Fixed bed adsorption from a high concentration feed

Chemical Engineering Science, 1963, Vol. 18, pp. 599-611. Pergamon Press Ltd., Oxford.

Printed in Great Britain.

Fixed bed adsorption* from a high concentration feed J. H. BOWEN? and M. B. DONALD Ramsay Memorial Laboratory

of Chemical Engineering,

University College, London

(Received November 1962) Abstract-The distribution, along a column, of water adsorbed from a stream of high humidity air onto discrete sections of activated alumina, was found gravimetrically. The corresponding fall in humidity of the air stream, as it passed through the column, was also estimated. In addition to a saturated zone, three zones of transfer were detected. Nearest the exit of the column, was a zone where water molecules were transferred, chiefly, to an adsorbed monolayer. Then, came a complex region of slower transfer to bilayer and residua1 monolayer positions. Finally, next to the saturated zone, was a zone where the rate of transfer increased and capillary condensation became the main transfer mechanism. A distribution of pore sizes was obtained. Experiments with various air flow rates showed that the relative humidity of the air entering the zone of monolayer adsorption was independent of air flow rate. This suggests that a method of sizing an adsorber to take a high humidity feed could be based on a concept of a self-contained “monozone”.

INTRODUCTION

THE complexity of the mechanisms involved in the transfer of a component from a moving stream onto a hxed adsorbent is implied by the absence of a general design method for determining the size of fixed bed adsorbers. In the relatively simple case of isothermal adsorption from a gas feed containing only a low concentration of adsorbable component, much can be done in the way of predicting performances by solving differential equations which describe the mass transfer of the adsorbate but assume that the carrier gas is not adsorbed. A common system which can approximate to these conditions occurs when air with a low relative humidity is passed through a bed of desiccant such as activated alumina or silica gel. The air emerges with a low moisture content which persists until the column reaches its break point, when the effluent humidity rises rapidly. In this case the breakthrough plot of effluent humidity against time is symmetrical about the mean value of humidity between that at inlet and that of effluent air before the break point. If the condition of the column before

breakthrough were analysed, the humidity of air (and the adsorbate concentration) would be found to fall from the value at inlet to the value at exit over quite a short length of column called the adsorption zone. These cases are indicated in Fig. 1 and, by making some simplifications, they can be analysed theoretically in such a way as to enable the performance for different duties to be predicted reasonably accurately [1, 21. The disparities between theory and experiment occur when the adsorption is complicated by a high concentration of adsorbable component in the feed and by temperature changes in the column due to the incomplete removal of the heat of adsorption. The latter can be allowed for, to some extent, by choosing a mean temperature of semi-isothermal operation but the former will introduce additional mechanisms for transfer which depend upon the precise structure of the adsorbent used and which cannot be predicted in the general case. After diffusing through the laminar film around a granule, a water molecule being transferred to the adsorbent surface is transported through the granule itself by one or more of four possible mechanisms.

* In most of this paper, the terms “adsorption”, “adsorption isotherm”, “adsorbate”, etc., are used in their most general sense and refer to the total water taken from the air by the adsorbent, whether it be retained on chemisorption sites, in physically adsorbed layers or as capillary condensate. In the section on capillary condensation, however, a distinction is drawn between the “sorption isotherm”, which is taken to include adsorbed layers and capillary condensate, and the “adsorption isotherm”, including adsorbed layers only. The distinction is clear in context. t Present address: School of Chemical Engineering, University of New South Wales, Kensington, New South Wales, Australia.

599

J. H. BOWENand M. B.

sensitive measure of the state of the adsorbent and the conditions of operation of the column, but is also some function, not necessarily known, of the moisture distribution on the column itself. An apparatus was designed to provide breakthrough curves and to enable the moisture distribution on the column at break point to be measured. The laboratory air supply at a pressure of 80 p.s.i.g. was fed into a pressure cylinder fitted with a reducing valve and gauge of the pattern used in oxygen cylinders. The air passed via a high pressure release valve to a water manometer and then through an integrating wet gas meter to the humidifying train. The humidifying train consisted of four bottles and a copper coil. The first bottle contained distilled water, the second distilled water and porcelain pieces. The third bottle was empty to collect large entrainment and the fourth filled with glass wool to remove smaller entrained droplets. The whole train was immersed in a constant temperature bath mamtained at 30°C by a mercury toluene regulator. The relative humidity of air leaving the train was measured by adsorption onto weighed alumina and found to be fairly constant at a mean value of 95 per cent for the various flow rates and columns studied. The variations in this humidity could not be reduced below 12 per cent but it will be seen later that these variations have no effect on break point conditions.

t

1s Time Breakthrough

DONALD

curve

Distance along column Progression of adsorption zone

/iDSORPTION

1. A breakthrough curve and water distribution curves such as would be expected of a column of desiccant fed with low relative humidity air. FIG.

If the pore spaces in the granule are large, the mechanism will be mainly that of bulk gas diffusion; if they are small compared with the mean free path of the gas molecules involved, it will be Knudsen diffusion. A third possibility is diffusion over the internal surfaces of pores, but this becomes appreciable only over surfaces that have a high proportion of their monolayer filled [3]. Finally, at high relative pressures, liquid condensation in the pores provides a fourth method of transfer. In so far as these mechanisms determine the rate of transfer of water into an adsorbent granule, they will effect the distribution of moisture within the adsorption zone itself. With the ultimate objective of finding a method of designing adsorbers to take high concentration feeds, this zone has been analysed for a column of activated alumina under various conditions of operation. APPARATUS An

external measure of the progress of the adsorption

zone (or humidity wave) through the bed is, of course, the effluent humidity. When the latter is plotted against time, a breakthrough curve is obtained which is not only a

COLUMN

After leaving the humidifying train, the air entered a column containing the alumina to be tested. The connecting tubes were wound with electric heating coils to prevent condensation and the temperature of the air into the top of the column was measured by a thermocouple. Preliminary work had brought out the importance of keeping the heat conditions the same for different columns if reproducible’ runs were to be obtained. For the first experiments, conditions were, as far as possible, kept isothermal. Because of the poor thermal conductivity of porous alumina, it is doubtful if truly isothermal conditions were, in fact, obtained, but the effect of any deviation from isothermal operation could not be detected when a jacketed glass cohnnn of 11 mm internal diameter was used with cooling water at 30°C flowing through the jacket. The adsorbent used in all runs was an 8116 B.S. grade of activated alumina. The samples came from one manufacturer’s batch and were discarded after being used once. This removed the need for a standard regenerating procedure. The mean humidity before the break point of the column was found to be unaffected by either inlet humidity or bed length and this was taken to show that there was no significant channelling and that, effectively, all the heat of adsorption was being removed. In order that the distribution of adsorbed water along the cohunn~itself could be measured, the ahnnina was divided into sections of known weight which could be re-weighed at the end of a run. The spacers to separate these sections had to satisfy certain requirements. They were required to hold up various sixes within the 8/16 grade so that small pieces of alumina did not drop from one section to the next. The spacers themselves had to constitute a minimum resistance to air flow and lend themselves to easy removal when sections were re-weighed. Finally, since a glass column was used to assist in the locating and the removal of the

600

Fixed bed adsorption

from a high concentration

spacers, they had to accommodate the slight variations in diameter which occur in standard glass tubing. A coil of fine copper mesh was eventually used, about f in. in length and lightly bound around the circumference with a metal thread. Themesh was frayed at oneendand it retained sufficient spring to take up variations in diameter. An eyelet was incorporated, by means of which the spacer could be pulled from the column. (Fig. 2) The column was operated vertically; it was 6lled through the top and emptied from the bottom.

feed

0.32

HLJMID~TY MEASUREMENT Only the air humidities into the column were measured by direct adsorption. Effhtent humidities were obtained using a type of frost point hygrometer developed by the Meteorological Office. This instrument consists, essentially, of a Wheatstone’s Bridge, one arm of which is a t?ne wire resistance wound round an anodized aluminium thimble. Methylated spirits cooled by solid carbon dioxide were sprayed into the thimble and the reduction in the resistance of the fine wires was shown as an out-of-balance in the Bridge circuit. The air to be measured was passed through a small space above the closed end of the thimble which was situated at one focus of a glass plate shaped as an ellipse. A bulb was placed at the other focus and, by internal reflexion, light from it illuminated the thimble. A chamfer around the edge of the hole cut in the ellipse to accommodate the thimble caused the liaht to strike the surface of the thimble with a glancing inc~ence, thereby throwing into relief the first signs of dew or frost formed on the thimble. The surface of the thimble was viewed through an eyepiece and the Bridge was balanced when the first frost appeared.

0

4

8

12 Distance

16

20

24

along column.

26

32

36

40

44

g length

FIG. 3. Distribution of adsorbate along various length columns at their breakpoint. Air flow = 053 l/min. Isothermal operation at 30°C. Relative humidity of the feed is 95 per cent.

plotted in Fig. 3. As the trend of the distributions became clear so it became convenient to increase the size of some sections where the rate of change of water concentrations with length was small.

WATERTRANSFERFROM

EXPERIMENTAL PROCEDURE Using the copper mesh spacers described, the activated alumina to be tested was fed to the column in known increments-say 2 g weight-of adsorbent. Water at 30°C was supplied to the jacket of the column and humid&d air, also at 3O”C, was passed down the column. So that the pressure over the thimble did not change with air flow rate, only sufficient to create a head of about 9 cm water was diverted through the hygrometer. The remainder went, via a screw clip, direct to atmosphere. The frost (or dew) point of the air leaving the column was followed closely and corresponding vapour pressures obtained from tables. After an initial fall, due, mainly, to the displacement of ambient air from the finite space above the thimble, the efBuent humidity remained fairly constant during the major part of the drying run, until the cohmm break point was approached. When the frost point began to rise consistently, values were taken frequently until it reached -33”C, which was arbitrarily chosen as the break point. Unless a breakthrough curve was being plotted, the run was stopped at this point, both the time and the total volume of air that had passed being noted. The alumina was taken from the column in sections and reweighed to give the amount of water taken up by each section. This procedure was repeated for columns of different lengths and the water distributions obtained are

AIRTO ALUMINA

Fig. 3 shows that the water content of the alumina in the column increases from its “dry” value taken as zero to an amount in equilibrium with the incoming air, in several stages. These were examined more fully. When humid air flows at a constant rate through an isothermal bed of alumina, the concentration of water at a point within the adsorption zone is a function of time of flow and distance along the column s = s(t, X) Neglecting second-order effects, the rate at which the adsorbate concentration increases at any point in the column is

Alternatively, and more conveniently, this may be expressed in terms of changes of humidity along the column. If c = c(x, t)

601

J. H. BOWEN and M. B. DONALD

the rate of transfer of water to unit length of column

and the rate of transfer per unit mass of alumina

For a constant air flow rate, the rate of transfer is proportional to the slope of the curve showing the variation of air humidity in the column with distance along it.

Mean adsorb&

FIG. 5.

__

s

50

.;I i

40

E 2 30

s ‘5 E ?j

20

. g/g

and relative humidities along the column. Isothermal operation at 30°C ’ Air flow rate of 053 l/min. * Sorption isotherm values.

TRANSIENTEQUILIBRIUM RELATIONSHIPS The air relative humidities (calculated as relative pressures) corresponding to Fig. 3 were found from transient equilibrium curves relating concentrations in the bulk air stream to mean water concentrations on the alumina granules. A relatively short column of, say 18 g was assembled and humidified air passed through it at the same rate as that used in Fig. 3. The run was continued beyond the break point and a breakthrough curve plotted. Fig. 4. The adsorbate concentrations at the 18 g point corresponding to the various break point volumes occuring in Fig. 3 were noted; the air humidities corresponding to the same set of conditions. The air humidities that occurred at the same point in the column after the same volumes of air had passed were read off the breakthrough curve. Other sets of conditions were obtained from different breakthrough curves. The transient equilibrium curve thus obtained is shown in Fig. 5 and is a function of air flow rate.

concentration,

Curves relating mean adsorbate concentrations

Distance along column,

FIG. 6.

g length

Distribution of relative humidity along column for the flow conditions of Fig. 3.

a

It can be used to prepare Fig. 6, which shows that, initially, water transfers quickly to dry alumina. There follows a period of slower transfer and, finally, the rate increases slightly until the adsorbent approaches saturation. Higher flow rates were tried and the results are shown in Figs. 7,8 and 9. As the flow rate increased, the third stage of transfer became less well developed. Furthermore, it appears that the change from one stage to the next occurs at a characteristic humidity which is independent of the flow rate. The change is not similarly related to granule mean adsorbate concentrations and this suggests that the mechanism of transfer is in some way controlled by the degree of saturation of the exterior surface of the granule.

IO

E w

0

!O

20

30

40

50 Volume

FIG.

60 of air,

4. Some of the breakthrough

70

80

90

too

1

curves used to compile Figs. 5 and 8. Isothermal operation at 30°C. Relative humidity of feed is 95 per cent.

EFFECTOF RELATIVEHUMIDITY

II0

The effect of reducing the humidity of the inlet air whilst keeping its temperature constant was investigated. Glycerol-water solutions were used 602

Fixed bed adsorption

from a high concentration

feed

Distance aloyg column,

Distance

along column.

g length

0

4

8

12

16

Disknce

FIG. 9.

Distance along column,

g length

20

24

along column,

28

32

35

40

44

g length

The distributions of relative humidity corresponding to Fig. 7.

to produce the required humidities. Mean inIet humidities were calculated from the weights of water adsorbed at break point. Fig. 10 shows that for inlet humidities greater than 56 per cent certainly, and perhaps less, the volumes to break point are approximately constant. These experiments, with various inlet relative humidities also enabled an adsorption isotherm to be plotted using the equilibrium adsorbate concentration at the inlet end of the column. In all experiments the volumes to break point were used rather than the time to break point because of the sensitivity of the latter to small differences in flow rate.

g length

FIG. 7.

Distribution of adsorbate along columns for different flow rates. Isothermal operation at 30°C. Relative humidity of the feed is 95 per cent. (a) Air flow rate of 1.07 l/min. (b) Air flow rate of 1.89 l/min.

DISCUSSION OF RESULTS

Meon

FIG. 8.

adsorbate

concentration,

g/g

Curves relating mean adsorbate concentrations

and relative humidities along the column. Isothermal operation at 30°C A Air flow rate of 1.04 l/min. 0 Air flow rate of 1.89 l/min. * Sorption isotherm values. The fourth line is re-plotted from Fig. 5 for comparison.

The distribution of moisture within the adsorption zone developed by a high humidity feed can be more complex than the simple sigmoidal form usually assumed to exist. Referring to Fig. 11, zone 4 at the inlet end of the column is in equilibrium with the incoming gas and there are three zones in addition. As already mentioned, the water distributions obtained for different air flow rates suggest that the progression from one zone to the next is related to the air humidity above the 603

J.H.

3

BOWEN

and M.B.

sensitive to the degree of saturation of the external surface. It is not easy to judge from Figs. 6 and 9 that relative humidity at which zone 2 changes to zone 3, but the low rate of transfer associated with zone 2 appears to persist until the relative humidity has risen to 70-75 per cent. However, the change from zone 1 to zone 2 can be estimated more accurately. It was taken to occur at that point in zone 1 where the rate of transfer. (as measured by the slope) ceases to decrease. A figure of 51 per cent is used. When these characteristic humidities are referred to the adsorption isotherm, which is the BET Type IV, they divide it into regions usually associated with the formation of a monomolecular layer, of multilayers and the occurrence of capillary condensation. It seems possible, therefore, that a monolayer forms in zone 1, that multilayers build up in zone 2 and that the main contribution to transfer in zone 3 is through the mechanism of Each zone will now be capillary condensation. considered in detail.

0.28 024

5 0.20 .z 0 : 0.16 $ $

0.12 ’

0.08 t

0

-.

4

6

12 Bed

16 length.

20

24

28

32

DONALD

36

g length

Fro. 10. The effect on the adsorbate distribution of varying the relative humidity of the feed. Air flow = 0.53 l/min. 94*4x0; 86.0% V; 81.6% 0; 75.1% *; 56.1% A ; 26.3 % 0; 10.0% x .

MONOMOLECULAR

Distance along column

Fro. 11. The four zones of the adsorbate distribution. Zone 1: Zone of monomolecular adsorption or monozone. Zone 2: Water molecules are adsorbed into a second layer on the outside of a granule but continue to occupy monolayer positions nearer the centre. Zone 3: The transfer of water is mainly by capillary condensation. Zone 4: The alumina in thii zone is saturated and no transfer of water occurs. rather than the mean water concentration in an adsorbent granule. If adsorption equilibrium is assumed to exist at the gas/solid interface, this may indicate that the mechanism by which water diffuses into the body of a granule is alumina

ZONE

The mean moisture content of an alumina granule corresponding to a relative humidity of 51 per cent decreased as the air flow rate through the column increased. In other words, the amount of water that has diffused into a granule in the time it takes for the air humidity outside the granule to rise to 51 per cent decreases with increasing flow rate. The maximum value of the mean moisture content equivalent to 51 per cent relative humidity is, of course, obtained from the equilibrium adsorption isotherm. (Fig. 5.) In this case, it is 0.10 g water per g of alumina, and if the postulate that transfer in zone 1 is to the monomolecular layer be valid, then it should be possible to relate this figure to the total internal surface area. Work done on the molecular areas to be used for surface area determinations suggests 10.8 A2 (Ref. [4]) for a water molecule. Using this figure, 0.10 g of water in a monomolecular layer corresponds to a surface area of 364 m”/g of alumina. Surface areas are conventionally quoted in terms of nitrogen adsorption and for the grade and quality of activated alumina used in these tests,

604

Fixed bed adsorption from a high concentration feed

figures varying from 250 to 290 m2/g were obtained [5]. The difference between these figures and the water area was considered to be greater than could be accounted for by the inherent uncertainty of the BET method. This apparent discrepancy would be explained if some of the water surface were not available to nitrogen. Work done by others on the preparation and pore structure of activated alumina suggests that such is the case. PREPARATION OF ACTIVATED ALUMINA

The manufacturer was unable to release details of the manufacture of his activated alumina, beyond saying that a multiple hydrate of alumina is precipitated which is substantially X-ray amorphous, but contains an easily recognisable proportion of boehmite of small crystallite size. The precipitate is activated by heating it to a temperature between 300 and 400°C [5]. The manufacturer’s catalogue [6] gave, as a typical analysis of this grade of activated alumina, Al,O,

85% by wt

H2O

12%

3% An accurate analysis of the samples used in the present experiment gave so3

A120J H2O

84.988 % by wt 11.759 3.253 %

SO, The aluminium was found gravimetrically by the hydroxy-quinolate method, after fusing the alumina with sodium carbonate. The SO3 was precipitated as barium sulphate. The production of an activated alumina from a hydrated precipitate has been investigated by several workers. Whilst there is agreement on over-all processes there is still uncertainty as to the detailed mechanism involved. The highest hydrates are the trihydrates, gibbsite and bayerite. When either of these is heated above 150-2OO”C,a mixture of monohydrate and anhydrous alumina is obtained, the proportion of each depending upon the time and temperature of dehydration. After heating for an hour in dry air between 300 and 4OO”C,the only constituents are the anhydrate and monohydrate. Several explanations have been offered

for the existence of both. Since the monohydrate is stable at temperatures below 4OO”C,the anhydrate must have been derived from the trihydrate by a mechanism distinct from that which produces the monohydrate. In his account of the pore systems in activated alumina [7], DEBOERstates that this dual behaviour is caused by the difficulty of removing water from the inside of granules at the start of the dehydration. Taking gibbsite as an example, he shows that it forms boehmite, xA1203 and 7A120J in three steps. At 160-165°C the normal decomposition of gibbsite to xA1203 starts at some active points. The water liberated diffuses out of the granule, but not quickly enough to prevent pressure being built up. The accumulation of steam within the granule enables boehmite to be formed at this temperature. More water is liberated, accelerating the hydrothermal transformation until the water pressure becomes so high it forces its way out. After this eruptive escape, normal decomposition of the trihydrate continues. DEBOER also states that the water which escaped prior to the eruptive discharge left spaces which were available to water but not to nitrogen molecules. Figs. 1 and 2 of his paper suggest that the composition of the dehydrated alumina between 300 and 400°C corresponds to a monohydrate less the amount of water that diffused out initially. Since the composition of the hydrated precipitate from which alumina used in the present work was prepared, is not known, it would be unwise to expect too close a parallel with the mechanism of dehydration of the carefully prepared trihydrate used by DE BOER However, it seems certain that the anhydrous portion of the commercial alumina is derived partly from an initial process of dehydration producing a surface area which is not accessible to nitrogen, and partly from the post-eruptive dehydration. After allowing for the presence of aluminium sulphate, it will be seen that the composition of the activated alumina is less than the monohydrate by an amount equivalent to O-025 g water per g of activated alumina. If this represents surface not available to nitrogen, the quantity of water that should be used to calculate the nitrogen surface area is 0~100-0~025 which corresponds to 271 m2/g. 605

J. H. BOWENand M. B. DONALD

An alternative possibility should not be overlooked, namely, that the change in transfer mechanism that occurs at 51 per cent relative humidity is only incidentally due to the formation of a monolayer and is caused primarily by the narrowing of pore spaces when adsorbed layers form. DE BOER found that most of the surface area in his samples was contained in fissures of 10 A width. Though it is not known how small a pore space must be for Knudsen diffusion to give way to surface diffusion only, it does seem unlikely that the former will persist when the formation of a monolayer has decreased the effective pore space to molecular dimensions. Work is continuing on this aspect of the problem. MULTIMOLECULAR ZONE

When the relative humidity of the air at any crosssection in the bed has risen to 51 per cent, a second layer of molecules starts building up and the transfer moves to zone 2. It is not possible in this zone to distinguish between water which is transferred to the second layer on the outside of the granule and that which is adsorbed into monolayer positions nearer the centre of the granule. Clearly this residual monolayer transfer must continue in zone 2 at least until a mean moisture content corresponding to the monolayer capacity is achieved. As the relative humidity outside the granule increases above 51 per cent, water can be transferred to the alumina by a third mechanism, namely capillary condensation. Again, it is not possible to distinguish that proportion of the water which is being taken up as condensate. Experiments with non-porous alumina would eliminate this third mechanism but since they would not suffer the same limitations on multilayer formation as those with alumina containing narrow pores, they were not carried out. Instead, the build-up .of second and subsequent layers in the absence of capillary condensation is predicted theoretically and the results obtained are considered to give at least an indication of the extent of the layer formation and, by difference, the range of the capillary condensation. If an instantaneous distribution of water in the air along the column is imagined to be held until

equilibrium between air and alumina is achieved, the adsorption isotherm can be used to calculate the corresponding distribution of water on the alumina. This is shown by the full line in Fig. 12 and it does, incidentally, represent the condition on the external surface of a granule if the extra granular laminar film does not constitute an appreciable resistance to the transfer of water. Equilibrium adsorption will be presumed to follow the limited form of the B.E.T. equation [8]. s,Wp/p*)

1 - (n + lXp/p*)”

f ~P/P*>“+ ’

1 f (K - wP/P*)

s = 1 - (P/P*)

- 4P/P*)

The shortcomings of the theory of BRUNAUER et al. have been discussed elsewhere, but their equation still provides as accurate a prediction of equilibrium adsorption as is available. The saturation capacity of the alumina suggests that the integral number of layers does not exceed four. This assumes, of course, that the capacity of each layer is the same as the monolayer. In addition, it assumes that the water transferring in the monomolecular zone to area not available to nitrogen and not featuring, therefore, in the monolayer capacity, does so uniquely, and is not repeated in subsequent zones. Taking n in the above equation as 4 and knowing from experiment that V = V, when (p/p*) = 0.51,

606

\

0

4

8

12

16

Distance

20

24

along column,

28

32

36

4c

44

g length

FIG. 12. Hypothetical equilibrium adsorbate distribution and B.E.T. values. The latter include an allowance for the 0.025 g of water per g of alumina transferred uniquely in the monozone. 0 B.E.T. values.

Fixed bed adsorption from a high concentration K can be calculated and equals 1.373. The relative humidity of air entering the column is 95 per cent. When (p/p*) = 0.95 V = 2*02V, indicating that, in the absence of capillary condensation, only one layer in addition to the monolayer would have been formed. The adsorbed volumes corresponding to relative humidities between 51 and 95 per cent can be calculated in terms of the monolayer capacity. To these values has to be added that quantity of water sorbed (this term is used deliberately since this water is probably chemisorbed) onto surface not available to nitrogen. The resulting adsorbate concentrations are shown by the dotted line in Fig. 12.

feed

exists in the surface of condensed phase as it passes from adsorbed layers to the meniscus of the capillary condensate. Since the value of 0 in the present experiments is not known, it will be taken as zero and a mental note made of the fact that pore dimensions calculated using this approximation will be slightly too large. Pore size distributions will be plotted in terms of the surface area per angstrom of characteristic dimension. The surface area will be related to volume by an expression of the form suggested by EVERETT[13].

where b is the mean characteristic dimension of the pores containing the volume V. For a parallel Because the structure of the activated alumina plate model, b is the mean distance between plates used in these experiments was not examined in whilst, for a cylindrical pore model, b is the mean detail, it would be unwise to attempt too elaborate pore radius. an intepretation of the capillary condensation zone. y is defined by EVERETTas a numerical factor But it is possible to find that proportion of the total dependent upon the detailed geometry of the water on the alumina which has been taken up system and on the way in which the mean pore size as capillary condensate, if adsorption itself is is defined. For uniform cylindrical pores and for equally spaced plates y = 1 but, even for some assumed to following the B.E.T. equation through simple, one parameter models, y can be as low as the zone. Several equations are available for relating the 0.104. The present work uses y in a somewhat extended relative pressure to the width of a pore in which sense by regarding it as a factor introduced to condensation will occur. Most of these equations assume a pore model, either a cylindrical [9, 101, equate the total surface area obtained from the distribution drawn assuming y = 1, to the total or a parallel sided fissure [ll], but the exception surface area of 271 m2/g found earlier. Used in is DERJAGUIN’S equation [12]. This does not depend on any specific pore shape but is the result of a this way, y also allows for the inaccuracies inherent in the assumption that the build up of multilayer fairly general thermodynamic argument ; it states follows the B.E.T. equation and that the adsorption r m” r~cos 13+ RT takes place under equilibrium conditions. It may -dP r = RT ln(p*/p) P p not, therefore, be truly constant. where As already mentioned, characteristic pore sizes may be calculated by DERJAGUIN’S method without r is the pore half-width for a parallel sided fisthe assumption of any pore model. He extends the sure or -(dV/dS) in the general case. m, the molal volume of condensate (18 cm3/mole) theory to give the total surface area in terms of surface tension of condensate (71.2 integrated areas under the sorption isotherm (inC-J the cluding capillary condensate) and the adsorption dynes/cm) e the angle of contact between the adsorbed isotherm layers and the condensate meniscus RT r ‘;ln(p*,p)] ds I- the adsorption in moles/cm’ referred to a total J sc s (total) = surface of 271 m’/g. CTcos 0 + RT r;ln(p*lp)] dF In general 0 is not zero because a discontinuity s ICAPILLARYCONDENSATION

p*

s

I

607

J. H. BOWEN and M. B. DONALD where s, refers to conditions under which capillary condensation no longer exists. Values of S are given in Table 1 and the surface area/A of pore half-width is plotted as a function of pore halfwidth. This gives the uncorrected distribution curve and its area is divided by the known surface area of 271 m*/g to obtain a mean y of 0.35. The distribution curve is then replotted (Fig. 13) with surface area values increase in the ratio 1 to y. If DERJAGuJN's~eqUationis not used, a pore model has to be assumed before the characteristic pore dimension can be calculated. Using, for example, COHAN’Sequation for condensation in open ended cylindrical capillaries P

3

P

= exP

-2om,

(

cos

R73.,

e

FIG. 14. The implications of the cylindrical model used to calculate nore surface area from COHAN’S condensation formula.

r=re+h AV=AV,w=w(rc+h)2L rc AA = 2n(rc + h)L Including correction factor y 2 Av2(rc+hI AA=AV-= Oy’ez r(rc + h)

)

and assuming zero angle of wetting, a net pore radius can be obtained for each value of the relative pressure. The thickness of an adsorbed layer at that relative pressure must be added to obtain the total pore radius. It is calculated on the assumption that the area of each layer is the same. This is not quite true for a cylindrical model but the error will be unimportant. The implications of a cylindrical model are given in Fig. 14. y is calculated as above and the corrected

'0 Pore radius,

i

(Bosedony=0*73) FIG.

15.

Pore size distribution derived using formula.

COHAN’S

distribution given in Fig. 15. Obviously the exact distribution must depend upon the condensing equation and the pore model used, but agreement between Figs. 13 and 15 should not be interpreted as showing that the pore spaces are, in fact, cylindrical. J 100 Pore half-width, A (Based on y = 0.35) FIG.

13.

Pore size distribution derived using DERJACWIN’S fOllllUli3.

THE EFFECTOF EBLATWEHUMIDITY The results of experiments in which the inlet relative humidity was successively reduced are shown in Fig. 10. These demonstrate that the 608

^. -

ZLI.0 S*EIl S*L

0.901

W6

80.0

E*IL

E*SL

1-P

LPI.0 94s

f-L

s+w

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J. H. BOWENand M. B. DONALD

complex form of the adsorption wave is indeed due to the high humidity of the feed. They also show that, for a fully developed monomolecular zone, the time (or volume) to break point does not depend upon the inlet humidity. It is this property which will be used in later papers as the basis of methods of design for adsorbers taking high concentration feeds.

Experiments with various inlet humidities showed that when these were high enough (greater than 51 per cent at 30°C) for the monomolecular zone to be fully developed, the progression of this zone along the column and, therefore, the time to break point was independent of the humidity at inlet. The use of this information in the design of adsorbers will be discussed elsewhere.

CONCLUSIONS

Acknowledgement-This work covers part of a study for a Ph.D. Thesis [14] undertaken in the Ramsay Laboratory of Chemical Engineering at University College London. Thanks are due to the Leverhulme Trustees for the award of a Studentship.

The work so far has been confined to isothermal adsorption on a column packed with activated alumina granules. Its immediate objective has been to investigate some of the complexities that occur when air nearly saturated with water is fed to such a column. The distribution of water on the alumina and in the air flowing through the column show clearly that several zones of transfer exist within the over-all adsorption zone. It is unlikely, therefore, that any theory based on the assumption of a simple sigmoidal humidity wave will be successful in predicting the performance of adsorbers taking a high concentration feed. In addition to a saturated zone at the inlet end of the column, where no transfer occurs, there are three zones associated, broadly, with the transfer of water to a monomolecular layer, the formation of a second layer and transfer by capillary condensation. In the monomolecular zone the relative sizes of the mean free path and the adsorbent pores indicate that Knudsen diffusion governs the passage of water molecules through the pores. But, as the external surface of the adsorbent granule becomes covered with a monolayer, the passage of molecules into the body of the granule is restricted. Under these conditions Knudsen diffusion gives way, probably to surface diffusion. Finally, the low rate associated with ‘the latter increases as transfer by capillary condensation becomes appreciable.

NOTATION A c h L nlv n

P P* r r0 R s

sm s t u

V V, W a” E K r’ 0 9

cm2 Column cross-section Concentration of water in air g water/m3 air at room temperature Thickness of adsorbed layer A Total length of pores of size r cm3/mole Molal volume of condensate Number of adsorbed layers mm Hg or dyn/cma Partial pressure of water mm Hg or dyn/cm2 Saturated vapour pressure Pore radius or half width Aorcm A or cm Condensation radius in COHAN'S formula ergs/mole “K Universal gas constant Concentration of water on alumina g water/g dry alumina Concentration of water in a monolayer g water/g dry alumina m2/g alumina Adsorbent surface area Time of air flow min Air flow rate I/min Volume of pores cm3 Volume of condensate cm3 g Weight of alumina, used as a measure of length Distance along the column cm Increment Intergranula voidage B.E.T. equation constant Pore geometrical factor moles/cm2 Concentration of adsorbed layers Surface tension dynlcm Contact angle between adsorbed layers & condensate meniscus

REFERENCES

;:; r31 141 [51 161

RQSENJ. B., J. Chem. Phys. 1952 20 387. R&EN J. B., Industr. Engng. Chem. 1954 46 1590. CARMAN P. C., Flow of Gases through Porous Media. Butterworths, London 1956. LIVINGSTONE H. K., J. Colloid Sci. 1949 4 447. Private communication with manufacturer 1961. Activated Alumina, catalogue of Peter Spence and Sons Ltd., Widnes, Lanes. 610

Fixed bed adsorption [71 [8] [9] [lo] [ll] [12] [13] 1141

from a high concentration

feed

BOER J. H. DE,2nd Int. Congr. Surface Activity ZZSolid/Gas Interface, p. 93. Butterworths, London 1957. BRTJNAUERS., EMMETTP. H. and TELLERE. J., .7. Amer. Chem. Sot. 1938 60 309. COHAN L. H., J. Amer. Chem. Sot. 1938 60 433. CRANSTON R. W. and INKLEYF. A.,Advances in Catalysis, Vol. IX, p. 143. Academic Press, New York, 1957. INNESW. B., Analyt. Chem. 1957 29 1069. DERJAGUINB. V., 2nd Znt. Congr. Surface Activity II Solid/Gas Interface, p. 153. Butterworths, London 1957. EVERETTD. H., Structure of Properties of Porous Materials Colston Papers, p. 95. Butterworths, London 1958. BOWEN J. H., Adsorption in Fixed Beds. Alumina, Air, Water-Vapour system. Ph.D. Thesis, London 1961. R&urn&-Des mesures gravimetriques ont permis de determiner la distribution de l’eau adsorbee dun courant d’air humide par une colonne d’ahunine active% On a &value Cgalement la variation de l’humidite du courant d’air au long de la colonne. En dehors de la zone satur&e il existe 3 zones de transfert. Pres de la sortie il y a une zone oti les molecules d’eau sont transferees principalement vers une couche monomoleculaire. Suit une region complexe oti le transfert, plus lent, se fait vers des couches bimol&culaires et des couches monomol&.tlaires residuaires. Finalement, pres de la zone saturee, il y a une zone oh la vitesse de transfert augmente et oti la condensation capillaire prevaut. Ces observations ont permis de calculer la distribution des dimensions des pores. Les experiences ont demontre que l’humidite relative de Pair entrant dans la zone a couche monomoleculaire est independante du debit d’air. On pourrait done baser le calcul dune colonne d’adsorption dans laquelle passe un courant d’air a forte humidite sur l’existence dune “monozone”. Zusammenfassung-Die Verteilung des adsorbierten Wassers sowie die entsprechende Feuchtigkeitsabnahme der durchstriimenden Luft kings einer Adsorbensschicht aus aktiver Tonerde wurde bestimmt. Zusatzlich zur Slttigungszone warden drei weitere Stofftibergangszonen festgestellt. In der N&he des Schichtendes entstand eine Zone, in der das Wasser in einer monomolekularen Schicht adsorbiert wurde. Daran anschliessend folgte eine Zone, in der hauptsachlich eine bimolekulare Schicht aufgebaut wurde. Unmittelbar vor der Sattigungszone wurde ein Gebiet mit erhijhtem Stofftibergang gefunden, wobei der Hauptaustauschmechanismus durch Kapillarkondensation beherrscht wurde. Die Porenverteilung wurde bestimmt. Versuche mit verschiedenen Striimungsgeschwindigkeiten der Luft zeigten, dass die relativen Feuchtigkeit der in die Zone der monomolekularen Adsorptionsschicht striimenden Luft unabhangig von der Luftgeschwindigkeit war. Die Dimensionienmg eines Adsorbers kann somit durch Bestimmung der Lange der monomolekularen Adsorptionsschicht erfolgen.

D

611