EngFnTring -Process development
Dialysis of Caustic Soda Solutions R. D. MARSHALL’ AND J. ANDERSON STORROW COLLEGE OF TECHNOLOGY, MANCHESTER 1, ENGLAND
Concentration distributions have been measured in the continuous countercurrent dialysis of 20 weight $& sodium hydroxide solutions in order to assess the mass transfer in terms of dialysis coefficients appropriate to specific positions along the contact path. Comparison of exact and approximate methods for the calculation of over-all coefficients shows that for design purposes it is adequate to use an over-all coefficient based on the logarithmic mean of the terminal concentration differences between the lye and water cells. Relative resistances to transfer in the liquor “films” and in the membrane have been assessed for various positions on the membrane and it has been shown that the reduction of either resistance will increase the over-all dialysis coefficient. .4pproximate design methods have been suggested from these analyses.
T
H E use of either dialysis or electrodialysis as a method of separation and purification has been confined in most of its applications to laboratory experiments (14, 26, 37) and small scale industrial processes (9,54, 36, 39, 40, 46). An important exception t o the generally small scale industrial application of dialysis is iound in the manufacture of viscose rayon. Caustic soda is recovered from steepage lyes of 17 to 20 weight % concentration contaminated with about 5% hemicellulose ( 1 , 3 , 5 , 6 , 16, 18, 31 , 39, 56, 41 , 42, 44, 4 5 ) . As the size of its particles is from 100 to 1000 A., the hemicellulose can be separated from the liquor by dialyzing through parchment or cloth membranes. The dial) zers commonly in use are either of the tank type, such as the Cerini unit (4), or of the filter-press type, such as the Heibig ( I S ) , Asahi, and more modern Brosites and Kooij dialyners. In the tank unit the diaphragms are suspended in the form of cloth bags reinforced with a wire mattress. The bags are connected in parallel, the contaminated liquor being fed to the bottom of the tank. Water is fed to the top of the bags and purified lye is withdrawn from the bottom. In the filter-press units vertical parchment membranes are sandwiched between alternate lye and water frames, the crude liquor and water being fed to the bottom and top of these frames, respectively. The membrane is usually supported by a metal lattice framework on either one or both faces. Of the various patented devices ( 1 , 3,6, 6 , 15, 31, 35, 4 5 ) the majority are designed either to increase the membrane life by control of the pressure difference across the membrane and by improvement in the design of the membrane supports, or to increase the capacity of the dialyzer by reducing the resistances to diffusion which occur in the boundary layers of liquid adjacent to the membrane surfaces. Attempts to achieve this are made by maintaining a tortuous passage for the liquors as they are pumped 1 Present address, Imperial Cheinioal Industries Ltd., Blaokley, Manchester, England.
over the membrane (3,35) or by spraying the liquors onto the faces of the vertical membrane and allowing them to flow downward under gravity. Despite the scope of the attempted applications of the process and the aceepted importance of the recovery of caust.ic lyes, few operating dat’a are in the published 1it)erature. The performance of the commercial dialyzers may be conveniently compared by estimation of an over-all dialysis Coefficient, but in only a few cases has sufficient information been reported (7, 69, 43) to permit such a comparison. This lack of comparative information explains in part the conservative attitude of dialyzer users and the low efficiencies tolerated. Dialyzers of the Cerini type have been tested, that were considered as working satisfactorily, although only giving an over-all dialysis roefficient of 0.0006-i.e., about half the attainable value ( 7 ) of 0.0013 gram of sodium hydroxide/(minute) (sq. cm.) or 0.0013 gram per ml. (g./cc.). Although the structural and operating information on an Asahi unit ( 4 3 )indicates a coefficient of 0.0086, giving this press unit a capacity six times that of the Cerini unit, it appears that a considerable proportion of dialyzers in use are of the latter type. Until methods of comparison are established and operating information published, the comparative advantages claimed for the various patented dialyzers cannot be assessed. The present work ( 2 5 ) was undertaken in order to develop the theoretical basis and derivation of dialysis coefficients, and to study the relationship between local and over-all coefficients in the countercurrent dialysis of caustic soda solutions over the concentration ranges occurring in the industrial recovery process. Local coefficients have been measured and analyzed to indicate the relative importance of the diffusional resistance offered by the membrane and the boundary films of liquor on each side of the membrane. Membrane resistance can be related to the membrane thickness and solution properties. Local dialysis coefficients can be estimated from these quantities using an approximate value for the combined liquor film resistances. EQUATIONS REPRESENTING DIALYSIS
On the basis of the Stefan-Xaxwell equation for the diffusion of material A through B in one direction, the resistance to the motion mag be expressed as proportional t o the concentrations of the components; the driving force for transfer is proportional to the concentration gradient. Although these assumptions are allowable for the gaseous phase, they are less sound for solutions, especially concentrated solutions. The following equation is thus an approximation. des _
dl
- - dca dl
=
OICACB(UA
- UB)
where ( u ~ U B ) is the relative velocity of the two components. Equation 1 is based on the assumption that the total number of molecules in unit volume is constant-i.e., c = (c,t C B ) is constant. The constant, 01, is a coefficient of resistance to diffusion.
+
2934
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
December 1951
If N A and NB are the molar diffusion rates of the components
N A = UACA; N B = UBCB
If the diffusion is considered as occurring along a path length, 2 (Figure l), between concentration limits C A = C A at ~ I = 0 and C A = C A , a t Z = Zl, then Equation 2 may be integrated, if a, c, N A , and N B are taken as constant with respect to 1.
2935
characteristics of the liquids a t various distances from the membrane surface. The membrane can be regarded as having a resistance equivalent to n times its thickness l2 of stagnant liquid. The diameter of the diffusing molecules is small compared with the membrane pore diameter and it is generally assumed that the factor, n > 1, is not due to electrical or mechanical restriction on the motion of the diffusing molecules but is due mainly to the -A 0-
therefore
-1
E)“
log*[‘
1
- ( +- (1 +
2)y
=
(1
+ $)
NA
(3)
p+e,+-e,--j
water memfilm branr
When CA, and C A , are small, or when N B / N A is near -1, an approximation to the logarithmic form may be used. Thus, when
-
h.H
(1+$)?
rlrk
water flow
and
w h-0-f-- NaOH
are small
transfer
Figure 1.
Diffusion System in the Dialyzer
or N A
k(CA1
- CAz)
The coefficient, k , contains the term
(4)
(which i) can be identified
with the diffusion coefficient, D, for the movement of A through B for the system when N A = - N E (2%). The characteristics of k depend on the diffusion coefficient and concentration term, on the assumptions that LY and care constant, and on the validity of the logarithmic approximation which deNE pends on the magnitudes of the terms (1 The
solid membrane structure reducing the area available for diffusion and to the fact that the diffusion paths through the membrane will not be straight lines of length 12 normal to the membrane face. Manegold (84) gives theoretical relationships for the ratio of effective thickness to actual thickness of membrane that lead to the values n = 1.5 for slits and n = 3.0 for pores running in all directions from one side of the membrane to the other. The transfer through the three resistances can be represented by: N A
+ E).:
variation in c in sodium hydroxide dialysis will be 3.5% over the range of concentrations from 10 to 20 weight % sodium hydroxide, and will contribute little to the change of k with concentration or position in the dialyzer. The average ratio, N B / N ~is, shown later to be about -1.8 and at the highest sodium hydroxide concentrations the replacement of the logarithmic term by an approximate form only introduces an error of up t o 4%. Thus the approximate Equation 4 is a reasonable basis for calculation of dialysis coefficients, and as indicated by Equations 3a and 4,the coefficient,k , should be proportional to D and inversely proportional to 11. In the cell represented in Figure 1, the caustic soda is transferred from the lye cell to the water cell; the resistance to the diffusional movement from the bulk lye concentration, C A ~ to , the bulk weak liquor concentration, CA*, can be represented by the sum of the resistances due to the motion to the membrane through the lye and away from the membrane through the water. This can be represented, respectively, by “effective film thicknesses” I, and 28 of stagnant films through which transfer occurs by diffusion only, and the diffusional resistance of the membrane of wet thickness Z2. The effective film thicknesses, Zi and b, are functions of the liquid velocities and of the physical
- CAS)
=
kl(CA1
=
kZ(CA,
(5)
=
kt(cAi
(6)
(4a)
- CAS) - CAa) K(CA1 - CA4)
(7)
where K , the local dialysis coefficient, depends on the individual resistances of the films and membrane: -1= - 1
K
1 1 k l f k z f &
(8)
The concentrations and diffusion rate defining K in Equation 7 are appropriate to a position height, h, above the bottom of the vertical membrane (Figure l), where the bulk concentrations are: CW
=
cA4; CL
=
CAI
For transfer through the element of membrane of vertical height 6h and of width a’:
The average value of the gram-mole rate, L’ or W’, taken from the inlet and outlet conditions varies by less than 3%-i.e., less than the variations in the volume flow rates, L and W-and thus may be taken as approximately constant over the total height of the membrane. The values of
6cL
6c&
and 6h may be estimated
INDUSTRIAL A N D E N G I N E E R I N G C H E M I S T R Y
2936
from the gradient of the curve of concentration versus height up the membrane to give the value of K a t any level in the cells. Eynon ( 7 ) has shown that an over-all dialysis coefficient, K O , may be obtained from initial and final concentrations and flom rates of the streams passing through the two cplls. A(h-A)m
KOA k
n ,
(10)
vhere Ac,, is the logarithmic mean of the differences in concentrations, Ac = (cL - cw), a t the bottom and top of the membrane. This derivation of K Oassumes that the volume flow rates and dialysis coefficients are the same at all positions on the membiane. However, as will be shown later, these quantities may
Vol. 43, No. 12
faces. Support of the swollen membrane is important owing to its inability to withstand more than small pressure difference8 across it; it was also necessary to keep the membrane as near the vertical plane as possible. With the long experimental times re quired owing to the low diffusion rates, it was necessary t o provide a constant temperature atmosphere around the cells. For this purpose the unit was held in a cradle within a lagged box (Fi ure 3) wherein the air temperature was maintained at 25' C. %he temperature of the air at the inlet was maintained to =t0.loC. and the temperature drop along the air-flow path through the box never exceeded 0.8" C. As the liquor flow rates were about 5 ml. per minute the %foot length of the inlet tubes within the box wm adequate in warming the liquids to the operating temperatures. A subsidiary 50-watt heater, controlled by a Variac transformer, was wound around the inlet tube and used when more rapid heating of calibrating solutions was required. Cross connections were fitted to the tubes so that a given solution could be fed to the bottom of both cells simultaneously. During dialysis the rates of the water and lye streams at the inlets to the cells were measured by small glass Niveau meters provided with overflow lutee that gave an adjustable constant level above the measuring orifices. The lye outlet line from the dialyzer was also provided with an adjustable lute so that the pressure on the two sides of the membrane could be approximately equalized.
Figure 2. Perspex Countercurrent Dialyzer
vary by 12 and 25%, respectively, from the top to bottom of the dialyzer. Because this over-all value may be readily obtained by measuring the end conditions in the dialyzer it is important to compare the approximate mean roefficient, KO, with the true mean coefficient derived from knowledge of the actual variations in local coefficients K and stream rates. I n the present work local coefficients have been measured in order to obtain the maximum amount of information on the process, and to compare these mean values of dialysis coefficient. Batch dialysis, wherein the bulk concentrations vary with time, can be represented by the integration of Equation 7 that gives the total solute transferred in time t :
?Y = K(Acm)t.4t
(11) Figure 3.
n her e
The integration to this form rests on the assumptions that K is affected neither by the concentration changes occurring in time t , nor by any hydrodynamic change affecting the effective film thicknesses that may occur during the exchange period. Furthermore, the volume of each liquor is taken as constant during the dialysis. CONTIKUOUS COUNTERCURRENT DIALYSIS
The dialyzer ahon-n in Figure 2 was made from Perspex, with Monel tube connections, and consisted of two sections which were clamped together with rubbe: gaskets on each side of the membrane thus forming the two cells of the unit. Lindapter clamps were fitted every 4 inches around the edges of the dialyzer. The membrane was supported on each side by a lattice of 24 standard wire gage nickel wires arranged every 3 inches of the height, the wires being embedded flush w:th the Perspex jointing
Arrangement of Apparatus
The measurement of concentration a t selected positions and distances from the membrane, or along the flow path of the liquors, by withdrawal of samples for analysis is extremely difficult if serious disturbance of the dialysis conditions is to be avoided a t the flow rates existing in the small unit. For the experiments on caustic soda solutions, in view of the sensitivity of specific resistance to the liquor concentration ( l e ) ,it was decided to use analysis by electrical conductivity measurements made in situ, thus avoiding disturbance of flow conditions. Such sensitive analysis also provide measurements as a function of time when the concentration and flow conditions are not in equilibrium. I n the present unit the liquor concentrations could be measured a t thirty positions in 5 minutes, which was a negligible period compared with the time required to attain balanced operation. The electrode systems used mere such that the measured resistances ranged from 7 to 70 ohms in the various liquor concen-
INDUSTRIAL AND ENGINEERING CHEMISTRY
December 1951
trations. A modified Wheatstone bridge was constructed to give an accuracy of 0.2%, when using an auxiliary capacity of 0.05 to 0.4 microfarad ( p f ) in parallel with the standard resistances in the bridge. The balance position was detected audibly using a 3000 cycle-per-second oscillator giving a sinusoidal wave form, that applied 0.2 volt potential difference between the electrodes. Fifty electrodes for sealing into the walls of the unit were made from platinum wire (29 standard wire gage) sealed into glass tubes
water and lye flows are normal to plane of diagram
L- ‘1
m
4
I
*
091’
water and lye flows normal to plane of diagram
i0 3 9
t/,y/Ay//J\ .1
Figure 4.
O 4T
Arrangement of Electrodes
Left. Electrodes A through I Right. Electrode J
of either ‘/*-inch or a/,,-inch external diameter, whose ends were
turned vertically to provide a mercury contact to the detector connections (Figure 4). The platinum wires were then platinized (I?‘). The main electrodes were laced 0.44inch from the inner face of the back wall of the cell, eacg associated pair being 1.5 inches a art, at nine positions spaced evenly along the contact path and agout the center line of the Perspex face. Similar measurement positions were provided on both sides of the membrane. At a position half the distance up the cells the electrode arrangement, J (Figure 4),was used in each cell to measure the concentrations at various distances from the membrane wall across a horizontal level, measurements being taken with electrode pairs J3-4, 3-5, 2-5, 2-6, 1-6, 1-7. The resulting concentrations were expressed as the mean of the distances between the center of the electrode platinum wire and the membrane for the respective pair. All the electrode pairs were calibrated in sodium hydroxide solutions over the intended range of operation and the calibrations were repeated after various dialysis tests. Using the conditions stated above and the platinized platinum surfaces, the electrode pairs maintained their calibration resistances well within the accuracy required.
hydrostatic pressure of less than 4 inch W.G. The ]ye outlet arrangement shown in Figure was used to the pressures in the cells a t the bottom of the dialyzer, where the membrane was weakest; the maximum pressure difference then occurred at the top of the unit. The flow rates were contr0l1ed to Rive about 90% recovery of sodium-hydroxide with a water rate twice the lye feed rate. These conditions are similar to those used industrially. As no guidance was U&4C“R” available from the literature, tests were made at a series of rates, giving the data in Table I. To minimize the time required to attain equilibrium conditions the experiments were started with 8 weight 0i‘m“Sh m % sodium hydroxide solution in both cells: Constant concentration disI tributions in both cells were generally obtained after about 48 hours’ feeding of 20 weight % sodium hydroxide lye and water to the lye and water cells, respectively. The distributions were checked after another 8 hours to ascertain whether further changes had occurred (see run 5, Table 11). During the first 24 hours the outflow lute had to be adjusted periodically to maintain the pressure balance a t the foot of the membrane. The data in Table I1 and Figures 5 and 6 are representative of those obtained in such tests. The tests from the J electrodes indicate in Figure 5 that the main fall in concentration, when considering the direction normal to the membrane, occurs near to, or inside, the membrane. The positions 0.44 inch from the membrane used for the main analyses along the flow paths are seen to be suitable for giving the bulk concentrations of the MEMBRANE
100
L. c Y
2 m
B P
P 2
3
4
80
60
0
TABLE I. RESULTSOF TESTS Run KO.
2937
Water Rate, Ml./Min.
Lye Rate Ml./Min.’
Approximate Recovery, %
20.0 15.4 5.5
10.0 8.0 2.8
40
40
70
90
.8
.6
.4
.2
DISTANCE
The experiments were confined to the dialysis of pure sodium hydroxide solutions, distilled water alone being fed to the water cell. The parchment membranes were allowed to swell in 8 weight yo sodium hydroxide for 12 to 15 hours before being fitted into the unit, thus avoiding the excessive bulging that would result if the membrane were fitted in an unswollen condition. The maximum swelling occurs in 14 weight sodium hydroxide solution, but preswelling at this concentration always resulted in failure of the membrane during the initial stages of the experiment. The concentration differences across the membrane occurring a t various levels in the cells gave an equivalent
0
.2
.4
FROM MEMBRANE
.6
.8 inch
Figure 5. Concentration Gradient Normal to the Membrane
streams, The distributions within the cells do not rest only upon the usual operating variables and physical characteristics considered to affect the effective film thickness in the case of solute diffusing into a moving stream of fluid. With the concentration differences across the membrane obtained in sodium hydroxide dialysis the flow conditions near the membrane are also disturbed by the influx of a solution of considerably different density. The stream of concentrated solution flowing downward
2938
INDUSTRIAL AND ENGINEERING CHEMISTRY
on the curve ( 8 7 ) . Thus the data for run 5 agreed well with the equations.
TABLE 11. DATAFROM RCN5
Stream Lye feed, L Water feed, W
Plow Rate, MlJhIin. 2.88 5.15
Lye out, L Water out, W
3 23 4.61
Rlole KaOH/min. Mole water/min. Total mole/min. Av. rate, niole/min.
I. MATERIALBALANCE Conon., Gram NaOHI Density, Axass Flow Rates, Gram/.ilin. Liter Gram/hIl. Total NaOH Water 228 1.208 3.48 0.656 2.82 0 0 . 998 5.14 -0 5.14 0.656 7.96 19.5 1.010 3.29 0.063 3.23 130 2 1.124 5.18 o.600 4 2 0 663 7.81 11. MOLARFLOW RATES Water Cell Lye Cell Input Output Input output 0.000 0.015 0.016 0.002 0.285 0.254 0.157 0.179 0,285 0.269 0.173 0.181 W' = 0.277 L' = 0.177
=
__
0.00 0.20 0.54 0.92 1.34 1.80
2.35 2.96 3.64 4.44 5.56
0.40 0.43 0.47 0.52 0.58 0.66 0.75
0.111 0.302 0.514 0.734 1.02 1.33
1.14 1.38
2.09 2.58 3.25
0.00
0.85 0.98
1.69
0.49 0.59 0.69 0.81 0.93 1.07 1.23 1.42 1.67 1.94 2.46
- 0.000526h
0.0488 0.524
+ 036625h
0.0556 1.00
+ 0.01532
cL =
- 0.000745h
(12)
(12a)
ci
Smoothed values of and e; could be taken. The differentials required for the estimation of the local dialysis coefficients, K , from Equation 9 were taken from the equations for
dc;
2~ and dc' -$obtained by the dif-
ferentiation of Equations 12 and 12a. The values of K based on the two sides of the membrane, having only (cL - C W ) common in their estimation, agree to within 5% (Table 11). The average value was plotted against the height, h, and the true mean value for K was obtained by graphical integration to give:
111. LOCALDIALYSISCOEZFICIENT BASEDox WATER-SIDEDATA
76.2 69.8 62.2 54.6 47.0 39.4 31.7 24.1 16.5 8.9 0.0
Vol. 43, No. 12
9.8
8.8 8.2
7.7 7.5 7.4 7.3 7.2 7.1 7.1 6.8
h=H
K,
= -
K6h = h=O
0.0075 mole ?\TaOH/(minute) (sq. cm.) = (mole/ml. ) 76 2 69.8 62 2 54.6 47.0 39 4 31.7 24 1 16.8 8.9 0.0
0 87 1.26 1.76 2.32 2.94 3.64 4.44 5.35 6.40 7.61 9.48
9 3 8.3 7.9 7.4 7.3 7.1 7.0 7.0 6.9 6 9 6 8
An approximate mean value, KO = 0.0071, was calculated from Eynon's equation ( 7 ) ,that resulted from the integration of Equation 7 based on the assumed constancy of K and L throughout the dialysis contact path. These quantities varied by 25 and 12%, respectively, from top to V. OYER-ALLDIALYSIRCOEFFICIENT^ bottom of the dialyzer (Table 11). HowTotal S a O H transferred, gram mole/min. 0.015 ever, the effect of the variations in these 1740 Membrane area, sq. c:m. Acni, mole/ml. 0.00121 two quantities tend to cancel each other, K O ,mole/(min.)(sq. em.) 0.0071 and the value, K O ,from Equation 10 is in a From Equation 12a. e From Equation 12. b From Equation 12a by differentiation. f From Equation 12 by differentiation. good agreement with the true mean c Calculated from smoothed c & values. Calculated from the smoothed c l values. value, K,. Thus for the caustic soda d From Equation 0. h Calculated from Equation 10. dialysis the average coefficient, K O , is adequate for design and comparison ournoses. near the membrane surface in the m t e r cell was clearly visible in The coefficients obtained clearly demonstrate the superiority the transparent Perspex unit. An analogous rising stream of weak liquor could be observed near the membrane in the lye cell due to the diffusion of water into the concentrated liquor. The effect of convection currents due to temperature differences in the cells was negligible and the flow rates were so small-e.g., 1 mm. per minute-that the velocity distributions vere also negligible. Thus the concentration distributions observed were due to the effect of this density-streaming from the membrane face superimposed on the distribution due t o diffusion through stagnant liquor. Without this streaming the over-all resistance in the dialysis would be considerably higher because of the need for transfer by diffusion through the whole of the cell liquids. The curves for mole fraction compositions in Figure 6 were used .
to provide the quantities,
L
A
2 and 2 by fitting equations to 6c'
6c'
them of the hyperbolic form:
where A , B , and C are constants. Approximate straight line forms were obtained for interpolation by plotting e' against c'
h
- c; - ho' where ho and &were eo-ordinates a t any selected position
0
20
40
60
h
80
cm.
Figure 6. Concentration Distribution in Countercurrent Dialyzer
December 1951
INDUSTRIAL AND BNGINEERING CHEMISTRY
of the press-type dialyzer to the Cerini design where KO = 0.0013 mole of sodium hydroxide (minute) (sq. cm.). The present values are less than those obtained from an Asahi dialyzer ( K O = 0.0086) operating on similar solutions (48) because the Asahi membranes were only 30% of the present membrane thickness. The relatively small reduction of the over-all resistance to diffusion by the large change in membrane thickness clearly indicates the presence of appreciable resistance to transfer in the liquor films near the membrane surface. ANALYSIS OF LOCAL DIALYSlS COEFFICIlENTS
To obtain the maximum information on the exchange process it is necessary to assess the contributions made to the total resistance to mass transfer by the membrane and the liquid films. In addition it should be possible to relate the resistance of the membrane to its physical properties and the properties of the solution. This would then permit the prediction of the probable performance of dialyzers for various concentration ranges and membranes. A small batch dialyzer was constructed and used as described in the following sections for the measurement of the membrane resistance.
2939
cells. The stirrers were adjusted to the required speed, and the batch dialysis time was then counted from the time when the feedptreams were stopped. The transfer was allowed to proceed until the concentrations chan ed by about 7 Grams per liter when samples were withdrawn, a n t the concentrations were readjusted to the initial conditions for the succeeding test. When using the highest speeds of the stirrer the final temperatures of the solutions increased by amounts up to 7" C. above the initial 25" C. owing to the energy dissi ation in the stirring and frictional effects. I n these cases the diayysis coefficient calculated from Equation 11 was corrected for the increased operating temperature by multiplying by the factor Dsh/De, where e was the mean temperature of the solutions during the test. The results of the experiments a t the concentrations mentioned are shown in Figure 8, and it is evident that the combined film resistance was approaching negligible values a t the highest stirrer speeds, although comprising an appreciable part of the total resistance in dialysis without stirring,
BATCH DIALYSIS
Equation 8 shows the relationship between the dialysis coefficient, K , and the individual resistances to mass transfer due to the membrane and the adjacent liquid films. To measure the relative importance of these resistances, batch dialyses were carried out in the apparatus shown in Figure 7, wherein the effect of stirring speed could be studied a t selected concentrations and concentration differences across the membrane. The dialyzer consisted of two cylindrical cells with a parchment membrane clamped between rubber ring gaskets as shown, the total membrane area for diffusion being 40 sq. cm. The liquors were stirred by agitators driven horizontally at equal speeds up to inch 1600 revolutions per minute (r.p.m.), and located about from the membrane. The unit was enclosed in the lagged box used in the previous tests and surrounded by air a t a controlled temperature of 25 f 0.1" C.
STIRRER r.p.m.
Figure 8.
Effect of Stirring on Batch Dialysis Coefficient
MEMBRANE RESISTANCE
identical compartments
Rl
LYE -
If local coefficients, K , in countercurrent dialysis could be esti-
n
mated from membrane dimensions and liquor film resistances, the over-all value, KO,from graphical integration of K would be available for dialyzer design. From batch dialysis the membrane coefficient, 4 , was found to be 0.0125 to 0.0138 mole of sodium hydro+de/(minute) (sq. cm.) over a concentration range of 10 to 150 grams per liter of sodium hydroxide. From Equations 3a and 4 the membrane coefficient, kz, is related to the diffusion coefficient, D; the membrane thickness, k; and the ratio of the effective thickness to the actual thickness, n:
kt =
D n,12
Thus, using a value for n, the dialysis coefficient, K , can be estimated for a particular case from a knowledge of the liquor film resistances, the diffusion coefficient of the solute in the solvent, and the dimensions of the membrane in the operating condition. Figure 7 .
Batch Dialyzer
The relative volume of the feed lines to the cells was kept small so that volumetric analyses could be made at the end of each test. In each experiment a new membrane was used, which was preswollen in sodium hydroxide solutions of concentration midway between those to be used in the lye and water cells. After the apparatus in the box had attained the standard temperature, strong and weak lyes of 81 and 31 rams per liter, respectively, at 25' C., were run t h r o q h the a t about 100 ml. per minute for 15 minutes with the stirrers revolving at 800 r.p.m. to attain a constant known initial concentration in each cell. This was checked by the analysis of samples withdrawn from the
eel%
A method was devised for measuring the thickness, la, of the swollen membrane in various caustic soda solutions. The vegetable parchment used in all the tests had a "density" of 137 grams per square meter. The sheet thickness when dry was determined on a standard paper-thickness machine, involving IO measurements on a wad of 10 sheets, giving a mean value of 0.0140 om. The wet thickness was found after steeping the membrane in sodium hydroxide solutions of different strengths for 24 hours. A wad of 10 sheets was pressed between the surfaces of glass disks of %inch diameter and 0.3-inch thickness. The compressive effect under various loads was determined by observing the digplacement of a mark on a glass rod attached to the upper disk USmg a Vernier microscope readable to 0.001 cm., the lower disk was supported rigidly. Loads up to 450 grams with the upper disk
INDUSTRIAL AND ENGINEERING CHEMISTRY
2940
were applied to the parchment and the wad thicknesses were plotted against the load, whence the "wet thickness" for the dialysis equations was found by e~trapolat~ion to zero load. The maximum reductions in wad thicknesa for the loads used varied from 0.005 cm. for the parchment swollen in the weakest sodium hydroxide solution to 0.046 om. for the most sn,ollen material. The results of such tests, all of which gave reproducible effects on unloading or loading, are shown in Table 111.
TABLE V. DATAFROM RUN5
(Dry thickness of sheet = 0.014 om.)
Thickness, Cm.
0.0 41.2 86.2 134.1 183.3 222.6
a 12,
6
0.022 0.030 0.037 0.044 0.043 0.039
F~~~ Equation 13 these values of membrane thickness give the values of R,hich are included with Table IV and tvhich agree with the range calculated from Manego]djs data (24). From the latter's estimations that the ratio of the length of the membrane capillaries to the membrane thickness is 1.5 to 3, ' and for a porosity of such membranes of about 7070, it is to be expect,ed that R lies between 2 and 4. The present results agree with this range (Table IV). TABLE IFr.
?VIEMBRANE
CHARdCTERISTICS
h,
1
69.8 62.2 54.6 47.0 39.4 31.7 24.1 16.5 8.9
118 125 133 135 137 139 141 143 143
K
Cm.
TABLE 111. WET THICKXESS OF PARCHMEKT MEMBRANE Smelling S o h Grams NaOH/Liter
Vol. 43, No. 12
1" k,
(k L) + 45 60 57 59 61 63 68 70 60
73 75 76 76
76
76 73 73 83
Effective Thickness of Combined Films", Cm. 0.05
0.05
0.06 0.06 0.065 0.065 0.07 0.075 0.055
Estimated from k2 = D/0.078. 1 Estimated as D (%
+ k3).
if D , is taken as the integrated mean of D between the concentrat'ions c ' and zero. The oholm values, D,, are actually complcx mean values over the wide range of experimental concentrations involved, although not from c = 0 to c = c', and are derived from the Stefan-Kawalki analysis of the unsteady state diffusion in the column: that actually depends on the assumed constancy Of throughout t'he When plotted against concentration, these values of D from the above relation agree v d h D , at zero concentration and fall about 3% below D , for the maximum experiment'al concentration of about 2 A' sodium hydroxide used in t'he measurement of D,. For the present purpose the data had to be ext,rapolated for solutions of twice this concentration. The actual concentration conditions across the liquor films and membrane at any poaition alone the contact Dath in the continuous countercurrent dialyzer were far from differential-e.g., 4 N to 2 A T sodium hydroxide-as can be seen in Table 11, across lengths such as li, Z2, and la. Thus the mean values of D t o be taken for the assessments on the basis of such composition differences and lengths will lie nearer the D , data than those for D. After consideration of the probable accuracy of the original data and the possible error of about 3% a t the highest required concentration on extrapolating the data by the method given below, it was decided that the i'jholm data would be used dlrectly, being sufficiently accurate for the present purpose. Further measurements of these diffusion coefficients for sodium hydroxide solutions probably ~ o u l d be profitable, particularly a t the higher concentrations hither to not covered. Diffusion coefficients for the precise conditions used in the dialyzer were not available and thus the Oholm data u ere extrapolated to concentrations up to 4 V ' sodium hydroxide using the I
&Iole/(Min.) k2, (Sq. Cm.)
DiP, Sq. Cm./Min.
Cm.
n
0.0125 0.0138 0.0124
0.00104 0,00103 0.00094
0.027 0.032 0.042
3.1 2.3 1.8
lzb.
nlz 0.084 0,074 0.076
hIean 0 . 0 7 8 5 Based on lye side hydroxide concentration as this seemed most suitable after oonsidering the Oholm technique whence the values D were derived. b Based on the mean lye and water side concentrations-Le., assuming swelling appropriate t o their average.
The product, nlz,is approximately constant and for a countercurrent dialyzer using parchment membranes at 25' C. the membrane coefficient can be estimated with sufficient accuracy from
D
k2
=
o m
FILM RESISTANCES
The combined film resistances of the two liquor sides can be estimated as ( l / k , l/&)from the measured values of K and the above relation for ks (Table V). This estimation is dependent on the knowledge of D , and it is noted here that the information on caustic soda solutions was limited.
+
DIFFUSION COEFFICIENTS FOR SODIUM HYDROXIDE IN WATER
The diffusion coefficients used in Tables IV and V were based on those of oholm (96). These are the mean values for the diffusion of sodium hydroxide from a given initial concentration into a column of water, the concentration distribution in the column a t a later time being analyzed by the method of Kawalki (18). The diffusion coefficients, D, for the mass transfer due to the differential concentration change 61 over the short
(g)
path length, SZ, are not available, but probably lie between the values, D , and D, estimated from oholm's data, D,, by the relation a - ( c j , D,) = D act
E::;;
approximate straight line obtained from the plot of Dq _ _ against c', as suggested by the Eyring function ( I O , SO):
where DOand 70 are the values appropriate to a very dilute solution a t the temperature being considered. The activities, a, of the solutions were found from the activity coefficients obtained by Harned ( l a ) . The diffusion coefficients xere also interpolated to the desired temperature of 25' C. by using the plot of log D against 1 / T , in view of the exponential relationship bctneen D and T (IO). The viscosities of the sodium hydroxide solutions ivere obtained by interpolation of the published data (8, 9, 1 1 ) using a plot of log 7 against c. The quoted (11)drrhenius equation 7 =
?;leBC
where q h is the viscosity of water and B is a constant, does not apply a t concentrations above 1 N sodium hydroxide for solutions tested a t 15' and 18" C. Interpolations of these data t o the desired temperature were made using a plot of log q against 1 / T .
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
December 1951
DIALYSIS OF SODIUM HYDROXIDE SOLUTIONS CONTAINING HEMICELLULOSE
DATAFOR KOOIJDIALYZER TABLE VI. OPERATING
Unfortunately the authors were unable to obtain data from the dialysis of solutions containing hemicellulose. Comparison with the data of Kooij (20)shows that the results obtained on pure sodium hyroxide solutions are similar to those found in practice. These are the only other data of which the authors are aware where the concentration distribution has been measured within dialyzer cells.
Total number of frames 81 (41 water, 40 lye) Total number of membranes 80 Effective membrane area, sq. om. 80.6 X 80.6 Concn. Gram/Liter of Presslye Wastelye Purelye Water
.;: 60
DIALYZER DESIGN
80
h cm. Figure 9. Concentration Distribution in ICooij Dialyzer The data in Figure 9 and Table VI were obtained from adjacent cells in a dialyzer using 80 membranes (working in parallel) each 80.6 sq. cm., of parchment similar in density but inferior in quality to that used in the present tests ( 2 1 ) . Local dialysis coefficients, K , were calculated from the gradients of the curves in Figure 9, assuming that each cell equally serves two membranes, using the equations: For the water side: ~ Z ) W = K(CL - cw)2a’
-
For the lye side: ( g ) L = K ( C L cw)2a’
*
-
Certain conclusions Can be drawn as to transfer conditions existing along the dialysis contact patch in equipment operating over the usual concentration range, in the recovery of sodium hydroxide from steeping press liquors in viscose production:
0 40
Analysis of Data from Concentration Distributions Mean CL cw, K x 103 Gram/Ml. Gram/(Min.)(Sd. Cm.) K X 1 6 8
the recovery of caustic does not lead to a lye outlet concentration below that a t which flocculation of the hemicellulose takes place. The conclusions drawn from the present tests are significant in considering the recovery of caustic soda from press lyes by dialysis.
Gcc
20
269 18 110 0
10 0.115 5.W 5.96 5.7 5.9 5.1 5.5 20 0.089 5.5 4.8 5.1 30 0.073 4.9 4.9 40 0.060 . 4.9 50 0.0475 5.0 5.6 5.3 5.7 7.2 6.4 60 0.034 a Values given in this column were based on water-side concentration distribution using a mean flow rate of 41.3 ml./minute. b Valuks in this column were based on lye-side concentration distribution, using a mean flow rate of 19.1 ml./minute.
200
0
Over-all Flow Rate, Ml./Min. 728 800 1650 1741
NaOH
h, Cm. 250
2941
The results in Table VI give from Equation 10 an over-all dialysis coefficient K = 0.0054 gram/(minute)(sq. cm.) which is of the same order as the local coefficients, again indicating that the former is satisfactory- for design purposes. The dialysis coefficients are lower than those obtained in the present tests; however, the method and accuracy of the measurements on the Kooij dialyzer are not known, the parchment used was inferior in quality (di),and the flow rates taken for the analysis are an average value for the whole of the dialyzer. Data from modern Kooij dialyzers operating over a concentration range up to 200 grams of sodium hydroxide per liter using membranes ot the same manufacture as those used by the authors give over-all coefficients of 0.0075 gram/(minute)(sq. cm.) which is in good agreement with the present tests (21). Thus the usual hemicellulose content of viscose press ]yes does not have any substantial effect on thecrate of dialysis providing
1. Local dialysis coefficients may be estimated from membrane thickness, solution properties, and film resistances. 2. The membrane repistance is substantially constant over the whole of the membrane surface, and may be estimated from (nEn)/D where n will vary from 1.5 to 4.0 depending on the degree of swelling for the common membranes of parchment or cellophane. 3. The resistance of the membrane and that of the combined liquor films are approximately equal, except near the top of the dialyzer unit. Advantage in capacity can be gained by reducing either resistance. 4. The effective thickness (II &) of the combined films does not vary greatly from top to bottom of the cells, and for design purposes an average value of 0.05 cm. could be taken. 5 . An over-all coefficient estimated from end conditions is approximately the same as the true mean value of local coefficients.
+
The absence of published information on the claimed improvements (1, 3, 16, 85) excludes the possibility of comparison, but the various devices for improving dialysis coefficients by providing tortuous paths for the liquors flowing near the membrane are unlikely to prove very effective unless combined with high bulk velocities, in view of the low rates of flow normally existing in the cells and the very vigorous movement required to attain the reduction in resistances shown in Figure 8. To attain appreciable increase in the dialysis coefficients it will be necessary to make the liquors flow across the membrane either under gravity, by agitators in the cells, or by pumping the liquor through a series of cells as in the Casey design. If pumping is to be avoided, it will be necessary to lead away from the membrane the falling and rising streams on the water and lye side, respectively, to increase the effective concentration difference across the membrane. It is important to note that without a motive force comparable to this streaming effect, the resistance to transfer would be considerably increased. The probable superiority of the press type of dialyzer lies in ita ability to use thin parchment or cellophane-type membranes rather than the relatively thick cloth membranes in the usual Cerini units, although tubular dialyzers have been made with thin
INDUSTRIAL AND ENGINEERING CHEMISTRY
2942
membranes (31, 46). A further improvement in the over-all coefficient is to be expected if still thinner membranes can be employed. At the present time it is difficult to obtain thinner membranes with the necessary strength when in the swollen condition. That such membranes were available in the past is proved by the Asahi parchment already mentioned. Tests on a cellophane-type membrane of 0.007-cm. dry thickness failed owing to the rupture of the diaphragm that swelled excessively in the sodium hydroxide solutions used. The development of thinner and stronger membranes would be of advantage in dialysis; to this end it may be profitable to review the support of the membranes and the control of the pressure differentials affecting the membrane. The advantages of the increase and control of temperature have been realized (1, $1, 55, 45). The diffusion coefficient of sodium hydroxide through water is increased by 50% if the temperature is raised from 15’ to 35” C., and, as expected, this causes an appreciable increase in the dialysis coefficient. Furthermore the counter diffusion of the water into the lye cells may be retarded by precooling the water feed or by incorporating cooling coils in the water cells. About 507, of the resistance to mass transfer in the dialysis of caustic soda lyes, and probably in other liquors, resides in the liquor films and is thus controlled essentially by the natural convection currents produced by the density differences near the membrane. As far as this resistance is concerned the diffusion characteristics of the materials involved may have little significance. ACKNOWLEDGMENT
The authors are grateful to C. Handford of this College for designing the oscillator and resistance bridge which proved so helpful in this investigation. Dobson and Barlow Ltd. of Bolton manufactured the Perspex dialyzer body and supplied the parchments required. H. Lindsay Ltd. of Bradford placed a t the disposal of the authors the Lindapter clamps. NOJIENCLATURE
total area of membrane, a”, sq. cm. a activity of solution a’ width of membrane, em. concentration of solution: CA and CB for components A c and B; c = (CA CB) for total concentration in binary mixture; CL and cw for sodium hydroxide concentrations in lye and rater streams, respectively; grammole/ml. = concentration: cl and cl/ for sodium hydroxide in lye c‘ and water etreams, respectively; mole fraction D = diffusion coefficient: De nnd 0 2 6 at 8’ C. and 25’ C., respectively; sq. cm./minute = vertical distance from bottom of cell to sampling posih tion, em. = vertical length of membrane, em. H = dialj-si? coefficient: K O for over-all mean value; K , for K true mean value; gram-mole/(minute) (sq. em.), niole/ml. = transfer coefficient: kl and ka for liquor films; klfor k membrane; gram-mole/(minute) (sq. em.), mole/ml. L = Ive flow rate, ml./minute, L’, gram-mole/minute 2 = length of transfer path: 11and /B for effective film thicknesses in liquor streams; 1, for wet membrane thickness; em. R = ratio of effective thickness to actual thickness for D membrane, n = k2lY = transfer rate, gram-mole/(minute) (sq. cm.) ( N ~ ) average transfer rate based on whole membrane; grammole/(minuJe) (sq cm.) T = temperature, K. t = period of time, minute u = linear velocity of component, ern /minute = water flow rate, ml./minute; W’, gram-mole/minute = constant in diffusion equations, cm.-minute/gram mole 0 temperature, ’ C. AC concentration difference: AC = (CL - cw); Acm for mean of end values; ( Ac)o for time 1 = 0; +(A C ) for ~ time t = 1; ( A c , ) ~ for mean from t = 0 to t = t; gram-mole/ml.
A
= = = =
w
.
+
=
7
Vol. 43, No. 12
viscosity of liquid, gram-cm./pecond
Subscripts A = componentA B = componentB L = lye stream rn = mean value
over-all value, or for datum value t = timet W = water stream 1,2, 3 , 4 = positions 0
=
LITERATURE CITED
(1) Bailey, D. H. (to Pfaudler Co.), U. S. Patent 2,247,143 (June 24, 1941).
(2)
Cammen, L. (to Preston Davie), Ibid., 1,974,235 (Sept. 18,
(3) (4)
Casey, H. W.,U.S. Patent 2,226,337 (Dec. 24, 1940). Cerini, L., Brit. Patents 265,126 (Jan. 29, 1926); 272,211 (June
(5)
Daniel, F. K. (to Hornkem Co.), U. S. Patent 2,365,457 (Dee.
1934). 1, 1926). 19, 1944).
(6) Daniel, F. K. (to Hornkem Co.), and Hutchings, 3. L. (to Bro(7) (8) (9)
sites Machine Co.), Ibid., 2,399,471 (April 30, 1946). Eynon, D. J., J . SOC.Chem. Ind. (London),52, l 7 4 T (1933). Faust, O., 2. anorg. allgem. Ckem., 160, 373 (1927). Giordani, F., Rend. acad. sci. fis. mat. e ?tat. reale XapoZi, 30, 111, 150 (1924).
Glasstone, S., Laidler, X. J., and Eyring, H., “Theory of Rate Processes,” New York, i\IoGraw-Hill Book Co., Inc., 1941. (11) Gmelin’s “Handbuch der anorganischen Chemie,” 8 iiuflsge, Heidelberg, C. Winter, 1927. (12) Harned, H. S., and Heoker, J. C., J . Am. Chem. Soc., 55, 4538 (10)
(1933). (13) Heibig, E., U. S. Patent 1,549,632 (March 15, 1932). (14) Hoon, R. C., and Dhaffan, C. L., J . Indian Chem. SOC.,17, 195204 (1940). (15) I. G. Farbenindustrie, Brit. Patent 459,654 (Aug. 2, 1938). (16) “International Critical Tables,” Vol. 6, p. 246, Kew Pork, McGraw-Hill Book Co., 1929. (17) Jones, G., and Bollinger, D. M., J . Am. Chem. Soc., 57, 280 (1935). (18) Kawalki, Wied. Ann., 52, 166, 300 (1894). (19) Iiooij, G. W. van B., Brit. Patent 505,527 (May 17, 1938). (20) Kooij, G. W.van B., Brit. Rayon Silk J., 26, KO.302, 74-6 (1949). (21) Kooij, G. W. van B., private communication. (22) Kratz; L., Kolloid-Z., 80,33-43 (1937). (23) Lovett, L. E.. Trans. Electrockem. SOC.,73, 163 (1938). (24) Manegold, E., and Kalauch, IC.. Trans. Faraday SOC.,33, 1086 (1937); Kolloid Z., 8 6 , 9 3 (1939). (25) hIarshall, R. D., M.Sc. thesis, Manchester, England, 1949. (26) Oholm, Z. physik. Chem., 50, 309 (1904). (27) Perry, J. H., Ed., “Chemical Engineers’ Handbook,” 2nd ed., p. 252, New York, AIcGraw-Hill Book Co., Inc. (1941). (28) Ibid., p. 1140. (29) Ibid., 3rd ed., p. 764, 1950. (30) Powell, R. E., Roseveare, W‘. E.. and Eyring, H., IND.ENQ. CHEM.,33, 430 (1941). (31) Reichel, F. H., and Russell, A. 0 . (to Sylvania Industrial Co.), Can. Patent 435,652 (July 2, 1946); U. S. Patent 2,411,239 (Nov. 19, 1946). (32) Rubber-Stichting, Brit. Patent 542,540 (Jan. 14, 1942). (33) Saddington, A. VI., and Julien, A. P., U. S. Patent 2,111,808 (March 22, 1938). (34) Schneiderwirth, H. J.,IbicE., 1,864,767 (June 28, 1932). (35) Skolnik, hl., Ibid., 2,252,213 (Aug. 12, 1941). (36) Slagle, E. A., and Roberts, L. VI., Sewage Works J., 14, 1021-9 (1942). (37) Spandau, H., and Gross, W., Be?., 74B, 362-73 (1941). (38) Stefan, Sitzber. Akad. Wiss. Wien, Math. naturw. Klasse Abt. I I , 63, 63 (1571). (39) Stevens, H. P., and Dyer, J. TT‘. TV., U. S. Patent 2,127,791 (Aug. 23, 1938). (40) Sylvania Industrial Corp., Brit. Patent 506,589 (June 6, 1939). (41) Tachikawa, S., U. S. Patent 1,865,965 (July 26, 1932). (42) Vohrer, H., Brit. Patent 511,739 (Bug. 23, 1939). (43) Vollrath, H. B., Chem. & M e t . Eno., 43, 303-6 (1936). (44) Weber, G. H. (to Brosites Machine Co.), U. 8. Patents 2,225,024 (Dec. 17, 1940); Ibid., 2,312,015 (Feb. 23, 1943). (45) Zender, J. ( t o Sylvania Industrial Corp.), Ibid., 2,361,000 (Oct. 24, 1944); Ibid., 2,411,235 (Nov. 19, 1946); Can. Patent 435,651 (July 2, 1946). (46) Ziro, Kato, J . SOC.Chem. I n d . Japan, 42, supp. bind., 376 (1939). RECEIVED August 9, 1950. This work was carried out by R. D. Marshall under the supervision of J. Anderson Storrow during the tenure of a Textile Machinery Xilakers Association research scholarship and has been presented as a thesis to the College of Technology, Manchester 1, England.
