DATA CORRELATION EQUATIONS

Mol Fraction

DATA CORRELATION EQUATIONS

Tie Line Correlations Useful correlations of ternary data may be obtained by using the methods of Hand [J. Phys. Chem., 34(9), pp. 1961–2000 (1930)] and Othmer and Tobias [Ind. Eng. Chem., 34(6), pp. 693–696 (1942)]. Hand showed that plotting the equilibrium line in terms of mass ratio units on a log-log scale often gave a straight line. This relationship commonly is expressed as

log = a + blog (15-23)

where Xijrepresents the mass fraction of component i dissolved in the

phase richest in component j, and a and b are empirical constants. Subscript 2 denotes the solute, while subscripts 1 and 3 denote feed solvent and extraction solvent, respectively. An equivalent expression can be written by using the Bancroft coordinate notation introduced earlier: Y′ = cX′b_{, where c}_{= 10}a_{. Othmer and Tobias proposed a simi-}

lar correlation:

log = d + e log (15-24)

where d and e are constants. Equations (15-23) and (15-24) may be used to check the consistency of tie line data, as discussed by Awwad et al. [J. Chem. Eng. Data, 50(3), pp. 788–791 (2005)] and by Kirbaslar et al. [Braz. J. Chem. Eng., 17(2), pp. 191–197 (2000)].

A particularly useful diagram is obtained by plotting the solute equilibrium line on log-log scales as X23/X33versus X21/X11[from Eq. (15-23)] along with a second plot consisting of X23/X33versus X23/X13 and X21/X31versus X21/X11. This second plot is termed the limiting solubility curve. The plait point may easily be found from the intersec- tion of the solute equilibrium line with this curve, as shown by Treybal, Weber, and Daley [Ind. Eng. Chem., 38(8), pp. 817–821 (1946)]. This type of diagram also is helpful for interpolation and lim- ited extrapolation when equilibrium data are scarce. An example diagram is shown in Fig. 15-20 for the water + acetic acid + methyl isobutyl ketone (MIBK) system. For additional discussion of various

1− X11 X11 1− X33 X33 X21 X11 X23 X33

correlation methods, see Laddha and Degaleesan, Transport Phenom- ena in Liquid Extraction (McGraw-Hill, 1978), Chap. 2.

Thermodynamic Models The thermodynamic theories and equations used to model phase equilibria are reviewed in Sec. 4, “Ther- modynamics.” These equations provide a framework for data that can help minimize the required number of experiments. An accurate liquid-liquid equilibrium (LLE) model is particularly useful for applications involving concentrated feeds where partition ratios and mutual solubility between phases are significant functions of solute concentration. Sometimes it is difficult to model LLE behavior across the entire composition range with a high degree of accuracy, depending upon the chemical system. In that case, it is best to focus on the composition range specific to the particular application at hand—to ensure the model accurately represents the data in that region of the phase diagram for accurate design calculations. Such a model can be a powerful tool for extractor design or when used with process simulation software to conceptualize, evaluate, and optimize process options. However, whether a complete LLE model is needed will depend upon the application. For dilute applications where partition ratios do not vary much with composition, it may be satisfactory to characterize equilibrium in terms of a simple Hand-type correlation or in terms of partition ratios measured over the range of anticipated feed and raffinate compositions and fit to an empirical equation. Also, when partition ratios are always very large, on the order of 100 or larger, as can occur when washing salts from an organic phase into water, a continuous extractor is likely to operate far from equilibrium. In this case, a precise equilibrium model may not be needed because the extraction factor always is very large and solute diffusion rates dominate performance. (See “Rate-Based Calculations” under “Process Fundamentals and Basic Calculation Methods.”)

LLE models for nonionic systems generally are developed by using either the NRTL or UNIQUAC correlation equations. These equations can be used to predict or correlate multicomponent mixtures using only binary parameters. The NRTL equations [Renon and Prausnitz, AIChE J., 14(1), pp. 135–144 (1968)] have the form

lnγi= + ∑

τij−

(15-25)

whereτijand Gij= exp(−αijτij) are model parameters. The UNIQUAC

equations [Abrams and Prausnitz, AIChE J., 21(1), pp. 116–128 (1975)] are somewhat more complex. (See Sec. 4, “Thermodynam- ics.”) Most commercial simulation software packages include these models and allow regression of data to determine model parameters. One should refer to the process simulator’s operating manual for specific details. Not all simulation software will use exactly the same equation format and parameter definitions, so parameters reported in the literature may not be appropriate for direct input to the program but need to be converted to the appropriate form. In theory, activity coefficient data from binary or ternary vapor-liquid equilibria can be used for calculating liquid-liquid equilibria. While this may provide a reasonable starting point, in practice at least some of the binary parameters will need to be determined from liquid-liquid tie line data to obtain an accurate model [Lafyatis et al., Ind. Eng. Chem. Res., 28(5), pp. 585–590 (1989)]. Detailed discussion of the applica- tion and use of NRTL and UNIQUAC is given by Walas [Phase Equi- libria in Chemical Engineering (Butterworth-Heinemann, 1985)]. The application of NRTL in the design of a liquid-liquid extraction process is discussed by van Grieken et al. [Ind. Eng. Chem. Res., 44(21), pp. 8106–8112 (2005)], by Venter and Nieuwoudt [Ind. Eng. Chem. Res., 37(10), pp. 4099–4106 (1998)], and by Coto et al. [Chem. Eng. Sci., 61, pp. 8028–8039 (2006)]. The use of the NRTL model also is discussed in Example 5 under “Single-Solvent Frac- tional Extraction with Extract Reflux” in “Calculation Procedures.” The application of UNIQUAC is discussed by Anderson and Praus- nitz [Ind. Eng. Chem. Process Des. Dev., 17(4), pp. 561–567 (1978)]. Although the NRTL or UNIQUAC equations generally are recommended for nonionic systems, a number of alternative approaches have been introduced. Some include explicit terms for association of

∑ kτ kjGkjxk _∑ k Gkjxk Gjixj _∑ kGkjxk ∑_jτjiGjixj _∑ jGjixj

molecules in solution, and these may have advantages depending upon the application. An example is the statistical associating fluid theory (SAFT) equation of state introduced by Chapman et al. [Ind. Eng. Chem. Res., 29(8), pp. 1709–1721 (1990)]. SAFT approximates molecules as chains of spheres and uses statistical mechanics to calcu- late the energy of the mixture [Müller and Gubbins, Ind. Eng. Chem. Res, 40(10), pp. 2193–2211 (2001)]. Yu and Chen discuss the applica- tion of SAFT to correlate data for 41 binary and 8 ternary liquid-liquid systems [Fluid Phase Equilibria, 94, pp. 149–165 (1994)]. Note that at present not all commercial simulation software packages include SAFT as an option; or if it is included, the association term may be left out. The SAFT equation often is used to correlate LLE data for poly- mer-solvent systems [Jog et al., Ind. Eng. Chem. Res., 41(5), pp. 887–891 (2002)]. In another approach, Asprion, Hasse, and Maurer [Fluid Phase Equil., 205, pp. 195–214 (2003)] discuss the addition of chemical theory association terms to the UNIQUAC model and other phase equilibrium models in general. With this approach, molecular association is treated as a reversible chemical reaction, and parameter values for the association terms may be determined from spectro- scopic data. Another activity coefficient correlation called COSMO- SPACE is presented as an alternative to UNIQUAC [Klamt, Krooshof, and Taylor, AIChE J., 48(10), pp. 2332–2349 (2002)].

Other methods are used to describe the behavior of ionic species (electrolytes). The activity coefficient of an ion in solution may be expressed in terms of modified Debye-Hückel theory. A common expression suitable for low concentrations has the form

logγi= + bzi2I (15-26)

where I is ionic strength, ziis the number of electronic charges, and a

and b are parameters that depend upon temperature. Ionic strength is defined in terms of the ion molal concentration. Equation (15-26) represents the activity coefficient for a single ion. For a compound MX that dissociates into M+and X−in solution, the mean ionic activity coefficient is given by γ±_{= (γ}+_γ−₎1/2_{. Activity coefficients for most elec-} trolytes dissolved in water are less than unity because of the strong attractive interaction between water and a charged species, but this can vary depending upon the organic character of the ion and its concentration. For more detailed discussions focusing on extraction, see Marcus, Chap. 2, and Grenthe and Wanner, Chap. 6, in Solvent Extraction Principles and Practice, 2d ed., Rydberg et al., eds. (Dekker, 2004). For general discussions, see Activity Coefficients in Electrolyte Solutions, 2d ed., Pitzer, ed. (CRC Press, 1991); Zemaitis et al., Handbook of Aqueous Electrolyte Thermodynamics (DIPPR, AIChE, 1986); and Robinson and Stokes, Electrolyte Solutions (But- terworths, 1959). The concepts of molecular association have been applied to modeling electrolyte solutions with good success [Stokes and Robinson, J. Soln. Chem. 2, p. 173 (1973)].

Modeling phase equilibria for mixed-solvent electrolyte systems including nonionic organic compounds is discussed by Polka, Li, and Gmehling [Fluid Phase Equil., 94, pp. 115–127 (1994)]; Li, Lin, and Gmehling [Ind. Eng. Chem. Res., 44(5), pp. 1602–1609 (2005)]; and Wang et al. [Fluid Phase Equil., 222–223, pp. 11–17 (2004)]. Another computer program is discussed by Baes et al. [Sep. Sci. Tech- nol., 25, p. 1675 (1990)]. Ahlem, Abdeslam-Hassen, and Mossaab [Chem. Eng. Technol., 24(12), pp. 1273–1280 (2001)] discuss two approaches to modeling metal ion extraction for purification of phosphoric acid.

Data Quality Normally, it is not possible to evaluate LLE data for thermodynamic consistency [Sorenson and Arlt, Liquid-Liquid Equilib- rium Data Collection, Binary Systems, vol. V, pt. 1 (DECHEMA, 1979), p. 12]. The thermodynamic consistency test for VLE data involves calculating an independently measured variable from the others (usually the vapor composition from the temperature, pressure, and liquid composition) and comparing the measurement with the calculated value. Since LLE data are only very weakly affected by change in pressure, this method is not fea- sible for LLE. However, if the data were produced by equilibration and analysis of both phases, then at least the data can be checked to determine how well the material balance closes. This can be done by plotting the total

−azi2I1/2

1+ I1/2

TABLE 15-1 Selected Partition Ratio Data

Partition ratios are listed in units of weight percent solute in the extract divided by weight percent solute in the raffinate, generally for the lowest solute concentrations given in the cited reference. The partition ratio tends to be greatest at low solute concentrations. Consult the original references for more information about a specific system.

Solute Feed solvent Extraction solvent Temp. (°C) K (wt % basis) Reference

Ethanol Cyclohexane Ethanolamine 25 2.79 1

Acetone Ethylene glycol Amyl acetate 31 1.84 2

Acetone Ethylene glycol Ethyl acetate 31 1.85 2

Acetone Ethylene glycol Butyl acetate 31 1.94 2

Trilinolein Furfural Heptane 30 47.5 3

o-Xylene Heptane Tetraethylene glycol 20 0.15 4

o-Xylene Heptane Tetraethylene glycol 30 0.15 4

o-Xylene Heptane Tetraethylene glycol 40 0.16 4

Toluene Heptane Sulfolane 25 0.34 5

Toluene Heptane Sulfolane 50 0.36 5

Toluene Heptane Sulfolane 75 0.31 5

Toluene Heptane Sulfolane 100 0.33 5

Toluene Hexane Sulfolane 25 0.34 6

Xylene Hexane Sulfolane 25 0.30 6

Toluene n-Hexane Sulfolane 25 0.34 6

Xylene n-Hexane Sulfolane 25 0.30 6

Toluene n-Octane Sulfolane 25 0.35 6

Xylene n-Octane Sulfolane 25 0.25 6

Toluene Octane Sulfolane 25 0.35 6

Xylene Octane Sulfolane 25 0.25 6

1,2-Dimethoxyethane Water Dodecane 25 0.46 7

1,4-Dioxane Water Ethyl acetate 30 1.29 8

1-Butanol Water Benzonitrile 25 3.01 9

1-Butanol Water Ethyl acetate 40 5.48 10

1-Butanol Water Methyl t-butyl ether 25 7.95 11

1-Heptene Water 1-Propanol 25 3.95 12

1-Octanol Water Methyl t-butyl ether 25 10.9 13

1-Propanol Water 1-Heptene 25 1.36 12

1-Propanol Water Butyraldehyde 25 4.14 14

1-Propanol Water Cyclohexane 25 0.34 15

1-Propanol Water Di-isobutyl ketone 25 0.93 14

1-Propanol Water Methyl tert-butyl ether 25 3.79 11

2,3-Butanediol Water 2,4-Dimethylphenol 40 1.89 16

2,3-Butanediol Water 2-Butoxyethanol 70 1.79 17

2,3-Dichloropropene Water Epichlorohydrin 20 181 18

2,3-Dichloropropene Water Epichlorohydrin 77 69.5 18

2-Butoxyethanol Water Decane 22 0.45 19

2-Methoxyethanol Water Cyclohexanone 70 0.54 20

2-Methyl-1-propanol Water Benzene 25 1.18 21

2-Methyl-1-propanol Water Toluene 25 0.88 21

2-Propanol Water 1-Methylcyclohexanol 20 3.66 22

2-Propanol Water 2,2,4-Trimethylpentane 20 0.045 23

2-Propanol Water Carbon tetrachloride 20 1.41 24

2-Propanol Water Dichloromethane 20 3.56 22

2-Propanol Water Di-isopropyl ether 25 0.41 25

2-Propanol Water Di-isopropyl ether 25 0.98 26

3-Cyanopyridine Water Benzene 30 1.55 27

Acetaldehyde Water Furfural 16 0.97 28

Acetaldehyde Water 1-Pentanol 18 1.43 28

Acetic acid Water 1-Butanol 27 1.61 29

Acetic acid Water 1-Hexene 25 0.0073 30

Acetic acid Water 1-Octanol 20 0.56 31

Acetic acid Water 20 vol % Trioctylamine + 20 vol % 20 0.61 32

1-Decanol + 60 vol % dodecane

Acetic acid Water 2-Butanone 25 1.20 33

Acetic acid Water 2-Ethyl-1-hexanol 20 0.58 34

Acetic acid Water 2-Pentanol 25 1.35 35

Acetic acid Water 2-Pentanone 25 1.00 30

Acetic acid Water 4-Heptanone 25 0.30 30

Acetic acid Water 70 vol % Tributylphosphate + 20 0.31 36

30 vol % dodecane

Acetic acid Water Cyclohexanol 27 1.33 29

Acetic acid Water Diethyl phthalate 20 0.22 37

Acetic acid Water Di-isopropyl carbinol 25 0.80 38

Acetic acid Water Dimethyl phthalate 20 0.34 37

Acetic acid Water Di-n-butyl ketone 25 0.38 39

Acetic acid Water Ethyl acetate 30 0.91 40

Acetic acid Water Isopropyl ether 20 0.25 41

Acetic acid Water Methyl cyclohexanone 25 0.93 38

Acetic acid Water Methylisobutyl ketone 25 0.66 42

Acetic acid Water Methylisobutyl ketone 25 0.76 38

Acetic acid Water Toluene 25 0.06 43

Acetone Water 1-Octanol 25 0.81 44

TABLE 15-1 Selected Partition Ratio Data (Continued)

Solute Feed solvent Extraction solvent Temp. (°C) K (wt % basis) Reference

Acetone Water 1-Pentanol 30 1.14 44

Acetone Water 2-Octanol 30 0.66 44

Acetone Water Chloroform 25 1.83 45

Acetone Water Chloroform 25 1.72 46

Acetone Water Dibutyl ether 25 1.94 38

Acetone Water Diethyl ether 30 1.00 47

Acetone Water Ethyl acetate 30 1.50 48

Acetone Water Ethyl butyrate 30 1.28 48

Acetone Water Methyl acetate 30 1.15 48

Acetone Water Methylisobutyl ketone 25 1.91 38

Acetone Water Hexane 25 0.34 49

Acetone Water Toluene 25 0.84 38

Acrylic acid Water 89.6 wt % Kerosene/10.4 wt % 25 6.50 50

trialkylphosphine oxide (C7–C9)

Aniline Water Methylcyclohexane 25 2.05 51

Aniline Water Methylcyclohexane 50 3.41 51

Aniline Water Heptane 25 1.43 51

Aniline Water Heptane 50 2.20 51

Aniline Water Toluene 25 12.9 52

Benzoic acid Water 87.4 wt % Kerosene/ 25 36.0 53

12.6 wt % tributylphosphate

Benzoic acid Water 89.6 wt % Kerosene/10.4 wt % 25 1.30 50

trialkylphosphine oxide (C7–C9)

Butyric acid Water 20 vol % Trioctylamine + 20 vol % 20 6.16 36

1-decanol + 60 vol % dodecane

Butyric acid Water 70 vol % Tributylphosphate + 20 2.51 36

30 vol % dodecane

Butyric acid Water Methyl butyrate 30 6.75 54

Citric acid Water 25 wt % Tri-isooctylamine + 25 14.1 55

75 wt % Chloroform

Citric acid Water 26 wt % Tri-isooctylamine + 25 41.5 55

75 wt % 1-Octanol

Epichlorohydrin Water 2,3-Dichloropropene 20 11.4 56

Epichlorohydrin Water 2,3-Dichloropropene 77 13.4 56

Ethanol Water 1-Octanol 25 0.66 57

Ethanol Water 1-Octene 25 0.036 58

Ethanol Water 2,2,4-Trimethylpentane 5 0.027 59

Ethanol Water 2,2,4-Trimethylpentane 40 0.041 59

Ethanol Water 3-Heptanol 25 0.78 60

Ethanol Water 1-Butanol 20 3.00 61

Ethanol Water Di-n-propyl ketone 25 0.59 38

Ethanol Water 1-Hexanol 28 1.00 62

Ethanol Water 2-Octanol 28 0.83 62

Ethyl acetate Water 1-Butanol 40 11.1 10

Ethylene glycol Water Furfural 25 0.32 64

Formic acid Water 20 vol % Trioctylamine + 20 vol % 20 1.77 36

1-decanol + 60 vol % dodecane

Formic acid Water 70 vol % Tributylphosphate + 20 0.37 36

30 vol % dodecane

Formic acid Water Methyisobutyl carbinol 30 1.22 65

Furfural Water Toluene 25 5.64 66

Glycolic acid Water 89.6 wt % Kerosene/10.4 wt % 25 0.29 67

trialkylphosphine oxide (C7–C9)

Glyoxylic acid Water 89.6 wt % Kerosene/10.4 wt % 25 0.067 67

trialkylphosphine oxide (C7–C9)

Lactic acid Water 20 vol % Trioctylamine + 20 vol % 20 0.65 36

1-decanol + 60 vol % dodecane

Lactic acid Water 25 wt % Tri-isooctylamine + 25 19.2 55

75 wt % chloroform

Lactic acid Water 26 wt % Tri-isooctylamine + 25 25.9 55

75 wt % 1-octanol

Lactic acid Water 70 vol % Tributylphosphate + 20 0.14 36

30 vol % dodecane

Lactic acid Water iso-Amyl alcohol 25 0.35 68

Malic acid Water 25 wt % Tri-isooctylamine + 25 30.7 55

75 wt % chloroform

Malic acid Water 25 wt % Tri-isooctylamine + 25 59.0 55

75 wt % 1-octanol

Methanol Water 1-Octanol 25 0.28 57

Methanol Water Ethyl acetate 0 0.059 69

Methanol Water Ethyl acetate 20 0.24 69

Methanol Water 1-Butanol 0 0.60 70

Methanol Water 1-Hexanol 28 0.57 71

TABLE 15-1 Selected Partition Ratio Data (Concluded)

Solute Feed solvent Extraction solvent Temp. (°C) K (wt % basis) Reference

Methanol Water Phenol 25 1.33 72

Methyl t-butyl ether Water 1-Octanol 25 2.61 13

Methyl t-amyl ether Water 2,2,4-Trimethylpentane 25 131 73

Methylethyl ketone Water 1,1,2-Trichloroethane 25 3.44 74

Methylethyl ketone Water Hexane 25 1.78 75

1-Propanol Water Ethyl acetate 20 1.54 69

1-Propanol Water Heptane 38 0.54 76

p-Cresol Water Methylnaphthalene 35 9.89 72

Phenol Water Ethyl acetate 25 0.048 77

Phenol Water Isoamyl acetate 25 0.046 77

Phenol Water Isopropyl acetate 25 0.040 77

Phenol Water Methyl isobutyl ketone 30 39.8 78

Phenol Water Methylnaphthalene 25 7.06 79

Phosphoric acid Water 4-Methyl-2-pentanone 25 0.0012 80

Propionic acid Water 20 vol % Trioctylamine + 20 vol % 20 2.13 36

1-decanol+ 60 vol % dodecane

Propionic acid Water 70 vol % Tributylphosphate + 20 1.02 36

30 vol % dodecane

Propionic acid Water Ethyl acetate 30 2.77 81

Propionic acid Water Toluene 31 0.52 82

Pyridine Water Chlorobenzene 25 2.10 83

Pyridine Water Toluene 25 1.90 84

Pyridine Water Xylene 25 1.26 84

t-Butanol Water Ethyl acetate 20 1.74 69

Tetrahydrofuran Water 1-Octanol 20 3.31 85

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feed composition used in the experiments along with the measured tie line compositions on a ternary diagram. The feed composition should lie on the tie line. For very low solute concentrations, this plot may be unrevealing. Alternatively, a plot of Y″i/Z″iversus X″i/Z″i(where Y″i is the

mass fraction of component i in the extract phase, X″iis the mass frac-

tion of component i in the raffinate phase, and Z″iis the mass fraction

of component i in the total feed) should give a straight line that passes through the point (1, 1). The tie line data also may be checked for consistency by plotting the data in the form of a Hand plot or Othmer- Tobias plot, as described in “Tie Line Correlations,” and looking for outliers. Another approach is to plot the partition ratio as a function of solute concentration and look for data points that deviate significantly from otherwise smooth trends. If the NRTL equation is used, refit all the binary data sets by using the same value for model parameter α. A value of 0.3 is recommended by Walas [Phase Equilibria in Chemical

In document Perry Hambook (Page 30-35)

DATA CORRELATION EQUATIONS

Mol Fraction

DATA CORRELATION EQUATIONS

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