d
R. F. BADDOUR, D. J. GOLDSTEIN, AND P. EPSTEIW Massachusetts Institute of Technology, Cambridge, Mass.
ONSIDERABLE published data are available for ion exchange columns operated under saturating conditionsthat is, a column saturat,ed with ions A is treated with a solution of ions B until saturated with B. Practically, however, an ion exchange column is oft’en run under partly saturating conditions-elution wit,h one ion is begun with the column only partly saturated with the other. Since this important case has received relatively little treatment, this paper reports both theoretical and experiment’al investigation of cation exchange in partly saturated columns operating under nonequilibrium conditions. The system used was one for which rate and equilibrium data H + solutions and Donex 50. These have been taken, Na+ data ( 3 ) were taken by simple saturation experiments, and it will be shown that these are sufficient to predict the performance of partly eaturated columns.
-
EQUATIONS FOR ELUTRIATlON CURVE
The experiment to be described mathematically is as follows. The column is initially saturated with ions A + and the void space is filled either with a solution of the same ions or with pure water. A band solution of ions B + of concentration co meq. per cc. is introduced into the column at a rate of V cc. per second until B total volume of QB cc. has been introduced. At this point, addition of band solution B + is stopped and, immediately, an eluting solution of A+, also of concentration co, is added at the same velocity, V , and in the same direction. Before the cycle is repeated, the addition of A + must be continued until the effluent from the column contains no Bf. The cycle begins with the introduction of band solution. After a total volume of Q plus the volume of the voids has flowed out, of the column, the concentration of B + in the effluent is designated as c. A plot of c/cp versus Q is called the elutriation curve. This has a bell shape instead of the S-shape of the elutriation curve for mturation performance. Equations for the elutriation curve have been rederived recent,ly by Goldjtein (4). In his article, extensive literature referenceR are given. A11 the theoretical results presented in this paper were taken from Goldstein’s work. The important assumpt>ionsmade by Goldstein in his derivations are as follows;
where
Equation 1 with 2 was derived by Thomas (6) and used for studying saturation performance; Equation 1 with 3 was first present,ed by Hiester and S’ermeulen ( 5 ) . EVALEATIOX O F J-FUKCTION. Values of the J-funciion involved in the above solution may be obt’ained from a, table prepared by BrinkIey ( I ) , noting that Brinkley’s function equals 1 J(z,y). The funct’ion can also be evaluated readily from asymptotic expansions developed by Goldstein (4). The table and the abbreviated expansions listed below were found to be adequate for evaluat’ing J in t’he range used in this work. The proccdurc for caiculating a point was bricfiy as foIIoas. As many of the four J-functions as possible were taken from the
-
TABLEI. ISTZRT’ALS FOR APPLYING L I M I ~ I FORVS AG r > 1
Y < z(r -
Z(i
-
Y< Interval
Mixing and diffusion in the axial direction are negligible. 3. The rat~eof exchange betveen B + and A + on the resin is given by an equation of the form 2.
d B R / d t = i c B s A ~- ( ~ / K ) B R A s
In this equation A and B refer to concentrations in meq. per cc. of A + and B+, respectively, and S and R refer to solution and resin, respectively. The rate and equilibrium constants always refer to the equation for the ion in the band solution replacing the ion in the eluting solution. Thus, in the process described above, k and K refer to ion B + replacing ion A + on the resin. The solution in terms of dimensionless groups for r 1 is
+
Preeent address, F KO.575, Yedado, Havana, Cuba.
2192
2(1/T
-
l/r)
E&%:-
Equation
Interval
r < l
1. Concentrations in the resin and in the solution a t any radial cram section are separately uniform.
1
Y > 117)
Interval
Y 2 c(l/’r 1.)
Equation
Interval
tion
- 7) Equation
0 200
400
600
800
(000
/PO0
I400
/600
/BOO
2000
INDUSTRIAL AND ENGINEERING CHEMISTRY
2194
Of the thirteen experimental runs made (t?), six were selected to illustrate the following effects. EFFECTOF VELOCITY. Two runs are shown in Figure 1 for the elution of a band of H - with a solution of sodium chloride. The same columns and milliequivalents of band solution were used for the two runs, but the velocity in run 5 was 25 times that in run 6 . The effects of the increased velocity were a reduction in the height of the peak and a broadening of the band width. These effects are in agreement with predictions made from the equations.
02
0
80
I20
I00
140
I60
I80
200
220
240
Y
Comparison of Runs w i t h Constant
Figure 3.
Dimensionless Groups
I O
08
0 6
C CO
LIMITING FORM
0 4
02
Vol. 46, No. 10
DIYENSIONLESS GROUPS. In order to determine whether the dimensionless groups arising from the theoretical development were the significant ones involved in these systems, two runs were made in xhich the column height \vas varied more than twofold and the velocity and band milliequivalents were adjusted to give the same values of x and Y . In Figure 3 the results are plotted as c/co versus the dimensionless group, y, in order t'o make the comparison. The data for run 9 are shown as a line in this figure for comparison with run 14, since the points for run 9 are shown in Figure 2 . The two runs plot,ted on a volume scale would not coincide, of course. For example, the peak for run 9 occurs a t approximately 1150 cc., while that for run 14 occurs at approximately 2780 cc. The agreement between the two runs indicates that the dimensionless groups used are the primary ones. APPLICABILITY O F EQUATIOSS.In all the runs, a good agreement was obtained between the experimental curve and the curve calculated using the complete equations. Over the range of variables covered, the curves calculated using the limiting forms were a reasonable approximation of those calculated using the complete equations, with the coniparison improving with the larger values of x and Y . For one of the five cases, shown in Figure 4 for an z of 280 the curves calculated with the different formulas gave equivalent r e d t s . AXIAL ~ I I X I S GI n. order t o determine how serious mixing in the axial direction might be, two runs were made in which a band of 0.1-Vhydrochloric acid was eluted vrith distilled water through a column in the hydrogen form. The results showed that with water pushing out the hydrochloric acid very litt,le mixing occurred, but with hydrochloric acid pushing out the water, the mixing was appreciable. From this it was concluded that with sharp density gradients and with the denser solution on top, mixing can be severe. In the elution experiments performed in this work, sharp density gradients did not exist and it is believed that no great amount of mixing occurred. CONCLUSIOYS
0 1200
1400
1800
I800
2000
2200
2400
2600
2800
Q ,CC
Figure 4.
Result for Large Values of x
For calculating the elutriation curve, equilibrium and rate data are required. These were obtained from previous n-ork (3); K for sodium in solution replacing hydrogen in the resin is 1.5. The rate constant for the same exchange and for a particle diameter of 0.0446 cm. is given by
_1 k
2.01
- 2.38Vu.84+ 0.049
+ 1.432
Curves calculated by both the limiting form and the complete equation are compared with experimental points in Figure I. For both runs the complete equation gave curves which agreed well with the data. For the low velocity run, the fit with the limiting form was much better than for the run at higher velocity. An increased velocity results in a decrease in the value of the dimensionless group, x. rigure 2 sho\vs two runs EFFECT O F EQUILIBRIUM COXSTAXT. for which the dimenslonless groups. x and I', were maintained constant but T was inverted-Le., S a + was eluted with H+in run 9 and H + was eluted with S a + in run 4. In run 9 a vciocity 2.5 times that used in run 4 was necessarj- t o keep the groups constant. The results show that eluting with the more selective ion gives the narrower band and the higher peak, It was expected that a sharper band would be obtained with the sharp front pushing out the diffuse front.
Experiments performed on the elutriation under nonequilibrium conditions of ion exchange columns partly saturated Ivith H + and N a + gave results that agree well Lyith predictions made on the basis of data collected on the same columns operated with saturation. Two methods of calculation are presented, both involving equations containing dimensionless groups that have been experimentally determined to be the major ones. One method involves the use of the complete equation. This method gives excellent results under all the conditions of the experiments but is somewhat tedious to use. The other technique uses a set of limiting forms which are simple to use and give good results in all these experiments, results equivalent to the complete equation under certain conditions. iixial mixing was investigated experimentally and found not to be a serious problem under the conditions of the tests. ACKNOWLEDGMENT
The original manuscript was reviewed by E. R. Gilliland and H. S. hfickley, whose criticisme and suggestions were helpful in the preparation of the final draft. h-OMERCLATURE
concentration of ions of band solution in effluent solution a t any instant, meq./cc. eo = concent,ration of band or eluting solution poured into column, meq.icc. c
=
J(x,y) IC
=
=
1 - e-li
x'
e - $ I,(Z l/&)dx,
function occurring in
equation of elutristion curve (tabulated by Brinkley, 1 ) rat,e constant, cc./(sec.)(meq.)
October 1954
INDUSTRIAL AND ENGINEERING CHEMISTRY
K
= equilibrium constant, dimensionless
QB
= volume of band solution run into column, cc. of liquid eluted from that was added to =
Q
r = Re =
u V
= =
z
= =
2 y
=
Y =
column during run (measured by subtracting voids volume from volume of eluent), cc. 1/K particle Reynolda number dimensionless group, c/c,. volumetric flow rate, cc. of liquid leaving column/sec. dimensionless group, ka/V total resin in column. mea. dimensionless group, 'kc,Q]V dimensionless group, k c o Q ~ / V
2195
LITERATURE CITED
(1) Brinkley, s. R., Jr., S. Bur. Mines, Rept. 3172, 1951. (2) Epstein, P., and Goldstein, D, J., M.S. thesis, in chemical engineering, M.I.T., 1953. (3) Gilliland, E. R., and Baddour, R. F., IND. ENG.CHEM.,45, 330 (1953). (4) Goldstein, S., Proc. Roy. SOC.(London),A219, 151-85 (1953). ( 5 ) Hiester, N. K., and Vermeulen, T., J . Chem. Phys., 16, 1087
u.
(1948).
(6) Thomas, H. C., J . Am. Chem. Soc., 66, 1664 (1944).
RECEIVED for review January 30,
1964.
ACCEPTED June 16, 1954.
Reactivity of Deposited Carbon E. R. GILLILAND AND PETER HARRIOTTI Massachusetts Institute of Technology, Cambridge, Mass.
REVIOUS studies of the oxidation of carbon with steam, P o x , , wen, and carbon dioxide have shown that the chemical reactivity of carbon under given reaction conditions, defined as the atoms gasified per minute per atom of solid carbon, depends both on the type of carbon and on the specific surface (area per unit weight), which is a measure of the relative number of carbon atoms exposed to the reacting gases. An extremely reactive type is carbon that is deposited on a porous carrier so that nearly all of the carbon atoms are on the surface or accessible to the reacting gases. Such carbon deposits often form on catalysts that are exposed to hydrocarbons or carbon monoxide at high temperatures. Dart (6) and Hagerbaumer and Lee (11) studied the regeneration of commercial cracking catalysts with air. Their results showed that the deposited carbons were several thousand times as reactive as coke or coal. From the literature (6, 12, 1.4, 16,S I , 32), the high reactivity of soot deposits to air, carbon dioxide, steam, and even hydrogen, can be inferred, but few quantitative results can be obtained. The authors investigated the reactivity of deposited carbons by studying the deposition and regeneration of such carbons from solid catalysts. In each run, a carbon deposit was formed on a catalyst, and the deposit was partially gasified, with emphasis on the gasification rate measurements. Most of the data presented are for the reaction of hydrogen with carbon deposited on a nickel-silica gel catalyst. The runs with hydrogen covered temperatures from 800' to 1400' F. and were mostly at atmospheric pressure. Some runs were made with catalysts other than nickel, and in a few runs the carbon was gasified with steam, oxygen, or carbon dioxide. EQUIPMENT AND PROCEDURE
The experimental runs were made in a batch fluidized reactor, 2.5 inches in diameter and 12inches high (Figure 1). The reactor was heated with exkrnal electrical windings, Reacting gases passed in order through a metering orifice, a preheating section, a supporting screen, about 6 inches of fluidized solids, a disengaging section, a cyclone, a filter, a condenser, and a gas eample line. For a few equilibrium runs the gases were recycled with a diaphragm pump. The gas flow rates corresponded to superficial velocities of 0.2 to 0.5 foot per second in the reactor for both regular and equilibrium rum. Axial traverses generally showed a constant temperature from the screen to the top of the fluidized bed. Furthermore, calculations indicated that there was neg1 Present address, Chemical Engineering Department, Cornell UniTrersity, Ithaoa, N. Y .
ligible temperature difference between the gas and the catalyst particles and between the center and the surface of the particles, even a t the most rapid reaction rates obtained. Sampling. Gas samples were taken by displacing a sodium sulfate-sulfuric acid solution and were analyzed by conventional Orsat techniques. Solid samples were taken by evacuating the sample flask and quickly opening the stopcock to the reactor to suck out a slug of gas and solids. The flask was flushed with nitrogen before sampling, and the sample was kept under nitrogen until it was analyzed. Some samples were reactive enough to decrease in carbon content in air at room temperature, and accidental exposure of the samples to air while they were still warm is one explanation for some analyses which were obviously too low. The solid samples were analyzed €or carbon and occasionally for hydrogen by burning with oxygen in a combustion train (Figure 2 ) . A sample was placed in one half of the Vycor U-tube; in the other half was 2 grams of copper oxide-silica gel catalyst to ensure complete combustion to water and carbon dioxide. Water was collected with Dehydrite (magnesium perchlorate), and carbon dioxide was collected with Ascarite (potassium hydroxide on asbestos). A furnace on sliding supports was placed around the U-tube to heat it to 1200' F. Combustion was usually complete in 15 minutes. The combustion train was also operated a t 700' F. to estimate the reactivity of the carbons to oxygen. At 700' F. the rate of combustion was slow enough to be conveniently determined by periodic weighings of the bulb of Ascarite. Catalyst. The nickel catalyst was prepared by soaking 28 to 200 mesh silica gel (Davison Co.) in a solution of nickel nitrate and heating the solid to decompose the nitrate. The catalyst was reduced with hydrogen in the reactor at the start of the run to give a catalyst with 15% nickel, The original area of the silica gel was over 500 square meters per gram. Surface areas for the used catalyst were not determined, but a rough estimate was made from room temperature adsorption tests. For sample K-2 No. 1 (4.4% carbon), a t 25" C. ethane isotherm showed 0.27 mg.-mole adsorbed per gram at 600 mm. of mercury; a comparison with isotherms for silica gel and Columbia G charcoal (16) indicated that the area was probably in the range 100 to 200 square meters per gram. A 10% copper catalyst was prepared in the same way. Also used was a commercial catalyst of the Fischer-Tropsch type which contained 28% cobalt, 5% thoria, and 67% silica and had an area of 300 square meters. Procedure. The procedure for a typical run was as follows: A charge (200 t o 600 grams) of catalyst was made through the top of the reactor. The reactor was heated to 1100" F. Any carbon was oxidized with air (15 minutes). Catalyst was reduced with hydrogen a t 1100" F. (15 minutes). (The amount of water collected in the condenser indicated that reduction was nearly complete in less than 10 minutes at 1100' F.)
