dialysis for separating solutes of different molecular weights

E-

EXFERIMENTAL -EXTRAPOLATED RANGE RANGE

asymptotic values at low pressures are indicated as short dashed lines on the ordinate. Plutonium removal at high efficiency by the surface reaction is approximated best by selecting f for x = 0, since over most of the reaction area x is very near zero; this approximation underestimates the final concentration. Conclusions

pa MFs- m rn H g

Downloaded by FLORIDA STATE UNIV on September 13, 2015 | http://pubs.acs.org Publication Date: January 1, 1967 | doi: 10.1021/i260021a019

Figure 4. Pseudo-first-order rate constant from rate equations

Thus the difference between 1and $‘ is only 2% in an interval when f is decreasing by 10%. T h e first approximation to computed from the data of Tables I and I1 is plotted as a function of PoHsoin Figure 3. For values o f j less than 40 orpoH20greater than 1.0 mm. of Hg, the first and second bed segments were used because the rapid decrease in concentration present in the first two beds was masked in the last bed by even small collection of product from the gas-phase reaction. T h e curves in the figure illustrate the statements, made earlier, about the relative hydrolysis rates. T h e dependence o f f on the pressure of hexafluoride becomes small at pressiires less than 0.001 mm. of Hg. The dependence at higher values is indicated in Figure 4. The values were computed from Equations 10, 11, and 12. T h e moisture values are conservative lower limits and were selected from the frequency distribution of atmospheric moisture a t Argonne to have probabilities of 0.001 and 5% of having lower values than 0.25 and 1.8 mm. of Hg, respectively. T h e

T h e measured reaction rates of plutonium and uranium hexafluoride provide a basis for understanding and estimating the performance of air cleanup systems used on process facilities containing PuFe or UFe. The remaining limitations to predicting performance of practical systems are probably restricted by the uncertainty of high efficiency air filtration performance with small particles in the size range of 0.02- to 0.2micron diameter. Acknowledgment

The author acknowledges the efforts of L. J. Marek and B. J. Misek in the construction of equipment and the collection of data, computer programming by A. J. Strecok, and the interest shown by W. J. Mecham, D. Ramaswami, J. Fischer, and A. A. Jonke. literature Cited

(1 ). Argonne National Laboratory, Chemical Engineering Division, Summary Report, April, May, June 1963, U. S. At. Energy Comm., ANL-6725,164 (1964). (2) Argonne National Laboratorv. Chemical Engineerine Division “Semiannual Report, Juli-December, 19u63, U. “S. At. Energy Comm., ANL-6800,247 (1964). (3) Cathers, G. I., Bennett, M. R., Jolley, R. L., Znd. Eng. Chem. 50,1709 (1958). (4) Florin, A. E., et al., J . Znorg. Nucl. Chem. 2, 379 (1956). (51 Guuta. A. S.. Thodos, G.. A.Z.CI2.E. J . 8.608 (1962). (6) HoLgen, A. O., Watson, K. M., “Chemical Process Principles,’’p. 922, IViley, New York, 1947. (7) Mandleburg, C. J.. et a/., J . Inorz. ’Vucl. Chem. 2, 365 (1965). ( 8 ) Steindler, M. J., “Properties of Plutonium Hexafluoride,” ‘c. S. At. Energy Comm., ANL-6753 (1963). ( 9 ) FYalas, S. M., “Reaction Kinetics for Chemical Engineers,” p. 160, McGraw-Hill, New York, 1959. 1

,

RECEIVED for review March 31, 1966 ACCEPTEDSeptember 22, 1966 Work performed under the auspices of the U. S. Atomic Energy Commission.

DIALYSIS FOR SEPARATING SOLUTES OF DIFFERENT MOLECULAR WEIGHTS Process Optimization C . C . OLDENBURG

Stauffer Chemical Go., Richmond, Calif.

IALYSIS

has been u!jed as a physical separation method on a

Dcommercial scale fix over 30 years to recover recycle caustic in rayon manufacture. Liquor fed to dialysis equipment is an aqueous solution containing about 17% sodium hydroxide and 27, hemicellulose (4, 8). About 90% of the sodium hydroxide passes through the membranes to result in a diffusate containing 9% sodiurn hydroxide. The hemicellulose mole1 Present address, Chevron Research Co., Richmond, Calif.

cules are so large that they do not pass through the membranes. The dialyzate contains all the hemicellulose and about 10% of the I i a O H present in the liquor. This particular application of dialysis recovers a valuable low molecular weight inorganic (NaOH) from a less valuable, larger molecular weight organic material (hemicellulose). The diffusate contains the valuable product, and the dialyzate is the waste stream. Other similar applications include sulfuric acid VOL. 6

NO. 1

JANUARY 1 9 6 7

111

Dialysis i s a useful tool for separating low molecular weight impurities in the manufacture of larger molecules


such as pesticides, pharmaceuticals, and related organics. The effects of dialysis process variables are analyzed. Correlations are presented to aid in selecting conditions such that product loss, investment, operating cost, and other economic factors can be optimized.

recovery from nickel sulfate in copper refining (7) and nitric acid recovery from iron nitrate in stainless steel pickle baths (2). I n the manufacture of pesticides, pharmaceuticals, and related organic chemicals, the opposite application of dialysis is often desired. For example, chlorination, phosphorylation, and sulfonation syntheses can result in aqueous solutions of valuable organic products along with such salts as NaCl, CaC12, or Na2S04. A low molecular weight impurity must be removed from a valuable product of larger molecular weight. Thus, the diffusate is the waste stream and the dialyzate contains the valuable product (Figure 1). The requirements of such a dialysis process are different from those in the case of caustic or acid recovery. A highly purified product is usually required, necessitating a high removal of the impuritye g . , >95%. The product may be of only moderate molecular weight and dialyze through membranes at a slow but finite rate. Such loss of product with the diffusate must be minimized, since the product is usually valuable. The purpose of this paper is to analyze the effects of variables in a dialysis process used to remove a low molecular weight impurity from the product. Correlations are presented to aid in selecting conditions such that product loss, investment, operating cost, and other economic factors can be optimized.

[WATER

I!

D I F F U S A T E ~ 219

Before evaluating dialysis as a means of performing a separation, it is necessary to know the dialysis coefficients for both species in the solution to be separated. Simple batch laboratory experiments can be performed to find a membrane that is favorably selective and reasonably porous to the low molecular weight material. Such tests may involve suspending a membrane bag full of the solution in a beaker of water and analyzing the water after a given period of time. Once the membrane is selected, however, the dialysis coefficients are best determined simultaneously by processing the feed solution in a bench-scale continuous dialyzer (7). Such equipment 112

I&EC PROCESS DESIGN A N D DEVELOPMENT

Y.?

Dialysis process definitions

1.

Impurity Product H, D, E, 1, W. Rate, Ib./hour x , y, z. Concentration, wt. %

2.

,-I---+--

Problem Definition

Dialysis Coefficients

YI*

Figure 1 .

WATER

LIQUOR NO. I

Figure 2 depicts a typical dialysis process for impurity removal. The feed aqueous solution to the dialysis operation would normally contain a fixed ratio of impurity to product, although total concentration can be varied. Dialysis must reduce this ratio to a value set by product purity requirements. Optimization involves studying all economic factors; product loss to diffusate and total membrane area are important. Process variables to consider are the ratio of water to liquor used, the number of stages, and the amount of concentration before each stage. In dialysis for caustic or acid recovery, the water-liquor ratio is low, in order that the diffusate does not become unnecessarily diluted. In the case under study, water-liquor ratios are made higher, to increase concentration difference across the membranes and thus decrease the area required. Similarly, more than one stage is usually advisable because impurity removal must be greater than 95%, whereas, in caustic or acid recovery, one stage at 90% recovery is normal.

IL

22

STAGE

WATER DIALYZATE N 0 . I

DIFFUSATE NO. I

I-

WATER

WATER

CONcENTRAT,ON

LIQUOR NO. 3 ETC.

can be purchased for a few hundred dollars or can be homemade (5, 6). Another approach is to determine membrane coefficients as described by Lane and Riggle (3) and Mindick and Oda (6). This involves measuring mass transfer through a membrane in a cell wherein the solutions on both sides of the membrane are highly agitated to eliminate film resistance. The over-all dialysis coefficient can then be estimated by adding in film resistances calculated from diffusion coefficients using an effective film thickness of about 0.05 cm. (7, 5). A more general approximation is to assume that over-all dialysis coefficients are one half the membrane coefficients (7). I n any case, the dialysis coefficients should be measured using the actual feed solution because of ion interaction in simultaneous diffusion of two or more competing electrolytes through a membrane (7). Values of the dialysis coefficients are most important in the optimization of process conditions. They should be determined over wide concentration ranges. At the same time, the coefficient for counterdiffusion of water, or water transport number (9), should be determined. Also, the relationship between solute concentrations in grams per milliliter and weight fraction should be developed from density-composition data.

Rate Expression and Material Balances

t-

Figure 1 depicts the parameters of the dialysis operation. The rate of transfer of the impurity or low molecular weight material through the membrane is

W1 = UiAACi

36

(11

or

s > -

32 28-

=

where

24

I


=

q =

I

I

4

8

I

t

4

2

0

I

I

I

I

8

6

'

IO

4 Figure 3.

Ihtroducing the following terms

p

p = 1.5

20 -

concentration driving force, g./ml. TV1 = transfer rate, lb./hr. A = membrane area, sq. feet U = dialysis coefficient lb./(hr.) (sq. ft.) (g./ml.)

nl =

-

Effect of water rate on membrane area

-UIA _ - (impurity dialysis coefficient)

Ezi -, the fractional removal of impurity required Lx 1

(membrane area), ml./g.

W1

(impurity membrane transfer rate) Ratio of water to liquor Lb. dialyzate/lb. liquor X I . 0.1 0 ( 1 0% impurity in liquor) nl. 0.80 (80% removol of impurity)

q. p.

D

-, the ratio of dialyzate to liquor L

H -, the ratio of water to liquor L

and substituting known relationships between weight fraction and volumetric concentration, Equation 2 can be written in the form

and solving Equations 4 and 5 simultaneously by equating the rearranged expressions for A , the relationship between n2 and nl can be written nz = f ( k , nl, nz, XI, xz, k, q )

(4) where x 1 is the weight fraction of impurity in the liquor. Optimum Water-liquor Ratio

I n any dialysis stage, the greater the ratio of water to liquor, the less will be the required area. Infinite water provides maximum concentration difference across the membrane. The relationship between water-liquor ratio and area is given by Equation 4. A computer program written for Equation 4 was helpful in preparing plots of U1A/W1 us. q for various combinations of X I , nl, and p . Results showed that the curves have substantially the same shape for

and

x1

= 0.005 to 0.10

fll

=

0.70 to 0.98

p

=

1.1 to 1.8

(6)

Equation 6 involves a trial and error solution. With the aid of computer calculations, several plots of n2 us. nl were prepared for various combinations of values of all parameters. Figure 4 gives typical curves. The greater the amount of impurity dialyzed, the greater is the loss of product to the diffusate. The most important variable in this relationship is k, the ratio of the dialysis coefficients of product and impurity. Other variables that have a relatively minor effect on the relationship

Figure 3 gives typical curves. Required area a t a waterliquor rate of about 5 to 8 is only 10% greater than a t infinite water rate. Decreasing the water-liquor ratio below 3 rapidly increases required membrane area. 0'

Product loss vs. Impurity Removal

An equation similar to Equation 4 can be derived for the product,

I

I

0.7

0.6

I

0.8

I

0.9

1.0

"I

Figure 4. n2.

nl.

k. XI.

Introducing a term for the ratio of dialysis coefficients for the product and impurity

'

0.5

XI.

p. q.

Product loss vs. impurity removal

Fractional transfer of product through membrane Fractional transfer of impurity through membrane Ratio dialysis coefficients of product and impurity 0.10 = ( 1 0 wt. % impurity in liquor) 0.1 0 = (10 wt. 70product in liquor) 1.5 Ib. dialyratellb. liquor 10.5 Ib. water/lb. liquor VOL.

6

NO. 1

JANUARY 1 9 6 7

113

shown in Figure 4 are the concentrations of impurity and product in the liquor, the ratio of water to liquor, and the amount of water counterdiffusion. For a given value of k in the range 0.01 to 0.20, the other parameters can vary over the ranges x1

= 0.01 to 0.20

x2

=

0.10 to 0.20

p

=

1.1 to 2.0

q = 5 to 20

without affecting the nz us. nl correlation more than about 15%. I t can also be shown that the number of stages has little effect on the relationship. Practically speaking then, total product loss is mainly a function of total impurity removal and ratio of the dialysis coefficients.


Optimum Concentration

The liquor should be concentrated as much as possible before each dialysis stage to maximize the concentration difference across membranes. However, dialysis coefficients generally decrease rapidly above a certain concentration because of viscosity increase. Experimental data on the effect of concentration on dialysis coefficients should be used to optimize liquor concentration, since the product of dialysis coefficient and concentration driving force should be maximized. Optimum Number of Stages

The greater the number of stages, the less will be the total required membrane area because of increased concentration differences. But the addition of stages requires additional piping, controls, instrumentation, and concentration equipment, If the impurity removal requirement is less than 90%, one stage is often optimum. Above 95% impurity removal, two or more stages are normally preferred. The following table gives the number of stages of equal fractional removal of impurity required for a given total impurity removal: Total impurity removal,

%

No. of staees Impurity removal in each stage, yo

1

99 2 3

4

1

98 2 3

4

1

95 2 3

4

99 90 78 68 98 86 73 61 95 78 63 53

Using the above values along with Equation 4, an example was developed from the following assumptions : nl = 0.98 (98% total impurity removal) x1 = 0.10 (10% impurity in the liquor fed to each stage) p = 1.5 lb. dialyzate/lb. liquor in each stage q = 10.5 Ib. water/Ib. liquor to each stage Results were as follows: No. of Stages 1 2 3 4 co

114

Relative Total Membrane Arta 3.19 2.08 1.56

1.26 1 .oo

l & E C PROCESS D E S I G N A N D D E V E L O P M E N T

Use of two or three stages would probably be optimum, depending on other factors. Conclusions

I n the removal by dialysis of a low molecular weight impurity from a valuable product where the ratio of dialysis coefficients is in the range of 0.01 to 0.20 product loss increases exponentially with impurity removal. Variables other than ratio of dialysis coefficients have little effect on the product loss-impurity removal relationship. Although higher waterliquor ratios result in lower membrane area requirements, at ratios near 7 the required area is within 10% of that required at infinite water rate. Optimizing the number of stages requires evaluation of many economic factors. Generally, for greater than 95% impurity removal, more than one stage is optimum, Nomenclature

A = total area of membrane, sq. ft. C = concentration of solute, g./ml. D = dialyzate flow rate, lb./hr. E = diffusate flow rate, lb./hr. H = water flow rate, lb./hr. k = U T / U l ,ratio of dialysis coefficients for product and impurity L = liquor flow rate, lb./hr. n = weight fraction of solute in liquor transferred through membrane p = D / L , ratio of dialyzate to liquor, a measure of counter diffusion of water q = H / L , ratio of water to liquor U = dialysis coefficient, lb./(hr.) (sq. ft.) (g./ml.) W = membrane transfer rate, lb./hr. x = concentration of solute in liquor, weight fraction y = concentration of solute in dialyzate, weight fraction z = concentration of solute in diffusate, weight fraction

SUBSCRIPTS 1 = impurity 2 = product x = liquor y = dialyzate z = diffusate literature Cited (1) Chamberlin, N. S., Vromen, B. H., Chem. Eng. 66, 117 (May 4, 1959). (2) Keating, R. J., Dvorin, R., Industrial Waste Conference, Purdue University, May 3-5, 1960. (3) Lane, J. A. Riggle, J. W., Chem. Eng. Progr. Symp. Ser. 55 (24), 127 (1959). (4) Lee, J. A., Chem. Met. Eng. 42,482 (September 1935). (5) Marshall, R. D., Storrow, J. A., Ind. Eng. Chem. 43, 2937 (1951 ). (6) Mindick, Morris, Oda, R., Symposium on Innovations in Separation Processes, North Jersey Meeting, ACS, Oct. 27, 1958. (7) Turviner, S. B., “Diffusion and Membrane Technology,” ACS Monograph Series, Reinhold, New York, 1962. (8) Vollrath, H. D., Chem. M e t . Eng. 43, 303 (June 1936). (9) Vromen, B. H., Znd. Eng. Chem. 54,20 (June 1962).

RECEIVED for review April 5, 1966 ACCEPTEDAugust 30, 1966

dialysis for separating solutes of different molecular weights

Recommend Documents