Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978
420
Hydraulic Studies in Sieve Tray Columns Walter J. Thomas” and Oluwasola Ogboja Chemical Engineering Department, University of Surrey, Guildford, England GU2 5XH
An extensive study is presented of the performance of two columns of different geometry and size each with 1 in. diameter holes. The significance of these factors on pressure drops across the dry and wet trays is considered with special reference to residual pressure drop. Experiments were made in which sampling of the vapor between trays was carried out as a means of establishing the extent of entrainment of liquid under different flow conditions. The results were examined on the basis of existing theory. Weeping and dumping for 1 in. diameter holes was examined.
Introduction The sieve tray is the simplest and cheapest type of gas-liquid contacting device. It is being used increasingly in industry, and researchers are beginning to produce design data after a lapse of many years. Available data tend to be for comparatively small holes in the range 1/8 to 3 / 8 in. diameter. Small holes have a number of disadvantages such as a susceptibility to blockage due to dirt and resinous material, a tendency to high pressure drop, and limited capacity. Investigations of the characteristics of trays with larger holes is called for as little seems to have been published. Holes of diameter 1 in., and even larger, are in use but are uncommon and their performance is not reported. In the present studies experiments have been carried out with two trays with 1 in. diameter holes. One tray was rectangular and the other round. The columns were designed to investigate the effects of both size and geometry on the tray and column performances. Hydraulic studies have been made using air-water to ascertain the effects of air and liquid rates on pressure drops, frothing, weeping, and entrainment. The study was restricted to a regime on the trays of a “frothy mass”, and most importantly related to 1 in. diameter holes. Theory Pressure Drop Relationships. Established equations (eq 1-9) referred to previously by Thomas and Haq (1976)
are shown in Table I. hF and h L both refer to a measured dynamic head a t the tray floor, while hc is the sum of the dynamic and momentum heads. The idea of a momentum head, hM,as introduced by Sargent and Bernard (1966) to allow for the head lost by vapor leaving the tray holes does not account for all such losses occurring on a tray. A residual pressure drop, hR, as given by Mayfield et al. (1952), is greater in value than hM. It is logical to suggest that hR be subdivided so that hR = hR’ hM (10)
+
The total pressure drop across the wet tray will then be ht = hDp + hF hM + hR’ (11) Dry plate pressure drop has been studied in considerable detail by Hughmark and O’Connell (1957) and McAllister et al. (1958). A useful summary is given by Chase (1967). Nearly all the examples considered were for small holes and column diameters. The applicability of the correlations to large holes and columns must be open to doubt. Their general findings nevertheless remain acceptable and are given in Table I. The discharge coefficient C in eq 7 was given by Hughmark and O’Connell in the form of a single curve on a C vs. Dolt plot. They attach considerable importance to tray thickness. Later McAllister et al. (1958) developed the expression given in eq 8. Here plate thickness is of small importance as the friction head loss in the hole, hfr, is quite small compared with the other terms. In the present studies hf < 1% hDP. Smith and Fair (1963) used a combination of eq 6 and 9 for design. According to these authors, the discharge coefficient, C,,, is a function of approach velocity, Dolt, Re, and the condition of the hole “lip”. Further, the exponent of 2 on both C,, and U , is not constant either. Liebson et al. (1957) produced a correlation of C,, with tray and hole dimensions based on published work, which Smith and Fair (1963) used in conjunction with eq 9 to calculate dry plate pressure drop. The aeration factor P is dependent on definition. On the basis of Mayfield et al. (1952), Chase (19671, and Smith and Fair (1963)
Table I eq no.
pressure drop equations
references Mayfield et al. (1952) , Smith and Fair (1963) Thomas et al. (1967,1976) Sargent and Bernard (1966) Sargent and Bernard (1966) Smith and Fair (1963) Hughmark and O’Conell(l957) McAllister et al. (1958)
As used previously by Thomas and coworkers (1967,1976) hF + h M h, + how Equation 13 gives values for /3 lower than those given by eq 12 as (hF + hM) < ( h +~ hR). In d cases depends upon hC
Od
0.186 ( u o / C v o ) ~
Smith and Fair (1963)
(PVIPL)
0019-7882/78/1117-0429$01 .OO/O
0
= h,
+ how
1978 American Chemical Society
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Ind. Eng. Chem. Process
Des. Dev., Vol.
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hDp and how,so that (a) hole imperfection, (b) absence of reliable data on C, the hole discharge coefficient, (c) difficulty in measuring or calculating how,influence the accuracy of the values of 0. Two definitions of 4, the froth or foam density, can be used. 4h
hL = ZF
B= (Smith and Fair,1963)
(14)
(Thomas et al., 1967, 1976) (15) More correctly on the basis of eq 11 taking into account the division of momentum loss through the hole, and an undefined hR’
Hutchinson et al., (1952) demonstrated a relationship between /3 and 4.
P = YZ(1 + 4)
(17)
Foss and Gerster (1956) studied an air/water simulator from which they obtained values of /3 and 4 as functions of F A . The A.1.Ch.E. Research Studies (1958) considered other systems. Within reason any of the definitions for 0should be acceptable providing consistency is maintained. Chase (1967) refers to the work of Eduljee (1966) and Calderbank (1956) on froth height and foam density, respectively.
zF= 2.2 + hF + 0.67 (Fa)’ Pf
out that the froth height has a limited accuracy of measurement, (to 1/2 in.), due to sloshing and frothing on the tray. They studied three tray spacings of 12, 15, and 18 in., and hole diameters of lll6,l/*, 3/16, and 1/4 in. Their equations are as follows
- A , = 1 - 0.1 (C’)2/3n113
(Eduljee, 1966)
(18)
(Calderbank, 1956) (19)
PL
Equation 19 is stated as applying up to G’/Aa = 12.7 (n/A,)’i2. The applicability of eq 18 and 19 needs to be examined especially as neither contains a liquid flow term. Liquid in Vapor Entrainment. The principal published works are those of Smith and Fair (1963), Van Winkle (1967) with detail provided by Souders and Brown (1934), Bain and Van Winkle (1961), Fair and Matthews (1958), and Zenz (1954, 1967). Van Winkle (1967) is especially useful in providing a tabulated report on entrainment studies and for giving the generalized conclusions that entrainment is increased for (a) decrease in tray spacing, (b) increase in superficial vapor velocity, (c) increase in weir height, (d) increase in liquid flow rate, (e) decrease in surface tension, and (f) increase in hole diameter. The results of the many published studies are diverse and not well correlated. Little is known about the mechanistic problems either of generation or collection in the upper tray. Hunt et al. (1955) presented a generalized correlation for entrainment in a 6 in. diameter column with a static liquid system. This eliminated the effects of liquid flow rate and weir height but was disadvantageous in being unrepresentative of practice. Their correlation is
where S‘= S - B (or S - ZF). When using water the surface tension group is ’unity. Bain and Van Winkle (1961) developed Hunt’s work by application to an operating tray with downcomers and an upper entrainment collector tray. Quite rightly they point
[0.094 + 0.014hW2]L +I 1000
(21)
I was given by a series of equations depending upon weir height. A typical equation for I is given below
”)’
2-in. weir: I = 3.57 - 1’23G + 0.996( 1000 1000
(22)
the coefficients differ with h,. Bain and Van Winkle correlated some 900 points of entrainment data with the following equation
where K and Bo are constants for each hole diameter. The functions off and g were given graphically. The Bain and Van Winkle correlation will be considered to test their validity for 1 in. diameter holes. Entrainment is reported as liquid carry-over in the vapor, ( E lb of water/100 lb of air), and is the result of collection on a special mesh. A criticism of this otherwise excellent paper is that the “Collector Tray” differs from the normal tray. It is uncertain how representative the entrainment vdues are. The value of the Hunt et al. (1955) and Bain and Van Winkle (1961) work is that they measure entrainment below flooding conditions. The Fair and Matthews (1958) and Smith and Fair (1963) correlation, to be discussed next, is associated with flooding studies. It has been suggested by Bain and Van Winkle (1961) that larger hole sizes may give higher entrainment than is predicted, leading to optimistic design. Fair’s Correlation (1963). Fair allows for the interaction of vapor and liquid flows by a parametric ratio related to their kinetic energy
FLV
=
V W
dY, PL
This is an unusual parameter inasmuch as it is not a ratio of F factors. F L V was coupled with a capacity parameter C S based ~ on the work of Souders and Brown (1934).
The vapor velocity, un, is based on the “net” area of the tray available for liquid disengagement. The equation needs correction where the surface tension of the liquid differs from = 20 dynlcm.
The values of F L V can be calculated for given values of L,, vw,pv, and p ~ From . the correlating graph (Csb)u=20 vs. F L V at different tray spacings as given by Smith and Fair (1963) and Van Winkle (1967), the (CSb),,=PO values corresponding to F L V values are obtained. The u, flooding values corresponding to the F L V values can now be calculated from eq 26 at the correct spacing (in our case 24 in.).
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 4, 1978
431
If operating values of u, called u, design are chosen less than u, flooding for a series of constant L,/ V, values, then a series of parametric curves can be drawn where each curve is uniquely related to a new term called To flood =
u n design X
~
100 (constant L,/V,)
(27)
un flooding
In this way, on a log log plot of J /vs. , FLv,curves can be drawn using published experimental values of the fractional entrainment, J / , where e V,+e
+v=-=-
e” l+ev
-
-
-
When the entrainment flood point is approached, J/ 1.0; and for no entrainment e 0 and 0. Fair points out limitations to the use of his correlation (1)h, < 0.15s; (2) low to nonfoaming system; (3) A , / A ,
