INDUSTRIAL AND ENGINEERING CHEMISTRY
216
FUTURE WORK
The field of low temperature polymerized latex is still in a state of rapid development. iin important problem remaining unsolved stems from the fact that gum tensiles of latices prepared with high-solids formulas are not so high as for latices prepared in low-solids formulas and subsequently concentrated by creaming. I n order to obtain information on this difference, a n investigation of the effect of different water levels and of various modifiers is planned. Another development project in a much more advanced state is a latex in which, by a simple formulation change, coagulation characteristics closely approaching those of natural latex are obtained. Since this latex should have important advantages in applications such as foam sponge, it will be sampled out in the near future. ACKNOWLEDGMENT
The authors wish t o express their appreciation to C. I-.Hawn, R. A. Reynolds, and F. A. hlauger of the Development Department and t o ‘61. C. Keklutin and J. A. Reynolds of the Research Department for their valuable assistance in this project. Thanks are due to Walker-Wallace, Inc., for supplying the model H.E.R.E. Paraflow plate heat exchanger and to G. &I. Irving of that organization for help during the plate heat exchanger evaluation.
Vol. 43, No. 1
Cooperation of the Turbine Equipment Company in piIot plant evaluation of the De Lava1 IMO pump is gratefully acknowledged. The authors wish to thank the Office of Rubber Reserve for permission to publish this paper. LITERATURE CITED
Chittenden, F. D., McCleary, C. D., and Smith, H. S., IND. EXG.CHEM.,40,337 (1945). Debye, P., J . A p p l i e d Phys., 15, 233 (1944). Feldon, M., and Gyenge, J., private communication. Grande, Paul, I b i d . Grande, Paul, and Harrington. E. W., Ibid. Hobson, R. W., and D’Ianni, J. D., IND. ENG.CHEM.,42, 1572 (1950). India Rubber World, 121,No.5, 549 (1950). Ibid., 122, No. 1, 71 (1950). Peaker, C. R. (to United States Rubber Co.), U. 9. Patent 2,393,261 (Jan. 22, 1946). Rubber Age, 65, No. 8, 681 (1949). Smith, H. S.,Werner, H. G., Madigan, J . C . , and Howland, L. H., IND.ENG.CHEM.,41, 1584 (1949). Thitby, G. S., Wellman, N., Floutz, V. W., and Stephens, H. L., IND. ENG.CHEM., 42,445 (1950). RECEIVED June 7 , 1950. Presented before the Division of Rubber Chemistry a t the 117th Meeting of the AXERICAXCHEMICAL SOCIETY, Detroib, hiich. The work reported i n this paper was carried o u t under the sponsorship of and in collaboration with the Office of Rubber Reserve, Reconstruction Finance Corporation.
development
B. J. LERNER’
AND
C. S. GROVE,
JR.
SYRACUSE UNIVERSITY, SYRACUSE, N. Y.
A new
theory of the mechanism of loading and flooding in packed columns, operating with countercurrent liquidgas flow, is advanced. An expression for the linear pore velocity of the gas in wetted packing, V,, is derived in terms of the superficial liquid and gas rates. Visual and pressure drop data for two-phase flow systems show that, for a given liquid-gas pair, there exists a single critical linear gas pore velocity, (F‘Jc, a t which the gas flow becomes discontinuous. The various phenomena attendant on disruption of phase continuity i n countercurrent packed towers are reviewed and analyzed, and previous qualitative observations of entrainment are placed on a quantitative basis. Present evidence indicates t h a t the mechanism of flow interruption is wave formation a t the liquid-gas interface. Application of the pore velocity
expression to loading and flooding data results in accurate correlations of these limiting flow points, and the wave theory presented serves as the basis for complete elucidation of the nature of plots of the pressure drop versus flow. Flooding and loading are redefined in terms of the critical linear pore velocity and the free area distribution within a packing. The lower critical point (load point) is postulated as occurring when ( V J 0is reached at the minimum free cross-sectional area of the packing. Flooding is observed when the gas velocity approaches (F’,)o for the statistical mean of the various free cross-sectional areas of the packing. The general nature of the equations developed is indicated by the fact t h a t they may be used to correlate “hammering” in steam-condensate return lines, as well as data on packed column limiting flow.
I
tions against the data obtained. In the course of the work it waa found necessary to review the entire problem of critical flow phenomena and to arrive a t a plausible, fundamental theory of the mechanism of the transition to flow discontinuity, based on an area of common agreement and observation.
N SPITE of the considerable amount of work that has been
done in recent years on the critical flow conditions existing in packed columns, there still remain certain areas of confusion as to the basic definition of terms, interpretation of data, and the most practical correlation for design work. The initial object of this investigation was to obtain critical data on flow and pressure drop for 1-inch clay rings, 1-inch porcelain saddles, and the new 3/4inch saddles, and to check critical flow criteria and existing correla1 Present address, Department of Chemical Engineering, University of Texas. Austin, Tex.
SURVEY O F PREVIOUS WORK
Preliminary investigation of the literature dealing with the critical conditions of flow in packed towers reveals a marked in-
January 1951
”
.
INDUSTRIAL AND ENG INEERING CHEMISTRY
consistency of terminology and a high degree of semantic confusion. One of the earliest investigators of this problem, Peters (33), defined the transitional condition of countercurrent flow for a liquid-gas system as “the maximum vapor velocity which a given column can withstand without priming.” This definition was later refined by White (33) on the basis of the logarithmic pressure drop-gas velocity curve. With reference to the two breaks in the logarithmic plot, White defined the loading point of a column as “the gas velocity a t which, for a given liquor rate, the logarithmic pressure drop-gas velocity curve first deviates from a slope of approximately two.” The flooding point was defined as ‘‘that velocity a t which the same curve turns abruptly almost vertically upward.” This latter point was said to be accompanied by a marked spraying of the liquid. Sherwood (50) in 1937 used these critical velocities of White’s interchangeably and changed Baker, Chilton, and Vernon’s (4) data on loading velocities to flooding data. This may be readily seen by a comparison of Sherwood’s work with Baker, Chilton, and Vernon’s original data. A further anomaly arises from the fact that, although Baker, Chilton, and Vernon used the term “loading,” they tendered no definition. However, in 1938, Sherwood, working with Shipley and Holloway (SI),used White’s definitions for his own determinations of the loading and flooding points, Although he defined the flooding point as a graphical flood point, the flooding condition was actually taken “by visual observation of the liquid flowing over the packing and down the walls of the tower.” Inasmuch as Sarchet (86) has since reported an appreciable discrepancy between visual and graphical flood points, this would seem t o render Sherwood’s data inconsistent with his own definition, as the visual points were found by Sarchet to be from 15 to 20% above or below the graphical flood points, the magnitude and direction of the deviation being a function of packing size. Sarchet further concluded that the graphical determination of the critical flow velocities was more dependable than visual observation. Although the lower break point, defined by Mach (16) and White (53) as the “loading” velocity, is generally used in industry as the limiting criterion for tower operation, considerably fewer data have been published on loading conditions than are available for flooding velocities. The data that have been published are somewhat contradictory. Elgin and Weiss (8),measuring both holdup and pressure drop, found no abrupt break point, but rather a gradual transition and suggested that the loading point be properly represented as a zone. On the other hand, Piret, Mann, and Wall (34) concluded from their data on a column 2.5 feet in diameter, packed with round gravel stones 1.75 inches in diameter, that a definite break in the holdup occurs at a point corresponding to the pressure drop loading point. Unfortunately, these investigators were not able to extend their data very far beyond the loading point because of the limited capacity of their blower. The basic correlation of flooding velocity used for design purposes in most instances is that of Sherwood, Shipley, and Holloway (SI). While originally accurate only within 40%, the correlation has been improved by further work on packing characteristics (15). Bertetti (6)attempted a semitheoretical correlation of flooding velocity, and Bain and Hougen (3)sought to extend the Sherwood correlation to wider ranges of fluid viscosity and surface tension. Zenz (36)has recently advanced a mechanism and a correlation for the limiting velocities of flow in packings based on an analogy to fluid flow through valves and orifices. Zenz smoothed the normal log-log plots into continuous curves, and by application of basic thermodynamic relationships defined the flood point as the gas velocity corresponding t o a constant “critical pressure drop” above which the log-log pressure drop-gas velocity curves become vertical. The existence of a definite critical velocity for twophase flow through orifices-i.e., a break point in the log-log plot-would obviate the basic premise of this latter theory. All
211
the correlations mentioned above are based entirely on pressure drop observations. A valuable source of fundamental information about critical flow velocities, that has been generally overlooked, is an early series of articles (6, 11, 93) dealing with flooding velocities for two-phase liquid-gas flow in pipes. There has been a good deal of recent activity in this field ( I O , 18, 19), but thus far no attempt has been made to link the phenomenon of limiting flow in packed columns to the two-phase flow work in pipes, other than the analogy between limiting flow curves recently pointed out by Gazley (10). Because these latter papers deal with flow systems that are much simpler than those existing in packed columns, they offer a more basic study of the fluid mechanics involved in transition flow, and provide a qualitative standard for comparison of flow effects involved in critical countercurrent velocities in packed columns. THEORETIGAL BEVELOPiMENT
-4lthough the development of a theory of discontinuity was predicated on the experimental results obtained, it is felt that an inversion of chronological order will facilitate interpretation of the data presented. The one requirement imposed on all correlations tested was that they provide the quantitative relationship between the superficial liquid and gas rates for both loading and flooding conditions (Figure 9). After several unsuccessful attempts at correlation based on the mechanisms of discontinuity suggested by Sarchet (367, Zenz (35), and Bertetti (6),it was concluded that the variables under consideration-Le., the superficial rates of flow based on the empty cross-sectional area of the tower-could not be directly related with the desired degree of accuracy. It was felt that if the superficial rates could be converted to the actual flow rates through the interstices of the packing, then these latter variables would repreeent a better picture of the actual flow aonditions, and would probably be more amenable to correlation. In the case of countercurrent liquid-gas flow in packed columns, qualitative analysis of the problem of converting superficial to actual flow rates leads directly to the general form of the quantitative relationships. If, as a first approximation, i t is assumed that the liquid flows through the packing under a constant head, then any increase in themaas liquid throughput will result in an increase in the cross-sectional area through which the liquid flows, rather than an increase in the linear liquid velocity. It is implicitly assumed that the liquid-packing interaction forces remain constant, and that the velocity of the liquid is simply related to the free fall velocity under the given gravity head. Thus, if the increase in cross-sectional area through which the liquid flows is proportional to the increase in liquid rate, the mass velocity of the liquid phase remains substantially constant. On the other hand, the total flow area for both gas and liquid must remain constant, so t h a t the area pre-empted by the i n c r e m in liquid rate diminishes the area available for gas flow. Thus, the actual mass rate of flow of the gas increases with an increase in liquid rate, although the superficial gas flow rate is unchanged. If now the limiting criterion for continuous gas flow be the velocity of the gas phase, it should be possible to achieve the loading and flooding conditions by an increase in liquid rate alone, at constant gas rate. Evidence that the actual gas flow rate is the limiting variable has been advanced by Furnas and Bellinger (9), Piret, Mann, and Wall @4), and Elgin and Weiss (8), who found that the liquid holdup is independent of the gas rate up to the loading point, at which point i t increases sharply. Furthermore, the fact that Elgin and Weiss were able to obtain flood points with zero gas flow is confirming evidence for the expectation of a point of discontinuity with increasing liquid rate. The above reasoning m a y be placed on a quantitative basis by the use of the data of Jesser and Elgin (12)on the relation between liquid rate and liquid holdup in packed columns. The objective of the analysis will be to derive an expression relating what appears
INDUSTRIAL AND ENGINEERING CHEMISTRY
218
to be the critical variable, the actual gas flow rate, to the superficial liquid and gas rates. Following the definition of Jesser and Elgin, the term “holdup” as used in this paper refers only to the dynamic, or operating holdup, which is that portion of the total holdup which varies with liquid rate. The static holdup, which is independent of liquid rate, is therefore included in the wetdrained fractional voids. Essentially this same procedure waa utilized by Cooper, Christl, and Peery ( 7 ) in their computation of the linear velocities of gas flow in packed columns.
Vol. 43, No. 1
Ga = AoGo/A, Substituting Equation 6 into Equation 7:
(7)
For the purpose of visualization it is advantageous to change from a mass flow rate in pounds per hour per square foot to a pore velocity in feet per second, V,:
v, = 3600p~Fwd[lGo-
Ho/(Ha),nl
For water as the liquid, the data of Jesser and Elgin ( 1 2 )show:
Ho = bLo”
(10)
where b and s are constants for any given packing. Equation 10 in Equation 9 and solving for GO:
E N TT R RAAP I N M E N T ~ ~ ,
Go = 3600Vnp~Fwd[l- bLos/(Ho)mI
MANOMETER
12- INCH SECTIONS
AIR ORIFIGE
CALMING SECTION -SIPHON
i DRAIN
Figure 1. Tower Assembly
Considering now a differential height, from the definition of operating holdup :
Thus far, the actual mechanism of channel closure has not been considered. However, the literature contains considerable material on two-phase flow transition in pipes that is relevant to the problem of the mechanism of closure in packed column channels. Boelter and Kepner ( 6 ) , investigating two-phase flow in horizontal pipes, found that with increasing gas velocity waves are generated on the surface of the liquid. As the gas velocity was further increased, the amplitude of the waves was observed to grow larger, until the amplitude became sufficiently large to cause the gas flow to become discontinuous. Although Boelter and Kepner employed parallel horizontal flow and an oil-air system, the same observations were made by O’Bannon ($3) and Houghten et al. (11) for vertical and inclined countercurrent flow for air and water and steam and water. Recentlv, Martinelli and eo-workers (17,19) and Gazley (10) have published extensive observations of the role of wave formation in channel closuxe.
A L = kHo (1) where A L is the cross-sectional area through Tvhich liquid is flowing, H Ois the dynamic holdup in cubic feet per cubic foot of packing, and k is a proportionality constant. The critical holdup corresponding to the point transition of flow discontinuity a t zero gas rate may be designated as Inasmuch as the critical flow point is marked by a break in the holdup, ( H o ) , is not the holdup t h a t completely occupies the free void space in thepacking, but rather the holdup immediately preceding the attainment of the critical point a t zero gas rate. I n terms of relative velocity, zero gas throughput is obviously not equivalent to zero gas velocity relative t o the falling liquid, but is nevertheless a reproducible reference flow for a given apparatus with a fixed free fall of liquid. Therefore, taking the zero gas throughput condition as the primary reference point, is a constant, and will result in liquid closure of the flow channel. Equation 1 then becomes:
AT = k(Ho)m
8,
+ AL =
li’udA0
(3)
where A , and A L are the gas and liquid flow areas, respectively, Ao is the cross-sectional area of the empty tower, and F % d is the wetdrained fractional voids. Equation 3 may be transposed to the form:
A , = . 4 ~ ( 1- A L / A T )
(4)
Substituting Equations 1 and 2 into 4:
A , = A r i l - Ho/(Ho)ml
(5)
or
A,
=
VANED CONE
(2)
where A T is the total area available for flow, and may also be defined as: AT
(11)
Because ( H o )is~a constant, the superficial liquid and gas rates are now related through the actual pore velocity or, conversely, the pore velocity may be expressed as a function of LOand Go.
I O - INCH SECTION
WATER IN-
Substituting
FudAo[I - H o / ( H ~ ) m l
(6)
By a simple material balance for the gas stream, the relation between the actual and superficial mass gas rates is given by:
Figure 2.
Entrainment Trap
The fact that a minimum gas velocit,y is necessary for inducing and sustaining waves on a liquid surface (25) leads to the conclusion that the limiting velocity of two-phase flow is directly related t o the wave-formation gas velocity. For small channel diameters, of the order of magnitude of twice the gravitational wave amplitude, the limiting two-phase flow gas velocity and the critical velocity of wave formation will be identical. Inasmuch as wave formation is primarily an interfacial phenomenon, the shape of the channel should have little effect on the inception velocity of the waves. For channel diameters larger than the critical minimum (twice the wave amplitude), the initiation of waves due to attainment of the critical gas velocity decreases the area available for gas flow and the velocity in turn increases, SO
January 1951
INDUSTRIAL AND ENGINEERING CHEMISTRY
that an unstable situation results, terminating in channel closure. Therefore, the period between wave initiation and channel closure is necessarily short (10). Within the limits of channel size ordinarily encountered in packed columns, the size and shape of the channel should have only a minor effect on the mechanism of closure, or the critical gas velocity of closure. I n view of the arguments cited, the following postulates about flooding in packed columns in countercurrent two-phase flow may be advanced: The mechanism of flooding in packed columns is wave formation on the liquid surface of sufficient amplitude to close the gas flow channel. Because the gas velocity appears t o be the determining factor, there exists a definite velocity of gas flow a t which waves will close the flow channel. This gas velocity is defined as the velocity of wave closure, ( Vo)c. ”
*
219
by the Maurice A. Knight Co. The packings were loaded into the column by filling it with water and dropping the packing in by hand until a depth of 4 feet was obtained. After wet installation of the packing, the tower w~tsdrained and air was blown through the packing for 2 hours to ensure dryness. The dry runs were made on the packing by blowing air through the dry packing and measuring the pressure drop with the water manometer connected t o the tower piezometer ring located directly below the packing support plate. The leg of the manometer was open to the atmosphere, and because the manometer connected to the top section of the column above the packing showed a negligible pressure differential at maximum air rate, the manometer below the packing indicated the pressure drop directly. For a given setting of the air control valve, readings of the air orifice pressure drop, column pressure drop, air temperature, and barometric pressure were recorded. Column pressure drops of less than 2 inches of water were measured with a n inclined manometer, and those of less than 1 inch were measured with the micromanometer.
It is now postulated that for any given liquid-gas system in countercurrent flow the velocity of wave closure is a constant, dependent primarily on the physical properties of the liquid and gas, and to a minor e x t m t on the size and shape of the channel. On this basis, Equation 11 becomes the correlating equation for limiting flow in packed columns. The data supporting this postulate and the effectiveness of the correlation developed are presented below. , EXPERIMENTAL APPARATUS
M
I
The tower used in this investigation consisted of five 18-inch sections of &inch diameter cast-iron pipe, with Van Stone flanged joints (Figure 1). Because of the unavailability of material a t the time research was initiated, i t was found necessary t o utilize 350-pound high pressure steam flanges in the fabrication of the individual sections. Water was supplied by a large centrifugal pump capable of delivering 20 gallons per minute a t 30 pounds per square inch gage, and was metered by means of a standard orifice manometer which was calibrated by direct weighing. The water was distributed over the packing by a five-legged spray head designed t o give equal annular area distribution. It was found that, in operation, the pump caused some pulsation of water flow and, in order t o eliminate this, two damping orifices were installed in the supply line. This reduced the maximum water rate obtainable in the tower to 13,000 pounds per hour per square foot. T h e liquid rate of flow was controlled by means of a globe valve in the water line. Air was supplied t o the column through a 2-inch elbow welded to the calming section. The air supply was so designed as t o enable the attainment of the superflood zone (8, 2 1 ) . Air was drawn from a compressed air tank, maintained a t 70 pounds per square inch by a compressor delivering 30 cubic feet per minute of free air. The air rate was metered by a sharp-edged orifice designed t o specifications taken from the fluid meters report ( 1 ) . This orifice was calibrated against a standard Pitot tube used in conjunction with a micromanometer reproducible with a precision of 0.05 mm. Tower pressures were measured by means of standard water manometers connected t o each section immediately below the flanges through three-tap piezometer rings. To prevent plugging of the manometer lines a t high liquid rates, manometer shields, tapered 4-inch metal strips, were placed over each manometer tap. Inasmuch as several investigators had called attention t o the fact t h a t the nature of the packing support had a definite effect on the flow characteristics in a packed column, care was taken to design supports which had a greater free area than the packings supported. Flat cast-iron rings were cut with a n inside diameter slightly larger than the inside tower diameter, and coarse wiremesh screen with 0.75- by 0.75 inch openings was soldered to the inside of the ring. The mesh has an effective free area of over 90%, and because the ring to which it was soldered did not project into the tower proper, a minimum cross-sectional area at the support was avoided. A perforated plate, 0.125 inch thick, that had previously heen used as a packing support, was available, and the pressure-drop characteristics of th:s plate were determined separately. EXPERIMENTAL PROCEDURE
The three types of packing t h a t were used in this investigation were 1-inch clay Raschig rings, 1-inch porcelain Berl saddles, and the new a/,inch clay Berl saddles. All packings were donated
The wet runs were made by establishing a definite water velocity, and setting the air control valve for some small air velocity. Readings similar to the dry runs were then taken, after which the air velocity was increased slightly and the readings were repeated. The readings were continued up to the maximum air rate, and the entire procedure was repeated for a new water rate. Because i t was indicated on the basis of the preliminary runs that a critical breakpoint could be approached a t constant gas rate by increasing the liquid rate, runs were made a t constant gas rate and varying liquor rate. The air control valve was set at some definite velocity, and the above procedure was repeated, using the water rate as the variable. Entrainment runs were made simultaneously with the above wet runs; the entrainment was collected and metered by a special trap designed for this purpose (Figure 2). The initial and final readings of the graduate were recorded for a known amount of time after equilibrium flow had been reached. These latter data were all taken in duplicate and the results averaged. DISCUSSION OF R E S U L T S
Flooding on Perforated Plate. The 0.125-inch thick perforated steel plate that was available from a previous investigation had random perforations, which were uniformly 7/3* inch in diameter. There were approximately 326 holes in the area encompassed by the tower wall. This gave a value of 43.2y0 for the plate free space, which was less than the free volume value for any of the packings, so t h a t i t was decided to determine the flooding charac-
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
220 18
16
lZ 2
i
IO
0' 0
#2 - e w
a! 5
6
K
I-
z w
4
e
-
channels, the flood break point waa sharp, and the flood line was very nearly vertioal. For packings with irregular channels and small ratio of tower diameter t o packing size, the flood line tended to deviate at a large angle from the vertical, and the break point becomes less sharp. The vertical break point phenomenon is particularly noticeable in the data of White and Othmer (Sg) on Stedman packing. As with the data obtained with the perforated plate, the loading zone is entirely absent in Stedman mesh packing. I n a qualitative sense, Figure 3 provides the key to the explanation oi the pressure d r o p g a s velocity curves and the nature of the loading and flooding points. It is obvious that if a second perforated plate with slightly larger orifices were to be placed in series with the plate tested, the flooding point for the same liquid rate would occur a t a higher mass gas flow rate for this second plate. I n othei words, there would be a definite velocity interval between flooding on the plate of smaller orifice and flooding on the second plate. It is evident that for a fixed total flow area there will be only one point of discontinuity of gas-continuous flow. Adding the separate pressure drop-velocity curves together, or a series of such curves, one would obtain a preliminary break point, where the minimum free cross-sectional area became flooded , and a second break point where the largest free area became flooded. Considering a packed column to consist of an infinite number of differentially free cross-sectional areas between the limits of minimum and maximum areas available for flow, it then becomes apparent t h a t there nil1 be a zone of flooding bounded by a lower break point, the loading point, and a n upper break point. If the free cross-sectional areas of the packing follow the normal statistical distribution law, neither critical point will be very sharp, and a close air velocity traverse of the loading and upper break point will show them to be narrow zones, as Elgin and 'weiss (8)found them to be. Theoretically, the upper limit t o the flooding zone would be that air velocity necessary t o flood the largest free cross-sectional area of the packing. This limit is characterized by a negative, or clockwise, change of slope on the plot of log-log AP versus Go. Using visual standards, this gas velocity would seldom be reached, because the packing already appears to be flooded. This may be the reason that the superflood point, the true upper limit of the flood zone, has been observed by only two other investigators. I n view of the evidence cited for wave closure, it is more plausible to assume t h a t the graphical flood point corresponds to the attainment of the critical
.
14
n I
2 AP/N:
Figure 4.
3
4
INCHES He0 PER FOOT
Entrainment vs. Pressure Drop
1-inch Raschig rings, Lo
=
6670 Ib./hr./sq.ft.
teristics of the plate alone, using the micromanometer to measure the small pressure drops involved. The data on pressure drop versus superficial gas mass velocity for the plate are plotted in Figure 3. The striking feature of this plot is that the flood zone is marked by a discontinuity of the AP curves. This point waa repeatedly checked by visual observation, and i t was found t h a t the flow conditions changed from preflooding to the superflood zone a t a single reproducible value of gas velocity. By visual observation, i t was also found t h a t a turbulent layer of water appeared on top of the support plate simultaneously with the pressure drop break point. The gas flow a t this point changed from continuous to bubbling. The literature was rechecked for evidence of similar behavior, and it was found that for regularly spaced and uniform packing
Vol. 43, No. 1
January 1951
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
gas velocity at the statistical mean free area of the packing. I n this case, use of the term for fractional voids, F,a, in Equation 11 would apply only to log-log flood points (assuming correspondence to mean area) and not the loading points, since F w d is properly the mean void, and not the minimum. A knowledge of the statistical distribution of free areas would serve to clarify this point completely, and investigation of this property is currently under way. The above discussion may be summed u p in the form of tentative new definitions of the log-log critical flow points: The loading point is that point a t which the critical gas velocity of wave closure is achieved a t the minimum free cross-sectional area of the packing. The flooding point is that point at which the critical gas velocity of wave closure is achieved a t the statistical mean free crosssectional area of the packing.
0
a
*
Entrainment Curves. Although entrainment has received repeated qualitative mention in published work on critical velocities, no attempt has been made t o put these observations on a quantitative basis. The initial series of entrainment investigations were begun in 1942 (1.3)and the results subsequently confirmed (2,27). Figure 4 is a plot of the entrainment in cubic centimeters per minute against the pressure drop for a 2-foot depth of 1-inch Raschig rings with the gas rate as the variable. This plot is typical of all entrainment curves obtained. It was thought a t first that the discontinuous nature of the curve might be caused by the rising of the flooding level above the distributor head, but for the check runs in which the tower was packed over the distributor head, the same characteristic curve was obtained. Visual observation established the fact that, for all packings, the f i s t entrainment peak occurred shortly after a film of water appeared on top of the packing. Visual study of the nature of the entrainment with the trap removed from the tower also revealed that the entrainment consisted of finedrop spray or mist up to the point where the entrainment again begins to increase. This latter break point, corresponding to the ‘Lvalley”on the entrainment plot, was marked by the beginning of large-drop or splash entrainment, intermingled with rapid, intermittent highvelocity puffs of mist. A comparison of the entrainment curves with the corresponding log-log pressure drop-air velocity plots (Figure 5 ) reveals several interesting relationships. The entrainment peak occurs somewhat above the graphical flood point, on the steepest slope of the pressure drop plot. The veiy marked entrainment minimum observed shortly after this point is reached seems to be due to the formation of a water “blanket” on top of the packing, which apparently corresponds to the transition point at which the air changes from the continuous phase to the discontinuous phase a t the top of the packing. The second upward break point on the entrainment plot was found to correspond to the log-log superflood point. The irregularity and instability of the pressure drop in the immediate vicinity of this point and the rapid intermittency of entrainment are apparently indications of the unstable equilibrium between two states of flow. It should be remembered that because of the time interval in whichentrainment was measured, the values of entrainment for this particular transitional flow zone represent an average value; the instantaneous rate of entrainment fluctuated from almost zero to “spurts” of intermingled mist and splash-drop carry-over. Although the lower log-log break, the loading point, does not appear on the entrainment plot, ample evidence exists for the assumption that the point a t which the fine mist entrainment first becomes visually noticeable occurs at approximately the same pressure drop as the graphical load point. This observation has also been made by Elgin and Weiss (8) and others (2.3, &?), However, because of the relative insensitivity of the trap at small values of entrainment, no accurate quantitative verification of this suspected correlation could be obtained in this investigation.
221
The interpretation of the entrainment data in the light of the critical flow mechanism proposed is straightforward. The dne mist entrainment which appears in the vicinity of the loading point is probably due to the attainment of the critical velocity of closure at several areas deep within the packing. Visual evidence advanced by Schoenborn and Dougherty ($8) indicates t h a t the minimum free area generally occurs at the supports because of the orienting effect of the supporting surface on the packing. Thus, there will be a film of water closing the air flow channel at, or near, the bottom of the packing. The resultant spray occurring as the air continually breaks through this film is filtered through the main body of the packing, so that only the fine mist droplets escape. As the air velocity is further increased, the critical velocity of wave closure is reached at the larger free areas, still within the packing, and the amount of mist entrainment is increased. AB was noted above, it is in this region t h a t the graphical flood point occurs, indicating a spread of free areas corresponding to a range of about 200 to 400 pounds per hour per square foot in the maw flow rate for 1-inch Raschig rings, depending on the liauid rate. With still further increase in the gas rate, the maximum free area, which occurs in the neighborhood of the top of the packing, becomes flooded, effectively sealing off the mist entrainment. Agitation of the water layer on top of the packing is relatively gentle at this point, becoming more violent as the air velocity is increased, and as the hydrostatic head of liquid increases. Thie region covers a rather narrow zone of air mass flows and corresponds to the superflood point. The increasing entrainment that is observed as the superflood zone is traversed is due t o splashing of the layer of liquid on top of the packing; larger and larger drops are carried over as the gas velocity increases. This zone of tower operation is characterized by “slugging” flow of the gas (18)and is very similar to the type of flow observed in fluid-solid systems ($0). Superflood Zone. All of the constant liquid rate curves (Figure 5) show the superflood break point. Because air was supplied by the buildin? air compressor, it was possible t o extend the pressure drop readinga to the higher ranges necessary for attainment of this break point. From theoretical considerations, one would expect that under a constant hydrostatic head of liquid, an intermittent flow of air would cause a pressure drop proportional to t h e 1.8 to 2.0 power of the mean gas velocity. Rouse (26) has developed a n expression for the pressure drop in terms of the gas velocity under conditions of rapid expansion and compression, which leads to this relationship. However, an inspection of t h e curves reveals that the superflood lines on a LIP2’s. GOplot have slopes in the range of 0.8 to 1.2, in the region of the break point, Lewis, Gilliland, and %uer (14) present data for the expansion of a column of water under the bubbling conditions of flow encountered in this zone of operation. It wasobserved t h a t the increase in height of the water column varied as the f i s t power of the air rate, which would seem to indicate a firstrpower relationship between pressure drop and gas velocity. Because the liquid in the packing is not, a continuous phase, the total head a t superflood is apparently less than the head of liquid equivalent to the height of the packing. This is indicated by the pressure drop data, since the pressure drop in the superflood zone is between 6 and 8 inches of water per foot of packed height for the 1-inch and 3/4-inch packings. Close to the superflood break point, the rapid flow changes cause a large fluctuation of pressure drop as the gas flow alternates from static to dynamic. However, as the gas rate is increased, the alternation becomes much more rapid and the pressure steadies to an average value. This point is best borne out by the pressure drop data for the perforated plate, since the pressure drop increased smoothly for an increase in the superflood gas rate. A recent application of superflood operation is the new Scofield packing ($99)for distillation purposes. Although there is ample evidence indicating higher transfer efficiencies in the discontinu-
INDUSTRIAL A N D E N G I N E E R I N G C H E M I S T R Y
222
Vol. 43, No. 1
10.0
I.O
8.0
L.0
I .o
0.6
0.3
0.L
0.1,
Figure 6.
Pressure Drop vs. Liquid Rate Curves for Countercurrent Air-Water Flow in Packed Columns
ous two-phase flow zone, the effect of factors such as entrainment, bubble size, and gas velocity is still undetermined. Constant Gas Rate Curves. During the preliminary entrainment runs, it was noticed that the entrainment critical points could be approached through the variation of the liquid rate a t a constant gas rate. It RBS realized that from the fundamental definition of a critical point as a unique set, of values for both liquid and gas rate for which the flow mechanism changes, varying the liquid rate a t constant gas rate would be expected to produce a break point. However, an inspection of the literature showed all pressure drop-liquid rate plots to be smooth curves. The data taken to resolve this contradiction are plotted in Figure 6. These curves were found to he similar in almost all respects to the pressure drop-gas rate plots. I n general, the plots gave a four-segment line with three break points apparently corresponding to the loading, flooding, and superflooding points of the gas rate plots. The break points obtained from the constant gas rate plotE scatter rather badlv, indicating that the critical flow points are extremely sensitive to variations in liquid rate and distribution. I n the light of the three different mechanisms of liquid transfer through packings found by Jesser and Elgin, increasing the Iiquid rate may result in a change in liquid flow mechanism rather than a direct increase in liquid flow area. Moreover, any surge or variation in liquid rate serves to induce wave formation, so that a transient condition results in a permanent shift to channel closure and bubbling flow. For these reasons it map be concluded that the AP-varying liquid rate curves are not very reliable for determination of critical break points. Critical Point Correlation. I n order t o use Equation 11 as a correlating equation for limiting flow velocities, reliable data on the relation between holdup and liquid rate are needed. Holdup data have been presented by Furnas and Bellinger (9) for a few packing materials, and by White and Othmer (34) for Stedman mesh packing, but by far the most comprehensive and definitive work on this subject is t h a t of Jesser and Elgin ( 1 2 ) . The latter authors present their data for water in the form of the empirical equation :
Ho = hLo"
(12)
where h and s are constants that were evaluated for various sizes of rings, saddles, and spheres. Furthermore, the holdup for liquids other than water, HA, was related to the physical properties of the liquid by the equation:
HL =
(13)
Ho~sn.'/pa0~7aasn
where p a , ps, and ua are the relative viscosity, density, and surface tension of the liquid, respectively, and n,the exponent of the relative surface tension, is a function of liquid rate. Thus all the unknown factors in Equation 11 Kith the exception of the critical pore velocity and the critical holdup can now be evaluated. Given any two points on the limiting velocity curve, ( V g ) oand (Ho),may be obtained by substitution of these values in the general form, and the specific correlating equation may be written for the entire curve. As was pointed out above, however, the term wet-drained voids, Fwd, is properly applicable only to the flooding condition. I n the absence of any information on the distribution of free areas within a packing, the critical pore velocity may be evaluated for the flooding condition, and on the assumption t h a t the critical velocity is the same a t loading, the ratio of the mean to minimum areas may be calculated. ,4n equivalent method would be to use the same value of Fcod i n Equation 11 for both loading and flooding correlations, in which case the ratio of the calculated critical velocities would he the same as the area ratio. The correlation method is perhaps best illustrated by an example. Figure 7 is the plot of the loading and flooding data for '/Q-inch Raschig rings. From the data of Jesser and Elgin ( 1 2 ) the holdup for this packing is evaluated as:
Ho = Selecting two points that lie on the best curve through the experimental flooding points, GO = 880 and 680 for liquid rates of 750 and 3000 pounds per hour per square foot, respectively, these values may be substituted into the simplified form of Equation 11:
Go = ~ [- l0.031L0°.631/(Ho)ml and (Ho), and a solved for. Solution of the two simultaneous equations resulting yields a = 1019 and ( H O ) , = , ~ 14,63. [Jesser and Elgin h values are taken a t Lo = 1000; consequently values for Ho are greater than 1.0, and should be divided by (1000)' t o yield holdup in cubic feet per cubic foot of packing.] Treating the loading data similarly, the relation between the liquid and gas rates for the critical velocities can then be stated as: Flooding.
Go = 1019 (1
Loading. Go= 610 (1
-
)
14,59 0.031L00.6a' 0.031Lo~.63') 15.0a
The predicted flooding points fit the experimental data with an
INDUSTRIAL AND ENGINEERING CHEMISTRY
January 1951
FLOODING VELOCITIES:
.
N
G
u. lo3 a I
> m 4
w I-
4
a v)
4
IOf-J 4
k0
0
c
3920 (1 - La O.'/1088)
Go
IO
1 -
T I L L S O N 132)
@ WHITE
LT
0
(34)
$( S A R C H E T 126)
A s.a
0. 128)
CRITICAL LIQUID RATE
IO
lxloe
LB./HR./FT.
lxloa
Figure 7 .
223
Returning to the application of the correlation to limiting velocities in packing materials, it is interesting to examine the data of Sohoenborn and Dougherty (28) for flooding in 1/2-inch Berl saddles for oil-air systems. Because Jesser and Elgin have established the relationship between holdup and the physical properties of the liquid (Equation 13), the correlating equation may be applied to liquids other than water. By inspection of Equation 11, it would seem that if the critical holdup, (H&, varied in the same way with the physical properties of the liquid as did the operating holdup, then the correction terms would cancel, and the equation would be the same as for water. However, in the absence of any data on the variation of (H& with liquid physical properties, this assumption was deemed unwarranted, and the data were treated in the same way that the waterair data were, correcting the operating holdup in accordance with Equation 13 and evaluating (Ho), as a constant. The calculated results are tabulated in Table I ; on the basis of the limited data available, it appears that no simple relationship exists between the critical velocity and the physical variables of the liquid. Wave inception velocities are known to be functions of the Weber and Froude numbers; and it is likely that with more adequate data, the correlations presented can be generalized to all cases of flow discontinuity in two-phase flow.
IX I 0 4
Critical Flow Velocities
TABLE I. FLOODING IN 1
l/z-inch Raschig rings
average deviation of 5.5%, and if the two points that lie far off the curve are eliminated, the average deviation is less than 3%. It should be remembered that the over-all function for holdup in terms of liquid rate was used-Le., 0.631-whereas Jesser and Elgin recommend three different values for this packing, depending on the mechanism of liquid transfer through the column. In view of this approximation, the agreement may be considered excellent.
SADDLES
/ 2 - 1 BERL ~ ~ ~
[Data of Schoenborn and Dougherty (88)1 Specific Critical Specific Specific , Surface Velocity, Equation Density Viscosity Tension Feet/Sec.
-
HzO
G'b
10 C oil
G'o
1428(1
-
B100oil
Go = 1045(1
-
= 1268(1
-
A)
1
1
6.72
Sz)
12.98
0.489
7.76
3)
35.1
0.517
5.66
1
0.889
0.900
From the flooding correlation equation for the l/rinch Raschig rings, the critical pore velocity was calculated as 6.08 feet per second, using a mean Fwd = 0.61, based on the various reported values. The ratio of the minimum to mean free area was calculated as 62.0%, by the method outlined above, correcting for the value of 0.586 for the wet-drained voids as determined by Tillson (32) in his load point determinations. This variation, while of a reasonable order of magnitude, is nevertheless appreciable, and should be subject to experimental determination.
c
Before proceeding with further correlation of critical flow in packings, the general nature of the equation developed may be demonstrated by its application to the two-phase horizontal flow data of O'Bannon (22) for air and water in a 1-inch pipe. I n order to use the equation for this case, it is necessary to know how the holdup, or film thickness, varies with the water rate. Direct data for this are not available, but a ood approximation may be made by use of the data of Jesser a n t Elgin. The assumption is made that the holdup in the pipe varies with the liquid rate in the same manner as it does in packing-that is, the exponential value of liquid rate is taken as 0.6 for this case, the average of the exponential value for the packing materials. On substitution of the two extremes of the experimental data, the term H' = bLoa/ ( H o )can ~ be evaluated and thecritical velocity of wave closure calculated for each point. For a range of liquid rates of 3430 to 82,300 pounds per hour per square foot, the mean value of the critical linear velocity was calculated as 14.50 feet per second, with an average deviation from the mean of only 2.95%, an exceedingly small variation in view of the range of liquid rates. The range of superficial air rates was 1to 4.5 cubic feet per minute, corresponding to the 24fold variation in liquid rates.
For the purpose of qualitative comparison, O'Bannon's data for countercurrent pipe flow are plotted in Figure 8; the striking similarity to the critical flow plot for packing materials is readily seen. The correlating equation for the limiting horizontal flow velocities for the 1-inch pipe data may be written as:
LIQUID RATE, LBS./HA.
Figure 8.
Limiting Countercurrent Air-Water Flow Velocities 1-inch horiaontal pipe Data of O'Bannon (22)
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
224
Figure 9.
Vol. 43, No. 1
Correlation of Limiting Flow Velocities Water-air coiintercurrent flow
The correlating equation has been applied to data on and 1-inch Raschig rings and Berl saddle@,for both loading and flooding conditions, and the resulting equations are summarized in Table I1 and Figure 9. The critical pore velocities a t flooding are listed, and the corresponding predicted ratios of mean to minimum free areas in the packings are stated. No reliable flooding data we available for the 1-inch Berl saddles; the data scatter too badly to permit correlation. Not all reported data have been plotted. Because of the confusion that exists as to whether a given break point is a load or flood point, especially where visual standards are used, some selection must be made. In general, if the data of several investigators for a particular packing fell on two widely separated curves, and uncertainty existed as to the critical velocity criterion employed, th2 upper set was taken as the flooding line and the lower one as the loading curve. Because methods of packing and free void values vary, critical flow plots for packed columns should be reduced to a single “reference” value of voids. While this procedure has been followed in the evaluation of the correlations, it is limited to those cases where experimental free void data have been reported. The agreement in the ratio of the minimum to mean free areas for the and 1-inch Raschig rings is an additional point of support of the basic theory of a constant velocity of discontinuity. Because area distribution in packing is a function of shape only, the ratio of minimum to mean free area should remain unchanged with change in packing size.
Application of Correlations. The advantage of the equations presented over the usual Sherwood correlation (Sf)is that if either the gas or liquid late is known, the limiting flow rate for that condition can be immediately solved for. Sherwood’s correlation requires either a known value of GOor a known ratio of Loto Go. It is apparent that in its present form the correlation presented here requires evaluation of constants for each new packing or flow system. However, only t w o points on the desired limiting flow rurve need be known in order to determine the equation for the entire curve. Because of the inherent uncertainty in the present methods for determining critical points, particularly the flood point, a certain amount of caution should be exercised in the uae of the equations. In most cases, the loading correlation will be more reliable, inasmuch as the load point marks the initial departure from continuous flow and can be referred to a single area value, Inasmuch as the correlations apparently justify the mechanism from which they were derived, it is believed that by a direct attack on the basic flow phenomena involved, the relationships here developed may be generalized to a single correlating equation. NOMENCLATURE
A,
free cross-sectional area available for gas flow, square feet A L = free cross-sectional area available for liquid flow, square feet A0 = cross-sectional area of empty tower, square feet AT = total free cross-sectional area available for flow, square feet F w d = vet-drained fractional voids G, = actual gas mass velocity in pore TABLE 11. LIMITINGFLOW CORRELATIONS space, pounds per hour per square foot Paoking, (Ve)c, Min. Size Loading Flooding Feet/Sec. Mean’ % ’ Go = superficial gas mass v e l o c i t y , based on empty tower, pounds I/pinch B.S. Go = 915(1 Go = 1268(1 79.5 per hour per square foot H , = operating or dynamic holdup of B.S. Go = 1360( 1 - L0%k02’) ........ (6.40)“ .. liquid, cubic feet per cubic 8.32 foot Qo = 610(1 - 0 . 0 3 1 L a ~ ~ 3 ’ Go = 1019(1 - 0.031L 0 1 3 1 6.08 62.0 I/n-inohR.R. (Ho),= critical dynamic holdup caus15.03 ing flooding a t zero gas veloc62.5 1-inch R.R. B = 1010( 1 - o--’ o ~ ~ ~ 6 s 00 ’ ) = 1620( 1 - 0 . 0 2 5 ~ ~ 0 4 3 1 8 . 4 8 ity, cubic feet per rubic foot H‘ = bL’,,/(Ho), = fractional free flow space occupied by liquid 1-inch pipe ...... 00 = 3920(1 14.50 .. (horir.) Lo = superficial liquid mass rate, based 5 Based on loading. on empty tower, pounds per hour per square foot
~~~~~~~~~~~
-&) I .
T~+) T) ~
2;;)
=
January 1951
INDUSTRIAL AND ENGINEERING CHEMISTRY
h p / A T = pressure drop per foot of packed height, inches of water per foot V , = linear pore velocity of gas, feet per second b, s, k , n = constants pa = relative viscosity p s = relative density U, = relative surface tension ACKNOWLEDGMENT
The authors are indebted to Donald W. Deed for his helpful suggestions, and for his initiation of the entrainment studies a t the Cooper Union School of Technology. LITERATURE CITED
i*
i
(1) Am. Soc. Mech. Engrs., New York, “Fluid Meters Report,” 4th ed., 1937. (2) Bacaewski, Z., undergraduate thesis in chemical engineering, Cooper Union, 1943. (3) . . Bain. W. A.. and Hougen, 0. A,, Trans. Am. Znst. Chem. Engrs., 40,29 (1944). (4)Baker, T., Chilton, T. H., and Vernon, H. C., Ibid., 31, 296 f 1935). (5) Reiietti,’J. W., Ibid., 38,1023 (1942). (6) Boelter, L. M.K., and Kepner, R. H., IND.ENG.CHEM.,31, 426 (1939). (7) Cooper, C. M.,Christl, R. J., and Peery, L. C., Trans. Am. Inst. Chem. Ezlgrs., 37,979 (1941). ( 8 ) Elgin, J. C., and Weiss, F. B., IND. ENG.CHEM.,31,435 (1939). (9) Furnas, C.C.,and Bellinger, F., Trans. Am. Znst. Chem. Engrs., 34,251 (1938). (10) Gazley, C . , Jr., Ph.D. thesis in chemical engineering, University of Delaware, 1949. (11) Houghten, F. C., Ebin, L., and Lincoln, R. L., J. Am. SOC.Heating Ventilating Engrs., 30,139 (1924). (12)Jesser, B. W., and Elgin, J. C., Trans. Am. Inst. Chem. Engrs., 39,277 (1943). (13) Lerner, B. J., undergraduate thesis in chemical engineering, Cooper Union, 1943. (14)Lewis, W. K., Gilliland, E. R., and Batter, W. C., IND.ENG. CHEM.,41,1104 (1949).
225
(15) Lobo, W.E., Friend, L., Hasmall, F., and Zenz, F., Trans. Am. Inst. Chem. Engrs., 693 (1945). (16) Mach, E., Forsch. Gebiete Ingenieurw., 6,Forschungsheft, No. 37, 59 (1935). (17) Martinelli, R. C., Boelter, L. M. K., Taylor, T. M., Thomsen, E. G., and Morrin, E. H., Trans. Am. Soc. Mech. Engrs., 66,139 (1944). (18) Martinelli, R. C.,and Nelson, D. B., Ibid., 70,695 (1948). (19) Martinelli, R. C., Putnam, J. A., and Lockhart, R. W., Trams. Am. Inst. Chem. Engrs., 42,681 (1940). (20) Matheson, G . L.,Herbst, W. A,, and Holt, P. H., IND.ENG. CHEM.,41,1099 (1949). (21) Molstad, M. C.,Abbey, R. G., Thompson, A. R., and McKinney, J. F.,Trans. Am. Inst. Chem. Engrs., 38,387(1942). (22) O’Bannon, L. S., J . Am. SOC.Heating Ventilating Engrs., 30, 157 (1924). ENR.CHEM.,14,476 (1922). (23) Peters, W. A., IND. (24) Piret, E. L.,Mann, C. A., and Wall, T., Ibid., 32,861 (1940). (25) Rouse, H.,“Elementary Mechanics of Fluids,” pp. 322-40,New York, John Wiley & Sons, 1946. (26) Sarchet, B.R., Trans. Am. Inst. Chem E w s . , 38,283 (1942). (27) Schlaifer, S., undergraduate thesis in chemical engineering, Cooper Union, 1944. (28) S,choenborn, E. M.,and Dougherty, W. C., Trans. Am. Inst. Chem. Engrs., 40,51 (1944). (29) Scofield, R. C., paper presented at 42nd Annual Meeting, Am. Inst. Chem. Engrs., Pittsburgh, Pa.,Dec. 4,1949. (30)Sherwood, T. K.,“Absorption and Extraction,” pp. 138-55, New York, McGraw-Hill Book Co., 1937. (31) Sherwood, T.K., Shipley, G. H., and Holloway, F. A. K., IND. ENG.CHEM.,30,765 (1938). (32)Tillson, P.,S.M. thesis in chemical engineering, Massachusetts Institute of Technology, 1939. (33) White, A. M., Trans. Am. Inst. Chem. Engrs., 31,390 (1934-35). and Othmer, D. F., Zbid., 38,1067 (1942). (34) White, R. E., (35) Zena, F. A.,Ibid., 43,415 (1947). RECEIVED January 7, 1950. Presented before the Division of Industrial and Engineering Chemistry a t the 117th Meeting of the AMERICAN CHEMICAL SOCIETY, Houston, Tex. Abstract of P a r t I of a dissertation submitted b y B. J. Lerner in partial fulfillment of the requirements for the degree of doctor of philosophy at Syraouse University.
Velocities and Effective Thermal Conductivities in Packed Beds MAXIM0 MORALES, C. W. SPINN,
AND
Engfinnedering B O W S
development
J. M. SMITH
PURDUE UNIVERSITY, LAFAYETTE, IND.
r
Fluid velocities in packed beds are of primary importance in determining heat transfer and mass transfer rates. Because no data were available on the variation of these velocities with radial position, this information was obtained in a bed 2 inches in inside diameter, packed with 1/p, I/d-, and a/e-inch cyIindrica1 pellets and through which air was passed. The results indicated that, at bed depths
above 2 inches, the velocity decreased both near the tube wall and near the center, giving a maximum value at a point between the center of the tube and the wall. These conclusions, which are not in agreement with the widespread assumption that the velocity profile in packed beds is uniform, explain some problems encountered in heat and mass transfer in packed beds in this laboratory.
T
solution of the differential equations relating temperature, conversion, and position in the catalyst bed. The effective thermal conductivity has been determined experimentally by measuring temperatures in a packed bed in which no reaction takes place-that is, by passing an inert gas such as air through the catalyst bed. Under such conditions the equation relating the temperature and position in the bed takes the form
HE temperature in every part of the catalyst bed in gas-solid
catalytic reactors must be predictable if reliable design methods are to be developed for estimating the conversion. In nonadiabatic reactors the situation is particularly difficult because of radial temperature variations. It is customary to approach the problem of radial temperature gradients by introducing the concept of the effective thermal conductivity as a measure of the radial heat transfer rate in the packed bed. A knowledge of this conductivity along with certain simplifying assumptions permits
