packing size [=6(1 e)/a p ] and K' is the Ergun-Brauer wall factor: (5.8-12) The friction factor in Eq. (5.8-11) is taken as constant at 2.45 for vapor Reynolds numbers of 2100 or higher. For lower Reynolds numbers, (5.8-13) (5.8-14) Finally, the ratio of irrigated to dry pressure drop is obtained:
TABLE 5.8-3 Constants for Billet Pressure Drop Equations Packing Material f <t> X C h Pall rings Metal 2.45 0.81 0.525 1.0 Ceramic 1.95 0.92 0.64 1.15 Plastic 2.45 0.83 0.57 0.75 NSW rings* Plastic 1.025 1.0 0.61 0.75 Bialecki rings Metal 2.45 0.79 0.596 1.0 Also known as Nor-Pac packing, product of NSW Co., Roanoke, VA. (5.8-15) where <f> geometric packing factor X = aperture correction factor e = packing void fraction Values of the several constants, each determined experimentally for a particular packing type (but for a range of sizes), are given in Table 5.8-3. A final approach to the problem of estimating pressure drop for random packings should not be overlooked: test data from the packing vendors. These data usually are based on air-water and are taken in the vendor laboratories. They are presented in charts such as that shown in Fig. 5.8-13. In the example shown, pressure drop is given as a function of gas mass velocity. For gases other than air, the abscissa should be multiplied by the square root of the ratio, air density to the density of the gas under consideration: Pf^S?!M.- ^^ MS RAIl AP-INCHES WATER/FT. ffccking AIRMASSVELOCITY FIGURE 5.8-13 Typical vendor data on random packing pressure drop. One-inch ceramic Raschig rings, air-water system (Norton Co.).
EXAMPLE 5.8-1 For the conditions of Example 5.7-1, that is, the top zone of a methanol-water fractionator, and for the case of 50 mm Pall rings replacing the sieve trays, estimate the pressure drop in the top 0.5 m of packing, using (a) the Eckert graphical method and (b) the Billet analytical method. Solution, (a) From Example 5.7-1, the value of the flow parameter is For the ordinate scale parameter of the Eckert chart (Fig. 5.8-12), From Fig. 5.8-12, Thus, for a packing height of 0.5 m, Pressure drop = 2.0 mm Hg/m (0.33 in. H 2 O/ft) (b) Using the Billet method, AP = 1.0 mm Hg Since Re K is greater than 2100,/ = 2.45. By Eq. (5.8-11),
Finally, by Eq. (5.8-15), STRUCTURED PACKINGS The pressure drop through structured packings may be estimated according to the method of Bravo et al. 24 as outlined below. The method applies to conditions below the loading point. Equation (5.8-6) may be adapted to allow for vapor flow through the channels of the packing: (5.8-16) The effective gas velocity inside the flow channel takes into account the slope of the corrugations, as proposed in an earlier paper by Bravo et al.: 24 (5.8-17) where B is the angle of inclination of the flow channel from the horizontal. The equivalent diameter of the flow channel d^ is taken as the side of a corrugation or crimp of the packing (see Table 5.8-4). The friction factor for Eq. (5.8-16) is obtained from the general relationship (5.8-18) where C 1 and C 2 are constants for a particular packing type and size. The Reynolds group of Eq. (5.8-18) is defined as (5.8-19) This friction factor is applicable to gas flow only and incorporates both turbulent and laminar contributions. Since the shapes of the flow channels of the structured packings are geometrically similar, one would expect that a single set of constants for Eq. (5.8-18) would cover all packing sizes. When the packing is irrigated, the influence of the presence of liquid may be related to the operating holdup, using a form alternate to that given earlier as Fig. 5.8-6. Bemer and Kallis 22 concluded that the following simple form is adequate: (5.8-20) where A' and a are constants for the packing type. Equation (5.8-8) is then adapted for the total pressure drop: (5.8-21) where
Flow Channel Triangular cross section Flow channel arrangem Flow channel cross section FIGURE 5.8-14 Geometric factors for estimating structured packing pressure drop (Ref. 24). (5.8-22) Figure 5.8-14 shows the flow channel geometry factors. Bravo et al. 24 found that for the corrugated-type structured packings only the constant C 3 was variable; values of the other constants in Eqs. (5.8-18) and (5.8-22) are C 1 = 0.171, C 2 = 92.7, and a = 0.5. Thus, the final working equation is (5.8-23) Values of the constant C 3 are given in Table 5.8-4. EXAMPLE 5.8-2 In the preceding example, the use of 50 mm Pall rings was considered for the methanol-water fractionator of Example 5.7-1. For the case of a 12.5 mm crimp height structured packing of the sheet metal type (Flexipac 2, Gempak 2A), estimate the pressure drop in the top 0.5 m of the packed bed. Solution. For the No. 2 structured packing and from Table 5.8-4, TABLE 5.8-4 Pressure Drop Parameters for Structured Packings Equivalent Angle* Diameter Packing (degrees) (mm) Constant C 3 Flexipac 1 45 9 3.38 2 45 18 3.08 3 45 36 4.50 4 45 72 7.26 Gempak IA 45 36 4.50 2A 45 18 3.08 3A 45 13.5 3.87 4A 45 9 3.38 Sulzer BX 60 9 3.38 Angle of channel from horizontal.