Tlds case is based uj)OIl [abomtoJ)' data obtained ill ({II industrial laboratory />riOl" to lite design of a contillllOus extractiol! /n'ocess. Tile names of tile actual c/lemicals being cOllsidered lI(u'e been c/I(mged for /mr/JOses of comme1'cial security. Some discussioll is directed to
lW1"d IIle use of faclorially designed eX/.Jerimellts ill gathering and analyzing cltemical engineering data. The im/J01"t(IIICe of utilizing tile
/Jroper /01'111 of inde/Jelldent variables ilZ tile fOl'lnulalioll of designed eX/Je1"imelll s is also em/J/Ulsized
Tile design computations in lids clla/Jte1' lead /0 a classical/ill(JIl
cial emluatioll in ll'hicll ca/.Jital and operating costs are balallced in the determination of all optimum design. III tills case only a prelimi
nary desigl/ is required, al/d liberal use of appmximations greatly simplifies the calculation effm'l. An ol'er-all underslandillg of lite process economics is obtained by all allalysis of a limiting case in
zclliell all illfillite lIumber of ext1'aclion slages is used.
Fenway Chemical Company Boston, M:l!,;!,;llr.hu!,;p.tt!';
To: Michael Higgins, Group Leader
From: William Sullivan, PreSident
As you know, the company is currently operating a batch process for the production of Fenway acid salt in our Back Bay plant. First, Fenway acid is produced by sulfonating Fen-aromol-A with mono
chlorosulfonic acid. This reaction is carried out in a stirred-tank reactor containing an aromatic solvent. Sodium hydroxide is then
51
52 C/wple y 3
added to the mixture to produce the stable sodium salt of Fenway aCid;
this neutralization is necessary to prevent hydrolysis of the sulfonate group. The salt is extracted into water and then amidated to the sodium salt of Brighton acid, the desired end product.
Since the aromatic solvent lowers the yield of the amidation step, it must be removed before the reaction can proceed. Moreover, a highly pure aromatic solvent is necessary for the recycle to the sul
fonator, because water reacts with the monochlorosulfonic acid. This separation is at present achieved by a cumbersome and costly series of washing and stripping operations carried out on each batch of pro
duct.
Since the batch extraction process is currently operated at peak capacity and increases in product demand are anticipated, it is de
sired to investigate the possibility of a continuous extraction opera
tion. Your design group is requested to complete a preliminary pro
cess design that will allow the extraction of Fenway acid to be carried out on a continuous basis. The present batch operation is carried out at 70°C, with a PH in the aqueous phase of 8. Since only a preliminary design is requested, you may wish to restrict your attention to these same conditions. However, the manufacturing technical group has ob
tained sufficient data to allow consideration of temperatures between 20° and 70°C and of pH values from 8 to 12.
The plant has available several agitated kettles that could easily be adapted to a continuous mixer-settler operation for the proposed extraction. Since this eqUipment is currently idle, you are requested to direct at least some attention to a continuous mixer-settler opera
tion; however, any ideas you may have about other types of processes would also be appropriate.
The design requirements for other sections of the process specify the following:
1. Feed to the continuous extraction and purification system
(
after addition of NaOH to form the acid salt)
:Aromatic solvent 3, 000 lb
/
hr Fenway acid salt 680 lb/
hr(
Plus negligible water which accompanies the NaOH)
2. Product of the continuous extraction and purification system(
to be fed to the amidation reactor)
: Aromatic solvent 5. 6 lb/
hr Fenway acid solvent 666. 0 lb/
hr Water I, 995. 0 lb/
hrThe following sections summarize the data relevant to your design, which have been gathered by the plant technical group.
Molecular Weights
Although both the Fenway acid and the aromatic solvent are com
posed of mixtures of several components, the following average
mole-Process im/JYocemellt for Liquid-Liquid Extractioll 53
cular weights may be ascribed to these compounds:
Compound
Sodium salt of Fenway acid Aromatic solvent
Water
Suggested Nomenclature
Molecular weight
24 6 123 18
A Refers to the sodium salt of Fenway acid
B Flow rate of the bottoms or product stream, lb moles/hr C Capacity of a process unit, cu ft
D Diameter of a fractionating column, in.
f Fugacity, atm
F Feed rate to a fractionating column, lb moles/hr
J( Distribution or partition coefficient, dimensionless L Liquid flow rate in a fractionating column, lb moles/hr
nz Mass flow rate of a process stream, lb/hr; or quantity of material present, lb.
n Molal flow rate of a process stream, lb moles/hr; or quantity of material present, lb moles
S Refers to the aromatic solvent T Temperature, °C
V Vapor flow rate, lb moles/hr or lb/hr
W Refers to water
x Mole fraction in a liquid phase
y Mole fraction in a vapor phase
(3 Per cent of the total Fenway acid salt appearing in the aqueous phase
"y Activity coefficient
Superscripts
o Refers to a component in its standard state
54 Chapter 3 Subscripts
AS Refers to component A in the solvent phase
A w Refers to component A in the aqueous phase
D Refers to the solvent content of the bottoms stream from a frac-tionating column
s Refers to the aromatic solvent
sw Refers to the aromatic solvent in the aqueous phase
ss Refers to the aromatic solvent in the organic phase
v Refers to the solvent content of the overhead product from a fractionating column
w Refers to water
ws Refers to water in the organic phase
ww Refers to water in the aqueous phase
Mutual Solubility Data
The mutual solubilities at 20°C of the pure aromatic solvent and water were obtained from the International Critical Tables. They are
Water in solvent: 0. 24 g/100 g Solvent in water: 0. 19 g/100 g
Liquid-Liquid Equilibrium Data
An experimental program was carried out to establish the relative solubility of Fenway acid in the water and the solvent phases. A 23 factorial program was carried out; the factors and setting levels for these experiments are as follows:
Factor Levels
Temperature 20° and 70°C
pH 8 and 12
W:S weight ratio 1. 0 and 2. 15
The data obtained from these experiments are summarized in Table 3-1.
Process IlIlprOl'elllelll for Liquid-Liquid Extradioll 55
Table 3-1. Results of the Liquid-Liquid Extraction Studies
Experiment I: 20°C;PH = 8; 1l1w/ms = 2. 15
Aqueous phase Organic phase
Component K- g mole mole fro K g mole mole fro
A 35. 90 0. 146 0. 00818 3. 66 0. 0149 0. 0125
W 318. 6 17. 70 0. 991 0. 585 0. 0325 0. 0272
S 1. 94 0. 0158 0. 00089 141. 2 1. 148 0. 960 356. 4 17. 86 1. 00 145. 4 1. 195 1. 00
Experiment II: 20°C;PH = 8; mw/ms = 1. 0
Aqueous phase Organic phase Component � g mole mole fro .II g mole mole fro
A 13. 10 0. 0533 0. 00405 3. 10 0. 0126 0. 00617
W 236. 0 13.10 0. 995 0. 991 0. 0550 0. 0269
S 0.873 0. 0071 0. 00054 242. 8 ---1. 975 0. 967 250. 0 13. 16 1. 0 246. 9 2. 043 1. 00
Experiment III: 20°C;PH = 12; mw/ms = 2. 15
Aqueous phase Organic phase
Component � g mole mole fro K g mole mole fro
A 33. 4 0. 136 0. 00798 3. 42 0. 0139 0. 0114
W 304. 5 16.90 0. 991 0. 546 0. 0304 0. 0249
S ---1. 21 0. 00985 0. 00058 144. 4 1. 175 --- 0. 964 339. 1 17. 05 1. 00 148. 4 1. 219 1. 00
Experiment IV: 20°C;PH = 12; mw/ms = 1. 0
Aqueous phase Organic phase
Component � g mole mole fro ,.g g mole mole fro
A 18. 39 0. 0748 0. 00565 4.33 0. 0176 0. 00874
W 237. 0 13. 15 0. 993 0. 844 0. 0468 0. 0233
S 0. 563 0. 004 6 0. 00035 240. 0 1. 950 0. 969 256. 0 13. 23 1. 00 245. 2 2. 014 1. 00
56 Chapter 3
Table 3 -1. Results of the Liquid-Liquid Extraction Studies (cont.)
Experiment V: 70°C;PH = 8;
mlV/ms
= 2. 15Aqueous phase Organic phase Component � g mole mole fro Ii. g mole mole fro
A 42. 0 0. 171 0. 00972 4. 33 0. 0176 0. 014 7
W 313. 0 17. 40 0. 989 0. 537 0. 0298 0. 0250
S 3. 09 ---0. 025 0. 00142 141. 0 1. 145 0. 960 358. 1 17. 60 1. 00 145. 9 1. 192 1. 00
Experiment VI: 70°C;PH = 8;
111w/n1S
= 1. 0Aqueous phase Organic phase
Component � g mole mole fro Ii. g mole mole fro
A 14. 10 0. 0573 0. 00440 5. 50 0. 0224 0. 0107
TV 234. 0 13. 00 0. 995 1. 150 0. 0640 0. 0306
S 0. 825 0. 0067 0. 00051 246. 0 2. 00 0. 958 248. 9 13. 06 1. 00 252. 6 2. 086 1. 00
Experiment VII: 70°C;PH = 12;
mlV/ms
= 2. 15Aqueous phase Organic phase
Component � g mole mole fro g- g mole mole fro
A 39. 2 0. 159 0. 00845 3. 20 0. 0130 0. 0108
IV 336. 0 18. 65 0. 990 0. 480 0. 0267 0. 0222
S ---2. 35 0. 0191 0. 00101 143. 0 1. 163 0. 967 377. 5 18. 83 1. 00 14 6. 7 1. 203 1. 00
Experiment VITI: 70°C;PH = 12;
n1w/ms
= 1. 0Aqueous phase Organic phase
Component £. g mole mole fro K g mole mole fro
A 14. 65 0. 0596 0. 00474 4. 76 0. 0193 0. 00943
W 225. 0 12. 50 0. 995 1. 19 0. 0661 0. 0323
S 1. 18 0. 00960 0. 00077 241. 0 1. 960 0. 958 240. 8 12. 57 1. 00 24 6. 9 2. 045 1. 00
Process 11ll/)rOl'emellt for Liquid-Liquid Extraction 57
The Statistics Department has analyzed these data uSing a standard computer program and has obtained the following correlating equation:
{3 = 86. 11 + 9. 82 - 1. 56
)
- 0. 425 (pH - 10)+ 0. 0215 (T - 45) + O. 478
(
mW - 1. 56)
(pH - 10)'YI1s
+ 9. 25 X 10-3 -1. 56
)
(T - 45) - 8 X 10-3 (pH -10) (T -45)+ 5.05 x - 1. 56
)
(pH - 10) (T - 45) (3. 1) wheremw/m
s represents the ratio of the mass of water to the mass of solvent in each batch extraction and {3 denotes the percentage of the total Fenway acid which is found in the aqueous phase. According to the statistics group, this equation is valid within 90 per cent confidence limits for the ranges of the variables over which the data were taken.Vapo r-Liquid Equilibrium Data
Vapor-liquid equilibrium data were obtained for aqueous solutions containing various amounts of aromatic solvent and Fenway acid.
These data showed that Fenway acid is virtually nonvolatile at the temperatures of interest in this problem (approximately 105°C). Data were obtained not only for mixtures containing various amounts of Fenway acid but also for mixtures having different values of pH in the aqueous phase. As shown in Fig. 3-1, the relative volatility of the sol
vent mixture is quite unaffected by the variations in PH and acid con
centration, and all the data may be correlated by a single line.
Cost Correlations and Design Instructions
The following approximate cost-correlation equations may be use
ful in evaluating the economics of any of the process designs to be considered:
1. D = 0. 4 7 (V)1/2
2. Cost of distillation tray = $16(D) 3. Cost of reboiler = $470(V)O. 24 4. Cost of condenser = $15(V)O. 6
58 C/Zapter 3
Figure 3 -1. Vapor-liquid equilibrium data for solvent-water mixtures containing Fenway
8. Cost of controls for a mixer-settler combination = $3,000/
extraction stage.
It is to be noted that these equations yield estimates for the uninstal
led equipment costs. The installed equipment cost may be approxi
mated by multiplying the uninstalled cost by four.
Although the residence time in the mixer-settler equipment will eventually have to be ascertained by a detailed mass transfer analy
sis, the following approximate values may prove useful for prelimin
ary design calculations: mixer residence time = 10 minutes, settler residence time = 20 minutes. At these values of residence time, an over-all stage efficiency of 100 per cent may be assumed. Reference (7) may be consulted for a discussion of the factors that may affect the efficiency of mixer-settler units. An average specifiC gravity of 1. 18 for the two-phase mixture may be used in computing the required equipment capacity.
Low-pressure steam is available at $0.80/1000 lb, and cooling
water charges are approximately $0.02/1 000 gallons. The cooling water is available for 80°F, and it is desired to maintain the tempera
ture rise of the cooling water at values below 40°F.
PYocess ImpYOl'eIllCII/ foy Liqllid-Liqllid Extractioll 59
PREPARATION OF A PRELIMINARY DESIGN Examination and Evaluation of Experimental Data
Before proceeding with an analysis of preliminary process de
signs, an examination and evaluation of the experimental data is in order. One important factor in determining the process economics will be the extent to which water and the aromatic solvent are mutual
ly soluble. The mutual solubilities will be particularly critical, since the final product specifications allow only a small amount of solvent in the aqueous extract that is fed to the amidation reaction step. Any excess solvent must be removed, and this should probably be accom
plished by a stripping or distillation process.
The original memorandum indicates that at 20°C water is soluble in the solvent to the extent of 0. 24 g/100 g and the solvent is soluble in water to the extent of 0. 19 g/100 g. After converting these values to a molar basis, it is useful to compare the mutual solubilities of the pure solvents with those obtained from the liquid-liquid extraction studies in which the acid salt was present. This comparison is imple
mented in Table 3-2.
Table 3-2. Mutual Solubilities of Water and the Aromatic Solvent
Experiment Temp.oC pH nlw
/
m s x sw xwsPure solvents 20 7 0. 00028 0. 0161
(lit. values)
I 20 8 2. 15 0.00089 0. 0272
II 20 8 1.0 0. 00054 0.0269
III 20 12 2. 15 0. 00058 0.0249
IV 20 12 1.0 0. 00035 0. 0233
V 70 8 2. 15 0. 00142 0. 0250
VI 70 8 1. 0 0. 00051 0.0306
VII 70 12 2. 15 0. 00101 0. 0222
VIII 70 12 1. 0 0. 00077 0. 0323
The data at 20°C reveal that the presence of the acid salt and the variations in pH have only a modest effect on the mutual solubilities of the two solvents. At constant temperature, the variations in pH and salt concentration do not appear to produce any Significant or consis
tent changes in the mutual solubilities. The scatter in the data ob
tained at 70°C may arise from difficulties in maintaining accurate temperature control at the higher levels of temperature. For the pur
pose of a preliminary design, the effects of PH and salt concentration will be neglected, and average values of the mutual solubilities will
60 CI/(/pter 3
be assumed to apply at each temperature level. These mean values of x s wand x ws are as follows:
Temperature
xsw xws
0.00059 0.0256 0.00093 0.0275After the design has been completed, it will be important to inves
tigate the effect of variations in the values of x sw and xws on the estimated process economics. If variations of the magnitude shown in Table 3-2 are found to affect the estimated financial return signifi
cantly, a more exact experimental determination of the mutual solu
bilities would be required.
Consideration of the Liquid-Liquid Equilibrium Data
The application of factorial experiments is a very powerful tech
nique in obtaining and correlating experimental data for design work.
Using statistical methods, a great deal of information may be gathered by expending only a minimum of experimental time and effort. These methods are particularly helpful when the theoretical basis of a pro
cess operation is poorly understood. References (J, 3, 4,5) serve as an excellent introduction to statistical designs and their application to practical chemical engineering problems.
By use of statistical methods, Eq. 3. 1 has been derived as the proper correlating equation for the experimental results shown in Table 3-1. This equation relates the fraction of the total Fenway acid found in the aqueous phase to variations in the temperature, pH, and amounts of solvent present. Its use in carrying out design calculations presents two very Significant difficulties. First, the validity of the equation is limited to the ranges of the variables for which the ori
ginal data were obtained. It is quite possible that the design specifi
cations will require the application of the correlating equation well beyond the range of variables for which the data were taken. For ex
ample, the ratio of water to solvent was varied by only a factor of 2 in the laboratory experiments, and it is unlikely that the optimum con
tinuous process would happen to correspond to solvent flow rates in this range. Application of the equation outside these limits would be quite risky and could lead to highly erroneous conclusions.
The second difficulty, somewhat related to the first, results from the poor selection of variables that were used in setting up the ex
perimental design and in expressing the experimental results. The selection of temperature and pH as variables appears to be reasonable;
however, the use of the ratio mw/ms has no reasonable basis, and the quantity (3 does not appear to be an appropriate form of the response variable. For example, if very large values of
1I1W/1I1S
(outSide the range of the original data) were inserted in Eq. 3. 1, values of (3 > 100 per cent could be obtained. This sort of physical impossibility mightProcess Improvement for Liquid-Liquid ExlYaclion 61
have gone unnoticed if the equation had been combined with other alge
braic expressions. In view of these observations it is worthwhile to search for a more satisfactory basis of expressing the experimental results before proceeding with the design considerations.
In a thermodynamic system in which a solute is distributed between two immiscible solvents, equilibrium will be obtained when the chemi
cal fugacity of the component in one phase becomes equal to the fugac
ity of the same component in the other phase. When this concept is applied to the present case,
which in turn may be expanded as
fA�'YAlVxAlV
=fAos 'YAS xAS
Therefore, at equilibrium one obtains
(3. 2)
Now fO, the fugacity of a component in its standard state, is independent of composition, and at constant temperature Eq. 3. 2 may be written as
(3.3) In dilute solutions, the activity coefficients may be assumed to be in
dependent of concentration, and a further simplification is effected, whereby
(3.4) The quantity]{ is termed the distribution or partition coefficient, and Eq. 3. 4 is conventionally known as Nernst's law. It proves quite use
ful in correlating the results of liquid-liquid extraction experiments.
It is to be recognized that the distribution of Fenway acid between the two phases is not determined solely by physical phenomena. Since a neutralization reaction is also taking place, the simple form of Eq.
3.4 is not strictly applicable. However, as an initial approximation, it may result in a data correlation that will be useful for preliminary design calculations.
Casting the data of Table 3-1 in the form suggested by Eq. 3. 4 results in the data listed in Table 3-3. They indicate that the
parti-62 Clzapter 3
Table 3-3. Liquid-Liquid Experimental Data Expressed
in the Form of a Partition Coefficient
Experiment Temperature,OC pH K = XAW
/
XASI 20 8 0. 655
II 20 8 0. 656
III 20 12 0. 699
IV 20 12 0. 647
V 70 8 0. 661
VI 70 8 0. 411
VII 70 12 0.782
VIII 70 12 0. 503
tion coefficient is independent of pH and the relative amounts of sol
vent. The average value of the partition coefficient at 70°C is 0.590, while that at 20°C is 0.663; only a 10 per cent variation is found over a 50°C variation in temperature. This is probably not satistically significant in view of the scatter in the data at the higher temperature level. Therefore, Eq. 3-1 may be discarded, and the liquid-liquid extraction data may be expressed in terms of a single average value for the partition coefficient, 0.63. Since the partition coefficient has been found to be quite invariant over a wide range of experimental conditions, the designer may use this value confidently for virtually any design condition. This broad application would not have been possible if the design calculations were to be based on Eq. 3-1.
The results of this discussion emphasize the need for good judg
ment in the selection of the proper method for correlating experi
mental data. The use of statistically designed experiments is an in
valuable aid, but it is not a substitute for a meaningful analysis of a problem. It should be pointed out that the results of the type shown in Table 3-1 are conventionally correlated in the form of a triangular diagram as illustrated by Hougen, Watson, and Ragatz (2). However, in the present situation the concentrations of the solute are so small that a triangular diagram would be neither meaningful nor useful.
Vapor-Liquid Equilibrium Data
The vapor-liquid equilibrium data appear to be well presented and properly correlated. Figure 3-1 should be directly applicable to the design calculation. In particular, the relative invariance of the rela
tive volatility with changes in pH and Fenway acid concentration is a very convenient feature of the data and will grea tly reduce the re
quired computational effort.
Process Improvemellt for Liquid-Liquid Extractiol/ 63 PRELIMINARY PROCESS DESIGN CALCULATIONS
To produce a Fenway acid product having the specified purity, a process must accomplish the following objectives:
1. Extract the acid salt from the aromatic solvent.
2. Remove the aromatic solvent from the aqueous acid salt solution prior to the amidation step.
Since the original memorandum specified that a continuous mixer
settler design should be conSidered, a process of the type shown in Fig. 3-2 should be appropriate. In this design scheme, the feed stream containing the crude Fenway acid salt is mixed with recycle and auxil
iary water, and the combined stream is metered continuously into the
Feed stream
Figure 3-2. Block flow diagram of a one
stage continuous extraction process.
mixer. The effluent from the mixer is separated into organic and aqueous phases in the settler. The small amount of dissolved organic solvent in the aqueous phase is removed by a stripper from which the final desired product is removed. It is important to note that the aqueous stream fed to the stripper is saturated with organic solvent, and further that the mutual solubility of the water and solvent is quite insensitive to temperature variations. Therefore, if a rectifying sec
tion were added to the stripper, all the plates in such a section would
tion were added to the stripper, all the plates in such a section would