Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 3, 1978 215
Projection of the Slugging Bed Height in a Recirculating Fluidized Bed Wen-Ching Yang" and Dale L. Keairns Research Laboratories. Westinghouse Electric Corporation, Pittsburgh, Pennsylvania 15235
Experimental data on the slugging bed height of a recirculating fluidized bed are presented, along with a theoretical model developed following the theory of Matsen et al. (1969). The experiments were performed in a semicircuiar, transparent, Plexiglas unit of 0.29 m diameter and 6.1 m height. The developed model was then used to project slugging bed heights in a 15 ton/day recirculating fluidized bed coal devolatilizer process development unit (0.51 m diameter, 4.88 m bed height). The estimated slugging bed heights from the process development unit compare favorably with the model's predictions. The slugging frequency was also discussed and found to be dependent on the draft tube gas flow rate, a phenomenon different from that in conventional fluidized beds.
Introduction Westinghouse is developing a two-stage fluidized bed coal gasification process to produce low heating-value gas for combined-cycle power generation (Archer and Keairns, 1974). A recirculating fluidized bed with caking coals has been successfully demonstrated as a first-stage coal devolatilizer in a pilot-scale Process Development Unit (PDU) (Salvador and Keairns, 1976,1977). The recirculating fluidized bed concept is briefly illustrated in Figure 1. Dry coal is introduced into the devolatilizer below the bottom of the draft tube through a coal-feeding tube concentric with the draft tube gas supply. The coal feed and recycled char at up to 100 times the coal feed rate are mixed inside the draft tube and carried upward pneumatically in dilute phase at velocities greater than 4.6 m/s (15 ft/s). The solids disengage in a fluidized bed above the top of the draft tube and then descend in an annular downcomer surrounding the draft tube as a packed bed a t close to minimum fluidization condition. Gas is introduced a t the base of the downcomer a t a rate necessary to permit the downward flow of the solids. The recirculating solids effectively prevent agglomeration of the caking coal as it devolatilizes and passes through the plastic stage. Laboratory studies are being carried out in a cold model to investigate different physical phenomena in a recirculating fluidized bed to support the pilotplant operation. The slugging behavior in a recirculating fluidized bed is reported here. On the basis of two-phase theory (Davidson and Harrison, 1963), gas in excess of that required for minimum fluidization will pass through gas fluidized beds in the form of bubbles. Coalescence of gas bubbles usually occurs rapidly above the distributor plate, and the bubble size increases with an increase in bed height. When the bubble approaches the reactor diameter in size, it becomes a slug which rises at regular intervals and divides the main part of the bed into regions of dense and lean phases. The bed is then said to be slugging. Slugging generally occurs in reactors of laboratory and pilotplant scale. According to Stewart (1965),slug flow will occur in gas fluidized beds when (U - U,f)/0.35 (gD)1/2is greater than about 0.2 with HID > 1. Slugging in ordinary fluidized beds has been extensively studied and documented (Davidson and Harrison, 1971), but slugging in recirculating fluidized beds with an internal draft tube has not. The recirculating fluidized bed concept has been reported elsewhere (Yang and Keairns, 1974, 1975 a, b). The basic difference between slugging in an ordinary fluidized bed and a recirculating bed is that, in the former, the bubbles have to coalesce to reach the slug size, and, in the latter, the slug-size bubbles are usually generated right a t the outlet of the draft tube. Transition to
slugging is usually compiete when the bubble size reaches '13 to l/2 of the reactor cross section. The study of slug flow is important in designing reactors that allow for adequate freeboard. The gas-solids contact efficiency is also an important consideration, especially for scaling up from laboratory or pilot units, where slug flow usually prevails, to large commercial units. The necessity of expanding the reactor diameter a t the proper reactor height to cut down the slugging is also a question which can be answered through studying the slugging phenomenon. When dolomite is used in the devolatilizerldesulfurizer for sulfur removal (see Archer et al., 1972, for detailed description of the process), the efficiency of char-dolomite separation may be affected. Experimental Apparatus The experimental data were obtained by using a Plexiglas column of 30.48 cm outside diameter, 28.58 cm inside diameter, and 5.1 m height. The detailed design of this column and its associated auxiliaries are described by Yang and Keairns (1975b) and Yang et al. (1976). The recirculating bed unit is illustrated in Figure 2. Experimental Conditions The bed material used was Ottawa sand with a particle size distribution as shown in Table I and a weight mean particle diameter of 740 bm. The operating draft tube velocities ranged from 4.80 to 8.84 m/s, and the freeboard velocities were between 0.90 and 1.63 m/s. Two bed heights were investigated-0.58 and 0.89 m above the top of the draft tube. The draft tube was 1.83 m high and had an inside diameter of 9.55 cm. Both flat and conical type (60' included angle) distributor plates were used. The distances between the distributor plate and the draft tube inlet were 7.62 and 15.24 cm for the flat plate and zero (measured from the top of the conical plate) for the conical plate. Experimental Techniques Slugging Bed Height. The slugging bed heights were observed, and the differential pressure drops over the downcomer height and between two pressure taps 1.24 and 1.74 m abnve the draft tube top were recorded. The differential pressure drops from these two pressure taps above the draft tube are shown in Figure 3 for different draft tube velocities (draft tube velocities of 4.8,5.9, and 7.7 m/s, respectively) and different slugging frequencies. At lower slugging frequencies and lower draft tube velocities, discrete air bubbles or slugs could be observed. The bed tended to return to its minimum
0019-7882/78/1117-0215$01.00/0 0 1978 American Chemical Society
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Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 3, 1978 Car Out 6 I
'
SdldS Out
1 t//- 1
10
Draft Tube Downcomer
Alternitlve Solids Fnd
-c
Lqnd 1
U-J
I
Gas and Soilds F n d
---
Sdld Flaw Gas Flow
Figure 1. Recirculatingbed concept.
height after the gas slug passed by (see Figure 3a). At higher draft tube velocities and slugging frequencies, however, the solids in the draft tube flow had enough momentum to penetrate the roof of the still-forming air bubble at the top of the draft tube. The discrete air bubbles no longer existed, and the slugging became more irregular, as shown in Figures 3b and 3c. Nevertheless, three different bed heights can usually be distinguished-the maximum bed height, the most frequent bed height, and the minimum bed height. The maximum bed height was the result of two factors. The first was rapid bubble formation. After the first gas slug passed through the bed and before the bed returned to its minimum height, the second gas slug arrived and pushed the bed height to an even higher position (see peak e in Figure 3c). The second factor was the dynamics of the bubble formation at the draft tube top. Usually, a bubble was already forming at the draft tube top before the bed height reached its highest position. On several occasions, however, the subsequent gas slugs coalesced because solids penetrated the bubble roof, and the next bubble had to be initiated at the draft tube top from an essentially slumped bed. If this occurred, the bed tended to slug higher than its usual height. These peaks can be seen as peaks a and b of Figure 3a and c and d of Figure 3b. Except for these occasional slugs which reached a higher bed position, most slugs reached a relatively constant bed height within a few inches of each other. This bed height will be referred to here as the most frequent bed height. When the gas bubble passed through the bed, the bed returned to a relatively constant minimum position or minimum bed height. The maximum bed height occurred a t irregular intervals and could be up to 0.6 m higher than the most frequent bed height. Slugging Frequency. The slugging frequency was observed three ways. First, slugging frequency was timed every 20 cycles with a stopwatch. Each time the bed surface rose and then returned to the minimum position was counted as one cycle. Thus, the irregular occurrence of the maximum bed height took a longer time to complete one cycle (see peaks a through e in Figure 3). Second, the fluctuation in differential pressure drop was observed in pressure taps located above the draft tube. Since the fluctuation of the differential pressure signaled the passing of an air slug, every up and down move-
SolYt lnleb
2
Solids O u t l d
I
owtm
4
DwncMntr
5
Alr Inlet to O M Tub
6
Air Inlet to Darncomer
7
MJur6blclpper Spatw
6
Mlushblc h e r S p u r
9
Dlrtrltubr PI& Is)
10
RhwWIcFmntPl&
Figure 2. Schematic of the semicircular unit (not to scale). Table 1. Particle Size Distribution of Ottawa Sand
Mesh size
Nominal opening, wm
18
1000
...
20 30
850
18.77 78.90 0.21 0.21 1.91
35 40 pan
600 500
425
...
Wt%
ment of the pressure reading was counted as one cycle. The fluctuation of two differential pressure probes was timed with a stopwatch for 20 cycles. These two methods were used exclusively before the installation of two differential pressure transducers and a two-pen chart recorder. The differential pressure transmitters used were Honeywell Model 41103 with a response time of 60 ms at 65% of full scale. After the installation of these instruments, however, the slugging frequency was extracted from the recorder chart tracings shown in Figure 3. These are averaged values obtained with two different chart speeds of 9.5 and 38.1 cm/min. Every time the differential pressure increased from a valley to a peak and then returned to a pressure close to or lower than the original valley was counted as one cycle. Development of Predicting Model The development of a predicting model for slugging bed
Ind. Eng. Chem. Process Des. Dev.. Vol. 17, No. 3, 1978 I
f =
0.62
-i
Fig. 3b
16 QeC.
I
217
I ,
-i
Figure 4. Comparison of experimental results with eq 1. See Table I1 for legend.
f =
k
0.83
16
See.
upward relative to the surrounding solids through a height of solids, H , - Hd. During this time the bed surface will rise to a hedheight, H , as expressed in the following equation
i
Fzg. 3c
Figure 3. Differential pressure tracmgs between two pressure taps 1.24 m and 1.74 m above the draft tube top, respectlvely. or, rearranged
height in a recirculating fluidized bed follows closely the theory proposed by Matsen e t al. (1969). If the air slug forms outright a t the mouth of the draft tube outlet, it will travel a t a velocity of
UB 0.35-
.
Equation 2 is similar to the slugging equation for the ordinary fluidized bed (eq 3) except for the factor ( H , - Hd)/H,. Also, in
Table 11. Legend for Figure 4
Distributor Symbol plate 0 Flat
Distance between Static bed distributor height Draft plate measd tube and draft tube from top height, inlet, em of draft tube m 7.62 88.9 1.83
Draft tube i.d., cm 9.55
A
Flat
7.62
58.4
1.83
9.55
V
Flat
15.24
88.9
1.83
9.55
Flat
15.24
58.4
1.83
9.55
Zero (measured from top of conical plate) Zero (measured from top of conical plate 17.78
88.9
1.83
9.55
58.4
1.83
9.55
0
A
0
Conical (60' included) angle Conical (60" included) angle Flat
Bed diameter Bed cm material 28.58 Sand; 740 pm; av size 28.58 Sand; 740 pm av size 28.58 Sand; 740 pm av size 28.58 Sand; 740 pm av size 28.58 Sand; 740 pm av size 28.58 Sand; 740 pm av size
Operating conditions Ambient Ambient Ambient Amhient Ambient Ambient
50.80 Husky char; 121 "C and 816 pm av size ambient pressure Flat 17.78 123.19' 2.59 12.70 50.80 Devolatilized 871 "C and Minnehahacoal 1519.5 kPa (15 atm) -6 +IO0 mesh a Use the minimum bed height as estimated from the differential pressure measurement,
4
91.44a
2.59
12.70
218
Ind. Eng. Chern. Process Des. Dev., VoI. 17, No. 3,1978
~H-Hd
I
H.-Hd
-1+
u - umr
(4)
0.35-
A coniparison of eq 3 and 4 shows that the slugging in a recirculating fluidized bed can he treated as that in an ordinary fluidi zed bed if only the bed height above the draft tube is taken into consideration.
FaEuU4 Y o I U m a t r k f ~ l n D M T U b , ? I s
Figure 5. Experimental slug frequency in a recirculating fluidized bed. -H =1+ Hmr
u-
Umr 0.35m
(3)
the bed height a t minimum fluidization, H,r, is replaced with H,, the static bed height. The recirculating fluidized bed with an internal draft tube cannot be minimally fluidized because of the possibility of gas bypassing between the draft tube and the downcomer. This substitution, however, will introduce negligible error if H . is measured by allowing the bed to settle gradually after fluidization. Equation 2 can also be rearranged to give
1
Comiparison with Experimental Results - 2 " ^C "..."":-...*"I A"+" Slllggurg 0ne" ~^:l-L n. g ~ l a^__^.. UG:YC.II c. a r m UL c ~ p n r i u r u r a uard i were plotted according to eq 1 in Figure 4. The legend for Figure 4 is summarized in Table 11. Four sets of data have a flat distributor plate located at 7.62 and 15.24 cm from the draft tube inlet with two different static bed heights at 58.4 and 88.9cm above the draft tube outlet. A conical distributor plate with a 60' included angle was used in two other sets of experiments. The draft tube height was 1.83 m and its inside diameter was 9.55 cm. The bed height data used for this comparison were the most frequent bed heights observed. The maximum bed height which occurred only occasionally was up to 0.61 m above the most frequent bed height. (Note that the actual diameter of the column rather than the hydraulic diameter was used.) The seventh set of data was estimated from the differential pressure probe records obtained during the initial try-out runs prior to the Cold Flow Dynamic Tests (Test Plan 005) and the Hot Tests (Test Plan 008.2) in the PDU (Process Development Unit). The scatter of the data is
I7
Bubble through Bed
'
Air
Bubble
Figure 6. Development of air bubble captured by high-speed movie
1
Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 3, 1978 219
the result of a different slugging mechanism that was observed in a recirculating fluidized bed, as will be explained later. Nevertheless, the correlation is useful for design purposes. The favorable comparison of the actual bed height with the PDU data is especially encouraging. Slugging Frequency. Through material balance, Matsen and Tarmy (1970) derived an equation for bubble frequency as shown in eq 5
-
(5) where lz was the number of column diameters between gas slugs, an empirically determined constant. With data from a 13.97-cm i.d. column, k was determined to be 2.44. Since the gas slugs formed above the draft tube in the present unit were far from ideal and were more difficult to measure, the solid slug frequency was measured both visually and by use of a chart recording pressure drop fluctuations. The rise of a solid slug up the bed and its return to close to its minimum position was counted as one cycle. The results of visual observation compared favorably with those from the chart recorder tracings; only those results recorded on a chart, however, are presented in Figure 5. The frequency is seen to depend on the volumetric flow rate inside the draft tube. The straight line passing the origin can be approximated by eq 6.
f = 23.26Fd (6) This observation differs from the theory of Matsen and Tarmy (1970) and from eq 5 which shows that the frequency is independent of gas flow rate. Equation 6 suggests slugs are formed by generating bubbles of constant volume close to the mouth of the draft tube before detachment occurs. The maximum volume of a bubble that will not leak to the emulsion phase in this case can be calculated as 1/23.26 = 0.043 m3. The semicircular unit has an inside diameter of 28.6 cm and a cross-sectional area of 0.032 m2. A bubble whose volume is 0.043 m3 will occupy a section of the column 1.34 m high. Gas slugs close to these dimensions were actually found. The development of a typical gas slug was captured by high-speed movie films as shown in Figure 6. The gas bubble continues to grow, because of the momentum of the solids in the draft tube gas, until it breaks through the top surface of the bed. The space occupied by the gas slug shown in Figure 6 is comparable to 0.043 m3. Presumably, the concentration of solids in the draft tube gas will also affect the slug frequency.
Discussion and Conclusions The experiments performed in the semicircular model are a t ambient conditions. The applicability of the developed correlation to the high-temperature and moderate-pressure conditions prevailing in the PDU should be evaluated. At higher temperatures the bubble frequency tends to increase, and the minimum fluidization velocity tends to decrease (Mii et al., 1973; Yoshida et al., 1975). The net effect of higher bubble frequency and lower minimum fluidization velocity is higher slugging bed height. The quantitative effect is still hard to ascertain. Fluidization characteristics under pressure have also been studied by Knowlton (1974) over a pressure range of 103.4 to 6895 kPa a t ambient temperature. He observed that the fluidization became noticeably smoother in the pressure range of 1034 to 2069 kPa. He also noticed a decrease of minimum fluidization velocity with an increase in pressure. This observation is consistent with results obtained at Westinghouse Research on slugging behavior up to 650 kPa (Westinghouse, 1974). Since the PDU is operating a t the
borderline pressure, where the effect of pressure becomes gradually noticeable, the actual pressure effect on the slugging bed height in the PDU may be comparable to that observed in the semicircular model. This is evident from the good agreement between the PDU data and the semicircular model data (Figure 3). Another phenomenon that is different in the ordinary fluidized bed and the recirculating fluidized bed is that an increase in gas velocity tends to increase slugging bed height in an ordinary fluidized bed. Increasing gas velocity by increasing the draft tube velocity in a recirculating fluidized bed, however, sometimes will decrease the slugging bed height. The higher the draft tube velocity the higher the gas-solids jet from the draft tube will penetrate into the bed above the draft tube. That means the jet will degenerate into bubbles a t a higher bed height and thus reduce the slugging bed height. The quantitative effect still cannot be derived. This phenomenon contributes partially to the large scattering of data obtained (see Figure 3). A correlation for predicting slugging bed height in a recirculating fluidized bed with an internal draft tube was developed and compared favorably with the experimental data obtained in the semicircular unit and from both the cold flow and hot operation tests in the PDU. Slugging frequency was also found to depend on the draft tube gas flow rate. The derived correlation was used to project slugging bed heights in the PDU a t different operating conditions. The present correlation will also be useful in designing commercial size equipment. Nomenclature
D = reactor diameter, m f = slugging frequency, s-1 F d = volumetric gas flow rate in the draft tube, m3/s g = gravitational acceleration, m/s2 H = bed height, m Hd = height of the draft tube outlet, m H,f = bed height a t minimum fluidization, m H, = static bed height, m k = constant PDU = process development unit U = superficial fluidizing velocity, m/s U,f = minimum fluidizing velocity, m/s Literature Cited Archer, D. H., Vidt, E. J., Keairns, D. L., Morris, J. P., Chen. J. L.-P., "Coal Gasificationfor Clean Power Generation",ProceedingsThird International Conference on Fluidized Bed Combustion, NTlS No. PB-231 977, Nov 1972. Archer, D. H., Keairns, D. L., U S . Patent 3 847 563 (1974). Davidson. J. F., Harrison, D., "Fluidized Particles", p 190, Cambridge University Press, 1963. Davidson,J. F.. Harrision, D., "Fluidization",Chapter 5, Academic Press, New York, N.Y., 1971. Knowlton, T. M.. "High-Pressure Fluidization Characteristics of Several Particulate Solids: Primarily Coal and Coal-Derived Materials", Paper No. 9b Presented at the 67th Annual AlChE Meeting, Washington, D. C., Dec 1-5, 1974. Matsen. J. M., Hovmand, S.,Davidson, J. F . , Chem. Eng. Sci., 24, 1743 (1969). Matsen, J. M., Tarmy, B. L., AIChESymp. Ser., SS(lOl), l(1970). Mii, T., Yoshida, K., Kunii, D., J. Chem. Eng. Jpn., 8 ( l ) , 100 (1973). Salvador, L. A., Keairns, D. L., "Advanced Coal Gasification System for Electric Power Generation, R&D Report 81-Interim Report 5", NTlS No. FE-1514-57, Oct 15, 1976. Salvador, L. A., Keairns, D. L., "Advanced Coal Gasification System for Electric Power Generation, Quarterly Progress Report," NTlS No. FE-1514-61. Jan 1977. Stewart, P. S. B., Ph.D. Dissertation, Cambridge University, 1965. Westinghouse Electric Corporation report to USERDA, "Advanced Coal GasificationSystem for Electric Power Generation", (NTIS Number PB236971), issued May 1974. Yang, W.-C., Keairns, D. L.. AlChE Symp. Ser., 70 (141), 27 (1974). Yang, W.-C., Keairns, D. L., Ind. Eng. Chem., Process Des. Dev., 14, 259 (1975). Yang, W.-C., Keairns, D. L., "Comparison of Recirculating Fluidized-Bed Performance in Two-Dimensional and Three-Dimensional Beds", Proceedings
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Ind. Eng. Chem. Process Des. Dev., Vol. 17, No. 3, 1978
of the International Fluidization Conference, Asilomer Conference Grounds, Calif., 1975, published as "Fluidization Technology", D. L. Keairns, Ed., Hemisphere Publishing Corporation, 1976. Yang, W -C., Margaritis, P. J., Keairns, D. L., "Simulation and Modeling of Startup and Shutdown in a Pilot-Scale Recirculating Fluidized Bed Coal Devolatilizer", Paper presented at the 69th AlChE Annual Meeting at Chicago, Ill., NOv 28-Dec 2, 1976. Yoshida. K., Fujii, S.,Kunii, D., "Characteristics of Fluidized Beds at High Temperature", Proceedings of the International Fluidization Conference, Asilomar Conference Grounds, Calif., June 15-20, 1975, published as
"Fluidization Technology", D. L. Keairns, Ed., Hemisphere Publishing Corporation. 1976.
Received for review February 3,1977 Accepted December 21,1977 This work is being performed as part of the Westinghouse coal G ~ ~ ification program and has been funded with federal funds from the Energy Research and Development Administration under Contract EF-77-'2-1514. The content of this publication does not necessarily reflect the views or policies of the funding agency.
Representation of NH3-H2S-H20, NH3-C02-H20, and NH3-S02-H20 Vapor-Liquid Equilibria Didier Beutier and Henri Renon* Groupe Commun Reacteurs et Processus, €NSTA-€cole
des Mines, 75006 Paris, France
A new method of calculation of NH3-H2S-H20, NH3-C02-H20, and NH3-S02-H20 vapor-liquid equilibria between 0 and 100 O C in the large range of concentrations encountered in sour water stripping processes is presented. The model is based upon the work by Edwards et al. (1975) on solutions of volatile weak electrolytes and extends its validity by a better representation of activity coefficients. Good prediction of ionic activities is achieved by applying Bromley's and Pitzer's ideas and taking ion-molecule interactions into account. No more than two empirical parameters are adjusted to improve the representation at very high ionic strengths for the acid gas partial pressure.
Introduction An accurate representation of NHs-H~S-H~Oand "3C02-H20 vapor-liquid equilibria is of interest in the calculation of sour water strippers. It was recently attempted with the aid of Van Krevelen's correlation (Beychok, 1967), the validity of which is limited to ammonia rich systems and does not extend up to the high dilution required. A precise representation of dilute solutions is necessary, especially to understand the difficulties commonly encountered in oil refineries to reach very low levels of ammonia. Besides, high concentrations of NH3 and H2S are found in the reflux streams of strippers and Van Krevelen's correlation cannot be extrapolated to such levels (Gantz, 1975).The design of strippers could be achieved with more confidence by a model that is valid in the whole range of concentrations. Vapor-liquid equilibria for these systems and NH3-SO2-HzO as well are needed in the calculation of gas cleaning process involving acid gas absorption. Clearly, a general model for the calculation of all acid gas absorbers and strippers is needed. This work is based upon the thermodynamic framework developed by Edwards et al. (1975). They propose an appropriate reduction of binary equilibrium data for NH3-H20, H2S-H20, C02-H20, the validity of which is confirmed by a fair representation of ternary equilibria NH3-H2S-H20 and NH3-C02-H20 at high dilution. The framework is summed up below.
which expresses the partial pressure of a neutral molecule Pa present in the gas phase, e.g., NH3 as proportional to its activity a t moderate pressures. Edwards estimates Henry's constants, Haas a function of temperature from experimental data. Ionization is expressed by
Binary Solute-Water Equilibria The solubility of volatile weak electrolytes in water results from two equilibria: gas-liquid and ionization. In the case of ammonia, for instance
The functions H,(T), K , ( T ) ,and parameters pa, given by Edwards provide a fair representation of solutes "3, COz, H2S, and water equilibria between 0 and 100 "C. Good agreement was generally found for solutions between 0 and 2 m as shown in Figure 1for the system NH3-H20. Therefore, the adjustment proposed by Edwards for the H2S, and C02 was kept as a basis for this three solutes "3, work on ternary equilibria. For solute S02, a new reduction of vapor-liquid data between 20 and 100 "C is proposed here and results are shown in Figure 2. For all solutes, numerical
The gas-liquid equilibrium is accounted for by
Pa = H,a, 0019-7882/78/1117-0220$01.00/0
a+a-
K, = an In eq 1and 2, activities are expressed on the scale of molalities mk (moles per kg of solvent) and evaluated from the usual reference state for solutes in water. Activities are given, for any molecular or ionic species k , except water, by ak
= mkyk
(3)
with lim y k = 1 Zmi-0
where 1 stands for any solute species. Mass balance, eq 2 and a correct evaluation of activity coefficients Y k allow the calculation of ma,the true molality of the undissociated solute, from mAp,apparent molality of the dissolved solute. Then eq 1and 3 give its partial pressure a t given T and mAp.The activity coefficient of a is estimated by In Y a = 2Paama
0 1978 American Chemical Society
(4)
