Pressure Drop in Bubble-Cap Columns
T
a d 13 lJccau6e uf the flow of HE pressiire drop suffered A neio method is preseriied Sur. coriipulirig /tie ,slot,s, and the v a p o r . This caiiiiot be acciiIiy the vapors in passing ji(Ft,i.f zvlpor lhrorlgh rately calculated, but ~tSair idea tlirougli a plate is an extent to urhich the slots are occupied by vapor. of tlieOrdprofrlragrlitude I,e esaent,ial element in the design The other elenlmfs ./ pressure d r w are also oljtained by considering tile f but~,le-cap coiuirins. TI)^ considered. Experirnen,ts wilh bubble caps conriarrowest cross section as an overflow height mist be great orifice. It will o r d i n a r i l y he cnougii to overcome this drop, taining a single triaiigulur or rectangular notch, found that this drop is quite and this may set a lower limit to bubbling air, hydrogen, ar,d diozide negligible in comparison with the distance between plates, althrough water arid n,aphlha, give f u t mrifirrriathe tlrougli usually this distance will lion Of lhe Some uvrk Orl a nlodel bi~bble At B, the surface of the liquid he fired by other considerabions. plate is also presenled. In vacuum columns tlie dron under tlie cap, the liquid is fairly quiescent,, and tliere will be little nrwy tie (if great importance, cause t i l e pressure drop cawed by tlie plates teiids to raise t.hc or no flow in tlie plane of llie papor. The pressure at B‘, just out,side the slot, will be the same as at B, the two points k i n g al,solute pressure just vliere a low pressure is most needecl-at tile bottom. Moreover, the proper design of caps, and tlwir at the same level and tlie liquid at the t,wo points being part nunher pcr plate, depends on a knowledge of the fraction of of t,he same niass; there will be no vapor bubbles below tliis the dots, teeth, or other mea.ns of subdivision vrhicli is actu- point. The driving force tending lo blow vapor tliruiigli the ally used by tlie rising vapors, and this information is also slot is eero and tliere will be no bi111blinp. At every higher point, liowever, say C, tlie presaurf. of tlie liquid out.sideis less required to determine tbe pressure drop. This pqier gives an analysis of the components of the tliari that of tlie vapor inside by the liquid height, BC (corrected pressure drop, considering especially the iinportant case in for the density of t,lio vapor). Tlie force available to bubble wliicli the Irubble caps have teeth, slots, or similar devices liquid outward is therefore equal to this lieiglit of liquid. along the lower edge. It prcsent.s a new fonnula from which (The effective ilerisity of the liqiiid may he somewhat reduced tooth opening and pressure drop tlirougli tlie teeth may be by tlie presenceof vapor ill it.) If every point in theopenspace criinputed, and gives the results of erperiment,s to show the in the slot is considared as an orifice, intcgrat,ion will give tlie total volume aliicli can pass througli Sor any given tooth ralidity of tlie formula. Tliere seems to he litt,lc availnhle on this subject i n tlie opening, and the opciiing will theresore be expressible as a literature. Walker, I,eris, and Meildams ( 3 ) and Cliillas function of the volume of vapor to he tianrlled. Integrations and Weir ( 1 ) do not refer to the change in tooth opening with for two important cases are girerr b e l i w ; other shapes can be vapor volurne (which they may have considered to be suffi- handled in a similar nianner, graphical integrat.ion being riently obvious), and their treatment suggests that the area of necessary in some cases. Since the pressure a t B’ is tlie same as that a t B, we may t,Iieslots is fixed, as is the case perhaps in certain types of cap. Robinson (.2) refers to tlie change in tooth opening and states say simply that pressure drop over tlre plate is equal to the that the extent of the opening can be coniputecl, hut i t is difference iii liead of liquid on the outside and inside of the diflicult to determine what niettiod of computation lie liad in cap, plus tlie usually negligible drop in the passages under the cap. The liciplit of liquid under the cap is, of course, known mind. when the tooth opening is known, but the question of the J3ASlS OF TI16 DERIV.4TlON static liead above the top of the not.ch is not so easy to solve. In E’igirrc 1 it diagrammatic cross section of a bubble cap in If we consider a cap wit,h a given submergence above the top action is shown. Vapors are ascending through the opening, of the slot and force vapor tlirougli the cap so as to produce .4 (the vapor nipple), and bubbling through the liqnid a t the little or no splashing, the head required will be equal to that slot B-C. There will be a certain pressure drop between A represented by the submergence. If, then, vapors are forced 524
1 Tu' D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y
May, 1934
through the cap so as to cause a steady condition of splashing and support a constant number of liquid droplets in the space above the cap, certainly the static head should remain as
525
The differential volume duo through dA = UdA = dV, = C
dGR
Wdh,
=
2(h - ha) B (in inches) 2A
=
(C)
= =
volume per cap = ( N ) (V,) number of slots per cap
VS
B U B B L E CAP SECTION
V N
dg
-
(2)
(0.001068)
h5l2
RECTANGULAR SHAPED SLOTS. In Figure 1, let h, ha, and R represent the same quantities as in the triangufar slot. At section with height ha: RECTANGULAR
5 LOT
TRIANGULAR
before and not increase or decrease because the same amount of liquid is present as when no vapors were flowing. However, in actual cases, a weir is present on the plate to govern the rate of overflow to the next tray below. The rate of flow over this weir is proportional to h3/2where h is the head of fluid flowing. I n a plate where a continuous foam is present over the weir, the rate should be governed by the height to which the foam rises. The density of the foam is inversely proportional to the height to which it rises, provided a uniform feed of liquid is supplied, but the rate of overflow to the next plate is proportional to the 3 1 2 power of the height so that there must be a decrease in static head of sufficient amount to provide a weight flow of foam equivalent to the weight of liquid entering the tray. Hence, the exact pressure drop will depend on the height of foam produced, the closeness of the overflow weir to the bubbling caps, and the relative height of the weir and the cap slots. If the weir were far removed from the splashing, then the pressure drop would be represented by a head of the liquid equal to the height in the quiet portions of the plate less the height under the caps, and would increase as the vapor velocity rose by the amount of increase in the slot opening. Actually the increase will be less than this and may even be negative. DERIVATION OF EQUATIONS FOR SLOTOPENING TRIANGCLAR SHAPED SLOTS. In Figure 1 : Let h = slot opening, inches density of vapor R = (density of liquid) - (density of vapor) h = max. head of gas flowing through slot, feet A = altitude of triangular slot, inches B = width of slot at base, inches
rR
ha Let 12R
=
head of gas at height ha,feet
At ha and through the section dh,, U
where U = velocity, feet per second
=
u
SLOT
FIGURE1. CROSSSECTION OF BUBBLECAP IN ACTION
C42g
12R
=cd2g&
The differential volume, dV., through the area dA is:
d$ -
V N
=
(C) (E') (0.00134)
= =
volume per cap = (V,) ( N ) number of slots per cap
h3/2
EXPERIMESTAL DATAON SLOTOPENING The data which were available for testing the equations were obtained from a series of experiments made by H. G. Schnetzler of this laboratory on bubble caps containing a single slot. The general arrangement of this apparatus is shown in Figure 2. Three different gases were passed t h r o u g h V-shaped and rectangular sh a p e d openings. ov The openings were v a r i e d f r o m 0 to 100 per cent. The V-slots were of three types: cut in t h i n m e t a l , cut square from 0.25-inch maBUBBLEC A P terial. and cut from FIGURE2. SINGLE-SLOT 0.25-inch material but with & beveled edge so as to make a sharpedged slot with the bevel on the upstream side. The rectangular slot experiments were made only with a slot cut in thin metal. LlOUlO
5 26 3.
,
INDUSTRIAL AND ENGINEERIXG
Vol. 26, No. 5
readings beyond the minimum flow were accepted as being accurate, and the average value of the G A S I N T O WATER difference between the minimum flow and the ob0000 A I R INTO NAPHTHA served zero readings was added to these, the e... AIR INTO WATER data could be plotted to give uniform results. V Figure 3 shows the data obtained when air z2 was passed through the three types of trianguw 1. a .Q lar slots into naphtha. The data plotted are 0.8 volume of gas against the height of the open slot -I *7 in inches. From the development of the formula 0 .6 -I for flow through a triangular notch, this will also ro 5 represent the lost head (in feet) of vapor flowing .4 if it is multiplied by the factor which changes it .3 from inches of liquid to feet of gas. Figure 3 also shows the results obtained by passing air through the various types of trian.2 gular notches into water. These data include runs in which the static head over the top of the notch varied from 0.6 to 2.16 inches. There is 8 r! 4 8 $ G $ slightly more spread in these data than in those CUBIC FEfT P E R S E C O N D obtained with naphtha, because there was an inFIGURE 3. DATAOBTAINED WITH TRIANGULAR SLOTS sufficient number of runs made in some instances to justify applying an average correction facThe experimehs included passing air through the slot into tor to the zero reading in all cases. It should be noted also water and also into a light petroleum fraction (Cleaner’s that there are two sets of points which are given for the flow Naphtha) a t various velocities and with various heights of of hydrogen and of carbon dioxide through the notch. It can liquid above the top b e shown that the of the notch. How2. volume of gases disever, the majority of charged through the the runs were made : orifice a t a given ab-GA5 I N T O WATER on the triangular slot 0 solute pressure will be with 1.5- and 2.1-inch I. in the ratio of the static heat of liquid a -9 square roots of their 0 .8 above the top of the densities. Then with slot. Inthecaseofair h y d r o g e n the flow blowing into water, u) .5 should be two runs are reported density of air .4 with static heads of 1 density of hydrogen and 0.6 inch, respec.3 t i m e s t h e flow for air a t the same abtively. In order to desolute p r e s s u r e and termine the effect of a .2 through the same change of gas on the performance of the size o p e n i n g . This 3 8 ;;3 8.7 ratio was applied to s 1o t , hydrogen and 886884 the runs made with carbon dioxide were CUBIC F E E T PER S E C O N D hydrogen and carbon passed t h r o u g h the WITH RECTANGULAR SLOTS FIGURE4. DATAOBTAINED d i o x i d e to make a trianmlar and the direct c o m p a r i s o n rectaGgular slots. The procedure used for taking the data for these experi- with air possible. The agreement is very good. The data obtained with the rectangular slot include only ments was as follows: three runs, one each with air, hydrogen, and carbon dioxide Gas was admitted to the cap until the liquid level inside reached the top of the slot. The reading on the pressure manometer at this time was taken as the zero reading on the static head above the slot. Additional air was admitted slowly until the first small bubbles appeared. This point was called the “minimum flow point,” and the pressure manometer was read again. Then a series of readings was taken with varying rates of gas flow until the ressure manometer indicated that the notch was wide open. &e same procedure was followed in all runs. I
-AIR
I
.
CHEMISTRY
2
INTO NAPHTHA
I I111111
3 8 8 8 W G
5 ::
8
4
8 8
When the data obtained from these experiments were plotted, discrepancies appeared a t the lower velocities, which caused a rather wide variation in the results. The data obtained while gas was actually flowing were very uniform, and it was observed that the minimum flow readings gave much more uniform results when used as zero readings than the observed zero reading. This is reasonable because the zero reading involved three observations, one of which was the observation of the liquid level and might have caused the inconsistency of the zero readings. It was found that, if the
0 STATIC n r A o UVCL
I I I I I 1 11
GAUGES
@
LIOUID LCVLL UNDCR U P
0
PRESSURE D R W MANQMLTER
FIGURE 5. MODELBUBBLE-CAP APPARATUS
INDUSTRIAL AND ENGINEERING CHEMISTRY
May, 1934
a
J y
c
s z
3
Y
Y
.2
2
2 3 4 5 678910 FLOWMETER R U S I N G
.4 .5.6.7.0.9!.
20
30 4 o W W
FIGURE6. STATICHEAD us. FLOWTHROUGH CAPS MODELCAP
80
FOR THE
flowing through water, These data could not be compared directly within themselves to correct the zero reading, but they agree quite well, especially in the cases of air and carbon dioxide. This is shown in Figure 4. The data obtained for air flowing through a triangular slot into naphtha may be represented by: V8 = (0.51)(0.067)h6/a V , = volume flow through one slot per second h = head of liquid, or opening of the slot, inches C = 0.51 B
a
(0.067) = (144)(6.5) ~
4?
(0.312) (144)(6.5)40-2
527
static head was determined by observing the reading on the inclined manometer, 3, when the liquid levels in gages 2 were even with the tops of the slots in the cap. The formula for flow through bubble-cap slots shows that the pressure drop through the slot opening is independent of the static head over the slots. The values obtained experimentally should have changed according to this formula, were it not for the change in the static head itself. The total pressure drop as measured is made up of static head plus drop through the slots, and any deviation from the value calculated from the formula is due to a change in the static head or liquid level over the tray. Seven runs were made on the model cap, using air and water. The initial head over the slots was determined by reading the inclined manometer when the liquid level, measured by gages 2, was a t the top of the slots. The level of the liquid over the cap (in the channel) was measured on gages 1. The initial static head over the slots was varied from 1 to 2.25 inches during the series of runs. The results of these runs are shown in Figures 6 and 7. I n order to compare and correlate the data, the initial static head over the slots has been subtracted from all of the readings. It has been shown that this should not affect the value of the change in pressure with change in flow through the slots.
64.4
Air, carbon dioxide, and hydrogen flowing through the triangular slot into water may be represented by the equations : Air : V = (0.51)(0.0775)h' Hydrogen : V = (0.51)(0.294)hS Carbon dioxide: V = (0.51) (0.0626)ha Air, carbon dioxide, and hydrogen through a rectangular slot into water may be represented by the equations:
Air: (0.078) =
V =(0.51) (0.078)h'l'
1 (rn 44
d&
= (0.25)(0.00134)
d$-
V = (0.51)(0.292)h7/4 Hydrogen: Carbon dioxide: V = (0.51)(0.0624)h7/'
The results show fair agreement with the anticipated results. It is perhaps a coincidence that exactly the correct power, 5/2, in the case of air bubbling into naphtha was found. For engineering purposes, however, it seems reasonable to assume that this equation is satisfactory for use in designing petroleum columns. If naphtha had been used in the rectangular-slot experiments, results might have been obtained which would correspond more closely with the theoretically anticipated value. EXPERIMENTAL DATAON TOTALPRESSURE DROP
I n order to study a particular practical case, the model bubble cap in Figure 5 was used. It contained fifty-four triangular slots 1.25 inches high by 0.625 inch a t the base, but in 0.25-inch material. The air flowing through the caps was measured with an orifice meter. Pressure drops and liquid levels were measured by level gages and manometers as shown. The manometer, 3, for measuring the drop through the cap was inclined to give readings of 6 to 1 ratio. It was connected to the air-distributing chamber below the cap. The liquid level under the cap was measured with gages shown a t 2. The height of the liquid over the cap was measured in gages a t 1, located at each end of the channel. At the beginning of a run the initial
* VAPOR VOLUME-CZFT. PER SEC.
'
FIGURE 7. OBSERVEDus. CALCULATED VALUES FOR MODELBUBBLECAP An examination of the data showed that there was a small but distinct lowering of the static liquid level in the channel with increased air flow. This decrease in level is plotted in Figure 6 against flowmeter readings (air flow). These data are scattered but it must be remembered that the changes observed were small and that water moving in the level glasses added to the difficulties of obtaining readings. The data are fairly well represented by a straight line on log paper, and the drop in liquid level varies from zero a t no flow to about 0.45 inch a t the maximum flow with slots open the full amount. These results confirm the theoretical considerations that the static head over the top of the slots might actually decrease as the vapor flow through the cap causes a foam to build up over the overflow weir. The effect is undoubtedly influenced greatly by the location of the weir and perhaps by the nature of the liquid and vapor on the tray.
528
INDUSTRIAL AND ENGlNEERING CHEMISTRY
Figure 7 shows the correlation of the data on actual pressure drop and the comparison of the actual opening of the slots with the calculated value. Curve 1 shows the actual pressure drop readings for all runs. The formula for flow through slots, represented by curve 3, Figure 7, gives values different from those of curve 1. It should be observed (curve 1) that no vapor flow took place until the slots were open to about 0.4 to 0.5 inch, and that the pressure remained practically constant from minimum to maximum flow. Curve 2, Figure 7 , represents the actual slot opening determined by adding the change in liquid level (static head) from Figure 6 to the apparent pressure drop (slot opening) shown in curve 1, Figure 7 . Curve 2 agrees fairly well with curve 3 with the exception of the values for lower rates of flow. For these rates, surface tension effects undoubtedly play an important part and seem to have more influence in the wooden experimental cap than they exerted in the case of single slots cut from metal. The lower rates of flow are not particularly important for the present purposes. This investigation has shown that for the rectangular bubble caps, the friction loss through the chimney uptake and space under the cap is negligible and need not be considered when estimating pressure drop. The pressure drop through
Vol. 26, No. 5
the slot opening can be expressed by a formula developed from theoretical considerations, using an orifice constant of 0.51. The static head above the slot tends to be a maximum a t vapor flows near zero, and, in cases where the overflow weir is located near to the bubble caps, the static head may decrease markedly with increased vapor flow. It is believed that the formulas given for tooth opening are accurate enough for engineering purposes, and that similar formulas for slots of other shapes using 0.51 as a coefficient will be found satisfactory. Since only two of the three factors governing the pressure drop are susceptible to calculation, the treatment given here cannot yield anything but maximum values. The data, however, should suggest methods of designing bubble trays having a low pressure drop.
LITERATURE CITED (1) Chillas and Weir, IND. EXG.CHEM.,22, 211 (1930). (2) Robinson, “Elements of Fractional Distillittion,” 2nd ed., p. 109, McGraw-Hill, 1930. (3) Walker, Lewis, and Mcddams, “Principles of Chemical Engineering,” 2nd ed., p. 625, McGraw-Hill, 1927. R E c E I v E D ~ ~ o v e m b 8, e r 1933. Presented before the Division of Petroleum Chemistry a t the 86th Meeting of the American Chemical Society, Chicago, Ill., September 10 t o 15, 1933.
Pa race ls~r s by PETER PAUL
RUBENS
(1577-1640)
Theophrastus Bombast von Hohenheim (14901541), who gave himself the name Paracelms, probably to indicate his superiority over Celsus, was a Swiss by birth. While primarily a medical man, Paracelsus was largely responsible for the departure from the Galenic .plymacopeia in favor of the chemical or “spagyric medicines, being the first to proclaim the doctrine that the life processes are chemical in nature. However, he was not a chemist, and was only slightly interested in “the beggerlie arte of Alcumystrie.” Throughout his entire life Paracelsus was a great student of all branches of natural history, as well as of the Hermetic mysteries, although something of a charlatan. H e lectured a t various universities, having been one of the first (in German and Switzerland) to abandon Latin and to use 6erman for his talks. For his time, he was a prolific writer. The original painting of which our illustration (No, 41 in the series) is a reproduction, is in the Royal Art Gallery in Brussels and must have been painted by the famous Flemish painter, Rubens, not less than sixty years after Paracelsus’ death.
*.*
A complete list of the first thirty-six reproductions in t h e series, together with the details for obtaining photographic copies of the originals, will be found with No. 37 in our issue of January, 1934, page 112. No. 35 was reproduced in our February, 1934, issue, page 207, No. 39 in the March, 1934, issue, page 331, and No. 40 in the April, 1934, iasue, page 419. A n additional reproduction will appear each month. The photographs of these paintings are supplied in black and white only.
