k kl
kz k, kL
k”, t 5
y 8
Subscripts i refers to conditions at interface o refers to initial conditions in liquid phase
= specific reaction-rate constant, l/second, reverse-direction,
first-order reaction = specific reaction-rate constant, l/second, forward-direction, second-order reaction = specific reaction-rate constant, l/second, reverse-direction, second-order reaction = specific reaction-rate constant, l/second, forward-direction, first-order reaction = liquid-film mass transfer coefficient (when accompanied by chemical reaction), moles/(sec.)( cm.2)(moles/liter) = liquid-film mass transfer coefficient (in absence of chemical reaction), moles/( sec.)(sq. cm.)(moles/liter) = time, seconds = distance into liquid film, centimeters = l / ( k l B , / D a ) (x), a dimensionless distance = k&t, a dimensionless time
LITERATURE CITED
(1) Cryder, D. S., and Maloney, J. O., Trans. Am. Inst. Chem. Engrs., 37, 827 (1941). (2) Danokwerts, P. V., Trans. Faraday Sac., 46, 300 (1950). (3) Sherwood, T. K., and Pigford, R. L., “Absorption and Extraction,” pp. 317 ff., New York, McGraw-Hill Book Co., 1952. (4)Stephens, E. J., and Morris, G. A., Chem. Eng. Progr., 47, 232 (1951 ). RECEIVED for review January 3, 1953.
ACCEPTEDApril 7, 1953.
Kinetics of Ion Exchange in the Calcium Cycle P. F R A N K H A G E R T Y 11’ YALE UNIVERSITY,
AND
NEW
H A R D I N O BLISS
HAVEN, CONN.
A t t e m p t s t o apply ion exchange t o t h e recovery of copper, zinc, and chromium from d i l u t e brass m i l l wastes have been disappointing because t h e regenerant is used rather Ineffectively. This makes considerably more difflcult t h e ultimate recovery of t h e metals. T h e use of ion exchange in t h e calcium cycle avoids this trouble, because t h e regenerant is itself regenerated and i t s degree of utilization in any one operation is n o t important. T h e rate process i s shown t o be one of diffusional control, and t h e parameters governing t h e behavior are reported. Copper and zinc behave very similarly, and they can be essentially completely removed in this manner. C h r o m i u m is n o t completely removed, because its speed of ionization i s low. T h e data and interpretation given here should permit design of large scale beds for this operation, and such large beds would be expected t o exhibit better performance t h a n t h e relatively short ones of these tests.
may be met in the brass mills.
covery of the metals, would represent a n important though partial solution of the waste-disposal problem, ion exchange in this par-
WATERS
RES“
BED*
-RESINBED
R E i E NE RATIOIN
H,s04 cAso4
LIME-
BED
zNck*
SOME
2 2 ~CACL,
CnS04 TO STREAM SOME CR,(SO,),
the hydrogen cycle, because the regenerant is
quiring the ion exchange t o be made in the sodium cycle. This will be discussed in a s u b s e q u e n t paper. Sodium would be necessary if the influent
The process sketched is the subject of a United States patent
(4). In order to establish its feasibility, the behavior of an ion exchange bed operating in the calcium cycle must be studied, and the fundamental kinetics delineated, so that rational design may be undertaken. This was the aim of this work. SCOPE
All runs were made with Amberlite XE-77, the analytical grade of IR-120, supplied by the Rohm and Haas Co., Philadelphia. The influent was in all cases
cuso4
Crz(SO4)a ZnSOd HZ604
77.7 p.p.m. Cu 42.2 p.p.m. Cr 81.6 p.p.m. Zn 360 p.p.m.
1.22 millimoles/liter 0.811 millimole/liter 1.25 millimoles/liter 3.67 millimoles/liter
which represents a reasonable average concentration to be expected from the brass mills, according to Curry (6) and Bliss (5). The chromium was obtained from stock solutions at least 9 months old. The columns were 1.08 to 1.10 em. in inside diameter, and all exhaustion and regeneration runs were downflow. The variables covered the following ranges:
The cell used was of the H-type as recommended by Lingane and Laitinen (13). One com artment held the standard calomel reference electrode. The otter held the solution, blown v i t h nitrogen gas to remove oxygen, and the dropping mercury electrode. The compartments were separated by a 2.5-inch agar salt bridge and a sintered-glass plate. The cell was held at 25.1" f 0.05" C. in a suitable thermostat. N o maximum suppressor was used. Inoperation, thecurrent flowing through thecell was recorded for the following potentials against the saturated calomel electrode: -0.20, -0.55, -0.60, -0.65, -1.20, -1.25, -1.65, -1.70, and -1.75 volts. The underlined potentials are of particular interest, as they are used for calibration of the system. If the current reading is high a t - 0.2 volt, incomplete removal of oxygen or a failure of the agar plug is indicated. The other three underlined voltages are for the plateaus of copper, chromium, and zinc, and the adjacent voltages are to ensure the establishment of the plateaus.
-
Bed weight (bone-dry hydrogen form), g. Ambient runs 3.62 to 21 3 4.52 to 13.3 High temperature runs Flow rates em /min. 4.3-74.5 Temneratuk. C. Akbient - ' 22-29.6, any one run constant to 0.5 88-99, any on? run constant t o 2 High temperature Particle sine mm. Average No. 1 0.848 (spheres onlv) No. 2 0.571 (spheres only) No. 3 0.387 (spheres,only) Regular 0.561 (not limited to spheres)
Only the regular was used for the high temperature runs. All regeneration runs were made downflow with 9.4% calcium chloride a t 25-27' C. and a t a flow rate of about 2 cm. per minute. I n all, 34 exhaustion and 26 regeneration runs were made. Successive exhaustion runs were made on completely regenerated, as distinct from fresh, resin. EXPERl M ENTAL WORK
The apparatus and procedure for ion exchange experimentation are unusually simple. High temperatures were reached by electrically heating the column and a storage vessel for the influent which was very near the column. The contents of the storage vessel were actually boiled and the vessel was provided with a reflux condenser. The column effluent was cooled with water before metering in a Rotameter. The regular resin, as received, was used in many cases. For the particle size study, however, the three size cuts indicated were made by elutriation, and then only the spherical particles of the given size were separated by tapping the material on an inclined plane along which the spheres rolled easily. Spheres used in studies were of the sizes designated as Nos. 1 , 2 , and 3. ANALYSIS
The determinations of copper, chromium, and zinc, in the effluents from the column, varying with time as they do, represent a considerable problem. The polarographic technique was selected. Full details of the method are given by Hagerty (9). The solutions were prepared as follows: Twenty-five or 50 ml. of unknown (copper must be held t o below 1.5 millimolar) were allowed to react for 5 minutes with 0.5 gram of sodium peroxide, after which 20 ml. of 5 M carbonate-free sodium hydroxide (supporting electrolyte) were added. After the sides of the vessel had been washed with 20 ml. of distilled water, the whole was heated to boiling and held there for 30 minutes t o decompose excess sodium peroxide. Then 5 ml. of 9% a ueous sodium arsenate were added and the contents held at ?he boiling point for another 15 minutes. This was necessary because the calcium hydroxide precipitate interferes with the zinc determination, but calcium arsenate does not. After cooling, the whole was transferred to a 100-ml. volumetric flask, which was then filled to the mark.
1254
0.0
1.0
2 .o
APPLIED P O T E N T I A L VERSUS S. C. E.,VOLTS
Figure 2. Polarogram of Copper, Chrom i u m , and Zinc i n 1 M Sodium Hydroxide Temperature, 25.1 O C. Capillary V I
The diffusion currents for the three substances were calibrated by means of the IlkoviE equation (11). Extensive calibration of the method was made, including suitable corrections for drop time which varies with voltage. A typical polarogram is shown in Figure 2. Because the diffusion currents with which concentration is related are the distances A B for copper, CD - A B for chromium (approximately), and B F - CD - AB for zinc (approximately), it is clear t h a t there is more error in the last than in the second and more in the second than in the first. Estimates of error introduced in this analysis are 2% for copper and chromium and 6% for zinc. The method proved very satisfactory, and several hundred determinations were made n.ith it. The hydrogen ion concentration was measured with a Beckman p H meter. DATA
The data sought in most studies of the kinetics of ion exchange are the breakthrough curves-i.e., the variation of effluent concentration with time. Representative exhaustion data are given in Table I, and a representative regeneration run is given in Table 11. The entire data are available from the American Documentation Institute. A typical plot of concentration history is shown in Figure 3, in which C/Co is plotted against effluent volume for run 36.
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 45, No. 6
Table I .
Run 36 Weight of bone-dry resin, g. Partiole diameter mm. Exchange schemi Velocity of influent, cm./min. Influent temperature, O C. Effluent composition Volume throu h Resin to M i 8 Point of Sample,
12.00 0.561 i 0.098 (not spheres) Downflow exhaustion 72.0 26.0
’ dt
cu
c/ CQ Zn 0.03 0.08 0.13 0.15 0.29 0.33 0.53 0.66 0.75 0.79 0.87
c*
H ion 0.64 0.94 0.96
.(I)
9
a
co
: ....
1 00
1:oo
It is clear that this assumes diffusional control and linear equilibrium and that the rate vanishes when C = Co, a = q as it should. The exact mathematical statement of the solution for this case is
l:oo 58.7
CO
= exp [-@s
+ A y ) l ( l o ( 2 Z / ~+ d A y , B z ) }
(4)
as given by Thomas (17)in which
General Observations. The concentration histories, when plotted, lead to several observations.
GI
Approximately 57% of the chromium is removed by the exchanger a t room temperature, and this fi ure is relatively little affected by the variables studied. The bekavior of chromium at temperature near the boiling point is not so simple and is described in detail later. The breakthrough curves for copper and zinc are almost identical. Hydrogen ion does not appear to exchange with calcium. Considering the very unfavorable equilibrium for such exchange, this is not sur rising. BreaktLough for copper and zinc occurred very near the start of the run for all ambient temperature tests, but there was a short period of essentially complete removal near the 1.2 boiling tem erature. I n short, beds of these 1engtEs exhibit only a small portion ’of their capacity before break1.0 through.
3
y
= fraction of copper not exchanged = bed weight = effluent volume
(rate constant on volume basis X
A = -kDS Co . entering concentration) a V (camcitv X volumetric flow rate) kD 8(rate const&t on volume basis) B
v
(volumetric flow rate)
I
Kinetics of Copper and Zinc Exchange. Because of the similarity between copper 0 0.8 Iand zinc, it is not surprising that they a a behave practically as one entity in this 0 0.6 phenomenon. As a consequence, the Y V authors have elected t o interpret these results with respect to copper only. 0.4 RUN NUMBER The theoretical analysis of ked-bed o CHROMIUM ion exchange problems depends on setWEIGHT - G M 0.2 ting up the differential equation of conE/ tinuity, imposihg on it a suitable rate equation, and integrating the result. The rate equation assumed must be I 2 3 4 5 6 7 8 9 IO 1) 0 EFFLUENT VOLUME ,V, LITERS consistent with the equilibrium relationship for the system. This analysis has Figure 3. Concentration History of Calcium Resin been accomplished for several cases; that of. linear equilibrium and a ratecontrolling step due to liquid diffusion appear to apply to this case. The function 4 is tabulated by Brinkley and Brinkley (6). This is admittedly a considerable simplification. The comEquation 4 has also been obtained for the wholly analogous case plexities due t o the presence of the three exchanging ions (copof heat transfer by Anzelius (1) and Schumann (14) and is the per, zinc, and chromium) cannot properly be taken into account, basis for the well-known Schumann curves presented by Furnas and any interpretation must be considered semitheoretical a t (8)and Hougen and Marshall (10). best. However, in support of the method of interpretation The procedure for evaluation 6f the fundamental parameters, based on linear equilibrium and liquid diffusional rate control, b ~ and 8 a,is as follows: the behavior of the band width may be cited. The breakthrough curve is plotted as C/C, vs. log y and the With other variables constant, the volume of effluent between slope is determined at C/Co = 0.5. It is simple to show that C/CO 0 and C/C, = 1(“band width”) expands as the bed length is increased, and as the influent velocity is increased. That the d log C/Co - d log C/Co band width increases as the bed length increases is particularly d logy d log Ay I
-*
- c*)
is the expression for the assumed linear equilibrium, we may write
INTERPRETATION OF EXHAUSTION RUNS
..
= kD8(C
Because
Effluent, Cr 159 0.02 0.42 670 0.43 0.05 1,082 0.10 0.44 1,591 0.42 0.18 2,199 0.43 0.25 2,805 0.47 0.32 3,926 0.38 0.45 5,042 0.42 0.56 7,143 0.45 0.74 9,244 0.47 0.85 10,370 0.48 0.88 Total exchange capacity of resin column, meq. 1 x 1 .
important, as this increase in band width is approximately as the square root of the increased bed lengt,h. This is characteristic of the Schumann curves (see below). I n addition, Selke and Bliss (16) found that this case applied to the exchange of copper for magnesium. The rate equation used is
Representative Exhaustion Results
June 1953
INDUSTRIAL AND ENGINEERING CHEMISTRY
I
J
1255
Table I I. Run 36
Representative Regeneration Results
Resin data Weight of bone-dry resin, g. Particle diameter mm. Resin compositioh (resin bed of exhaustion run 361, millimoles
12.00 (Ca) 0.561 i 0.098 (not spheles)
cu
6.28 5.14 6.06
Cr Zn Operating data Exchange scheme Regenerant solution wt. % CaClz Regenerant tempera'ture, C. Velocity of regenerant, cm./min. Volume of Regenerant through Resin, M1. 0- 42.8 42.8-135.8 135.8-280.8 280.8-382.8
Domnflow regeneration
9.4 26 1.94-2.04
Concn. in Regenerant Effluent, lIillimoles/Liter cu Cr Zn 106.7 13.8 2.98 0.01
35.3 25.0 2.56 1.28
103.5 11.1
0.0 2.42
Cumulative Fraction of Metal Recovered cu Cr Zn 0.726 0.294 0.732 0.933 0.746 0.902 0.999 0.999
0.82 0,845
Cumulative Av. Concn., Millimoles/Liter Cr Zn 106.7 35.3 103.5
cu
43 22.3 16.4
0.902 0.945
28.2 15.0 11.3
40.3 19.5 14.9
excellent except in the case of run 35, and this n-as undoubtedly due to fracturing of the larger particles on wetting, exposing more area than calculated. It is clear, according to this diagram, that the transfer coefficient, k i d , is linear in surface area, varies approximately as the 0.5 power of liquid velocity, and is independent of bed length. These certainly confirm the belief t h a t the rate-controlling step was liquid film diffusion. The equation of the line for the regular resin (0.561 mm.) is kDS = 2.75 Go.6
(6)
with G in grams (sq. em.) (min). The value for other sizes could be estimated by the usual simplification of assuming X inversely proportional to D. I 2 3 4 5 6 The effect of temperature on knS is shown in Figure 6, E F F L U E N T VOLUME,V, L I T E R S in which k&3 for the high temperature and lo; temperature runs is plotted. It is apparent that the mass Figure 4. Comparison of Data with Calculated Curves velocity effect is the same and that ~ D isS in general about 75% higher a t the higher temperature. An and the latter a t C/Co = 0.5 is a function of B z only. This empirical equation for these results is functionality has been plotted by Hougen and Marshall ( I O ) . Thus the slope of the log-log plot a t C/Co = 0.5 defines Bz. ~ D =S 4.8 Go.6 (7) Since x is known, B is defined and thence ~ D Sas, V is known. Any method involving the determination of slopes is subject Comparing the results a t the two temperatures in the usual way, t o some inaccuracy, and a certain amount of personal judgan activation energy of 1.8 kcal. is found, certainly a further indiment is involved. A is then determined by reading the value cation of liquid diffusional control. of A ~ on J the full Schumann curve for the value of Bz found at which C/Co = 0.5, and using the experimental value of y at this point. Other points than 0.5 would yield slightly different answers, because the fit is not perfect. As ~ D S ,CO, , and V are known, the value of the quantity, a, is determined from A. TEMP ERAT UR E
The results of these calculations on all runs are given in Table 111. A comparison between observed data and curves calculated on the basis of ~ D and S a, thus determined, for three runs is given in Figure 4. Mass Transfer Coefficient, kDS. This, in the units milliliters per gram of H resin per minute, is plotted in Figure 5 for all ambient temperature runs. The line for the regular resin size (0.561 mm.) is drawn through the points in what seemed to be the best manner. The other lines are drawn by estimating S, the surface area per gram of resin, relative to SR,the same for the regular resin. These factors X/SRwere derived, taking into account the distribution of particle sizes about a mean and are not quite the same as the reciprocal of D/DRas would be used for t h e simplest analysis. Thus S / S R was 0.64 for No. 1, 0.95 for No. 2, and 1.40 for No. 3 rather than 0.66, 0.98, and 1.45 as the simpler method would indicate. The agreement is certainly
1256
2
3
7
5 MASS
Figure 5.
10 20 30 50 VELOCITY GM J C M ~ S M I N
Mass Transfer Coefficient as a Function of Mass Velocity Effect of particle diameter
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 45, No. 6
Table I I I .
Summary of Calculations i n Application of Liquid F i l m Controlling Mechanism w i t h Linear Equilibrium
Run No.
Particle Diameter, Mm.
CrossSectional Area, Sq. Cm.
Resin Weight, G. H R / Sq. Cm.
52 51 64 60 39 27 55 58 36 37 43 34 33 41 42 38 40 14 32 29 35
0.561 0.561 0.561 0.561 0.561 0.561 0.561 0.561 0.561 0.561 0.571 0.571 0.571 0.571 0.571 0.571 0.571 0.387 0.387 0.387 0.848
0.91 0.91 0.91 0.93 0.93 0.93 0.945 0.945 0.93 0.91 0.93 0.92 0.92 0.92 0.93 0.93 0.93 0.92 0.92 0.92 0.945
4.05 4.05 "4.05 8.12 7.99 7.99 12.85 12.85 12.05 21.8 3.90 3.94 3 94 3.94 7.69 7.69 7.69 3.67 3.67 3.67 2.98
53 50 49 62 47 46 48 45 59 67
0.561 0.561 0.561 0.561 0.561 0.561 0.561 0.561 0.561 0.561
0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.93 0.945
4.51 4.51 4.51 8.29 8.00 8.00 8.14 8.00 13.2 12.85
AV.
(Calcium form of Amberlite XE-77) Total dlogC Volume U t o C/Ca = Y, dlo y Dead G./dq. 0.5, MI./Sq. a t C?Co = Volume, MI. MI. Cm. 0.5 Bo Cm. Min. Ambient Temperature Column Experiments, 24' t o 30" C. 1.08 5.25 4.48 1875 9 2050 0.80 2.50 20.8 9 1750 1600 0.60 1.44 9.2 1310 74.5 1200 1.58 11.4 4.35 4400 11.1 4720 3900 1.10 5.30 19.8 3650 20.4 0.82 2.68 71.7 3000 21.4 3200 15.6 4.48 6650 28.6 7000 1.90 20.0 8.25 5000 29.8 5260 1.30 0.95 3.75 72.0 4350 10.2 4660 69.3 10,000 60.5 10,900 1.20 6.70 1870 1.13 5.65 1750 11 4.4 0.76 2.26 20.0 1450 11 1540 0.65 1.69 38.6 1300 11 1390 0.54 1.18 73.2 1200 11.6 1280 3710 1.04 4.7 8.6 3450 8 5.0 20.0 3400 7.5 3760 1.07 2.5 72.3 2850 7.3 3060 0.80 19.6 1600 11 1710 0.90 3.30 2.2 1500 10.5 1600 0.75 38.6 1.56 10.8 1225 0.63 73.1 1150 19.6 950 9.9 1015 0.64 1.60 High Temperature Column Experiments, 90' t o 100' C. 2150 97 2210 1.54 10.7 4.3 2550 97 2640 1.04 4.7 21.5 72.1 2350 0.78 2.4 97 2420 4500 87 4750 1.62 12.2 4.24 8.45 4400 87 4640 1.70 13.2 20.4 4950 87 5230 1.28 8.00 5100 87 5410 1.25 7.40 36.9 73.4 5200 87 5520 77 7240 1.85 15.0 7700 1.24 7.25 50
....
....
hDs,
Ag at
G. HR/Min.
*...
....
c/co
0.5
=
4/CO,
4,
MI.
Meq.
G. H R
G. HR
5.81 12.85 26.4 6.1 13.1 24.1 5.45 12.85 22.4 21.3 6.4 11.5 16.6 22 5.3 13.0 23.5 17.5 23.2 31.2 10.55
4.75 2.0 1.15 11.0 4.75 2.15 15.0 7.8 3.25 6.2 5.15 1.80 1.36 1.0 4.2 4.5 2.0 2.8 1.8 1.25 1.25
559 542 405 602 543 500 569 435 449 541 527 490 441 385 541 541 49 8 549 534 416 438
1.37 1.33 0.99 1.48 1.33 1.22 1.39 1.07 1.10 1.33 1.29 1.20 1.08 0.94 1.33 1.33 1.22 1.34 1.31 1.02 0.83
10.2 22.4 38.5 6.26 13.9 20.4 33.5
9.8 4.3 1.9 12.0 12.8 7.5 6.95
535 638 680 588 600 560 709
1.31 1.56 1.66 1.44 1.47 1.37 1.73
22.8 40.9
14.5 6.8
568 640
1.39 1.57
a was determined for copper only, and certainly a n equal amount is required for the zinc and a considerable amount for chromium. Exactly how much is required for chromium is unknown because the average ionic charge with which chromium exchanges is unknown. Thus, the requirements for zinc and chromium probably bring the figure for a up to 3.4 meq. per gram, while the ultimate capacity is about 5.0. The higher value of a at higher temperature probably reflects a greater capacity for copper because of a smaller capacity for chromium.
Figure 6.
Mass Transfer Coefficient as a Function of Mass Velocity Effect of temperature
e
Capacity, a. In order t o understand the quantity, a, it is necessary t o rewrite the linear equilibrium relation as it was introduced in the rate equation
a
a'
a"
8This is plotted in Figure 7 . It is clear that there is no great significance t o a; it is merely the value of q in equilibrium with CO. It would take on other values with different influent concentrations, had they been investigated. However, a should be less than the ultimate capacity .of the resin and approximately constant for constant CO,and it certainly is so according to Table 111. The values of a average 1.27 meq. per gram of HR at room temperature, and 1.54a t the elevated temperature. These low values are due to the fact that June 1953
Figure 7.
Linear Equilibrium
Behavior of Chromium. The solutions of chromium sulfate in the presence of sulfuric acid contain a variety of complex forms, some nonionized and others ionized to a greater or lesser degree. Considerable simplification results if one considers them as of only two forms: ionized and nonionized. The work of Montemartini and Vernazza ( I S ) in which no ion exchange was involved leads to several important observations:
INDUSTRIAL AND ENGINEERING CHEMISTRY
1257
1. The equilibrium mixture of trivalent chromium sulfate contains 44% of the ionized form at 25" C. and practically none of the ionized form at 90" t o 100" C. 2. The rate of conversion oi nonionized to ionized form is very slow a t 24" to 30" C. 3. The rate of conversion is very fast a t 90' to 100" C.
1 - 1
o BATCH KINETIC EXPTS~
10
I
i
I
I
I
I
1
I
I
1
1
I
I
I
I
10-
10-4
ION EXCHANGE COLUMN EXP'TS
A
I
l
I \ I
I
; \ I
I
I
I I
I
1
\ I
I
I
l
l l l l l l l l l
.a24
,0028
(kS)
= 1.6 X 1015exp
(11)
The times of contact in nearly all the runs reported were such that less chromiuni was exchanged a t high temperature than a t ambient ones. Thus, the capacity of the resin for copper was increased, leading to a larger value of a. This is certainly confirmed by the fact that the largest values of a were obtained with the shortest contact times. UTILITY OF THE DATA
I
I
I
,0032
k
The good
The establishment of mechanism is of interest, of itself, but the application of the data and results t o design is of more value. Ion exchange probably would not be used in the calcium cycle for the recovery of copper and zinc, if a bed of large commercial size was expected to exhibit such poor performance as these beds-Le., breakthrough a t or near the very beginning of the operation. But, as it has been established that koS is independent of bed size, the manner of design for large scale exchange is clear. It should be possible to use such a parameter for design of any scale, although conservatism would require confirmation of these results and interpretation, particularly with respect to bed length, on a somewhat larger scale than here attempted. The increase in band width is approximately as the square root of the bed length, and therefore as bed length increases to commercial sizes the band viidth increases, but not nearly so much so, and the large bed will exhibit a much higher utilization of its capacity. The effect of bed length on increasing the capacity-Le.. giving a more favorable breakthrough-is shown in Figure 9, based on the esperimental data.
i
I
Vernazza a t three other temperatures are also plotted. agreementis apparent. The equation this line is
,0030
i / T [ I/OK.]
Figure 8. Rate Constant for C h r o m i u m Ionization as Function of Temperature
Observations I and 2 explain the ambient temperature data very well. The ion exchanger removes the ionized form completely, and the time of contact is too short to permit any great conversion of nonionized to ionized form. The figure of 57% ionized is somewhat larger than their 44%, but this is to be expected, as the authors' solutions were more dilute. Observations 1 and 2 indicate that the high temperature runs should be capable of explanation as a rate phenomenon-Le., the removal of the ionized chromium, however small, by the exchanger disturbs the equilibrium and more ionization can occur rather rapidly to compensate for this removal. I t is probable that the diffusional rate of exchange is faster than the rate of reaction-that is, the rate of reaction controls. Assuming the rate is first order and is irreversible because of the porn-erful effect of the exchanger,
dC - = dt
- kC
in which Cis the concentration of nonionized chromium. dVR Dividing both sides by Co and recognizing t h a t dt = -
V
(9) which may be integrated between
L
co
nonionized a t the high temperature), In- C
co
= 1(because it is nearly all
C
VR = 0 and -, V E ,we have
co
-k V'R
(10)
V
VR
The slope of a plot of the logarithm of C/C, versus - defines the
V
value of k , which is 38.6 reciprocal hours. This value of k is plotted against 1 / T in Figure 8, in vhich the results of Montemartini and 1258
An example will serve to show best how these data may be used. One million gallons per day of a solution containing 77.7 p.p.m of copper, 42.2 p.p.m. of chromium, and 81.6 p.p.m. of zinc is to be treated with an exchanger - in the calcium cvcle. The length of the bed with a design rate of 15 gallons/(sq. foot)(minute) and the percentage utilization of the resin are desired. The operation should cease when C/Co for copper is 0.05. Complete regeneration of the bed is assumed. This is relatively easy to accomplish with this system, but such is not always the case. The area is
l'oooJooo = 46.3 square feet and the diameter is defined by 15 X 60 X 24 7.67 feet. Using Equation 6 knS = 2.75
INDUSTRIAL A N D ENGINEERING CHEMISTRY
.\/a
Vol. 45, No. 6
and converting the units of ~ D toS ~ D ‘ (pounds/lb. S HR)(hour) and G to G‘, pounds/(sq. foot) (hour) we have
and with G’ = 7500 pounds/(sq. foot)(hour)
~ D ’ S= 1290
-.
The authors wish t o acknowledge the fellowship assistance of the Rohm and Haas Co. and E. I. du Pont de Nemours & Co. Appreciation is also expressed for the help of R. W. Southworth, who had a part in this work during the prolonged illness of one of the writers. NOMENCLATURE
pounds (pound HR)( hour)
The quantity a, it was shown before, has no great significance, because it varies as does CO. However, a/Co is the slope of the equilibrium line, and i t will be chosen for this example the same as was found here. This was
”“ = 450
ACKNOWLEDGMENT
pounds of solution pounds of H R
Then y = 8.33 X
I
loe pounds
a
= quantity on exchanger in equilibrium with CO,meq. per
B
= -kDS
C CO
= concentration, millimoles per liter
gram
C* G
= mass velocity,
G‘
=
k
=
= 69
~ D ‘ S=
kDS 2 V
qm
t T V V R 2
x = 52(7500)(46’3) 1290
=
14,000 pounds of H R
As the bulk density is about 25 pounds of bone-dry resin per cubic foot Length =
Y
z
14 000 = 12.1 feet 25(46.3)
-L--
This manner of operation almost all of the copper and zinc and about 60% of the chromium. This corresponds in 24 hours to 54,300 pound meq. of metals. The total ultimate capacity of the resin is 5.38 pound meq. per pound of HR or 75,300 pound meq. The utilization is, therefore, 72%. This is good enough so that the use of high temperatures is probably not warranted. REGENERATION
The regeneration results are not capable of any theoretical interpretation, because such theoretical problems are far outweighed by practical considerations. Chief among these is the longitudinal mixing. However, several observations are of much value: There is no significant difference between the behavior of copper and zinc, and both can be completely recovered. Chromium is considerably more difficult, but it can be completely recovered. High concentration of regenerant combined with high recovery is very much favored in longer resin beds. It is possible to get so]utions as strongas 100 per liter of copper and millimoles per liter of zinc with practically Complete recovery of these metals. However, chromium is Only about 50% recovered a t this point. T o go on and get nearly a]] the chromium back would require dilution to about one third of these figures‘ Regeneration in two stages Or more is indicated.
=
or meq. per ml.
C in equilibrium with q
= that value of
koS =
BX = 52
June 1953
= initial value of above
kDS coy = 1290 (8.33)(106) Ay = Vu 7500(46.3)( 450)
T h a t Schumann curve for which C/Co = 0.05 and A y = 69 exhibits
‘ I
V
grams (sq. cm.)(min.) mass velocity, pounds sq. foot (hour) first-order reaction velooitv constant for ionization of chromium sulfate complex, reciprocal hours mass transfer coefficient for liquid film diffusion on volml. ume basis, min. gram hydrogen resin pounds same, (hour)(pound hydrogen resin) quantity on exchanger, meq. per gram
= correction for area per unit weight for one size relative t o that of regular size = time, minutes = temperature = volumetric flow rate, ml. per minute or pounds per hour = volume of free space in resin bed = bed weight, grams or pounds = effluent volume, ml. or pounds = complex variable LITERATURE CITED
(1) Anzelius, A., Z . angew. Math. Mech., 6, 291-4 (1926). (2) Beaton, R. H., and Furnas, C. C., IND. ENG.CHEM.,33,1501-13 (1941) . (3) Bliss, H., Chem. E n g . Progr., 44, 887-94 (1948). (4) Bliss, H., U. S. Patent 2,628,165 (Feb. 10, 1953). (5) Brinkley, S. R.,Jr., and Brinkley, R.,U. S. Dept. Interior, Bur. Mines, Rept. 3172 (1951). (6) Curry, J. J., Connecticut State Water Commission, Hartford, 1947. (7) David, M. M., Jr., “Ion Exchange Treatment of Dilute Brass Mill Wastes,” D.Eng. dissertation, Yale University, 1950. (8) Furnas, C. C., U. S. Dept. Commerce, Bur. Mines, BuZl. 361 (1932). (9) Hagerty, P. F., 11, “Recovery of Metals from Dilute Brass Mill Wastes by Ion Exchange,” D.Eng. dissertation, Yale University, 1952. (10) Hougen, 0. A,, and Marshall, W. R., Jr., Chem. Eng. Progr., 43, 197-208 (1947). (11) Kolthoff, I. M., and Lingane, J. J., “Polarography,” revised reprint, New York, Interscience Publishers, 1946. (12) kingane, J. J., and Laitinen, H. A., IND.ENC. CHEM.,ANAL. ED., 11, 504 (1939). (13) Montemartini, C., and Vernazra, E., I n d . chim., 7, 432-5, 867-65, 1001-4 (1932). (14) Schumann, T.E. W., J . Franklin I n s t . , 208,405-16 (1929). (15) Selke, W. A., and Bliss, H., Chen. E n g . Progr., 46, 509-16 (1950). (16) Ibid., 47, 529-33 (1951). (17) Thomas, H. C., Ann. N . Y . A c a d . Sci., 49, 161-82 (1948). RECBIVED for review January 8, 1953. ACCEPTED April 9, 1953. Based on a dissertation presented by P. F. Hagerty I1 t o the faculty of the Yale School of Engineering in partial fulfillment of the requirements for the doctor of engineering degree. Material supplementary t o this article has been deposited as Document 3971 with t h e AD1 Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington 25, D. C. A COPY may be secured b y citing t h e document number and by remitting $8.75 for photoprints or $3.00 for 35-mm. microfilm. Advance payment is required. Make checks or money orders payable to Chief, Photoduplication Service, Library of Congress.
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