Solid-liquid equilibrium phase diagrams for salt solutions

Kaj Thomsen Associate Professor, Department of Chemical and Biochemical Engineering, Technical University of

Denmark kth@kt.dtu.dk

Phase diagrams

• Phase Diagrams

– Solid-liquid equilibrium

– Vapor-liquid

– Liquid-liquid

• Focus on solid-liquid equilibrium phase diagrams

Calculated and experimental phase diagram

• If a good model is available, the phase diagram can be calculated at any temperature

• By comparing experimental and calculated phase diagrams, you can get an idea about how good the model is.

• Phase diagrams are good as visible tools to understand what is going on in a process – Operating lines for fractional crystallization

processes can be marked in phase diagrams

Prediction of phase diagram

• Not possible yet to predict what solid phases might form

• The types of solid phases are determined experimentally

• The standard state properties of solid phases can be determined from experimental phase equilibrium data

Phase Rule

• F = Number of degrees of freedom

• C = Number of independent components

• P = Number of phases

• Intensive variables of a system:

– Temperature,

– Pressure,

– C-1 mole fractions for each phase

• 2 + (C-1)*P intensive variables

Phase Rule

• Equilibrium equation for each component describing its distribution between two phases

• If two phases are present C equations can be written relating the concentrations in the two phases

• If P phases: C*(P - 1) equations

• F = 2 + (C-1)*P - C*(P-1) degrees of freedom

• F = 2 + CP – P – CP + C = C – P + 2

One component system: water

• One phase: F = 1 – 1 + 2 = 2 : T and P can be varied and the same phase continue to exist

• Two phases: F = 1 – 2 + 2 = 1: T or P can be varied and there is still equilibrium between the two phases

• Three phases: F = 1 – 3 + 2 = 0: T and P can not be chosen – Triple point, invariant point

Binary systems

• F = 2 – P + 2 : There can be up to 4 phases in equilibrium with each other in a binary system

• Solid – liquid equilibrium can be determined by thermal analysis:

– Known amounts of salt and water are mixed, the solution is cooled. At a certain temperature the cooling stops because crystallization starts

– Does not require that you visually observe that all solid is dissolved

-60

-40

-20

0

20

40

60

80

100

0 10 20 30 40 50 60 70 80

Mass % CaCl2

Te

mp

era

ture

°C

Extended UNIQUACExperimentalSeries3

Ice

Ca

Cl2∙6

H2O

Ca

Cl2∙4

H2O

Ca

Cl2∙2

H2O

A

B

C

Binary diagram

• Eutectic point = invariant point

• Peritectic points

-40

-20

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60 70 80 90 100

Mass % MgSO4

Te

mp

era

ture

, °C

Extended UNIQUACExperimental

Mg

SO

4·6

H2O

Mg

SO

4·H

2O

Mg

SO

4·7

H2O

Mg

SO

4·1

2H

2O

Ice

Ternary phase diagrams

• F = 3 – P + 2 = 5 – P: up to 5 phases in equilibrium with each other

– 3 solid phases

– 1 liquid phase

– 1 vapor phase in invariant point

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-10 0 10 20 30 40 50 60 70 80 90 100 110

sa

lt f

racti

on

Calculated

Experimental

Temperature, °C

Mg

SO

4N

a2S

O4

3Na2SO4·MgSO4

Vanthoffite

Na2SO4·MgSO4·2.5H2O

Löweite

Na2SO4

Thenardite

Na2SO4·10H2O

Glauber salt

MgSO4·12H2O

MgSO4·7H2O

Epsom salt

MgSO4·6H2O

Hexahydrite

MgSO4·H2O

Kieserite

Na2SO4·MgSO4·4H2O

Bloedite

Ice

A

B

C

D

E

100

90

80

70

60

50

40

30

20

10

0

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100MgSO4

Na2SO4

H2O

T= 85.0°C

MgSO4·H2O

Kieserite

Na2SO4·MgSO4·2.5H2O

Löweite

3Na2SO4·MgSO4, Vanthoffite

AB

CD E

Salting out of NaCl by CaCl2

Salting out of NaCl by CaCl2

Schreinemakers method

Quaternary systems

• Systems with two anions and two cations

• Systems with three anions and one cation

• Systems with one anion and three cations

Jänecke coordinates

• For systems with 2 cations and 2 anions

• Equivalent fractions or charge fractions

• One axis for the two cations (0 – 1)

• One axis for anions (0 -1)

• Water content can be displayed

– By three dimensional plot

– By contour lines

– By marking the water content in the diagram

2.703.133.383.633.924.194.444.825.846.755.50

4.55 4.29 4.07 3.85 3.61 3.36 3.07 2.85 2.46 2.16 1.82

2.232.57

10.30

24.30 22.30 20.32 18.36 16.38 14.36 12.26 10.05 7.67 7.67 5.86

6.085.645.476.698.7610.6912.5414.3216.0817.8319.60

21.39 18.54 16.96 15.41 13.87 12.33 10.77 9.18 7.52 5.74 5.04

5.154.614.575.296.677.929.1210.4211.7413.0714.42

15.79 14.13 13.01 11.91 10.83 9.74 8.64 7.50 6.30 4.99 4.03

4.013.323.424.515.706.797.838.849.8310.8311.84

12.87 11.22 9.41 8.53 7.65 6.77 5.86 4.91 3.87 2.70

2.501.482.073.103.964.755.516.256.997.738.48

9.26 7.06 6.43 5.83 5.24 4.65 4.07 3.47 2.85

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

SO42-

Anion charge fraction NO3-

Moles of water per mole of ions given at grid intersections

K+

Ca

tio

n c

ha

rge

fra

ctio

n

Na

+

K2SO4

NaK3(SO4)2

Na2SO4 Na2SO4•10H2O NaNO3•Na2SO4•H2O

NaNO3

KNO3

Three anions, one cation 0

10

20

30

40

50

60

70

80

90

100

100

90

80

70

60

50

40

30

20

10

0

73.3

71.771.8

69.970.071.0

67.867.969.872.4

65.465.568.571.172.9

62.662.767.169.871.672.9

59.360.265.568.370.271.572.6

55.158.463.966.768.670.071.171.9

49.656.662.165.066.968.369.470.371.0

48.654.760.363.265.166.567.668.569.269.9

47.352.858.361.263.164.565.566.467.167.868.3

0 10 20 30 40 50 60 70 80 90 100

NaNO3

Na2SO4

NaCl

T= 50.0°C Mass percent water given at

grid intersections

Na2SO4

NaCl

NaNO3

NaNO3·Na2SO4·H2O

0

10

20

30

40

50

60

70

80

90

100

100

90

80

70

60

50

40

30

20

10

0

70.2

67.968.4

65.265.866.2

66.762.763.366.2

70.665.264.966.468.2

73.269.165.768.768.869.2

74.871.667.369.370.870.269.4

75.673.069.671.271.671.970.969.3

76.873.670.473.174.273.972.170.872.0

79.076.373.074.676.076.375.773.671.674.3

80.878.575.875.877.478.178.077.174.974.076.2

0 10 20 30 40 50 60 70 80 90 100

K2SO4

Li2SO4

Na2SO4

T= 100.0°C Mass percent water given at

grid intersections

NaK3(SO4)2

K2SO4Li2SO4·K2SO4Li2SO4

Na2SO4·Li2SO4 2Li2SO4·Na2SO4·K2SO4

Na2SO4

One anion, three cations

Quinary systems

• Phase diagrams for systems with 5 ions

• Can be shown as surfaces saturated with two salts

– Relevant for describing salt deposits with large NaCl content

– Can be used for separating the quinary system into ternary systems

Quinary system,

all points sat. with

NaCl

61.78 67.07 67.55 70.45 70.47 70.27 70.04 69.99 70.25 70.37 70.44

70.1370.0269.8469.5069.1469.2769.3168.9766.1266.0765.35

66.41 65.58 65.62 67.27 67.98 68.13 68.11 69.03 69.44 69.67 69.83

69.5269.3369.0468.5767.5566.8066.4365.8865.1065.7667.02

67.03 65.86 66.13 66.54 66.52 66.35 67.08 68.12 68.65 68.99 69.22

68.9368.6668.2767.6966.6066.6666.7766.7566.3965.7766.85

66.62 65.63 66.43 66.80 66.87 66.81 66.68 67.26 67.90 68.33 68.64

68.3568.0067.5366.8466.8066.8866.9066.7866.3765.4866.39

66.18 65.33 66.27 66.73 66.88 66.91 66.86 66.78 67.17 67.68 68.06

67.7867.3766.8166.8366.8966.9066.8466.6566.1565.2065.98

65.81 65.08 66.02 66.56 66.79 66.88 66.90 66.87 66.81 67.05 67.50

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Mg

++

Ca

tio

n C

ha

rge

fra

ctio

n

K+

Cl- Anion Charge fraction SO4--

T= 55.0°C

NaCl + Na2SO4

NaCl + KCl

NaCl + NaK3(SO4)2

NaCl + K2SO4·MgSO4·4H2O

NaCl + KCl·MgSO4·3H2O

NaCl + KCl·MgCl2·H2O

NaC

l + M

gSO

4·6

H2O

Mass % water given at grid intersections

Quinary system

all points sat. with

NaCl

1.17 3.41 5.02 12.72 16.04 18.08 19.52 20.95 22.46 23.41 24.08

24.223.5622.6721.2819.3717.8815.7812.395.764.332.97

5.13 5.78 7.46 11.93 15.45 17.62 19.16 21.58 22.87 23.71 24.32

24.4423.8623.0621.8619.6617.2714.9912.29.158.097.82

10.19 10.5 12.79 15.24 16.89 18.14 20.18 22.13 23.25 24.01 24.56

24.6824.1523.4322.3820.6319.6618.6117.2215.1612.5612.23

13.97 14.31 16.86 18.63 19.83 20.73 21.47 22.62 23.6 24.29 24.8

24.9124.4223.7722.8522.221.5520.7519.718.1415.7815.45

16.71 17.04 19.15 20.54 21.48 22.19 22.77 23.26 23.94 24.56 25.02

25.1324.6924.123.6823.2422.7122.0721.2219.9818.1117.79

18.72 19.04 20.67 21.8 22.57 23.15 23.63 24.04 24.39 24.82 25.24

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Mg

++

Ca

tio

n C

ha

rge

fra

ctio

n

K+

Cl- Anion Charge fraction SO4--

T= 55.0°C

Mass % NaCl given at grid intersections

NaCl + Na2SO4

NaCl + KCl

NaCl + NaK3(SO4)2

NaCl + K2SO4·MgSO4·4H2O

NaCl + KCl·MgSO4·3H2O

NaC

l + K

Cl·

Mg

Cl 2

·6H

2O

NaCl + MgSO4·H2O

Multicomponent systems

• Increasing complexity of phase diagrams with increasing number of components

• Phase diagrams can give a visual understanding of the process

• With an accurate thermodynamic model, separation processes can be optimized

– Input: composition and temperature of stream

– Output: composition of solid and liquid phase