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A.

ADSORPTION KINETICS

The modified Wheeler adsorption kinetics equation (1), initially derived from a continuity equation of mass balance between the gas entering an adsorbent bed and the sum of the gas adsorbed by plus that penetrating through the bed, shown in the polynomial form tb = (W~W/CoQ) -- (WepB/Cok~)

X In (Co/C~) E1-] has been successfully used by Jonas and R e h r m a n n (2) in studies on the kinetic adsorption of gases by activated carbons. I n this equation, tb is the gas breakthrough time in minutes at which the concentration C~ appears in the exit stream, Co the inlet concentration in g / c m ~, Q the volumetric flow rate in cmS/min, p8 the bulk density of the packed bed in g / c m 3, k~ the pseudo first order adsorp1To whom correspondence should be addressed.

tion rate constant in min -1, W the adsorbent weight in g, and W, the kinetic adsorption capacity in g / g at the arbitrarily chosen ratio of C~/Co. I n Eq. [-1-], pB is determined as a property of the granular size and shape of the adsorbent when filled by gravity settling in a container column, and the parameters Co, Cx, and (2 are set by the conditions of test. A plot of tb vs W, for any fixed flow rate and temperature, yields a straight line curve from whose slope and intercept the parameters We and k~ can be respectively calculated. B. A D S O R B E N T C A P A C I T Y

A series of equations have been developed (2), based upon the original work on prediction adsorption isotherms by Dubinin (3) and the concept of volume pore filling by Bering et al. (4), which permitted adsorbent saturation capacity values, calculated under equilibrium conditions, to be applied with only negligible error to the expected kinetic adsorption

538 Journal of Colloid and Interface Science, Vol. 50, No. 3, March 1975

Copyright I~ 1975 by Academic Press, Inc. All rights of reproduction in any form reserved.

ADSORPTION BEHAVIOR OF ACTIVATED CARBONS capacity for a well packed bed of fine grained activated carbon granules. These equations are summarized in the form

We = dz(,)Wo exp r-- (kR2T2/~ 2)

x (ln P0lP) 2] [-2] for direct substitution of calculated We values into Eq. [-1]. In this equation &(,) is the liquid density of the condensed test gas at the temperature T in °K, W0 the maximum space available for the condensed adsorbate in the adsorbent in cm~/g, k a constant related to the structure of the adsorbent in (cal/mole) -2, Po the saturated vapor pressure of the liquid adsorbate at T, P the equilibrimn pressure of adsorbate vapor at T, and B the dimensionless affinity coefficient which compares the strength of the adsorptive interaction of the adsorbate under consideration to that of a reference adsorbate. C. ADSORPTION ~RATE CONSTANT

The pseudo first order adsorption rate constant kv in Eq. [-1] has recently been shown (5), in the case of benzene vapor adsorption by activated carbon granules, to be a function of the superficial linear velocity V, of the gas-air flow into the carbon bed. The mathematical relationship found, which exhibited a 0.999 correlation coefficient with the experimental data over a 120 to 3000 cm/min velocity range, was

a+b =

1 + (a/b) exp

[--(a + b)cVz]'

[3-1

where a, b, and c were constants of the system. It is expected that one or more of these constants includes the effect of carbon granule size. Equation [3-] describes a sigmoidal curve of k~ versus V~, showing a minimum value b for k~ at a low Vz and a maximum value for k, of a + b at high flow velocities.

eters in Eq. [-1], and consequently U. The volumetric flow rate Q increases due to volume expansion with a proportionate decrease in bed residence time. The inlet concentration Co decreases due to volume expansion and, coupled with the increase in Q, satisfies the requirement for the gas flux (mass per unit area per unit time) to remain invariant. The kinetic adsorption capacity We decreases due to the fact that the physical adsorption process is characterized by a decrease in both free energy and entropy and a negative heat of adsorption (exothermic). This is shown more explicitly by the fact that a higher temperature requires a larger adsorption potential e = RT In Po/P,

Increased temperature in gas adsorption kinetics affects the Q, Co, We, and k~ param-

[4]

for gas adsorption by the activated carbon. An increase in temperature not only directly increases e but also indirectly through its effect on Po/P. Thus, Eq. [-2] can be rewritten as

We = dl,)Wo exp [-k~Vfl2],

[5]

which clearly shows that as e increases We decreases. The pseudo first order adsorption rate constant k,., at any fixed linear flow velocity, decreases as temperature increases. This has been shown by Jonas and Svirbely (6) in the study of carbon tetrachloride and chloroform adsorption by activated carbon. Quantification of the change in k~ as a function of temperature was approached by mathematic modeling based upon Langmuir kinetics which assumed that one gaseous molecule is adsorbed by one active site producing an occupied site, and that an equilibrium exists between these two states. From a kinetic viewpoint the equilibrimn can be shown as a Langmuir type equilibrium constant KL existing between the rate of adsorption (k~) and the rate of desorption (ka). Thus, K5

D . EFFECT OF TEMPERATURE

539

~

kv/kd.

E6]

A procedure for calculating the change in k~ resulting from a change in the temperature of adsorption is proposed as follows :

Journal of Colloid and Interface Science, Vol. 50, No. 3, March 1975

540

JONAS, BOARDWAY AND MESEKE

The Gibbs-Helmholtz equation (7) can be stated for this equilibrium constant KL as

AH °

d In K L -

[7]

d(1/T)

R

and for finite differences as In [ K L ( 2 ) / K L ( 1 ) ]

AH ° -

(1/T2) -

C8]

(1/T1)

R

If AH °, the standard heat of adsorption, is known for the particular vapor it can then be substituted into Eq. [-8]. If not, an approach to the value of the heat of adsorption can be obtained from the vapor pressure vs temperature relationship in the form In P(Torr) = -- (AB°/RT) -t- a.

E9]

Then, substituting A//° for a vapor into Eq. [8] for some T2, where T2 ¢ T1 and T1 is some standard or known temperature, it is possible to calculate the ratio KL(:)/KL(1). Knowing that the molecular diffusivity values for gases or vapors are usually a function of the -~ power of the absolute temperature (8) and assuming that to a first approximation the rate of desorption of a vapor from an activated carbon will be a linear function of its diffusivity, one can establish the relation kd(2) = (_T2/' kdo)

\T1/

[10] "

Recasting Eq. [-6-] in subscript form one can obtain the relationship KL(2)

KL(1)

k~,(,2)kd(1) -

En]

k~(1)kd(2)

and then snbstituting Eq. ElO] into gq. [11] yields k,~(2) .

KL(2)kvo) (T2) ~ .

.

•

.

KL(1)

from Stauffer Chemical Co., Westport, Connecticut and isopropyl methylphosphonofluoridate (IMPF or GB), 98~opure, from Edgewood Arsenal, Maryland. The carbon absorbent used in these tests was a bituminous coal, BPL grade, 12-30 mesh, activated carbon from Pittsburgh Activated Carbon Company, Pittsburgh, PA, having an internal pore surface area of 1000 m2/g. The activated carbon was then impregnated with an aqueous solution (12.0~o NHa) buffered by 10.9% carbonate ion and containing 8.5% cupric copper, 4.1% chromate ion, and 0.3(7o silver nitrate. The impregnated carbon was termed an ASC whetlerite carbon. Thirty and one-half pounds (13,847 g) of this impregnated carbon was filled in an M10 gas filter unit, forming a carbon granule bed with a mean depth of 6.99 cm. Since the cross-sectional area of the bed was 3130 cm2 the volume of carbon was 21,881 cm 8. The mean packed density of the carbon, therefore, was 0.633 g/cm ~. The M10 gas filter has a rated flow of 150 CFM (4245 X 103 cm3/min). B. ~QUIPMENT The kinetic adsorption tests were carried out in a modified Q126 vapor adsorption test apparatus. The apparatus consisted of metal and glass components in an overall metal frame and had three functional sections, one for vapor generation, another for drawing the generated vapor through the M10 gas filter unit, and the third for the detection of vapor penetration of the carbon bed. The vapor penetration was determined by continuously monitoring the exit line with a hydrogen flame emission detector (HYFED) for phosphorus Model SH202, manufactured by Meloy Laboratories, Springfield, Virginia.

[12]

T1 C. PROCEDURE

2. EXPERIMENTAL A. MATERIALS

The vapors used as adsorbents were dimethyl rnethylphosphonate (DMMP), 96.5% pure,

D M M P liquid was drawn by suction directly from a five gallon metal container, through a calibrated rotameter, and into two Spraco nozzles (air nozzle #2081 and fluid

Journal of Colloid and Interface Science, Vol. 50, No. 3, March 1975

ADSORPTION BEHAVIOR OF ACTIVATED CARBONS nozzle # F2), forming a fine spray which was then directed into a 55 gallon drum. Dry air entered a compartment on the side of the drum, near its center, and was pulled downward through a series of four 1700 W Chromalox finned air heaters. The heaters were controlled by a Fenwal temperature controller. The heated air was released in the bottom of the drum where it passed through the D M M P spray. The vapor laden air then passed through a particulate filter which collected any D M M P still present in aerosol form, permitting it to vaporize before challenging the gas filter. In addition to the Hyfed monitoring, bubbler samples were taken at both the inlet and outlet positions, the inlet sample being heated to prevent sample condensation. The auxiliary heat was provided when needed by heating tapes wrapped around the duct and/or sampling lines. A record of pressure drop due to flow and temperature profiles of the tests was kept. The temperature profile was obtained by using six thermistors positioned at various locations in the test apparatus. When the desired test concentration of D M M P was obtained (5 rag/liter or 5 X l0 -6 g/cm 3) the vapor was then directed at 150 CFM (4245 X 103 cm3/min) into the M10 gas filter. The time at which a D M M P concentration of 0.04 X 10-9 g/cm 3 appeared in the exit stream, representing a concentration reduction of 8 X 10-8, was termed the breakthrough time U for the test. 3. RESULTS AND DISCUSSION A. PURPOSE

The purpose of this study is to show that the relationships expressed by Eqs. [-4~-[-12-] can be used to calculate the effect of temperature on various kinetic adsorption parameters, as a result of which it then becomes possible to predict, by means of Eq. [1-], the breakthru times of D M M P vapor through a carbon bed at various temperatures. A necessary prerequisite for these calculations is the characterization of these adsorption param-

541

eters at a reference temperature, in this case 25.0°C. B.

CALCULATION P R O C E D U R E

Prior determination (2) of adsorption parameters for this carbon was made at 25.0°C on small gram quantities under conditions of an inlet D M M P concentration (Co) of 585 X 10-9 g/cm a and an exit concentration (C~) of 585 M 10-1I g/cm ~, to which the breakthru time (U) of the vapor corresponded. Under these reference conditions the kinetic adsorption capacity (We) was 0.299 g D M M P / g carbon and the pseudo 1st order adsorption rate constant (k~,) was 23, 645 rain -I. The detailed step-by-step calculation procedure is shown as follows : (1) The regression equation for D M M P vapor pressure vs temperature, over the range of 7 to 62°C, was found to be - 2807.7 log Torr -

-}- 9.368 T

with a coefficient of correlation r of 0.9977. From this equation the heat of liquefaction (AH °) was determined to be - 12,846 cal/mole. (2) Assuming that, to a first approximation, the heat of liquefaction for D M M P was equal to its heat of adsorption, the AH ° value was inserted into Eq. [8~ to calculate the ratio KL(2)/KL(1) for each of seven T2 values (namely, 40.3, 40.8, 41.3, 41.6, 41.8, 44.9, and 46.7°C) using 25.0°C (298.2°K) as the reference Ti temperature. (3) Ratios of the test to reference temperatures to the ~ power were determined for each of the above six temperatures. (4) Using the value of k~(1) for D M M P at 25°C, and the values of K L ( 2 ) / K L ( 1 ) and (T2/T1) -~ for the various temperatures, the resultant k~(2) adsorption rate constants were calculated from Eq. ]-12] for each of the seven temperatures. Values of these parameters are shown in Table I. (5) In accord with the mass flow conservation principle, the product of inlet concen-

Journal of Colloid and Interlace Science, Vol. 50, No. 3, March 1975

542

JONAS, B O A R D W A Y AND M E S E K E

identified as P0 values in g/cm 3, were calculated from the following relationships

TABLE I D M M P ADSORPTIONRATE CONSTANT AS A FUNCTION O~" TEA[PERATUEE

T~ Temperature °C °K 25.0 40.3 40.8 41.3 41.6 41.8 44.9 46.7

298.2 313.5 314.0 314.5 314.8 315.0 318.1 319.9

(T2/TI)]

1.0000 1.0779 1.0805 1.0832 1.0847 1.0856 1.1017 1.1111'

KL(eI/KLo)

1.0000 0.3470 0.3358 0.3251 0.3187 0.3146 0.2576 0.2298

Ads. rate constant k~ (min-9

V2 =

23645 8844 8579 8327 8174 8075 6710 6037

P0 -

tration Co and volumetric flowrate Q was invariant for each of the six temperatures. Thus, since all T2 temperatures were greater than the reference temperature T1 a volume expansion occurred in each case, causing Co to decrease and O to increase proportionately. The various values were calculated, assuming ideal gas conditions, by applying the appropriate ratios of the absolute temperatures. (6) From two known densities (9) for liquid DMMP, namely 1.1507 g/cm ~ at 30°C and 1.1547 g/cm 3 at 25°C, and the assumption of linearity over the temperature range of interest, liquid densities were then calculated for the six test temperatures under study. (7) The maximum concentrations of D M M P vapor which can exist in air at each of the temperatures under consideration, and

[-13~

V1 - - ,

T1

M p ,

]-14]

V2 760 where V1 is the volume of 24,400 cm 3 occupied by 1 mole of D M M P at 25.0°C, V2 is the volume occupied at the temperature T2 in °K, M the molecular weight of D M M P (124.1 g), p the vapor pressure in mm Hg, and p/760 equal to the fractional number of moles of vapor possible. (8) The above P0 values for each temperature were inserted, together with the inlet concentration pertaining to each test and identified as P values, into Eq. [-4~ to calculate the adsorption potentials. (9) Using values for this impregnated carbon of 4.45 X 10-8 (cal/mole) -2 for k, I for/~ (since in the case of only one vapor it can be considered as its own reference), 0.259 cm3/g as W0, the square of the e values calculated in the previous step, and the liquid density values calculated in step V6~, and inserting them in Eq. E5~, permitted calculation of kinetic adsorption capacities for each temperature. Values of these parameters, determined in accord with the conditions of test, are shown in Table II.

TABLE I I KINETIC ADSORPTIONCAPACITY AS A FUNCTION OF TEMPERATURE Temp. °C

25.0 40.3 40.8 41.3 41.6 41.8 44.9 46.7

Vapor press p (Torr)

Inlet conc. @ test temp. g/cm ~ X 10~

Max. vapor cone. P0 g/cm~ X 109

(Ads. Pot.E)2 (cal/mole) 2

0.897 258 2.6 2.8 2.9 3.0 3.5 3.9

5000 5479 5211 5247 2860 3213 4266 7409

5810 16400 16490 17730 18384 19006 21910 24280

7910 466,419 516,591 578,959 1,354,896 1,237,879 1,069,624 569,239

Liquid density

Kinetic ads. cap

g/cm~

g/g

1.1547 1.1425 1.1421 1.1417 1.1414 1.1412 1.1388 1.1373

0.299 0.290 0.289 0.288 0.278 0.280 ~ 0.281 a 0.287 ~

dz

We

Values break sequence of monotonic decrease as temperature increases because of increased inlet concentrations of test and consequent effect in Eq. [-27. Journal of Colloid and lnlerface Science, Voh 50, No. 3, March 1975

543

A D S O R P T I O N B E H A V I O R OF A C T I V A T E D C A R B O N S TABLE III D M M P BREAKTHRU TIMES I~OR M10 GAS FILTERS Mean bed temp. °C

25.0 40.3 40.8 41.3 41.6 41.8 44.9 46.7

Inlet conc. Co g/cm* X 109 @ 25°C @ bed temp.

5000 5760 5487 5534 3019 3394 4551 7948

5000 5479 5211 5247 2860 3213 4266 7409

Voh flowrate Q cm3/min X 10.3 @ 25°C @ bed temp,

4245 4245 4245 4245 4245 4245 4245 4245

4245 4463 4470 4477 4481 4484 4529 4554

%

Breakthrough time tb min

Deviation

Observed Calculated

117.0 126.0 129.7 193.7 177.2 120.6 66.6

176.3 119.4 123.6 120.6 215.8 191.6 129.5 68.5

+2.05 -- 1.90 -- 7.02

+11.41 +8.13 + 7.40 +2.85 Mean

C. DATA COMPARISON Adsorption parameters for the D M M P adsorbate--M10 gas filter adsorbent system which were invariant with respect to temperature, such as the carbon weight W and the bulk density OB, together with those dependent upon temperature and whose values were calculated in accord with the above described procedure and shown in Tables I and II, were inserted in Eq. [1] to obtain predicted breakthru times. The predicted values were then compared with experimental breakthru times, and both sets of values shown in Table I I I . Although no test was run at 25°C a breakthru time was calculated for that temperature. With respect to the other seven temperatures shown in Table I I I it can be seen that the calculated tb values compare closely with the experimentally observed values. The mean percentage deviation of the calculated from the observed values, without regard to sign, is

5.82%.

5.82

5000 X 10-~ g D M M P / c m 3 as the normalization concentration challenging the bed, an exit concentration of 0.04 X 10-9 g/cm 3, a volumetric flow of 4245 X 10~ cm3/min, a bed weight of 13,847 g, and a bulk density of 0.633 g/cm 3 the breakthru time will be 176.3 min as shown in Table I I I . At 35°C, representing a 10°C increase in temperature, the inlet concentration will be 4838 X 10.9 g/cm 3, the volumetric flowrate 4387 X 108 cm3/min, the kinetic adsorption capacity 0.296 g/g, the concentration reduction ratio Cx/Co 8.268 X 10-6, the adsorption rate constant 12,295 min -~, and the breakthrough time 156.3 rain. Analysis of the magnitude of changes in the various parameters, resulting in the 20.0 min decrease in breakthru time, showed that 87% (17.4 rain) of the decrease was due to lowering of the adsorption rate constant, 9% (1.8 min) of the decrease due to reduction in the adsorption capacity, and the remaining 40-/o (0.8 min) due to volume expansion and its associated effects on concentration and flowrate.

D. EFFECT OF TEMPERATURE ON REFERENCES

BREAKTI-IRU TIME

The effect of temperature on the breakthru time of a gas, such as DMMP, through a bed of ASC whetlerite carbon, as exemplified in Eq. [1-], can be calculated by normalizing the inlet concentration. Thus, at 25.0°C, with

1. WHEELER, n . , AND ROBELL, A. J., ft. Catal. 13, 299 (1969). 2. JoNAs, L. A , AND REHRMANN, J. A., Carbon (Oxford) 10, 657 (1972) ; 11, 59 (1973). 3. DUBININ, M. M., ZAVERINA,E. D., AND RADUSH~EVICR, L. V., Zh. Fiz. K h i m . 21, 1351 (1974).

Journal of Colloid and Inlerface Science, Vol. 50, No. 3, March 1975

544

JONAS, BOARDWAY AND MESEKE

Dum~IN, M. M., AND TIMOFEYEV, D. P., Zh. Fiz. Khim. 22, 113 (1948). DUm~N, M. M., AND ZAVERINA,E. D., Z]~. Fiz. Khim. 23, 1129 (1949). DUBININ, M. M., Chem. Rev. 60, 235 (1960). DUBININ, M. M., Akad. Nauk SSSR Otd. Khim. Nauk 1153 (1960). DUBININ, M. M., "Chemistry and Physics of Carbon," Voh 2, pp. 51-120. Marcel Dekker, New York, 1966. 4. BERING, B. P., DI3BININ, M. M., AND S]~RPINSI~Y, V. V., J. Colloid Interface Sci. 21, 378 (1966). 5. JONAS, L. A., AND REHRMANN, J. A., Carbon (Oxford) 12, 95 (1974). 6. JONAS, L. A., AND SVlRBEL,', W. J., J. Catal. 24, 446 (1972).

Journal of Colloid and Interface Science, Vol. 50. No. 3. March 1975

7. CAST]~LLAN, G. W., "Physical Chemistry," pp. 215-216. Addison-Wesley Publishing Co., Reading, MA 1964. 8. PERRY, J. R., "Chemical Engineers' Handbook," 4th ed., pp. 14-20. McGraw-Hill Book Co., New York, 1963. KNUDSEN, J. G., AND KATZ, D. L., "Fluid Dynamics and Heat Transfer," pp. 18. McGraw-Hill Book Co., New York, 1958. HIRSCH]~ELDER, J. E., BIRD, R. B., AND SPOTZ, E. L., Chem. Rev. 44, 205 (1949). HIRSCH~'ELDER, J. O., CURTISS,C. F., ANDBIRD, I~. B., "Molecular Theory of Gases and Liquids," pp. 581-2. John Wiley and SoDs, Inc., New York, 1954. 9. KOSOLAPOFF,G. M., Y. Chem. Soe. 3222 (1954).

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