signal and requires no complicated computations. It can easily be implemented for any semibatch gas-liquid reactor.
i-
"E:
50
30
0.0
4.0
8.0
12.0
16.0
20.0
24.0
28.0
Time ( M i n . )
A
One Controller
8
Two controllers
4.01
2.0 0.0
4.0
8.0
12.0
16.0
20.0
24.0
2a.o
Time (MI".)
Figure 7. Response to a set point change (8 to 6).
be made satisfactory throughout the entire reaction cycle. The two-controllersystem ~llsobrings about a significant reduction in the total amount of diluent gas required. The simulation study carried out indicates that the performance of a conventional single controller and the two-controller system are essentially equivalent !For small disturbances. However, when the process is subjected to large decrease in reaction rate, as is common when reactions are carried out on a semibatch basis, the two-controller system is superior. The two-controller system is based on only one feedback
Nomenclature C = difference between measured composition and set point value G1 = transfer function of first process element Gz = transfer function of second process element G,1 = transfer function of first controller Gc2 = transfer function of second controller KD = derivative constant KI = integral constant KP = proportional constant R = reactionrate S = Laplacevariable T = time V = volume of head space W = exhaust gas concentration after dilution W' = measured gas concentration X I = diluent flow relative to its steady-state value X Z = feed flow relative to its steady-state value Y = gas flow leaving the liquid surface Yi = gas flow to the reactor 2 = diluent flowrate 71 = time constant of first process element 7 2 = time constant of secord process element 7d = dead timedelay Literature Cited Emanuel, N. M., et al., "Liquid Phase Oxidation of Hydrocarbon." Chapter 1, Plenum Press, New York, N.Y., 1967. Luyben, W. L., AlChEJ., 14 (I), 37 (1968). HarriOtt, P., "Process Control," Chapter 8, pp 153-177 McG-aw-Hill. New York, N.Y., 1964. Hughmark, G. A., Hydrocarbon Process., 44 (4), 169 (1965). McAvoy, T. J., Id.Eng. Chem., Process Des. Dev., 6, 440 (1967). Shinskey, F. G., "Process Control System," Chapter 10, pp 278-280, McGraw-Hill, New York, N.Y., 1967. Sommerfeld, J. T., Schucker, R. C., lnstrum. ControlSyst., 45 (9), 63 (1972). Ziegler, J., Nichols, N., Trans. ASME, 64, 759 (1942).
Received for review June 2,1976 Accepted January 21, 1977
Presented at the AIChE 81st National Meeting, Kansas City, Missouri, April 1976.
Adsorption 01 Methylmercuric Chloride on Activated Carbon. Rate and Equilibrium Data R. Dean Ammons, Neil A. Dougharty, and J. M. Smith' Department of Chemical Engineering, University of California, Davis, California 956 76
The adsorption of methylmercuric chloride from aqueous solutions on activated carbon at 25 OC was studied in batch experiments and in packed beds with continuous liquid flow. The isotherm was reversible and nonlinear over the liquid concentration range 0 to 320 ppm, with an approximately linear section up to 20 ppm for which the equilibrium constant was 3000 cm3/(gof carbon). Breakthrough curves (BTC) were measured in packed-bed experiments as a function of particle size (0.057 to 0.263 mm diameter), bed length (0.79 to 4.7 cm), and liquid velocity (1.6 to 4.7 cm/s). The moments of the breakthrough curves were analyzed to establish the relative importance of the various individual processes contributing to the overall adsorption. Axial dispersion was found to contribute no more than 15% to the second moment while liquid-to-particle mass transfer contributed about 60 %
This paper reports a. study of the removal of a water-soluble mercury compound by passing the waste stream through
packed beds of activated carbon. The chief objectives were to determine the relative importance of the several mass transInd. Eng. Chem., Fundam., Vol. 16, No. 2, 1977
263
port processes and the adsorption step at the carbon site. I t was necessary also to determine the adsorption equilibrium isotherm at the conditions of our work, 25 "C and 1 atm pressure. There is considerable evidence (Jensen and Jernelov, 1969; Jernelov, 1969) that all forms of mercury can be converted to soluble methylmercury compounds by biological processes under the conditions that prevail in lakes, streams, and estuaries. Investigations in Japan and projections by others (Fujiki, 1963; Lofroth, 1970; Anflat et al., 1968) suggest that methylmercuric chloride or methylmercuric hydroxide may be representative of methyl mercury compounds occurring in natural waters overlying mercury-containing sediments. Methylmercuric chloride also has been investigated (Smith et al., 1971) as a form of organic mercury in waste streams from industrial processes. For these reasons methylmercuric chloride (solubility in water = 0.020 g-mol/L at 25 "C) was chosen for our study. A summary of its properties is available (Ammons, 1975). Pulse-response techniques have been used successfully to evaluate mass transport and adsorption rate constants in packed beds (Schneider and Smith, 1968; Suzuki and Smith, 1971; Mehta et al., 1973). We first planned to use this technique wherein a pulse of adsorbate is introduced into the feed to the bed and the concentration peak of adsorbate in the bed effluent is measured with a suitable detector. The mass transport and adsorption rate constants can then be calculated from the first and second moments of the effluent peak. The chief restriction is that all the transport and adsorption steps in the bed be first order. Due to the high adsorption capacity of activated carbon for methylmercuric chloride, no practical combination of bed length, particle size, flow rate, and pulse concentration could be found such that the effluent peak could be analyzed accurately by available methods. These peaks were invariably of low concentration and flat. Hence, the approach was changed and breakthrough curves (BTC) were measured in response to step functions of methylmercuric chloride concentration introduced to the bed. Since moments can be calculated from the breakthrough curves, the data were evaluated by the moment method already developed. Due to the high capacity and slow desorption, the BTC exhibited long tails which made the mercury-carbon system a difficult one to analyze. However, the BTC approach was satisfactory for establishing the importance of the several transport processes. Experimental Section Solutions of CH3HgCl were prepared from distilled water and commercially available methylmercuric chloride (with a stated purity of more than 95%). Concentrations of the mercuric salt in the aqueous solutions were determined by spectrophotometric analysis in a Beckman DK-SA ultraviolet spectrophotometer. Solutions were prepared by weighing dry CH3HgCl (fO.OO1 g) and adding distilled water in a volumetric flask. The solutions were stored in glass-stoppered Pyrex bottles. Analysis of solutions exposed to laboratory lighting for 3 days and other solutions maintained in darkness gave the same results. A 100 ppm solution stored for 2 months changed less than 1%in concentration. It was concluded that neither adsorption on the walls of the glassware or light had a significant effect on the concentration. Calibration curves were prepared for the spectrophotometer by plotting the maximum absorbance vs. known concentrations from 5 to 500 ppm. The maximum absorbance occurred at wavelengths within the range 190 to 195 nm. For equilibrium isotherm measursments liquid samples were analyzed in a closed cell inserted in the spectrophotometer. For BTC data a 1-cm length continuous-flow cell was used with the spectrophotometer operated as a time-scanning instrument 264
Ind. Eng. Chem., Fundam., Vol. 16, No. 2, 1977
a t a constant wavelength of 194 nm. When operated as a continuous-flow instrument, distilled water flowed through the reference cell at the same flow rate as the solution passed through the sample cell. The precision of the spectrophotometer in the range used was within 1%. The activated carbon used was Filtrasorb 200 (a coal-based material supplied as granular particles about 0.9 mm in diameter) from the Calgon Corporation. Its particle density, pp, was determined by mercury porosimetry to be 1.02 g/cm3, based on several measurements on a sample of particles of average diameter equal to 0.263 mm. The density, pt, of the solid phase of the particles was 2.20 g/cm3 as determined with a helium pycnometer. The porosity calculated from these two densities is 0.534. The manufacturer specifies a BET surface area of S , = 800 to 900 m2/g which corresponds to an average pore radius (F = 2p/p,Sg) of 12 A. Manufacturer's information indicated that the pore volume was distributed over a wide range of pore sizes, as is the case for many activated carbons. Before use the carbon was ground and sieved to the desired size range. In analyzing the data these particles were assumed to be spherical with a diameter equal to the arithmetic average of the sieve openings. The particles were then washed five times in distilled water, boiled in distilled water for 30 min, and dried to constant weight at 110 "C. For equilibrium measurements the carbon was used as taken from the drying oven. For BTC experiments the dried carbon was again boiled with distilled water prior to preparing the packed bed. Otherwise, air trapped in the pores had an adverse effect on the method used to obtain a uniformly packed bed. Adsorption Equilibrium Experiments. The adsorption isotherm was established by analyzing liquid samples taken from mixtures of carbon particles and solution. The procedure consisted of contacting various masses of carbon particles (dp = 0.114 mm) with 50-cm3portions of 50 and 500 ppm solutions of CH3HgC1. The solutions were covered and then mixed continuously in a rotating machine for 10 days. Preliminary tests indicated that equilibrium was closely approached after 24 h. Small, known volumes of liquid were withdrawn and analyzed to determine by difference the concentration of adsorbed carbon. Each portion then received the following treatment. Ten cm3 of distilled water was added, the mixture was rotated for a second 10 days, and small samples of liquid were analyzed. Then 50 cm3 of the solution was removed and discarded and 50 cm3 of distilled water was added. After a third 10-day rotation period samples of liquid were again analyzed. This sequence of steps yielded three different points on the isotherm, one based on adsorption, one for mild desorption, and one for strong desorption. The desorption steps determined the reversibility of the adsorption. The air temperature in the temperature-controlled hood where the measurements were made varied from 23.8 to 25.3 "C. Breakthrough-Curve Experiments. A Chromatronix, liquid-chromatograph column was used to hold the packed bed. It was a precision-bore glass tube, 0.250 in. i.d. with a total length of 13 in. The upper and lower bed supports consisted of two layers of fine-mesh stainless steel screen. The connecting lines of the apparatus were made of 0.024-in. i.d. Teflon tubing. The solutions were in contact only with glass and Teflon with the exception of the support screens. Preliminary experiments indicated that significant amounts of CH3HgC13 were not adsorbed by these materials. The inlet and outlet lines of the column terminated a t the bed support screens. These lines were as short as possible in order to reduce the effects of dispersion and residence time outside the packed bed and between the injection valve and spectrophotometric detector. However, this was not an important factor for the CH3HgCl-water-carbon system because first and second moments for the packed bed are very large (Table 11).
Table I. Experimental Conditions for Breakthrough Curves ~~
BTC no. 1 2
3 4 5 6 7 8 9 10
~
Particle diameter, d,. mm
Bed length, 2 , cm
Bed void fraction, a
0.057 0.0825 0.0825 0.0825 0.114 0.1 14 0.227 0.5127 0.2127 0.263
0.79 2.10 1.91 2.10 1.73 2.05 ‘3.88 3.93 4.01 4.68
0.362 0.428 0.404 0.443 0.372 0.425 0.401 0.406 0.420 0.415 CH3HgCl solution
Constan! head
Liquid flow rate, Q , cm3/min
Interstitial velocity, u , cm/s
25.8
3.2 2.6 4.3 4.7 3.4 3.3 1.6 1.8 3.3 3.4
25.5
39.4 47.8 28.5 31.7 15.0 16.9 33.7 31.8
Reynolds no. 2.0 2.4 3.9 4.3 4.4 4.2 4.0 4.6 8.4 10.1
Prior to a run, distilled water flowed through the bed for at least 10 min to purge air from the detector cell. Then the spectrophotometer was calibrated at zero and 100%absorbance and the stability of the base line (zero absorbance) observed for 5 min. Feed lines of both distilled water and mercury solution were pressurized during this time. Then the step function input of mercury solution was introduced with the injection valve. Flow was continued at constant rate until the bed effluent solution showed the same absorbance as the feed.
&-€l;rTkl Packed bed of activated carbon
Spectrophotometer with continuous
Distilled Water
Wtste Water
Waste CH3~gci
Figure 1. Apparatus for breakthrough curve data.
In addition to the column the essential parts of the apparatus were the sample injection valve and the spectrophotometric detector, as shown in Figure 1. The injection valve was a two-position rotary type of Teflon and Kel-F which permitted smooth switching from a flow of distilled water to the same flow rate of CH:3HgC1 solution, without air leaks and with minimum pressure fluctuation. Initially, the bed was formed by locking the outlet bed support in place, pouring in the desired amount of dried carbon, and compressing the bed with the inlet bed support. Such beds exhibited channeling, as large amounts of CH3HgCl were detected in the bed effluent almost immediately after introducing the step input. After experimentation, the following packing method was found to result in maximum packing density and minimum channeling. The dried carbon was boiled in distilled water and added in four equal portions to the column as an aqueous slurry. After each addition, the bed was compacted with a vibrator, compressed by hand, and further compressed by pressuring, alternately, both ends of the bed with distilled water at 200 psig for 10 min. After each pressure cycle, one bed support was loosened, used to compress the bed by hand as far as possible, and retightened. When the bed length did not change (usually after four cycles) the bed length was mleasured and the BTC run procedure initiated. The bed density and bed void fraction were calculated from the bed volume and particle density. Table I gives the properties of the bleds for which BTC were measured.
Theory Mass transfer of CH3HgC1 in the bed is supposed to occur by the four processes: axial dispersion (dispersion rate constant EA)in the interparticle voids, transport from bulk liquid to particle surface ( k f ) ,intraparticle diffusion in the liquidfilled pores ( D e ) and , adsorption at a site with a rate constant k , . The adsorption process is assumed to be reversible and first order with an adsorption equilibrium constant, KA.This means that concentrations of CHBHgCl in the water must be low enough that the adsorption isotherm is linear. It i s also assumed that the bed is isothermal and that the liquid velocity is uniform across the column diameter. Moment Equations. For the model and conditions just described the first absolute moment F ~ and ’ the second central moment p2 of the effluent peak, obtained in response to a square pulse input, can be related to the rate and equilibrium constants EA,k f ,D e , k , , and KA.The results, which were derived previously (Schneider and Smith, 1968), are
where (3) 81
=
1-CY
(--)B
where t o / 2 and to2/12 are the contributions of the input pulse (injection time = t o ) to the first and second moments, respectively. Equations 2 and 4 show that the contributions of the four processes to the second moment are additive. The general procedure for analysis is to evaluate moments numerically from the observed breakthrough curves and then to use these moment values in eq 1 to 4 to determine the imInd. Eng. Chem., Fundam., Vol. 16, No. 2, 1977
265
BTC no. 4
(11
dp = 0.0825 mm. 2
= 2.10 cm,
Q = 41.8 cm.' min
" 1-
i l l BTC no. 9
= 0.221 m. z p = 4.01 cm. 9 = 33.1 c m 3 min. d
o
10
IO
120
160
zoo
LIQUID COUCEUTRATlOn, C L ,
210
ZIO
azo
aeo
pm
Figure 2. Adsorption equilibrium isotherm for aqueous CHjHgCl solutions of activated carbon at 25 "C.
'a
'c
-t
portance of each of the four transport processes to the overall performance of the adsorption bed. Moments from Breakthrough Curves. Equations 1 to 4 are obtained by solving the conservation differential equations for the bed in the Laplace domain. Since the solution for the effluent concentration in the Laplace domain for a pulse input ( 6 ) is related to that for a step input ( b ) ,moments can be calculated from breakthrough curve data. The relationship between the two concentrations is [cL(z,
= S[cL(z, s)]b
(5)
Using this relation and the properties of the Laplace transformation, the following equations can be derived (Ammons, 1975) for the moments
where C L is~ the concentration of CH3HgCl in the step input to the bed. The measured BTC's were employed to calculate pl' and ~2 using eq 6 and 7 . Then these moment results were compared with eq 1 and 2 to evaluate the significance of the individual processes to the overall adsorption operation.
Equilibrium Results The results of the adsorption and desorption, batch equilibrium measurements are shown in Figure 2. The agreement between adsorption and desorption points shows that adsorption of CH3HgCl from aqueous solutions on activated carbon is reversible. The points at the lowest liquid concentration, 5 ppm, are not as reproducible as at the higher concentrations, probably due to the limited precision of the spectrophotometric analyses. The moment theory requires that the adsorption be first order as well as reversible. Figure 2 shows that the isotherm is very close to linear for concentrations up to a few ppm and reasonably linear up to 20 ppm. Since the accuracy of the analysis is uncertain at very low concentrations, we used 20 ppm for the step-function concentration for the BTC experiments. The slope of the straight line drawn through data points up to CL = 20 ppm in Figure 2 gives a value of K A = 3000 cm3/g of carbon. Neither the Langmuir or Freundlich equations fit the isotherm data over a wide concentration range. However, the Temkin form C, = 0.054 In (0.174C~) (8) agrees with the data points in Figure 2 within 12% for liquid 266
Ind. Eng. Chem., Fundam., Vol. 16, No. 2, 1977
i c ) BTC no. 1
t
2
'b
Q
= 3.88 em. 15.0 c m 3 min.
V 1-
Figure 3. Typical H ' K for input Concentrations of 20 ppm.
concentrations from 10 to 200 ppm. The deviation is 20% at 300 ppm.
BTC Results-Correction for Channeling Ten breakthrough curves were measured for various values of particle diameter, packed bed length and liquid flow rate. The conditions for each BTC are given in Table I. In all cases CH,jHgCl appeared in the effluent stream a few seconds after the step function was introduced. The concentration then rose sharply to 15 to 25% of the inlet value, after which the concentration-time relationship followed the sigmoidal form of a normal BTC. The initial rise became more severe as the bed length decreased and particle size and flow rate increased. This suggested that some channeling occurred, even with the careful attention given to preparing a uniform, dense bed. In the short beds used some solution could presumably flow down the tube walls, or through connected interstices in the bed, without effectively contacting the particles as far as mass transfer of CH3HgC1 is concerned. Longer beds were not practical because the time required to obtain a BTC became prohibitive. The first moment (retention time) for a 4-cm length bed was about 4 h (Table 11) and a complete BTC required a much longer time. Representative BTC depicting the channeling effects are shown in Figure 3. To correct the BTC for channeling, a procedure was developed for predicting the fraction of the total flow which did not contact the particles. This was done by assuming that the concentration C', (Figure 3a) at the nearly flat section of the BTC curve was due entirely to channeling. When there was no distinct flat section, as in Figures 3b and c, the location of C,' was determined by first converting the BTC to the equivalent response curve for a pulse input (C6vs. t ) . The equation relating the two concentration vs. time curves is
where M is the quantity of adsorbate injected in the pulse
Table 11. First and Second Moments Calculated from Breakthrough Curves (After Correction for Channeling)
1 2 3 4 5 6 7 8 9 10
f Iwo
lZW0 1,
1c#o
1480 3 960 2 410 2 380 3 350 3 300 14 100 13 100 6 890 7 010
2.3 9.3 5.0 4.0
12. 17. 280. 200. 130. 200.
2WW
,,e
Figure 4. Response curve to pulse input predicted for BTC No. 9.
ment Apl’, for adsorption by the bed of particles alone, is given by API’ = 111’ - (p1’)in
(11)
Subtracting eq 1with K A = 0 from eq 1gives an expression for Ap1’ in terms of K A .
llffl
ISM
12W
This result shows that a plot of Apl’/((l - a ) / a )p vs. z / u should give a straight line through the origin with a slope of p 6 ( ~ / P .The observed p~ values were corrected for (pl’)in according to eq 11and the results are plotted according to eq 12 in Figure 5 . The correction for (pl’)in was always very small. For example, for BTC no. 3, p1’ was 2410 s and (pl’)in was 4
m woo
1ffl
S. 0
a
0.1
0.8
0.1
1.2
1.5
1.1
1.1
1.4
2.1
I I ,S*&
Figure 5. First-moment function for adsorption. input. The so-computed response to a pulse input is illustrated for BTC no. 9 in Figure 4. The effect of channeling, shown at the left side of the response curve, can now be separated by extrapolating the trailing edge of the channeling peak and the leading edge of the normal peak to zero concentration. This extrapolation, shown b y the dotted lines in Figure 4, is guided by the condition that the sum of the concentrations indicated by the dotted lines, at any time, must be equal to the concentration denoted by the solid line. The interstitial velocity used in analyzing the moment data by eq 1and 2 must also be corrected for channeling. These correction procedures are described in detail by Ammons (1975). The moments values calculated from eq 6 anid 7 using the corrected BTC are given in Table 11. Note that ithe second moments are very large.
First Moment Analysis Equations 1 and 3 slhow that the adsorption equilibrium constant can be determined from the first moment. However, the p1’ values in Table I][ include the retention time in the dead volume (V,) between injection valve and bed, and between bed outlet and detector. Further, the observed first moment includes the residence time in the void volume of the bed. To correct for these two effects, eq 1, with 3, may be applied to a hypothetical situation of a nonadsorbing adsorbate ( K A= 0). The resulting inert first moment would be (&’)in
=u
[ 1+ (
3 3 1
+
2
(10)
The data in Figure 5 do suggest a straight line with no effect of particle size, as required by eq 12. From its slope K A is calculated to be 3740 cm3/g, in comparison with 3000 cm3/g obtained from the batch equilibrium experiments. To see if the difference between these values was due to the method of correcting the BTC’s for channeling, first moments were calculated from the original BTC’s and plotted vs. z/u, where now the interstitial velocity also has not been corrected for channeling. The resultant K A was essentially unchanged. A t least part of the deviation between values is due to the nonlinearity of the isotherm up to CL = 20 ppm. In the first part of the BTC the average adsorbed concentration in the column is much less than that corresponding to equilibrium at CL = 20 ppm. As Figure 2 shows, deviations from linearity would correspond to larger slopes (and larger equilibrium constants) than the slope of a straight line from the origin to C L = 20 ppm. Hence, the larger value of K A obtained from the first moment analysis is reasonable. Except at the lowest CL, isotherm data points shown in Figure 2 are believed to be accurate to a few percent. The equilibrium constant of 3000 cm3/g may be somewhat high since it was obtained by supposing the isotherm to be linear up to CL = 20 ppm, which is not exactly correct.
Second Moment Analysis Second moment values are less consistent than first moment results. This is particularly so for this difficult liquid system where the slow desorption results in a long tail in the BTC. Hence, it was not possible to obtain accurate values for all the rate constants in the equation for the second moment. Nevertheless, valid conclusions can be reached for the relative importance of the four rate processes. The contribution of each process to p2 can be displayed by rewriting eq 2-4 in the form
Since (Y and /3 are knowin and VD was measured to be 2.0 cm3, (pl’)in can be calculated for any flow rate. Then the first moInd. Eng. Chem., Fundam., Vol. 16, No. 2, 1977
267
1.0
1.0
5.0 Y
"
1
1
__--.-
1
-
1
1
1
6.0
0.221 mn. /5.0
4.0
1.1
/
2.0
I
1Jlb m.
odp=o.051 m
0 1) = om m
1.WI A.
----0.1s-
le@ 0 a&
(.a o m m0.6
o.18
0.76
0.1
0.1
1
I
1.2
1.1
2.1
R 2 1 1 0 4 , un2
l/*,I*e./
(111,
1
Figure 7. Effect of particle diameter on contribution to second mo-
Figure 6. Second-moment function for adsorption.
ment. (14) (15)
where 60 is given by eq 3. Dispersion can occur in the dead volume. To evaluate its contribution, not shown in eq 13, a pulse of CH3HgC1 solution was passed through the system with no activated carbon present and with the variable bed length reduced to essentially zero. The second moment of the response peak at the detector for this experiment was three orders of magnitude less than the smallest second moment calculated for the ten BTC. Hence, no corrections of this type were made to the 6 2 values given in Table 11. Axial Dispersion. Correlations in the literature (Gunn, 1969,1971; Miller and King 1966;Perkins and Johnston, 1963; Wilhelm, 1962) in the range of Reynolds numbers and particle sizes (Table I) and Schmidt numbers corresponding to our experiments show the axial Peclet number to be nearly independent of velocity and particle size. Therefore, E A should be directly proportional to the interstitial velocity. Under these circumstances the last term in eq 13 is proportional to l / u . If kf (eq 16) is so large that 6, is insignificant, or if the velocity is so low that kf is determined by molecular diffusion alone, all the terms in eq 13 are independent of velocity except the last one. Then a plot of the left side of eq 13 vs. l / u should yield a straight line whose intercept is (6, 6i 6e). Since neither of these extremes is exactly met a t conditions of our work, a linear plot is not rigorous. However, such a plot, as shown in figure 6, is useful to show the significance of axial dispersion resistance to the overall adsorption rate. The lines for various particle sizes in Figure 6 were all drawn with the same slope as determined by the data for d , = 0.0825 and 0.227 mm. According to eq 13 extrapolation of these lines to infinite velocity gives (6, 6i 6e), while the vertical distance of any point above the intercept identifies the a x i d dispersion contribution. Since the lines are rather flat, the axial dispersion contribution is small. At u = 3.3 cm/s, (EA/ a)(l 60)2(1/u2) constitutes from 4 to 15% of k&!(z/u) depending on particle size. It may be concluded that axial dis-
+ +
+ +
+
268
Ind. Eng. Chem., Fundam.. Vol. 16, No. 2, 1977
persion was rather unimportant, even though the extrapolation based upon kf being independent of velocity is not exactly true. The relative unimportance of axial dispersion is not unexpected since the BTC were corrected for channeling, which is responsible for much of the so-called dispersion in a packed bed with liquid flow. The slope of the lines in Figure 6 corresponds to a Peclet number, d,u/EA, of 2.1 in comparison with values of 0.2 to 0.6 predicted from available correlations. The difference between values is reasonable since the data upon which the correlations are based were not corrected for channeling. This was verified by carrying out the same analysis using second moments uncorrected for channeling. Such an analysis yielded Peclet numbers similar to those predicted from the correlations. Liquid-to-Particle Diffusion. The intercept values in Figure 6 are the sum of the contributions to p z due to liquidto-particle diffusion ( f i e ) , intraparticle diffusion (&), and adsorption at the internal site (6,). Considerable experimental information has been obtained for kf. Hence, we can expect to predict this rate coefficient, and then ,6, with reasonable accuracy from available correlations. Such is not the case for the rate coefficients necessary to obtain 6i and 6,. For the conditions of our experiments the following correlation of Wakao et al. (1958) seemed most appropriate
Using this expression for kf, the values of 6, determined from eq 16 were about 60% of the total intercept in the range of velocities (see Table 11) covered by our experiments. In the calculations the molecular diffusivity D of CH3HgCl in water cm2/s, as calculated from at 25 "C was taken to be 1.79 X the Nernst equation (Reid and Sherwood, 1966).These results show that resistance to transport from bulk liquid to particle surface was mare important than intraparticle diffusion in this liquid system. (It is shown later that the rate of adsorption at an interior site, k,, is very fast so that the contribution of 6, to the total is negligible.) In gaseous systems, fluid-to-particle surface resistance is not as important, and often is negligible (Schneider and Smith, 1968). Adsorption Rate, k,. Equations 14-16 indicate that (6,
+
'
+
6i 6,) should vary linearly with R2 and give an intercept equal to 6,. The intercepts for the five particle sizes shown in Figure 6 are plotted vs. R2 in Figure 7. Since the intercepts in Figure 6 are subject to uncertainty, the data points in Figure 7 can include some error. Nevertheless, such uncertainties are insufficient to counteract the indication that the intercept in Figure 7 is near zero. This means that the rate constant k , is large, corresponding to rapid adsorption of CH3HgC1 on the sites of activated carbon. Such a conclusion is not expected in view of the polar characteristics of the adsorbate molecules and the adsorbent. Intraparticle Diffusion. The intraparticle diffusivity for the pore volume can be estimated from the expression
D,=
(f) D
where T is the tortuosity factor. Using a conservatively low value for T of 2.5 [Satterfield's (1970) summary of available data indicates tortuosity factors of 3 to 41, D , is 3.8 X cmz/s. In contrast, D e viilues calculated from the slope of the line in Figure 7, using eq 15 and 16, average about 2 X cm2/s. The range of values is due to the fact that 6, determined from eq 16 depends upon the velocity and particle size as calculated from eq 17. Tihe fact that De is about 60 times larger than D , provides strong evidence for surface diffusion. Calculation of the molecular diffusivities by other methods, as given by Sherwood and Reid (1966), gave values from 1.0 to cm2/s. These numbers do not deviate enough from 1.2 X the Nernst result to explain the difference between De and D,. The fact that the isotherm is slightly favorable (concave downward), rather than linear as assumed in the moment theory, could lead to high values of De, as shown by Dranoff and Colwell(l969,1971). However, such an error again could not explain the 60-fold increase of D e over D,. It is postulated that surface diffusion is the predominant process of intraparticle mass transfer. This result has been observed in other instances, for example by Komiyama and Smith (1974) in studies of adsorption of benzaldehyde in aqueous slurries of activated carbon and Amberlite particles. The effect of surface migration is to yield apparent values of the intraparticle diffusivity much larger than expected for liquid-filled pores. This reduces the importance of intraparticle mass transport and probably explains why fluid-toparticle transport was the dominant barrier in the overall adsorption process.
Acknowledgment The financial assistance of the Federal Water Quality Administration in the form of a Fellowship is gratefully acknowledged. We thank also the Calgon Corporation for supplying the activated carbon. Nomenclature C, = adsorbed concentration of CH3HgC1 on activated carbon, g-mol/cm3 CL = concentration of CHBHgCl in the aqueous solution, g-mol/cm3 C', = solution concentration at time when the true BTC (shorn of channeling effects) begins, g-mol/cm3 c = Laplace transform of the solution concentration d, = average diameter of carbon particle, cm D = molecular diffusivity of CH3HgC1 in water, cm2/s De = total effective diffusivity (based upon void plus nonvoid diffusing area) in the carbon particles, cm2/s D , = effective diffusivity (based upon void plus nonvoid diffusing area) in the pore volume of the carbon particles, cm2/s
E A = effective axial dispersion coefficient, cm2/s k , = first-order adsorption rate constant, cm3/(g)(s) K A = adsorption equilibrium constant for linear portion of isotherm, cm3/(g of carbon) k f = fluid-to-particle surface mass transfer coefficient, cm/s M = quantity of adsorbate in pulse, g-mol Q = liquid flow rate, cm3/s R = radius of carbon particle, cm F = mean pore radius in carbon particle, cm s = Laplace transform variable S , = surface area of the carbon particles, cm2/g t = time, s to = pulse injection time, s u = superficial velocity in the bed, cm/s v d = dead volume between injection valve and detector, cm3 u = interstitial velocity in the bed, u/a,cm/s z = bed length coordinate, cm Greek Letters a = interparticle void fraction in the bed (3 = intraparticle void fraction 60 = equilibrium function defined by eq 3 61 = second moment function defined by eq 4, s 6,, 6,, bi = contributions of adsorption, fluid-to-particle and intraparticle diffusion resistances to the second-moment function, eq 13-16, s p = density of liquid solution, g/cm3 pp = particle density, g/cm3 pt = true (solid phase) density of particles, g/cm3 p = viscosity of liquid solution, g/(cm)(s) pl' = first absolute moment of response peak to a pulse input (corrected for channeling), s (pl')in = first moment for a nonadsorbing ( K A= 0) component, s Ap1' = contribution of adsorption alone to first moment, s 1.r2 = second central moment of response peak to a pulse input, ( s ) ~ T = tortuosity factor, eq 18 Subscripts 6 = response to pulse input b = response to step-function input 0 = input condition
Literature Cited Ammons, R. D., M.S. Thesis, University of California, Davis, 1975. Anflat, T., Dyrssen, D.. Ivanova, E., Jagner, D., Sv. Kern. Tinskr., 80, 340 (1968). Colweil, C. J., Dranoff, J. S., Ind. Eng. Chern., Fundam.. 8, 913(1969). Colwell, C J., Dranoff, J. S., Ind. Eng. Chern., Fundarn., 10, 65 (1971). Fujiki. M., Kurnarnoto Igakkai Zasshi, 37, 494 (1963). Gunn, D. J., Trans. Inst. Chern. Eng., 47, T351 (1969). Gunn, D. J., Trans. Inst. Chern. Eng., 49, 109 (1971). Jensen, S.,Jernelov, A,, Nature, 223, 753 (1969). Jernelov, A.. in "Chemical Fallout," M. W. Miller and G. G. Berg, Ed., C. C Thomas Co., Springfield, Ill., 1969. Komiyama, H.. Smith, J. M., AlChEJ., 20, 728 (1974). Lofroth, G. "Methylmercury." Ecological Research Comm. Swedish Nat. Sci. Res. Council, 2nd ed, Stockholm, 1970. Mehta. R. V., Merson, R. L., McCoy, 6. J., AIChEJ., 19, 1068 (1973). Miller, S. F.. King, C. J.. AlChEJ., 12, 767 (1966). Perkins, T. K., Johnston, 0. C., SOC.Petrol. Eng. J., 70, (March 1963). Reid, R. C., Sherwood, T. K., "Properties of Gases and Liquids," McGraw-Hill. New York. N.Y.. 1966. Satterfield, C. N., "Mass Transfer in Heterogeneous Catalysis," M.I.T. Press, Cambridge, Mass., 1970. Schneider, P., Smith, J. M.. AIChEJ., 14, 762 (1968). Smith, S. B., Hyndshaw, A. Y., Laughlin, H. F., Maynard, S. C., presentedat 44th Annual Conf. Water Pollution Control Federation, San Francisco, Calif., Oct 1971. Suzuki, M , Smith, J. M.. J. Catal., 21, 336 (1971). Wakao, N., Oshima, T., Yagi, S.. Kagaku Kogaku, 22, 780 (1958). Wilhelm, R. H., Pure Appl. Chern., 5 , 403 (1962).
Receiued f o r review June 16,1976 Accepted January 25,1977
Ind. Eng. Chem., Fundam., Vol. 16, No. 2, 1977
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