INDUSTRIAL AND ENGINEERING CHEMISTRY
1922
Nomenclature
a = interfacial area of packing, square feet per cubic foot at = total surface area of packing, square feet per cubic foot
A = total area of packing, square feet A , = surface area of one packing unit, square feet D = diffusivity, square feet per hour f = constant G = gas rate, pounds per hour per square foot H = Henry’s law constant, pound moles per cubic foot (atmosphere) h = height of packing, feet j = transfer factor for mass in gas phase IC, = gas phase coefficient, pound moles per hour (square foot) (atmosphere) K,u = over-all gas phase coefficient, pound moles of solute transferred per hour (cubic feet) (atmosphere) kl = liquid phase coefficient, pound moles per hour (square foot) (pound moles per cubic foot) Klu = over-all liquid phase coefficient, pound moles solute transferred per hour (cubic foot) (pound moles per cubic fool) L = liquid rate, pounds per hour per square foot m = Y / X a t equilibrium, pounds of water per pound of air N = mass transferred, pound moles per hour n = constant P = pressure, atmospheres s = constant X = aounds solute per Dound of water: X * = eauilibrium value, pound-solute per pound of’wakr a = proportionality constant p = liquid density, pounds per cubic foot p = liquid viscosity, pounds per foot hour
‘
dxi = modified Reynolds number (7)
(-$)
= Schmidt number
literature Cited (1) Baker, T. C., Chilton, T. H., and Vernon, H. C., Trans. Am. I n s t . Chem. Engrs., 31, 296 (1935). ( 2 ) Borden. H. M., and Squires, W., Jr., S.N. thesis in Chem. Eng., Massachusetts Institute of Technology, 1937. (3) Dodge, B. F., and Dwyer, 0. E., IND. EXG.CHEM.,33, 485 (1941) (4) Doherty, T. B., and Johnson, F. C., S.M. thesis in Chem. Eng., Massachusetts Institute of Technology, 1938. (5) Fellinger, L. L., Sc.D. thesis, Massachusetts Institute of Technology, 1941. (6) Gamson, B. W.,Thodos, O., and Hongen, 0. A., Trans. A m , Inat. Chem. Engrs., 39, 1 (1943). (7) Grimley, S . S., Ibid., 41, 233 (1945). ( 8 ) Houston, R. W., and Walker, C. -4., ISD.ENG.CHEW,42, 1105 (1950). (9) Hurt. D. M.. Ibid.. 35. 522 (1943). (io) “International Critical Tables,;’ Kew York, hIcGraw-Hill Book Co., 1928. (11) Johnstone, H. F., and Singh, A. D., IND. ENG.CHEM..29, 286 (1937). (12) MoAdams, W.H., Pohlenz, J. B., and St. John, R. C., Chem. Eng. Progress, 45, 241 (1949). (13) Mayo, F., Hunter, T. O., and Sash, A. W., J. Soc. Chem. I d . (London), 54, 375 (1935). (14) Molstad, hl. C., McKinney, L. F., and Abbey, R. G., Trans. Am. Inst. Chem. Engrs., 39, 605 (1943). (15) Resnick, W., and White, R. R., Chem. Eng. Progress, 45, 377 (1949). (16) Sherwood, T. K., and Holloway, F. A. L., Trans. Am. Inst. C h a . Engrs., 36, 39 (1940). (17) Shulman, H. L., and Molstad, M. C., IND.E m . CHEY.,42, 1058 (1950). (18) Surosky, A. E., and Dodge, B. F., Ibid., 42, 1112 (1950). (19) Taecker, R. G., and Hougen, 0. A., Chem. Eng. Progress, 45, 188 (1949). (20) Weisman, J., and Bonilla, C. F., Im. ENG.CHEM.,42, 1099 (1950). REGEIYED for review August 2 , 1951. ACCEPTEDJune 6 , 1952.
.
For material supplernentary to this article order Document 3644 from American Documentation Institute, 1719 S St., N.W., Washington 6, D. C., remitting 61.00 for microfilm (images 1 inch high on standard 25-am. motion picture film) or $2.40 f o r photocopies (6 X 8 inches) readable without optical aid.
Subscripts 0 = top of column 1 = bottom of packing d = pertaining to mass transfer
-
Vd. 44, No. 8
development
ALAN S. MICHAELS Massachusetts fnstifute of Technology, Cambridge, Mass.
HE increasingly important process of ion exchange is, in essence a t least, analogous with the processes of absorption and extraction. The mathematical treatment and analysis of ion exchange data is, however, seriously complicated by the fact that the process is usually carried out in practice by passing liquid through a packed bed of solids, rather than by passing liquid and solid countercurrently t o each other. Conditions within the bed thus change with time and the relations derived to express the composition of the liquid and solid as a function of time and distance through the bed are in most cases too cumbersome to be of material value to the engineer (1-3,7-9). On the other hand, the treatment of mass-transfer processes
T
taking place under steady-state conditions in counterflow equipment is fairly straightforward; furthermore, one can usually employ laboratory data taken under such conditions for the design of a pilot plant or ronimercial unit with fair assurance that the unit will perform as expected. It is thus clear that the development of some similar, relatively simple analysis, applicable t o fixed-bed ion exchange, u ould be of material assistance and would put this new unit operation on a more sound engineering basis. The major object of this work has been t o develop such a simplified treatment. The method presented here has been tested on a fairly substantial amount of laboratory data and has
August 1952
INDUSTRIAL AND ENGINEERING CHEMISTRY
been found t o reproduce the experimental results with fairly high accuracy. Furthermore, it is believed t h a t laboratory data interpreted in this fashion can safely be used for the design of large fixed-bed ion exchange units. T o be sure, the method is limited in applicability t o certain specific types of ion exchange reactions; fortunately, however, those types to which i t applies are the ones taking place in a large number of present-day commercial ion exchange processes.
1923
exchanger in a region further on down the bed-that is, a given particle of solid does not “know” what is going on below it. It is this characteristic of fixed-bed operation which permits utilization of experimental S-curves for determining conditions within the exchange zone. After the e a u e n t ion concentration reaches 95% of the influent value, continued flow of liquor through the column results
Exchange Zone Method
If an aqueous solution of, say, sodium chloride is allowed t o pass down at a constant rate through a packed bed of acid-form cationexchanger particles, exchange of hydrogen ions of the solid for sodium ions takes place, and an effluent containing largely hydrochloric acid is obtained. Equilibrium relationships for the sodium-hydrogen exchange (as well as for most metallic cation-hydrogen exchanges on high capacity, strong acid-type cationic exchange resins, e.g., Dowex 50) are such t h a t sorption of metal ion is strongly favored; furthermore, the rate of exchange of ions is usually rapid. The result of these facts is t h a t the exchange process is largely confined t o a rather narrow region v , EFFLUENT VOLUME, c u m CENTIMETERS in the bed which, within a short time after Figure 1. Idealized Effluent Concentration vs. Volume Plot for a Fixed-Bed Ion liauor flow is bemn, moves down the bed at a Exchange Column constant rate determined by the liquor rate, solute concentration, and the specific capacity in gradual increase in effluent concentration until the influent of the exchanger. The solid above this region is essentially in concentration is reached; the residual exchange capacity of the equilibrium with the influent solution, and t h a t below, essensolid utilized in this stage of operation, however, seldom amounts tially in the pure acid form. It is thus likely t h a t within this to more than a few per cent of the total rapacity of the exband-the exchange zone-conditions will remain essentially changer. unchanged with time, except during the initial period of operaThe time, ez, required for the exchange zone to move its own tion of the column when the region is being established. [Sillen height down through the bed under steady-state conditions is and Ekedahl (6) also employed the constant-width exchangeproportional t o the volume of effluent, V Z (see Figure 1 ) : zone theory in a mathematical analysis of ion exchange column performance; their treatment is considerably different from t h a t ez = (1) presented later in this article, however.] This permits analysis of the kinetics of the exchange process from a relatively simple, where U L = liquor flow rate, centimeters per second, based on steady-state counterflow basis. total column cross section and A,, = total column cross-sectional Debition of Exchange Zone. It will be convenient for the area, square centimeters. subsequent discussion t o define as the exchange zone t h a t region Similarly, the time, eT, required for the zone to establish itself at of the bed within which (at steady state) the sodium ion conthe top of the bed and to move down out of the bed is proyorcentration in the liquid flowing through the bed falls from 95 tional to the total volume of effluent collected, V T : to 5% of its value in the influent. It is clear t h a t the choice of concentration limits t o define the zone is purely arbitrary; it eT = V T / ( U L ) ( A m ) (2) will usually prove advantageous, however, t o choose values which Except for the period of time during which it is being formed at have a n arithmetic average of 50% and which are not so close the beginning of the process, eF, the zone is descending through to 0 or 1 0 0 ~ ot h a t experimental measurement of concentration the bed at a constant rate determined by: becomes difficult. Calculation of Zone Height. If the concentration of metallic cation in the effluent from a fixed-bed ion exchange column is plotted as a function of the total volume of effluent collected, The height of the exchange zone must be determined by the relacharacteristic #-curves (see for example, Figure 1) are obtained. tion Evidently, at the instant when the effluent metallic cation concentration reaches 5% of its value in the influent, the exchange (4) zone has reached the bottom of the bed. This point may be designated as the break-through point. As operation of the The only unknown in Equation 4 is the zone formation time, column is continued, the concentration of metallic ion i n the OF. However, this time can be estimated quite closely‘in the effluent rises until i t reaches 95% of the value of the influent. following manner: At this point, the exchange zone has moved out of t h e bed, and The quantity of metallic cations removed by the exchange zone the exchanger is for all practical purposes exhausted. If, as from the break-through point t o exhaustion of the bed may be assumed above, conditions within the zone do not change with determined graphically from time, the effluent volume versus concentration 8-curve will give a true picture of the concentration variation across the exchange zone, since the exchange capacity of the solid in any cross section (5) of the bed is in n o way influenced by the condition of the solid
vz/(uL)(~,,)
INDUSTRIAL AND ENGINEERING CHEMISTRY
1924
where &E = total cations removed by exchange zone, V,T = volume of effluent collected up t o break-through, X O = concentration of metallic cation in influent, and X = concentration of nietallic cation in effluent. If, however, the solid in the zone had been completely in the acid form, this same region of the bed would have removed ~i quantity of ions equal t o (very nearly) QZ
ma*.
=
xovz
Vol. 44, No. 8
removed), the time of formation of the zone would be very short. A simple relation for estimating zone formation time which satisfies the limiting conditions is as follows:
eF = (1 - p ) e z
(8)
In othei words, the lower average metallic cation content of the exchanger in the zone (after steady state is reached), the shorter the time required t o form the zone initially. I n many cases the 8-curves are found t o be symmetrical, so that F = 0.50, and SF = 0.5 Bz. On a basis of these assumptions, one can calculate the height of the exchange zone from the S-curve and the relation
or for symmetrical curves
h,= 0
An alternative method of calculating the zone height, hz, is as follows : The residual ion exchange capacity of t h e zone, &e, can be calculated from Equation 5. If CT is defined as the specific total capacity of the exchanger-Le., metallic ion content per unit volume when the exchanger is exhausted-the zone height can be calculated from
Agreement between the two values of hz as determined by these two independent methods should prove an adequate test of the correctness of the assumptions regarding the initial time of formation and average degree of exhaustion of the exchange zone. Determination of Bed Capacities from S-curves. For any fixed-bed unit operating a t constant liquor flow rate for which the 8-curve has been determined (see Figure l), it is clear t h a t the total capacity of the bed can be calculated by graphical integration of the relation
= A,
Figure 9 .
Schematic Dia ram of an idealized Countercurrent Ion Exchange Unit
Hence t h e fraction of the exchanger present in the zone which still possesses the ability t o remove ions is
If F = 0 (Le., if the exchanger within the zone a t steady state is essentially saturated with the ions being removed), it would be expected t h a t t h e time of formation of the zone at the top of the bed would be nearly equal t o the time required for the zone to descend a distance equal t o its own height, ez, after steady state is reached. Conversely, i f F = 1.0 (Le., if the exchanger within the zone at steady state is essentially free of the ions being
(11)
where CT = specific molal total capacity of exchanger (milliequivalents per cubic centimeter of solid) and VEA= average volume occupied by solid in the bed. It is necessary t o specify the conditions undei which the exchanger volume is measured, since most high capacity exchangers undergo appreciable shrinkage or expansion during the exchange cycle. The average volume employed in the subsequent calculations is the arithmetic mean of the values for fresh and exhausted exchanger. Similarly, the effective or working capacity of the exchanger may be determined by calculating the area above the S-curve up t o the break-through point
Bed Capacity Determination by Zone-Height Method. If an ion exchange bed is operated to the break-through pointi.e., operated until the concentration of metallic ion in the effluent reaches 5% of its value in the influent-the only portion of the bed not essentially exhausted will be the band a t the bottom of the bed corresponding to the exchange zone. Since this region is partly saturated with metallic cation, the break-through capacity of the bed may be determined from the relation
INDUSTRIAL AND ENGINEERING CHEMISTRY
August 1952
COLUMNHElGHT:33.5 C M .
COLUMN HUGH T.' 22.5 CM.
0
1000
2000
1925
IO00
2
zoo0
SODO
4000
V , EFFLUENT VOLUME (MINUS HOLDUP) a CUBIC CENT/M€TERS Figure 3.
Experimental Effluent Concentration vs. Volume Curves
for Sodium-Hydrogen Exchange in Fixed Beds of Nalcite HCR
Influent 0.120 N sodium chloride Temperbtute, PIo C. Average resin particle size, 0.6 mm.
a simplified treatment of exchanger regeneration in fixed beds will The height of the exchange zone is a measure of the rate of ion exchange under a h e d average concentration driving force. The factors influencing this height, therefore, must be variables affecting the resistance t o ion transfer, t h a t is, temperature, exchanger particle size, ion concentrations or activities, and liquor velocity. Since the process occurring in the zone is but little influenced by the exhausted exchanger above it or the fresh exchanger below it, the zone height should be independent of both the over-all height of the bed and bed cross-sectional area. Thus, if the zone height is known for a given exchange process under conditions of specified temperature, influent solute concentration, exchanger particle size, and liquor velocity, the capacity of a bed of any desired height and cross section can be calculated from Equation 13 for the specified conditions. It is clear that as long as zone heights are relatively small (say, 3 feet or leas), they can be calculated by the methods outlined above from S-curve data obtained from simple, laboratorysize columns. If liquor velocity is the only variable t o be considered, a single column will suffice for the construction of a plot of zone height as a function of liquor velocity, from which R practical ion exchange unit can be designed. Lnnitations of the Proposed Method. The exchange zone method developed i n this study is applicable only to those fixedbed ion exchange processes in which a sharply defined, constantwidth exchange zone is formed. This behavior is generally characteristic of exchanges in which the ion t o be removed from the influent has a greater affinity for the exchanger than the ion originally present in the solid. Inasmuch as preferential sorption of this nature is highly desirable from the point of view of completeness of removal of the desired ion, one fmds that the majority of important industrial ion exchange processes fall in this category. It is clear, however, that the regeneration of ion exchangers must involve ion interchange opposite t o t h a t described above. I n these processes, only a diffuse exchange zone is formed, which broadens continuously as it descends through the bed. Application of the exchange zone analysis t o such cases is fruitless, since the basic premises upon which the analysis has been developed no longer apply. It is hoped, however, t h a t
soon be devised in order that a complete picture of ion exchanger performance will be available for design purposes. In very small laboratory units, errors may be encountered in applying the zone height method for interpreting the data, because of end and wall effects. The limits of column height and diameter a t which such effects become important have not been determined; the experimental data of this investigation gave no evidence of such complications for bed heights as short m 22.5 em. and for a bed diameter equal t o about 40 exchanger-particle diameters.
Theoretical Treatment of Ion Exchange in Moving Beds under Steady-State Conditions If the conditions within the exchange zone of a ked-bed ion exchange column are analogous to those existing in a steady-state, countercurrent unit, it should be possible t o apply straightforward adsorption or extraction theory t o this case and t o compare the results with the experimental observations. The mathematical development presented below is a simplified analysis of conditions extant in a n ideal countercurrent ion exchange column and is based on the following implicit assumptions: 1. Flow conditions and concentrations in both solid and liquid phases are uniform and constant across the column cross section. 2. Activity coefficients for all ions involved in transfer are unity. 3. Mass transfer coefficients are constant for any specific flow conditions and are independent of ion concentration,
Consider a column in which a liquid containing a sodium salt is flowing downward, countercurrent to a n acid ion exchanger. Fresh solid is introduced a t the bottom and exhausted solid removed at the top. The relative rates of feed of liquid and solid will be so adjusted that liquid leaving the bottom of the column is essentially free of sodium ions and the solid leaving the top is essentially saturated with sodium ions. This process evidently requires a column of infinite height, but this fact offers little complication, since conditions are to be determined in the middle of this column where the majority of the exchange is taking place (see Figure 2)
1926
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 44, No. 8
60 40
$
k
$
2o
8-
IO
: $
6
$ 0
4
? %
2 001
Figure 4.
2 4 6 S o l 2 4 6 SUPERFKlAL VKLOClTY, CENTIMETERS/SEC.
6 / O
Height of Exchange Zone as a Function of Superficial Liquor Velocity
Letting L = liquor rate, R = solid late, X = concentration of sodium in liquor a t any point, Y = concentration of sodium ion in solid a t any point, CT = concentration in solid of sodium ion when solid is saturated with the ion in contact with thc raw influent, h = distance down from a specified cross section of column, and A,, = column cross-sectional area, a material balance around the entire unit requires that
L(X0 - X , ) but, since X, = Y ,
=
=
n(c, -
U,)
(14)
0,
TJo
=
RCr
01'
S o = R/LCT
(1.5)
At any point in the colunm, it follows that
L X = RY
(16)
Now consider a section in the column of width dh. If the transfer of ions between liquid and solid is liquid-film controlled, the rate of exchange can be represented by:
-LdX
z $1
=
(KLu)(A,.)~~( XX * )
(17)
where K L =~ over-all mass transfer coefficient and X * = sodium ion concentration in equilibrium with a solid containing Y in?. of sodium ion per cc. In general, the equilibiiuin distribution of sodium and hydrogen ions between an ion exchanger and the surrounding solution can be expressed by the relation
LO '0
(3
0
$1
m
*
n
0
0
fi
9
* N
0
where s and E refer to concentrations (in any consistent units) in solid and liquid phases, respectively, and K is a constant. Electrical neutrality requires t h a t the sum of hydrogen and sodium ions in both phases be constant. The total cation content of the solution must be equal t o the initial sodium ion concentration, so that
H: = Xo
-X
(19)
Similarly, for the solid phase
0
$1 (3
d In
H,f=Cr-Y Hence, where Equation 18 applies, one may write
(20)
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
August 1952
[ Y~ l-xol xT 4 -
=
Solving Equations 15, 16, 17, and 21 simultaneously, it is found that
x
This equation can readily be integrated (over the interval --t XI, 0 ., h ) :
Equation 23 relates the ion concentration in the liquid phase to the distance through the exchanger bed under a fixed set of operating conditions, in those cases where a constant-width exchange zone is formed. This equation also describes the Scurve (see Figure 1) characteristic of the bed when operated under these fixed conditions. If X I= 0.95 XO, and X = 0.05 Xo, by the definition given above for the exchange zone, i t is clear that
For any value of h less than hz KLah(Acn)=
L
K In ( 1 9 ) ( X" - x 7 - In (wf) x) o(25) K - 1
Hence
Equation 26 relates the ion concentration in the liquid phase to the fraction of the distance through the bed defined as the exchange zone. Comparison of the curve represented by Equation 26 (for the appropriate value of K ) x i t h the corresponding curves obtained from experimental S-curve data will be useful for verifying the assumption of a constant-height exchange zone. If this assumption is justified, Equation 24 can then be used for the calculation of mass-transfer coefficients and related quantities.
-
4-
2
Experimental Demonstration of Zone
1927
versus volume curve was determined. The representative Scurves for all columns investigated are shown in Figure 3. To avoid confusion, experimental points for only one S-curve are shown on the diagram. Reproducibility of the data was found to be remarkably good throughout, the maximum variation in sodium ion concentration for a given effluent volume for any column seldom exceeding 0.01 me. per cc., or 8% of the influent concentration. The average variation in ion concentration at a given volume of effluent for any column was about 0.002 me. per cc., or less than 2% of the influent concentration. Analysis of Data. The total capacity of the resin for each column was determined by measuring the area over the effluent volume us. concentration plot u p t o the point at which t h e effluent concentration of sodium reached 95% of the influent concentration (i.e., 0.114 N ) , allowance being made for column holdup volume. Specific total capacities were determined by dividing the total milliequivalents of sodium removed by the average bed volume. A similar procedure was used t o determine the effective capacity (capacity a t break-through) of the resin. The fraction residual capacity, F , of the zone was determined as outlined above; zone heights were calculated by both of the suggested methods (Equations 9 and 10). The rate of descent of the zone and the ratio of zone velocity t o superficial liquor velocity, were also calculated. The results of these calculations are summarized in Table I. Several observations noted in Table I deserve comment. First, the fraction residual capacity of the zone averages 0.49 &. 0.02, emphasizing the symmetry of the S-curves over s fifteenfold change in liquor flow rate. Secondly, as anticipated above, the specific total capacity of the resin is only slightly affected by flow rate or bed height in the range investigated, the maximum deviation from the mean being only about 7%. Thirdly, the rate a t which the exchange zone descends through the resin bed is essentially directly proportional t o the liquor velocity as shown by the constancy of the UL/UZratio. Since this ratio in reality measures the maximum volume of solution (0.120 N in sodium chloride) from which one unit volume of resin exchanger can remove essentially all the sodium ions, the specific resin capacity should be equal t o ( U L / U Z )X (normality of influent) = (15.7) (0.120) = 1.89 me. per cc. of resin. This is in close agreement with the average value obtained by direct graphical integrationLe., 1.94 f 0.07 me. per cc. of resin. Correlation of Zone Height with Liquor Velocity. Agreement between values for hz calculated from rate data and capacity
2 0
Height Method Sodium-Hydrogen Exchange in Fixed Beds of Nalcite HCR. Ten glass columns, 22 mm. in diameter and of varying heights, were packed with the high capacity, sulfonic acid-type, cation exchange resin Nalcite HCR (Dowex 50). The average particle size of this exchanger was between 0.6 t o 0.7 mm. Beds roughly 8,12, and 16 inches high were employed. The columns, containing initially pure, acidform resin, were treated with a n 0.120 ( f O . O O 1 ) N sodium chloride solution over a wide range of liquor flow rates, and the effluent was collected and analyzed at intervals for sodium and chloride content. When the beds were exhausted, they were backwashed with distilled water and regenerated essentially completely with 3.99 N hydrochloric acid solution. Several exchange runs were made on each column a t a specific flow rate and the characteristic (average) concentration
4p*
2$
$b b e\ ?8
I 6 /
2 '
g$
u8
/e
0 2
0 1
UL
Figure 5.
0 3
, SUPERFICIAL
0 4
0.5
LIQUID VELOCITY
0 6
,
0 7
0 8
09
CENTIMETERS / S E C
Specific Effective Resin Capacity as a Function of Superficial Liquor Velocity Dotted areas represent probable error in experimental data
INDUSTRIAL AND ENGINEERING CHEMISTRY
1928
data is also satisfactory. The maximum discrepancy is about 18%; the average discrepancy between the two values is about 9%. I n Figure 4, zone height is plotted against mperficial liquor velocity on logarithmic coordinates. Drawing the best straight line through the points, the following equation is obtained: hz = 37.4
U~0.50
(27)
with hz in centimeters and U L in centimeters per second. This equation reproduces the experimental data within about 14%, an error which is not much greater than t h a t involved in the experimental measurements themselves. In familiar mass-transfer terminology, the zone height is merely the height of a number of transfer units (N.T.U.'s) determined by material balance and equilibrium relationships within the zone. Since the same resin, influent, temperature, concentration limits, etc., were employed in every case investigated, it is clear t h a t hz should be very nearly proportional t o the H.T.U. for the given flow conditions, the constant of proportionality being the same for all flow rates. The exponent on the velocity in Equation 27 (0.50) is in very close agreement with the value of 0.51 recommended by Wilke and Hougen (10) for calculating H.T.U.'s for gas film-controlled mass transfer in beds of packed solids at particle Reynolds numbers less than 350. (Flow conditions in this work were well within the streamline region, the largest value of D p U ~ p / being p about 5.) Under conditions where diffusion of ions through the gel structure of the exchanger (or chemical reaction within the exchanger) was the rate-controlling step in ion exchange, it is evident that the exchange rate would be independent of flow rate, and hence the zone height would be a linear function of the liquor velocity. The fact that zone height actually increases with the square root of the velocity indicates that the major resistance t o ion transfer is probably diffusion of ions through liquid surrounding the solid particles. Experimental and Calculated Specific Effective Capacities for Nalcite HCR, From a knowledge of zone height as a function of liquor velocity and of the specific total capacity of the exchanger, it should be possible (using Equations 13 and 27) t o determine the effective capacity of an exchange bed of any specified height and a t any specified liquor rate, under conditions of constant temperature, particle size, and liquor concentration. This has been attempted in Figure 5. The curves represent the calculated capacities for resin beds 22.5, 33.5, and 43.8 em. high, corresponding t o the bed heights employed in the experimental part of this investigation. The experimentally determined capacities are spotted on this plot for purposes of comparison. The maximum deviation between experimental and calculated values of capacity is about loyo,representing about twice the experimental error encountered in capacity measurements. It is probable that this error could be reduced by obtaining a number of additional experimental values for hz, but when it is realized that the 10 values determined in this work are the result of roughly 1400 independent volumetric analyses, it is doubtful that the gain in accuracy would be worth the expenditure in effort. Since agreement with experiment within 10% is adequate for most engineering work, it appears that the zone height method for estimating ion exchange bed capacities can be recommended as simple and reliable, within the limitations cited earlier in this discussion. Comparison with Theoretical S-Curve. For the sodiumhydrogen exchange on Nalcite HCR, under the conditions employed in this investigation, K = 1.20 (4). If Equation 23 is solved using this value of K , letting X = 0.95 Xo, the relation reduces to :
Vol. 44, No. 8
This equation is plotted (from X = 0.05 X Ot o X = 0.95 X , ) in Figure 6. The limiting values of X correspond t o the concentration range defining the exchange zone employed in correlating the experimental data. The abscissa of the graph is h/hz, where hz is the value for h when X = 0.05 X O(i,e., the bottom of the zone). If the experimental 8-curves for the 10 columns investigated are plotted on coordinates comparable with those of Figure 6 (Le., X / X O vs.
"-"),
the agreement between theory and vz experiment is found t o be remarkably good. I n most cases, the experimental points fall on or near the theoretical curve and only in rare instances are the deviations greater than experimental error. These results suggest that the simplified development employed here may closely depict the conditions occurring in monovalent cation exchange units employing high capacity resins such as Nalcite HCR. The values of X corresponding to the points of inflection of the theoretical curve can be calculated from the simple relation:
For K = 1.2, Xinf.is found t o be 0.522 X Ofrom Equation 29. The points of inflection of the experimental curves, it will be recalled, occurred at X = 0.49 X O ,which is in substantial agreement with theory. Evidently the shapes of the curves are determined solely by the magnitude of K and become increasingly unsymmetrical for larger values of this constant. For values of K 5 1, Equation 23 no longer applies; under such conditions, it is not possible to achieve steady-state operation and at the same time utilize the full capacity of the exchanger, When K is greater than but very nearly equal t o unity, mathematical difficulties are encountered in the application of Equation 23 and the determination of the height of the exchange zone. This is caused by the great width of the zone when the steadystate condition is reached and the slow, progressive widening of the zone which naturally precedes attainment of steady-state conditions. Similar difficulties will be encountered if the front boundary of the exchange zone is defined by a value of X very close to zero. These conditions represent regions where the exchange isotherm for the exchanger is essentially linear and point out the difficulty in applying the exchange zone concept in such cases. Estimation of H.T.U., N.T.U., and Mass Transfer Coefficient. [K~ah(Ac,)1 The term represents the number of transfer units
L
required for the removal of a specified amount of the metalllc ions in the effluent liquor. From Equation 24 between the limits X = 0.95 XOand X = 0.05 XO, it is found that the ?T.T.T = 32.4 for liquid film-controlled ion transfer. Assuming this relation is a fair representation of the actual situation nithin the exchange zone, it is then possible t o determine the H.T.U. from a measured zone height and to calculate the liquid-film mass tranefcr coefficient. Combining: (30)
with Equation 27 it is found that
K L= ~ 0.86
(31)
U L in cm./second, KLCL in me./second X em. X (me./cc.) The mass-transfer coefficients for sodium-hydrogen exchange under the conditions existing in this investigation are thus very high and the H.T.U.'s correspondingly very small (usually less than 1em.) when compared with other liquid extraction processes. The coefficients are of the same magnitude when expressed in
August 1952
INDUSTRIAL AND ENGINEERING CHEMISTRY
comparable units as those observed for the absorption of ammonia from air by water in quartz-packed ( l l / d - to la/,-inch particles) columns under conditions of turbulent gas flow (6). This observation is particularly surprising when it is realized that liquid flow in ion exchanger beds is mainly laminar and that diffusivities in liquids are several orders of magnitude less than diffusivities in gases. A possible explanation for these inordinately high mass-transfer rates may lie in the gel-like structure of the ion exchange resins-that is, the permeability of the resin particles to the ambient solution may be so high that the effective inter-
1.0 r
I
I
I
I
I
0.95
0.75 X
x, 0.5
I
O / f fUS/Ol CONTROLLING
0 0
0.2
0.4
0.6
0.8
1.0
h
h, Figure 6. Relative Variation of Metallic Ion Concentration in Liquor with Distance through Exchange Zone in an Idealized Countercurrent Exchange Column
Theoretical curve,
ka
= 1.20
facial area for ion transfer is larger by many orders of magnitude than the measured surface area of the particles. More detailed and fundamental investigation of ion exchange kinetics under idealized conditions will be necessary, however, before the mechanism of the exchange process is adequately clarified. Experimental Procedure
Laboratory Setup. The 2.2-cm. diameter glass columns used in this work were packed with acid-form Nalcite HCR, Pyrex cloth being used for bed supports, Solutions, Le., salt solution and regenerating acid, were fed to the columns via manifolds from elevated, 55-gallon, paraffin-lined barrels. The same solutions were used in all columns throughout the investigation. Column Operation. With the resin bed in the acid form and the column filled completely with distilled water, 0.120 N sodium chloride solution was allowed t o flow down through the unit, the rate being controlled by means of pinch clamps and measured by recording the volume of liquor collected in a known time interval. Upon exhaustion of the bed, the column was backwashed with distilled water until the wash gave no flame test for sodium; regenerant acid (3.99 iV hydrochloric acid) was then passed down through the column until the effluent was sodium free. Backwashing with distilled water was then resumed until the wash water was essentially free of acid. The column was then ready for another exchange run.
1929
Analytical Procedure. Sodium ion concentration in the effluent was determined by titrating aliquots fist with standard base t o a phenolphthalein end point and second with standard silver nitrate solution (in the presence of potassium chromate) to an orange silver chromate end point. The sodium ion concentration was thus equal to the difference between the chloride ion and hydrogen ion concentrations. Since the cationic resins do not remove anions, the silver nitrate titration was used only to spot check the total solute concentration. Variation in chloride ion content of the effluent was found t o be almost negligible. Experimental Precision and Reproducibility. The effluent liquid from each column was collected in 1-liter graduates and the accumulated volume recorded each time a sample was taken for analysis. The uncertainty in the volume determinations did not exceed 10 ml. Flow rates were determined periodically by measuring the time required to accumulate a certain volume of liquor. Changes in bed density caused by shrinkage of the resin during a run made flow rate control difficult, so that the reported rates may have been as much as 10% in error This is undoubtedly the most significant experimental error encountered in the investigation, Column holdup volume was determined by recording the volume of liquor collected when the effluent showed the first traces of acidity, and by completely draining the column and measuring the volume of liquid collected. The value determined by the latter method was in most cases 10 to 15 ml. higher than by the former. The reported holdup volumes are the averages for all columns of the same height, the mean variation being about 10 ml. This represents a possible error in total bed capacity of 1.2 me. of sodium or less than 2% of the average bed capacity. The volumetric analyses were of high enough precision t o warrant their exclusion as a significant source of error, An error of no greater than 0.5% is believed t o have been introduced in aliquoting 10-ml. samples for analysis. Bed height measurements were reproducible to within 0.5 cm. from run t o run for a given column but varied more than thls between columns of the same nominal height. The values reported are the mean values (and mean deviations) for all columns of the same nominal height. The reproducibility of the data points for the S-curves of a given column was generally excellent from one run t o another. The greatest discrepancies occurred, as might be expected, a t the steep part of the S-curves, but seldom exceeded 0.005 me. per ml. on the ordinate. Fortunately, even appreciable deviations in this region introduce little error into the subsequent calculations. The mean deviation of the experimental points from the mean 8-curves was about 0.002 me. per cc. The cumulative experimental error in the calculated capacities and zone heights, including the error of precision in graphically integrating the plots, is believed not t o have exceeded 10%.
Summary
A simplified treatment of the kinetics of fixed bed ion exchange, believed t o be of engineering utility, is presented. The treatment is applicable t o high exchange rate reactions and is based on the concept of an exchange zone in which the majority of the exchange occurs, and which descends through the exchanger bed a t constant velocity. B y use of the method, it is possible t o correlate laboratory data obtained from small columns and employ the correlation for the design of large ion exchange units. The effect of bed height and liquor velocity upon the capacity and rate of exchange of sodium for hydrogen ions on acidform Nalcite NCR (Dowex 50) was studied in the laboratory. The results show that useful exchanger capacity decreases with increasing liquor velocity and decreasing bed height and that
INDUSTRIAL AND ENGINEERING CHEMISTRY
1930
exchange rate increases with increasing liquor velocity but is unaffected by bed height. Useful exchanger capacities calculated by the zone height method are found to agree within 10% with the values determined by experiment. Theoretical treatment of conditions within the exchange zone of a fixed bed unit on an ideal steady-state, counterflow basis has yielded relations which quite closely duplicate the experimental results. These relations permit calculation of N.T.U.’s, and with accompanying experimental data, of H.T.U.’s and over-all mass transfer coefficients. These latter quantities should permit determination of ion exchange column performance over a wide range of operating conditions.
= total milliequivalents cation removed by exchanger bed
up to break-through point
= total milliequivalents cation removed by exchanger bed
a t exhaustion
= milliequivalents cation removed by the exchange zone = = = = = = = = = = =
Acknowledgment
= =
= = =
CT
= specific total capacity of solid ion exchanger, me. per
Literature Cited
cc. of packed solid
cc. of packed solid
D P = average particle diameter, em. F = fraction residual capacity of exchange zone hT hz
= mean bed height, cm. = height of exchange zone, cm.
K = equi!ibrium constant for ion exchange KLU = over-all mass transfer coefficient (based on liquid diffusion controlling), me. per second X em. X (me. per cc. driving force)
Engil”,”d” ring
RCCEIJTD for review October 1, 1951.
ACCEPTEDbrag 2G, 1952.
Corrosion Zirconium
P development O C W
I
Mineral Acids
LEX B. GOLDEN, 1. ROY LANE, JR., U. S. Bureau
of
AND
WALTER L. ACHERMAN
Mines, College Pork, M d .
ITSNIUhI and zirconium have only recently made their debut in the metals industry but their outstanding properties have evoked tremendous interest in their potential use as engineering materials. Both metals are particularly attractive from the standpoint of corrosion resistance and undoubtedly will assume a prominent role in chemical and allied industries, along with stainless steel and similar acid-resisting materials. The production of ductile titanium has advanced from the strictly experimental or small-scale pilot plant stage t o that of limited commercial production. An increasing number of industrial organizations are entering into the titanium production field, thue assuring the metal of an important position as an indus-
T
from break-through to exhaustion solid exchanger flow rate, cm. per second superficial liquor velocity, cm. per second rate of descent of exchange zone, cm. per second volume of effluent, ml. volume of effluent collected up to break-through volume of effluent collected upon exhaustion of bed, ml. volume effluent collected between break-through and exhaustion of bed, ml. average volume occupied by packed bed, cc. effluent metallic ion concentration, me. per cc. influent metallic ion concentration, me. per cc. metallic ion concentration on exchanger, me. per cc. of packed solid time of formation of zone, seconds time required for exhaustion, seconds time interval between break-through and exhaustion of bed, seconds liquid viscosity, c.g.s. units liquid density, grams per cc.
(1) Boyd, G. E., Adamson, 8.Vi‘., and Myers, L. S., Jr., J . A m . Chem. Soc., 69, 2836 (1947). (2) Ibid., p. 2849. (3) Nachod, F. C., “Ion Exchange: Theory and Application,” pp. 29-43, Sew York, Academic Press, Inc., 1949. (4) Ibid., pp. 55-6. ( 5 ) Perry, J. H., ed., “Chemical Engineers’ Handbook,” p. 1180, New York, McGraw-Hill Book Co., Inc., 1941. (6) Sillen and Ekedahl, Arkiv. Kemi Min. Grot., 22A, Xos. 15, 16 (1946); 25A, No. 4 (1947). (7) Thomas, H. C., Ann. N . Y . Acad. Sci., 49, 161 (1948). (8) Thomas, H. C., J . Am. Chem. Soc., 66, 1664 (1944). (9) Walter, J. E., J . Chem. Phys., 13, 229 (1945). (10) Wilke, C. R., and Hougen, 0. A . , Trans. Am. Inst. Chem. Engrs., 41, 448 (1945).
Nomenclature = bed cross-sectional area, em. = specific effective capacity of solid ion exchanger, me. per
liquid flow rate, cm. per second
=
The experimental data presented in this paper were obtained and compiled under the author’s supervision by 43 students in the department of chemical engineering (class of 1950) during a laboratory course in industrial chemistry. The author is indebted t o Edward J. Freeh, Laurent P. Michel, and Curtis C. Williams, 111, for their assistance in correlation of the data, to Edwin R. Gilliland and Herman P. Meissner for their helpful comments and criticism of the manuscript, and to Harold H. Carter, who so kindly prepared the plots and diagrams.
Ace CE
Vol. 44, No. 8
trial commodity. The rate of production for 1952 has been estimated a t 3500 tons per pear. Up t o the present time, substantial quantities of zirconium have been produced only by the U. S. Bureau of Mines a t Albany, Ore., with smaller amounts being produced by the Foote Mineral Co. a t Philadelphia, Pa. Since the publication in 1949 of quantitative corrosion data for ductile titanium and zirconium by Gee, Golden, and Lusby ( 8 ) , there have been several papers on the corrosion resistance of ductile titanium but very little has been published on zirconium. Fontana ( 7 ) reported that titanium shows surprising resistance t o nitric acid a t high temperatures and pressures. Hutchinson and Permar (IO) presented data on the corrosion resistance of commercially pure titanium in some inorganic and organic acids
