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OCTOBER. 1939 c
TABLEIV.
ELECTROMOTIVE FORCES AND PH VALUES OF SODIUM CARBONATE^ SOLUTIONS
Normality
E. M. F.b
of
0
b
NaaCOo
Trial 1
1.000 2.000 3,000 4.000 5.000 6.000
1.00816 1.02104 1.02932 1.03490 1.03808 1.03010
Trial 2 1,00809 1.02094 1.02930 1.03488 1.03800 1.03895
Average
PH
1.00812 1.02099 1.02931 1.03489 1.03804 1.03903
12.27 12.49 12.63 12.73 12.78 12.80
Anhydroua sodium carbonate. Between normal hydrogen snd calomel electrodes at 25.0' C. ~~
The specific gravity values (Figure 3 and Table I) were nearly straight-line functions of the normalities, and for given normalities nearly straight-line functions of the temperature. Values vary from 1.047 and 1.009 a t 22.5' and 98' C., respectively, for the 1.000 normal, to 1.262 and 1.214 for the same temperatures with the 6.000 normal solution. I n industry large quantities of solution are transported through pipea. Often the concentration is high and the temperatures vary. Viscosity is an important factor in costs.
1295
Instead of nearly straight-line functions the viscosities increase much more rapidly with higher normalities and decrease rapidly with higher temperatures (Figure 4 and Table 11). At the highest temperature measured, these changes almost compensate one another. The extremes are 0.01201 and 0.00347 poise for the 1.000 normal solution a t 22.5' and 98' C., respectively, and 0.05650 and 0.00960 poise for the 6.000 normal solution a t the same temperatures. Maximum values of specific conductance were obtained at 4 normal (Table 111). The curves in Figure 5 show that the maximum values occur a t about 4.25 normal. The values increase rapidly from 1 to 3 normal. The curves for potential and pH values (Figure 6) rise rapidly with increase of normality and then begin to flatten. The alkalinity of the solutions varies from a pH of 12.27 for the 1 normal to 12.80 for the 6 normal (Table IV). This paper shows that some of the properties of concentrated solutions cannot be predicted from those of dilute solutions. It is worth while to determine experimentally the properties of concentrated solutions of those salts used extensively in technical work.
SEPARATION PROCESSES Analogy between Absorption, Extraction, Distillation, Heat Exchange, and Other Separation Processes' MERLE RANDALL AND BRUCE LONGTIN University of California, Berkeley, Calif.
HEN a number of related fields of technical knowledge have developed independently, it is natural that each field will be supplied with its own distinctive viewpoints and methods of calculation. The recognition of an analogy between a number of fields is valuable in allowing the methods peculiar to each field to be applied in the analogous fields, thus expanding the arsenal of mathematical weapons available in each particular field. The close analogy between distillation and solvent extraction processes was pointed out by Saal and Van Dyck (16, 17) and used by them to develop a new method of solvent extraction. This analogy has since also been used successfully by Varteressian and Fenske and by others (d,4, 15,18) in elaborating new principles of extraction. Although it is now somewhat difficult to disentangle the early history of countercurrent extraction (cf. IO), it is relatively certain that even its earliest stages were considerably influenced by recognition of this analogy. Thus it is safe to
W
The first five appeared in 1938 1 This is the sixth paper in this series. and in February, July, and September, 1939,respectively.
An analogy exists between all types of processes in which the important considerations are those of material and energy balance, diffusion and rates of transfer, and equilibria. Application of this analogy has already permitted experience in fractional distillation to be utilized in developing solvent extractions and similar processes. This paper suggests broader applications of the analogy. Absorption in the case of variable reflux ratio is discussed. The analogy between heat transfer and absorption is brought out, and a concept analogous to the height of a mass transfer unit (H. T. U.) is proposed. say that the development of solvent extraction processes has profited greatly by previous experience in distillation through the aid of this analogy. The graphical methods previously discussed in this series (14) are essentially exact methods of representing complex material and energy balances together with equilibria. BoSnjakovi6 (1) presented methods of carrying out calculations in the H vs. N diagram for cases in which heat flow and diffusion are occurring simultaneously; with respect to this diagram they maintain the position which is held by the standard method of integrating diffusion equations for packed towers with respect to the y vs. x diagrams. Thus the fields of heat transfer, distillation, absorption, extraction, and all others which chiefly involve considerations of material and energy balance, flow of heat, diffusion, and equilibria may be considered analogous with respect to application of these methods.
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Solvent
FIGURE 1. TYPICAL POUXD OR MOLEFRACTION DIAGRAM
FIGURE 2. DIAGRAM OF FIGURE 1 IN FIGURE 3. DIAGRAM OF FIGURE 1 IN JANECKE FORM, SOLVENT-FREE BASIS JANECKE FORM, IMPURITY-FREE BASIS
The use of the center-of-gravity constructions and other graphical methods which have already been discussed in connection with distillation is familiar in the field of solvent extraction (6, 7, 16,17,18). The analogies between the various types of separation processes will be brought out by considering the application of these methods to other types of processes (in particular, absorption and heat transfer) in which their use is uncommon.
Typical Phase Diagram I n the usual absorption process a gas is treated with a liquid solvent to remove traces of an impurity. The system dealt with contains three components. A typical phase diagram is shown in Figure l. I n this case the solvent and wanted substance (e. g., pure gas) are only partially miscible, whereas the impurity is completely soluble in either alone. I n the usual case of absorption the solvent and wanted substance are completely immiscible to the extent that the region of two immiscible phases fills the whole triangle; the equilibrium tie lines each connect a point on side c of the triangle with a point on side a. The diagram of Figure 1 may be plotted on a Janecke type diagram (8) rather than the triangular diagram. If side c is desired as the base, it is necessary simply to express the compositions on the solvent-free basis, as in Figure 2. If side b is desired as the base, the compositions are to be
expressed on the impurity-free basis, as in Figure 3. Of the two forms, that of Figure 3 is perhaps the more convenient. I n both figures the saturation curve and tie lines represent the same equilibrium data as those of Figure 1. The dotted curves indicate the way in which the saturation curve changes with diminished miscibility of the two phases. I n each case when the solvent and treated substances are completely immiscible (the impurity remaining completely soluble in each), the saturation curve coincides with the two straight lines, a and c. The same diagrams are typical of solvent extraction processes. I n these processes it is often the wanted substance that is soluble in both phases, and the impurity that is insoluble in the solvent.
Graphical Design I n an absorption process the solvent is usually fed to the top of the absorption tower and the gas to the bottom of the tower. The compositions of these two streams are quite independent, and the tower functions as a simple column section (14) without the limitations imposed by any end equipment. The design diagram for a simple section based on the center of gravity construction may be used for a plate absorption tower in connection with any of the diagrams of Figures 1 to 3. As shown previously (14), it is necessary only that the
Solvent
O?/
3 0 wanted Impurity Substance Lbs. Imp./Lb. SOW- Free Mix.
0 Solvent
1.0
Wanted Substance. Lbs. Wanted Subs./Lb. Imp.- Free Mix.
A B C DIAGRAM FOR THREE-PLATE ABSORBER (EXTRACTOR), FROM DIAGRAMS OF FIGURES 1 TO 3 FIGURE4. DESIGN
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L bs. Imp / L b. Imp - free Mix.
two composition variables be expressed on the same basis (e. g., pounds per pound of impurity-free mixture for both axes in Figure 3). The diagram for a particular three-plate absorber (or three-stage extractor) is shown in Figure 4, plotted in three different ways. Such diagrams are familiar in the design of extraction equipment but uncommon in the study of absorbers. Usually the operation of an absorption or an extraction process is determined by the compositions of the raw material, fresh solvent, and desired product, together with the number of plates or stages available. As Figure 4 shows, fixing the compositions of fresh solvent and purified product serves to determine a line upon which point D must lie. Only one position of D along this line will make the three-stage construction finish at the given composition of raw material. As shown, D lies nearest the wanted-substance phase curve and indicates the necessity of a relatively small amount of solvent. If D should lie on the opposite side of the region of immiscibility, it would indicate the necessity of relatively large amounts of solvent.
Countercurrent Stream (Reflux or Recycle) Ratio I n the triangular diagram of Figure 4 the mass associated with each point in any center of gravity construction (14) is the total weight (or number of moles if mole units are used) of material in the phase represented. I n the first Janecke type diagram (Figure 4B) these weights are expressed as weights of solvent-free mixture; in the second they are ex_ - mixture. pressed as weights of impurity-free I n each diagram the ratio B D I A D is a measure of the ratio of quantity of material in the gas-phase stream to the quantity of material in the solvent-phase stream. In the triangular diagram it expresses the ratio of total weights of the two streams. I n the solvent-free basis diagram it expresses the ratio of the weights of solvent-free material in the two streams; in the impurity-free-basis diagram it expresses the ratio of the weights of impurity-free material in the streams. It may be designated as the countercurrent stream ratio (e. g., reflux or recycle ratio), expressed on a basis consistent with the diagram being used. Figure 4 shows that the countercurrent stream ratio varies from one interunit to the next for the case considered. It varies least when expressed on the impurity-free basis. If the saturation curve coincides with the two sides a and c (the usual case in absorption), rays through D are divided in variable proportion by the saturation curve in the first two diagrams. I n the third, the curves become two parallel straight lines, which cut rays through D in a constant countercurrent stream ratio. When the solvent and pure gas are completely immiscible, the only possible variation in the relative amounts of the two streams is that due to the transfer of impurity from the gas to solvent phase in a contact unit. If any separation is to occur, such a transfer must take place. If it does, the relative amount of impurities in the two streams must vary from one unit to the next. Hence the countercurrent ratio will be constant only if expressed on an impurity-free basis.
The y ws. x Absorption Diagram The design of absorption towers is usually carried out with the help of a y us. x type diagram, in which the coordinates are the ratios of impurity to solvent and to gas in these respective phases. I n the usual case (solvent and gas almost completely immiscible) these are the values given by the vertical coordinates of Figure 4C, in which compositions are plotted on an impurity-free basis. Hence the form which the usual absorption diagram takes when solvent and gas
M /
,
,
,
,
,
.
,
,
,
Lbs. lmp,/Lb. lmp,-Free Mix. in Gas
Phase ' FIGURE 5 . TRANSFORlvfATIOS O F THE IXPURITY-FREE-BASIS JBNECKE DIAGRAM OF FIGURE 4C INTO A y us. x DIAGRAM '
are partially miscible is to be obtained by laying of the vertical coordinates of the gas-phase points of Figure 4C as y coordinates against those of the solvent phase points as x coordinates (or vice versa). This has been done in Figure 5 by means of a graphical construction previously used in transforming distillation diagrams (14, 18). Other y us. 2 type diagrams may be similarly obtained by transferring the proper coordinate of one of the diagrams of Figure 4 to the y us. x coordinates. Figure 6 shows the construction of a y os. x diagram in which the weight fraction of gas is transferred from the triangular diagram to y us. x coordinates. The y us. x coordinates could have been chosen as mol fraction of impurity, in which case the side c of the triangle should be placed in the horizontal position, while placing side a in this position would give mol fractions of solvent as the y us. x coordinates.
Validity of the Straight Operating Line The operating line (or reflux curve) of Figure 5 is appreciablyZcurved (cf. 18) as a result of the fact that the saturation curves in the original Janecke diagram are not parallel straight lines. I n the usual case of nearly complete immiscibility, these saturation curves become nearly parallel and straight, so that the use of the straight operating line is justified. However, if any other y us. x coordinates than those based on the impurity-free mixtures were chosen, the operating line would remain curved even in this limit (except in trivial cases). I n general, the use of a straight operating line in any y US. x type design diagram can be made valid, or nearly so, if a proper choice of units is made. This choice is the one which 2 It also shows a peculiarity in connection with t h e m a x i m u m point, which will be discussed i n another article.
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tions based on the y us. x diagram may be replaced by the method of BoSnjakovid based on the triangular diagram.
Heat Exchange Analogies
/
/
Weight Fraction of Gas in Solv: Phase
FIGURE 6. TRANSFORMATION OF TRIANGULAR DIAGRAM OF FIGURE 4A INTO A g us. x DIAGRAM
will make the saturation curves of the corresponding phase diagram of the center-of-gravity type most nearly parallel. Thus the use of “latent heat fractions” proposed by Peters (IS)makes the use of a straight operating line valid in many distillation problems, since it will bring the liquid and vapor curves of the H us. N diagram into approximate parallelism.
Use of the Analogy From the preceding discussion it is seen that in the usual case of absorption with an immiscible solvent, the g us. x diagram is most suited for the solution of absorption problems; whereas in the usual solvent extraction problems the triangular diagram is necessary because there is a t least partial miscibility of all components. However, in the less usual case the triangular diagram may be required for the solution of absorption problems, while it may be possible to use the simpler y os. x type diagrams for some problems in extraction. The discussion has dealt so far only with countercurrent processes of the ideal multiunit type (plate towers, multiunit extractors). In the case of a packed tower the integration of diffusion equations replaces the stepwise construction. The methods developed by BoBnjakovi6 (1) for simultaneous integration of heat transfer and diffusion equations are readily applied by analogy to the problem of simultaneous diffusion of several components in connection with the triangular diagram. Thus in those cases in which the solvent is sufficiently volatile and the gas sufficiently soluble in the solvent to invalidate the use of a straight operating line, the customary method of integrating the absorption tower equa-
Evans (6) recently proposed the evaluation of countercurrent heat exchangers in terms of an equivalent series of ideal heat exchange units. The concept is closely analogous to that of evaluating a packed distilling tower in terms of the equivalent bubble-plate tower composed of ideal bubble plates. The analogy is further strengthened by the fact that an equation which plays a central role in the Evans method is essentially the analogous form of Kremser’s absorption factor equation (9),which is used in the evaluation of absorption towers. If one looks for an H us. N diagram analogous to that of Figure 4C, in which the variable, pounds impurity per pound of impurity-free mixture, is to be replaced by the molal heat content, it will be found in that of Figure 7 . This phase diagram is typical of any binary system of two partially miscible liquids with a critical mixing point (e. g., phenol and water). If these two phases are sent in opposite directions through a multiunit countercurrent contactor as indicated by the flow sheet of Figure 7, the behavior will be that indicated by the stepwise center-of-gravity construction shown in the phase diagram of Figure 7 . In the particular case illustrated, the entering B phase (B4)is hot, while the entering A phase (A1) is cold. The leaving B phase stream (B1) has been cooled by transferring its heat to the leaving A phase (&). Although there is some change in composition of the phases, the chief effect is that of heat transfer. A similar case of practical importance is the cooling tower in which water is allowed to flow down over tiered slats, partially evaporating into the air which rises through them. In a case recently tested by Boelter and co-workers (11), the equipment was such that the use of the plate concept seemed equally as appropriate as that of the packed tower as a means of correlating results. 8 4I
A4.
H
1 -N
FIGURE 7. FLOWSHEETAND DESIGNDIAGRAM FOR HEAT TRANSFER BETWEEN PARTIALLY MISCIBL~ PHASES The problem treated by Evans may be considered as a special case in which mixing of the hot and cold phases is prevented either by their immiscibility or by the interposition of thermally conducting walls. Thus it corresponds to the case in which the saturation curves of Figure 7 coincide with the axes of pure components. The calculation of heat balances; which Evans carried out algebraically, assuming constant specific heats, may therefore be carried out graphically; an H os. N diagram is used in which only two vertical lines (representing the heat contents of the two phases undergoing heat exchange) are significant. The calculation is simplified by making a nonuniform temperature scale on each of these two lines; the scale is obtained by laying off the
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INDUSTRIAL AND ENGINEERING CHEMISTRY
1299 .
heat content( Y z d T ) corresponding to each round value
.
HofSfream
ooc.
of temperature of the scale. The resulting diagram is shown in Figure 8. With this diagram the heat balance conditions may be calculated graphically by the center-of-gravity construction. For a countercurrent exchanger - the -point D is located a t such a position that the ratio B D / A D gives the proportion of the two streams (in this case the ratio 3/1 indicates 3.pounds of cooling Xiquid per pound of hot stream); the construction agrees with specified values of the temperature a t two points in the exchanger (e. g., entering hot stream and entering cooler liquid), The general center-of-gravity construction gives the heat balance without assuming constant specific heats, since this assumption was not made in-laying off the heat content (temperature) scales; and the construction may be used to include losses of heat to the surroundings by appropriate shifting of the net flow (D)point (14). The particular construction shown in Figure 8 corresponds to the case of ideal heat exchange units (as defined by Evans) from which the leaving streams are at the same temperature (thermal equilibrium). The construction readily gives the number of ideal units needed to perform the proposed cooling. Since the phase lines which correspond to the i 80 saturation curves of Figure 5 are parallel straight lines, the calculation may also be carried out on the corresponding y us. x type diagram, shown in Figure 9 with the use of a straight o p e r a t i n g line. T h e equilibrium line represents p o i n t s a t which b o t h phases h a v e t h e same temperature and is curved as a result of the fact that the specific heats of the FIGURE 8. HEAT BALANCE FOR A CHAIN OF IDEAL (EVANS) two phases do not vary in the same way. I n the HEATEXCHANGE UNITS(VARIABLE HEATCAPACITIES) case assumed by Evans, this line is straight, and the diagram reduces to that on which Kremser &sed his absorption factor equation-hence the appearance of an analog of Kremser’s equation in Evans’ paper. The usefulness of Evans’ method of ideal heat exchange units is practically limited to cases in which the over-all transfer coefficient is constant along the length of the exchanger, a condition not often met in practice. The usefulness can be somewhat extended, in the utilization of direct test data, by considerations analogous to those upon which the Murphree plate efficiency factor ( I d ) is based. But this concept should not be resorted to except in special cases. It has been pointed out by a reviewer that the analogy between a countercurrent heat exchanger and a packed tower is sufficiently close to permit the definition of a quantity analogous to the “length of a mass transfer unit” proposed by Chilton and Colburn (3) for the evaluation of packed towers. The number of heat transfer units would be defined in terms of the integrated transfer equation as
lg s% =
where T
=
= no. of heat transfer units
(1)
temperature of that phase whose specific heat is C and whose weight rate is W at osition x
A = temperature difference between pEases ’ U = over-all transfer coefficient A = heat exchange area per foot length of exchanger
FIGURE9. x us. y DIAGRAM FOR CHAIN OF IDEALEXCHANGE UNITS (VAR’IABLE HEATCAPACITIES)
Cooled Stream
20
0
40
Temperature of Cold Phase
The length of a transfer unit would be defined as W C / U A , provided this quantity is constant. Of the possibilities considered, this concept is most likely to lead to fruitful results in the definition of ideal heat exchange units. The use of these graphical methods (particularly the H us. N type diagram) is not limited to the case of ideal heat exchange units. Rather, it should prove of value as a means of expressing heat balances in the integration of heat transfer equations in cases for which the evaluation of heat balances by algebraic means is difficult as a result of rapid variations of specific heats, to heat losses, or to complexity of the process. Examples of such cases are cooling of a wet gas with condensation of a part of the vapor (IQ), and heating of a mixture in which a chemical equilibrium is disturbed by temperature changes. The authors do not intend to imply that these methods should supplant present familiar methods of solving heat exchange problems but only that they may serve to fill in gaps where the present methods have failed. It is also likely that the analogies between heat transfer and separation processes may be used in the opposite direction to supplement the present methods in design of separation equipment where the conditions are analogous to those already dealt with in heat transfer problems.
Acknowledgment Clerical assistance of the Works Progress Administration (0. P. No. 665-08-3-144) is gratefully acknowledged. Bruce Longtin, the junior author, is Shell Research Fellow in Chemistry a t the University of California.
Literature Cited (1) (2) (3) (4) (5) (6) (7)
(8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18)
Bolnjakovib, “Technische Thermodynamik,” Vol. 11, Leipzig, Theodor Steinkopff, 1937. Cannon and Fenske, IND.ENG. CHEM.,28, 1035 (1936). Chilton and Colburn, Ibid., 27, 255 (1935). Cornish, et al.,Ibid,, 26, 397 (1934). Evans, Ibid., 26, 860 (1934). Ibid., 27, 1212 (1935). Hunter and Nash, J. SOC. Chem. Ind., 51, 285T (1932), 53, 95T (1934) ; World Petroleum Congr., London, 1955, Proc., 2, 340; IND.EKG.CHEM.,27, 836 (1935) ; J . Inst. Petroleum Tech., 22, 49 (1936). JPnecke, 2. anorg. Chem., 51, 132 (1906). Kremser, Nutl. Petroleum News, 22, 43 (1930). Lewis, W. K., IND.ENQ.CHEM.,9, 825 (1916). London, A. F., thesis, Univ. Calif., 1938. Murphree, IND.ENO.CHEM.,17, 747, 960 (1925). Peters, Ibid., 14, 476 (1922). Randall and Longtin, Ibid., 30, 1063, 1188, 1311 (1938). Rogers and Thiele, Ibid., 29, 529 (1937). Saal and Van Dyck, World Petroleum Congr., London, 1933, Proc., 2, 352. Thiele, IND.ENG.CHEM.,27, 392 (1935). Varteressian and Fenske, Ibid., 28, 928, 1353 (1936) ; 29, 270
(1937). (19) Weise, 2.ges. Kuttednd., 38,17 (1931).
