FLUID MECHANICS IN CHEMICAL ENGINEERING
I
LEON LAPIDUS' Esso Research and Engineering Co., Linden, N. J.
Flow Distribution and Di usion in Fixed-Bed Two-Phase Reactors Column-packing performance under actual high temperature and pressure operation is important in hydrogenation and hydrodesulfurization of heavy petroleum feed stocks. Here is a w a y for characterizing the internal pore structure.
THE
"
present study was initiated to investigate distribution and liquid-catalyst contacting in two-phase cocurrent flow through packed beds. This type of operation has pertinent importance in many commercial processes, such as hydrogenation and hydrodesulfurization of heavy petroleum feed stocks. Numerous other catalytic processes with the same physical arrangement are currently under investigation and will undoubtedly soon become important in the petroleum industry. However, few actual data are available defining the contacting or flow distribution in this cocurrent process. In general, catalytic reactions require a uniform velocity distribution to achieve maximum reactor efficiency. Deviation from such a distribution results in decreased conversion and hence reduced reactor efficiencies (5). A time-of-contact or resistance-time technique was used to define the fluid flow behavior; basically the procedwe was a simple one. To the floiving phase under consideration was added, in some predetermined manner, a tracer material which lends itself to chemical or physical analysis. The manner of addition may be any one of many, but a step function in tracer concentration or a pulse of tracer lends itself best to analysis of the data. The effluent from the bottom of the bed was monitored for the tracer material and the resulting data on effluent tracer concentration us. time were taken as representative of the flow behavior of the fluid through the bed. These data are referred to as time-ofcontact or residence-time curves. The use of the residence-time curves to evaluate flow distribution is based upon recent publications of Gilliland (5) and Danckwerts (3, 4). Their Consultant, Department of Chemical Engineering, Princeton University, Princeton, N. J.
work delineated and defined the technique but was mainly applied to fluid bed problems. Kramers and Alberda (8) have discussed the utility of the different inputs. Experimental data were obtained for a Raschig ring tower using a sinusoidal tracer input. Sherwood (72) has also reviewed some of the implications of the method. The literature is replete with information on countercurrent flow distribution of two fluids through a packed column. Among the most significant are the work of Baker, Chilton, and Vernon (7) and Uchida and Fujita (74). Leva ( 9 ) summarizes the available data. Fluid holdup measurements are available, the work of Jesser and Elgin ( 6 ) and Shulman, Ulrich, and Wells (73) being the most representative and detailed in the field. However, in all this work the relationship among holdup, the quantity of fluid actually held in the column at any time, and flow distribution has not been considered. When holdup was measured, it was tacitly assumed that the flow approximated plug-flow conditions. No data are available for cocurrent flow of the two phases. Residence-time studies are reported in the present investigation for the system air-water and air-hydrocarbon flowing cocurrently downward in a packed column 2 inches in diameter. These data, as well as other previously unreported step-function input data for columns ranging in diameter from 3/4 inch to 6 feet, all indicate a close approach to plug flow for the liquid phase. Pulse-type inputs produce an adequate representation to the actual flow profile for porous or nonporous packing. By contrast, step-function inputs produce greatly distorted residence-time curves if porous packing is used. This distortion is a consequence of mass transfer of the tracer from within the packing.
1000 INDUSTRIAL AND ENGINEERING CHEMISTRY
By suitable manipulation, however, these latter curves can be transformed to indicate the true flow distribution and to characterize the rate of mass transfer. In addition to measuring the residencetime distribution, information was obtained relative to catalyst-liquid contact--namely, the extent to which all of the catalyst was covered with a moving liquid film. Catalyst-liquid contacting should be differentiated from flow distribution, as a liquid may have a uniform velocity through the bed but because of channeling may come in contact with only a part of the catalyst. The data, although not too clear on this point, indicate that only a fraction of the catalyst is wetted by the flowing liquid. Consideration is given to the possibility of employing a residence-time curve with a step input to evaluate an effective diffusivity representing mass transfer into and out of porous packing. The technique exhibits promise for use under experimental conditions approximating actual reactor operation.
Apparatus and Procedure The packed column was of borosilicate glass, 2 inches in diameter and packed to a height of 36 inches. The packing was supported by a perforated brass plate with a symmetric free area of approximately 40%. The liquid distributor was a flat spray head which covered almost the entire diameter of the column. Approximately 100 holes drilled in the bottom of the distributor served to impinge the liquid in the form of fine streams on the top of the packing. Water and air were taken directly from the laboratory lines, metered through flowmeters, and fed to the top of the column. The water was also passed through a mixed-bed ion ex-
change column before delivery to the distributor, to remove all traces of foreign cations. The hydrocarbon solutions were fed through a centrifugal pump drawing from the large storage reservoir. Below the packed section a small volume was provided to serve as a gasliquid separator. The gas was vented from this open volume through a 0.50inch tube, while the liquid was withdrawn directly from the bottom. The liquid, as it dropped past the disengaging volume, p.assed through a restricted opening. This restriction was used as the sampling point. Two types of packing material were used: spherical glass beads, 3.5 mm. in diameter, and l/s-inch cobalt molybdate-activated catalyst cylinders. Input Techniques and Tracers. The gas phase tracer was helium, which was monitored through appropriate flowmeters to produce an approximately 1% mixture of helium and air. A small vacuum capillary probe was placed in the outlet gas stream at the bottom of the column and a sample was continuously removed and sent to a mass spectrometer. The mass spectrometer measured the helium content and the output voltage was recorded on a high speed recorder. T o ensure a very sharp step function, an electrical, rather than mechanical-type, valve was employed to stop the helium flow instantly. Three different tracers were used for the water phase experiments-reagent grade magnesium sulfate, potassium chloride, and hydrochloric acid. Concentrated solutions of each were made up such that continuous addition of the solution to the water stream produced a mixed composition of 0.01N or lower. The volume of solute solution added was always less than 2y0 of the water stream volume. Samples of the effluent solution from the bottom of the column were collected in glass vials and analyzed by means of a Sargent Oscillometer. This instrument measures the dielectric strength of a solution which can be converted to electrolyte concentration. For a step-function input the solute solution was fed continuously into the water stream from a pressure reservoir with a quick-closing mechanical valve to cut the solute solution off. A hypodermic needle was used to inject tracer solution when a pulse input was desired. In the hydrocarbon systems, n-heptane and benzene were used in conjunction as either solvent or solute. The procedure was essentially identical to that for the aqueous tests, except that a solution of solvent and solute was made up previous to a run and circulated through the column. At the desired time this solution was cut off and replaced with a stream of fresh solvent. Analysis of the effluent was by refractive index.
The column proper was placed upon a beam balance which could detect 0.20-ounce changes in weight. As the dry weight of the column and packing was known, this balance allowed calculation, during operation, of the actual amount of fluid within the column. The dry weight of the column and packing was determined with air flowing through the column. After the dry weight of the column was obtained, the packing was removed and the column was packed for operation by allowing the pellets to settle through the liquid-filled column. I n calculating the weight of liquid holdup, no correction was applied for the increased pressure drop of the gas phase due to the presence of the liquid. I n all cases a t least 1 hour of solvent or solution flow was employed before a run actually started. This time interval was used to ensure uniform conditions throughout the packed section. Previous data taken in this laboratory have shown that after this time period of bed saturation the residence-time curves did not change, even when the column was operated for as long as 5 hours.
Methods of Calculation Step-Function Input. For a stepfunction input, an analysis of the effluent fluid will yield a plot of c, concentration of tracer in the effluent, us. t, time measured from the moment of discontinuing the tracer flow. This curve can have any of a number of different forms, as seen in Figure 1. In all the present experimental work the step function was obtained by saturating the bed with tracer until the effluent reached a constant composition. The tracer was then cut off. A represents the theoretical process of plug flow in which the exit concentration of tracer remains at c,, the initial concentration, until a volume of fluid equal to the fluid holdup has passed through the fixed bed and then immediately
MECHANICAL-
ELECTRICAL
t
SOLVENT IN
PACKED BE0
I
AiR IN
PERFORATED SUPPORT
+
SOLUTION OUT
Packed column and accessory equipment drops to zero concentration. This type of flow can never occur in practice because of viscous effects and molecular or eddy diffusion, but it can be used conveniently as a frame of reference against which all actual flow patterns can be compared. B represents the case of excessive back-mixing, commonly referred to as perfect mixing. The concentration of tracer from the bed is always equal to the uniform concentration throughout the bed. As with plug flow, this perfect mixing case must be a hypothetical one. Excessive back-mixing in a packed bed seems improbable. C represents an intermediate case. Some of the tracer spends less and some spends more than the average time in the bed. No matter what the shape of the resulting curve, the following material balance relation must hoId :
where
N
= holdup of fluid in the bed,
volume units
t-TIME
Figure 1.
Different possible experimental time-of-contact curves VOL. 49, NO. 6
JUNE 1957
1OOT
by Danckwerts ( 4 ) ; only basic details are given here. The d u e n t curve will have the form of a distorted pulse in which the tricer effluent concentration, c, varies with the time, t. From these data a further plot of cf or. I can be made. In tern of these two plots: CIdi
=-
JDcdl
--
JDcdi
figure 2. txpenmsntai 'magnesium sulfate time-af-+act curve, nonparm packing
F
. . . .
4
tb
,
,*.
-
volumetric flow rate of main
fluid phase
The integral can be evaluated by graphical integration of a c/c. m. t curve, and called 8, the mean residence time. 8 is equal to the time at which the concentration for a plug-flow procau drops from c. to zero. A more concise methcd of plotfing the data is c/c. ur. t/8. This dimepsionleas type plot is &led a resideace-me or time-of-contact curve, where i/8 indicates the number of holdup volumes that have passed through the packed bed in time 1. The fluent tracer curve can thus be used to calculate the holdup of fluid in the bed as well as to indicate the type of grcmn flow profile through the bed. Pnhe Function Input. If a quantity of tracer can be i n t m d u d into the en* stream (no other tracer being preacnt in the system) virtually instantaneously or within a time pviod much d e r than 8, then theoretically the d u e n t concentration can be u d to obtain the same information as with a stepfunction input. The method of convdng the pulse 4 u e n t curve into the form exhibited by the stepfunction e. fluent ha# b&n discussed rn detail
.."
rdi
AU the integrals may be evaluated graphically. The pulse-input data can 'thus be converted to a residence-time curve in the form c/c. ur. i/8 and compared directly with the stepfunction nwea. ResuIIs and Discussion
Liquid Phase &ntacting with Nonporous Packing. Residence-time data obtained in a bed packed'with solid glass beads represent a condition whereh the internal porosity of the packing is zero. Thedore, these data represent the flow disaibution through the column. Figure 2 is a semilog plot of a typical experimental run using a stepfunction input of magnesium sulfate t r a m . Also shown are theoretical C U N representing ~ the distribution through a plug flow and a completely mixed reactor, Gilliland, Mason, and Oliver (5) have shown that the dope of a time-of-contact curve may be taken as indicative of the spread in velocity distribution and can be quantitatively related to the conversion of a iirst-order chemical reaction. Actually the present time-of-contact curves are due not only to a spread in the-velocity distribution but also to a possible diffusion from stagnant pools of liquid at the contact points of the pellets. This latter phenomenon has been discussed in detail by Jcaser and Elgin (6) and Shulman and workers (73). Howeva, as the effluent tracer concentration drops to approximately aero within 30 seconds in the present experiments, the contribution of this stagnant pool diffusion is pmbably smalL Referring to Figure 2, the s l o p of the curyea for piston flow, completely mixed reactor, and the experimental data are, reapectively, - .=, -1.0, and -4.0. A midenwtime curve with a slope of -4.0 represents a close approach to plug flow. To illustrate this, calculationswcn made for a first-order chemical reaction with a flow distribution characarjzed by a slope of -4.0. These d t s are shown in Table I, where the ratio of -tor volume for actual flow
igure
3. Experimental time-of-can-
rad arvos for a variety of operating conditions, nonporous packing
to that required for plug flow is given for various levels of conversion. The & a t of this deviation from plug &w becomes important only at conversion levels of 95% or -tu. This distributiod is characteristic of what was o b mined in a single teat conducted in a commercial-sized unit. In all the data collected no significant deviation from a slope of -4.0 was noted. This included the use of different solvents (water and n-heptane), diKerent tracer materials and tracer inputs, and changes in liquid flow rate from approximately 1564 to 4000 pounds pa hour-sq. foot. Figure 3 is a plot of six experimental runs for a variety of conditions; the uniformity may be noted. The flow distribution through the bed of nonporous packing thus approximates plug flow. The experimental holdups as ealculated from the liquid phase mtacting data using glass beads as packing arc summarized in Table 11, which also gives the holdups obtained by weighing the column during its operation. No signific'ant &ect of the t r a m or the type of input used can be OW. The h y h r b o n y t e m leads to lowe6 holdups than the aqueous system. The liquid holdup increases exponentially with i n d flow rate, as TCported by other experimenters (6,73) for countercurrent flow. For the three water flow r a m , the holdups have been averaged irrespective of the type Of t r a m or the type of input. Cont.Ftiog Averup
WaterFiOw Rata, Lb./Hr.-
sp. Ft. 1600 27-
3wo
Holdup. cu. Ft./ Cu. Ft. Tower Volume 0.10112 0.119 0.121
Weight of EOUUR.
cu.Ft./ CU. Ft
T m
Volum 0,107.
0.115 0.127
The contact holdups deviate by approximately 3% from the weighed holdups. However, within the con-
tacting dues, differences of as much as 10% have been averagad. If the liquid holdups truly represent the total quantity of liquid held up in the bed, then the sum of the gas phase holdup plus the liquid phase holdup should equal the void fraction-of the packed bed. T o teat the validity of this point, a number of gas p k reaidenretime curves w a x evaluated using heliun as tracer (Table 111). The sum of the mmbined holdups is larger than the total void volume of 0420 cubic foot per cubic foot of tower volume as m e d by water displacement. The difference is, however, due to high valucs for the gas holdup, as there are, qbove and below the packed saction, open volumu which must be subtracted from the measured gas contacting volume. Small errors in meagurement of these two volumcs may be significant to the final answer. This problem d d become wy troublesome q the experimental equipment increases to commercial sue. A uniform flow distribution docs not ensure complete liquid-solids contaot. It is possible that a plug flow distribution could be obrained with only a fraction d the packing in contact with the liquid. For example, the liquid may move in preferred channels through the bed and bypass a large fraction of the bed. Because the aqueous and the h y d m a r b n systems all pmduee aurmdally identical timemfautact cwvw with, howcver, a wide range of holdup8 between them, this p d d channel flow would seem to be indicated. Liquid Phase Contpcting with Poroua Packing. Consideration is given h a c to t i m d - m n t a c t curves obtained using the 2-inch diameter column packed with p o r n 1 / ~X 118 inch cobalt molybdate catalvst nrlinders. me tirie-ofimntact c w c s for porous packing were found to be a function of example, pulse the paeu input-for of step function. Included in F i 4 is the NIye for nonporous packing under identical flow conditions. The p u k function pmdnces a curve whose slope and holdup is close to the gkss bead data, whereas the stepfunction curve has a comparatively low slope and a vuy krge holdup. This difference is due to maaa &er out of the porous packing. At the start of a pulse input run, the widn of the bed are & from tracer; as the pulse moved quickly down the bed, there is time for only a small amount of tracer to diffuse into the packing and later to diffuse back out The pulse input thus reports the flow distribution thmugh the intervoids of the bed with a possible tailing 9f the curve at low values of the d u e n t tracer concentration. By contrast, a t the #tart .of a step input all of the fluid inside
stant composition, c;. as the subsequent tracer-& solution moves down the bed, it displaces tracer h m between particles and also sets up a condition very favorable to diffusion out of the padring pore ~QucNre. As a ~ 1 1 8 6 quence, the step-input curve exhibits cxccssivc t a i h g . The area under this latter curve will represent the total liquid holdup, both inter- and intra-, in the bed. These c o d e r a t i o n s are very important, as they indicate that a pulse input should be used in mmmrrcial size units to characterize the flow distrihtion. The step-input rnare also a function of rate of bulk liquid flow. Figure 5 shows the t i m w f a n t a c t curvea under identical conditions, except for liquid flow rate. At low liquid rates the tracer has time to dEuse out into the moving fluid and h m a concentration which is high enough to be detected by the analytical measurements at the output of the column. At hi& flow r a t a mass
~
&e low concentrations which &t. ks a comequence, the step c u m will tend to approach the pulse c u m at high flow rates. The data in Figure 5 substantiate this point.
ing are sum&ked in T a c k IV. The step-input holdups are the largest and repremnt, as compared to the valuea obtained by weighing the column, an approach toward the total inter- (between packing) and intra- (within packing) void holdup of the bed. The pulse-input holdups are lower but are still larger than those for nonporous 1.0,
"
0
7
Figure 4. Comparilon of magnesium sulfate fime-of-contod cuwos, porous and nonporour packing VOL W, NO. 6
JUNE 1957
1003
Table IV.
Holdup Data for 2-inch-Diameter Packed Column
( 1/8-inch cylindrical porous pellets, 38 Ib./hr.-sq. ft. air flow, cocurrent downflow of air-
liquid)
Weight Contact Holdup Holdup, Cu. ft./cu. ft. Cu.Ft./Cu.Ft. See. tower vol. Tower Vol. 55.2 0.294 0.286) 46.4 0.248 o*286\ 35.7 0.191 28.2 0.214 0.309) 19.4 0.142 0.309 29.2 0.156 0.286 32.3 0.164 40.0 0.165 0.279 0.2861 52.3 55.2 0.295 0.286 37.9 0.288 0.3091 30.4 0.231 0.309 39.4 0.210 0.286) 74.7 0.232 0.254)
Liquid Flow, Lb./Hr.Sq. Ft. 2750 2750 2750 3900' 3900 2750 2370b 2950b 2750 2750 3900 3900 2750 1600
Z .
...
... ...
3210b 33.9 38.6 27206 2610b 47.6 47.5 2580b 3130b 50.8 1550 48.4 1290 61.4 120 1050 2060 56.0 Air rate, 70 Ib./hr.-sq. ft. Bed repacked.
Table V.
I
... )
0.188 0.200 0.215 0.214 0.275 0.124 0.128 0.203 0.233
* * *
::: ... ***
1 )
... ) ... "*
Comments MgSOc step input in water
MgSOd pulse input in water
KCI step input in water KCI pulse input in water KCl step input in water KCI pulse input in water KCI step input in water Benzene pulse input in heptane Benzene step input in heptane
Fraction o f Internal Catalyst Voids Filled with Liquid
(2-inch diameter column) Liquid mass velocity, lb./hr.-sq. ft. 1600 Liquid holdup, cu. ft./cu. it. tower vol. .0.232 Total 0.108 In external voids" 0.124 In internal voids Measured internal voids, cu. ft./cu. ft. 0.295 tower vol. % of internal catalyst void filled with 42 liquid Estimated from nonporous packing data.
packing. Holdups as high as 0.300 cubic foot per cubic foot of tower volume are measured for step inputs with porous packing, contrasted to approximately 0.120 cubic foot per cubic foot of tower volume for nonporous packing. The comparison is, in a sense, qualitative, as the dry void fractions of the two 10
08 06 05 04
03 02
c/co 01
0 08 0 06 O M 0 03
o o 2 ~ 30
40
50
60 70 80 t-SECONDS
90
100 110
120
Figure 5. Effect of liquid flow rates on effluent time-of-contact curves, porous packing
1 004
2750
3900
0.279 0.119 0.160
0.251 0.124 0.127
0.295
0.295
54
42
types of packing are not identical. In terms of order of magnitude, however, the comparison is valid. There seems also to be an effect of tracer used, potassium chloride tracer holdups being greater than those using magnesium chloride as tracer. This is probably due to the higher diffusivity for potassium chloride and a subsequent larger amount of detected tracer in the effluent. The fact that the step inputs are characterizing both the inter- and intravoids is very important. A comparison of holdup for the porous and nonporous beds (Tables I1 and IV) shows that only a fraction of the internal voids of the packing is filled with liquid. This indicates inefficient catalyst utilization. While the liquid flow patterns may approximate plug flow, complete contact of the packing may still be a serious problem. Calculations to indicate the significance of this point are given in Table V, wherein only 40 to 50% of the internal voids are shown to be filled with
INDUSTRIAL AND ENGINEERING CHEMISTRY
liquid. Laboratory tests have show= that when only a part of any pill is covered with liquid-i.e., dipping one edge into a pool of liquid-the majority of the internal voids become filled through capillary action. It thus appears that approximately 40 to 5070 of the packing is actually wetted by the liquid. If the entire bed was wetted, the majority of the internal voids within the particles would be expected to be filled with liquid. I t is possible that the low internal holdups are not a consequence of incomplete wetting but are due to occlusion of the gas phase within some of the internal voids. If this occlusion occurred and at the same time the particles were completely covered with a film of liquid, the gas would be trapped and could not be displaced. In a catalytic reactor there generally will be generation of a gaseous product as a result of the chemical reaction. Thus, the low liquid holdups may be an inherent problem in all two-phase fixed-bed catalytic reactors. Evaluation of Contacting in Commercial Units. Contacting data for commercial and pilot plant fixed-bed catalytic reactors are reported here. In all cases the residence-time curve was obtained by monitoring a step input of an impurity in the feed stream. The step-function input with porous packing results in a time-of-contact curve which includes both diffusional mass transfer out of the packing pores and flow distribution through the bed. As a first step, it is necesary to separate out these two effects. This separation may be approximately achieved by analyzing the data from the 2-inch-diameter column. An exampIe of the technique used is shown in Figure 6, where the data of Figure 4 are replotted. The lower straight-line portion of the stepinput curve was extrapolated backward to slightly lower values of the time (see circled region). This extrapolated 10
00 06
os 04
03 02
c/co 01
0 08 0 06 I
0.03 0.02
I
M g SO+ TRACER
0.04
0
I
2750 L B I H R - F T L H 0 38 LBIHR-FT' Ai:
10
PO
M
1 40
50
60
70
t-SECONDS
Figure 6. Illustration of approximate method for removing mass transfer from step input curves, porous packing
FLUID M E C H A N I C S
0
IO
20
30
40
x)
60
70
t- MIMUTES
Figure 7. Time-of-contact curve for commercial unit 6 feet in diameter
line is assumed to represent the contribution of mass transfer and is subtracted from the original curve to give the approximate time-of-contact curve representing only flow distribution. The validity of this method can be noted by comparing the approximate curve with the curve obtained for porous packing using a pulse input. A pulse input gives a time-of-contact curve which closely approximates the flow distribution in the external voids. Contact data for a commercial unit 6 feet in diameter, when corrected to give an approximate time-of-contact curve, indicate excellent flow distribution. Figure 7 shows the corrected curve compared to the tracer input curve. In Figure 8 these results are compared with the air-water data with glass beads from the present study as well as data in a pilot unit 3 inches in diameter. The slopes of all of these curves lie between -4.0 and -5.0 and are thus good approximations to plug flow. The range of bed diameters covered in this comparison varies from 2 inches to 6 feet-an indication that the liquid velocity distribution is not a function of bed diameter. Further data are also available representing the distribution through a column inch in diameter packed with nonporous silica chips. Because the time-of-contactcurve is almost identical with the three shown in Figure 8, it has not been plotted. In all these cases the ratio of the tube to particle diameters was greater than 10. For ratios of this magnitude, Baker, Chilton, and Vernon (7) have indicated that there should be a negligible effect of bed diameter on flow distribution. Holdup data from these studies in the columns 3 inches and 6 feet in diameter suggest that only 40% of the internal particle voids are filled with liquid (Table VI). This was indicated earlier to be the case also for the air-water data. In
all three cases the packing used was identical. While the total liquid holdup is higher for the pilot unit, the holdup of liquid in the internal voids is the same for the three units. Mass Transfer from Within Porous Packing. Having established that mass transfer may distort the time-of-contact curves, it is of importance to see if a quantitative significance can be placed upon this distortion. This discussion must be considered tentative and indicates the possibilities rather than furnishes conclusions as to its applicability. More refined data will be required before positive statements can be made. Wilhelm and Deisler (75) present another approach to the same type of problem, in which a sinusoidal tracer input is used. There are, however, advantages to the use of the present transient technique as compared to the pseudosteady-state sinusoidal input; ability to perform a test on large scale equipment and ease of determining the fluid holdup are outstanding examples. A physical model may be set up which represents in an idealized manner the behavior of the experimental packed beds. This model is based upon spherical, isotropic, porous pellets packed uniformly in a column. Plug-flow displacement of tracer from the intervoids of the column by pure solvent is assumed to take'place, as well as simultaneous transfer of tracer from within the intravoids of the pellets. The rate of mass transfer is characterized by an effective diffusivity, Deff,, and is assumed to be very slow as compared to any other possible mass transfer steps. The mathematical formulation of this model is identical in all respects to that presented by Kasten, Lapidus, and Amundson (7) and Rosen (II), describing the transient behavior of deep beds of ion exchange resin. Approximate numerical solutions by Rosen (70) predict the effluent tracer concentration as a function of the system variables. A set of these theoretical curves is reproduced in part in Figure 9. The curve for X = 0.02 was estimated by the approximation suggested by Rosen
Table
VI.
06
05 04
-
-
-
-
02
-
c/co
006
-
004
-
003
-
008
OO%l,
O L
0;s
Ib
I15
,A
IAO
t/8
,bo
Figure 8. Time-of-contact curves for towers of various diameters, mass transfer removed
(77). The abscissa Y/X is a modified version of t/Oa, where On is the holdup time in the external voids and the parameter on the curves, is a modified bed length and contains the effective diffusivity, Deff., for solid diffusion. Any set of time-of-contact data may be plotted in these units and from the corresponding value of X the effective diffusivity may be computed, as all other terms in X are known or may be estimated. Calculated values of D,ff.for a number of experimental runs are presented in Table VI1 with certain of the curves shown in Figure 9. These values were obtained by plotting c/c, us. Y / X on the same coordinate system as the theoretical curves of Rosen. O n this basis a corresponding value of X can be estimated for each experimental curve and the value of Deft.subsequently calculated. I n many instances it proved impossible to assign a value of X to a particular set of data, as the curve was obviously displaced from its correct position in the c/c, us. Y/Xfield. This may be a result of the use of estimated values for some of the physical parameters-Le., 0, was calculated using nonporous data. The actual physical
x,
Fraction of Internal Catalyst Voids Filled with Liquid
(2-inch, %inch and 6-foot-diameter columns)
Bed diameter, inches Holdup, cu. ft./cu. ft. tower vol. Total External void Internal void Total internal voids, cu. ft./cu. ft. tower vol. 70of internal voids filled with liquid a Estimated by approximate method.
Wax Hydrofiner 72
0.250 0.130' 0.120 0.295 40
Pilot Unit 3
Borosilicate Glass Column 2
0.300
0.232
0.210" 0.110
0.108
0.295 37
VOL. 49, NO. 6
0.124 0.295 42
JUNE 1957
1005
Figure 9. Thearetical. and &pori. mmtol timed-contad curves
. problem in which liquid is in cbntact
.,
with only a portion of the packing and 6lh only a portion of the void spaces is di5-t h m the ideal theoretical ' . d c i and may contribute to this & plaament. The values of Deft. in Table VI1 are in the range expected for pore dii€+u, 10-6 to 10% sq. cm.per second., This is encouraging and mg--the technique ,h considerable mait. However, the Frit consider-.' a h are,pnliminary in nature. Purther and morC rcfinal data will be re.quired bdbrc a positive or negative asslpis o f t h e technique can be made. .Further publications will be concerned with a detailed examination of the entire pmbh. The importance of cakulations of this type M that one may, by a timd-contact arpcriment, charactaiee both the flow " distribution and the maaa transfer or hvgilabnity of catalyst packing. ' T h e dective dX*vity is naUy zn indication . of the availabiity of the pores for mowmcnt of traccxinto and out of the pellets. By mitable choice of the tracer, the a, pciment can be carried out under actual reaction tempcxature and p m w and thus lend a cleartr insight into &e. mechanism of eankport within catalysts. Them may also .be c o d e r a b l e utility ' . to the w e of~~the'preacnt technique for single-phase gas flow &ugh packed catalytic 'reactors. The high. d-vity of gas tnreQs may require a alightly but diffaent mathematical anal+, the virtues ,we still preaent. Blue and -0thm (2) d t i g 1
,
'
'
''
have presented preliminary data along these lines. The timc-of-bntact curves may exhibit two or more breaks due ut&r to a distribution of pore sizes within the catalyst or to various types of intanal dXuaion--e.g., molecular or Knudsen diffusion. Both'the howup and the availability of each portion of the muye may be am5nable.fa detumination.. , In applying this technique to poioua-lid catalyzed gaseous reactions certain pmblcma can, howevk, be anticipa&. Adsorption of the traeci may complicate the analysis and considerable care may bc required in &oo+g a witahle tracer with mass transfer propertiea co'mpnnding to the reaction gases.
Cgnelurionr Timwf-contact oi residence-time experiments in a packed bed 2 i d e s in diameter with cncurrent flow of liquidair over nonporous pa&g indicate a dose approach ,toplug f ly for the liquid phase. The e 5 F t of the minor deviation from plug flow would not become important ,unless c h m + d convemiom of 95% or greater are desired. . By contrast, +deme-iime ex&ments with porous paproduce, & tortmi C U N ~the ~ , distortion being' a consequence of mass t r a d e r of.tracv voids of the from within the inpacking. F'ulse-type inplt,curvea are aftected 9 o d y a minot degree by the aLass tramfer and thus produce d t s almost identical to those for,~nonpomy packing. An approxima$ method punaits s e p aration of the contributions of Fa% fer and 0oy distribution..'Data for k e d beds ranging in size from */e inch m 6 feet, whcn corrected by the approxb i t e method, all exhibit appiwximately the Mme.appmach plug flow as those for nonpmoua p a w . Holdup data for the icactora show that only 40 to 50% of the voids within the packing are Wed with liquid. A corresponding. fraction of the packidg is t h w ' u n a v e b l e for reaction, indicat&g p+x --all liquid'
Nomenelaturn c
= tracer concentration in d u e n t
. 6
= influent tracer concentration
at any timet
usedtosaturatebed Ddt = internal poredifliaaivity of t r a m F = volumetric flow rate of main fluid phase H holdup of fluid im bed f = time of operation; measured from time of pulse injection or t i m e d cutoff of tracer in stephnctien input = mSdi6ed bed length parameter
-
x
troy
Y / X = mcdilied % / B parameter (70) 0 = mean holdup time offluid phaae Os = mean holdup time of fluid phase in interpartick region
Litemturn Cibd
.,.,--,.
4 ) IW., 5 , 2 6 (1954). 5) Gillilaud, E. R., Mamn,
E. A,,
Oliver, R. C., IND.ENO. Ckw.
45,1177 (1953). (6) Jcssx, B. W., Elgin, J. C., Tram. Am. inst. Chm. -6. 39, 277 I.".*\
6
Pand Packcd Tower Dtaip," U. S. Stonmarc Co., b, Ohio, 1953. h D . h0.&Ex. 46, Ryd
(9) h a y M., '"To&
p a c k i i contacting..
(io)
A single-step input timc-of-contact expviment yields-informationnot only on the fluid flow d i d b u t i o n but also on the mass ,tram+ h m witbin p o w paddng. Attrmpts to chapctuize thia l a m r maaa tranafer by means of an effective diffiaaivity show pmr+e. Because the qperiment can be .carried out at high.amperaturrsand ppraunura, considerable elucidation on .the, rate of p$M'ullion under d~tualreactor opera&ng conditions may be possible ' ' with this technique.
(12) ShS h d , T. K ., Chm. J3g. Prep. 51,303 (1955). (13) Shulman, H. L., Ulrich, C. F., Wells, N., A.I.Ch.E. JoMlol l>247 (1955). (14) Uchida, S., Fujita, S., J. Soc. I d . Japan 40, 238B (1937); 41. 275B (1938). (15) Wilbelm, R. It, Dcialcr, P. J., I ~ N D .tho. Chum 45,1219(1953).
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Engineering Co. for pvmission to publish this article. The work presented was .carried out while the author was employed by the Research and Engineering Co, as a tdmical consultant. The author also wishes to acknowledge the contributions of D. L. Baeder, E m Research and Engineering Co., whose advice and auggcations m a d l y aided in the formulation and develop ment of the ideas p-ted.
Atkndwl+sment The author wiahes t6 exprws his appreciatiun 'to the EsN R.esearch, and
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RBannro Ton review January 2,1957 AcapTBD April 15, 1957 MvLion of hdustrial nnd Engin Chemisby, Am, Symposium on% Mcchanicr in chermcd F%in*, Lafayctte, Ind., Dmmbcr 1956.
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