Ternary phase diagrams

The carbon dioxide – ammonia – water system

The phase behavior and the thermal properties of this system is important because of its potential use for removing carbon dioxide from flue gas in post combustion carbon capture processes.
One such process is the chilled ammonia process (Eli Gal, Ultra cleaning combustion gas including the removal of CO2, United States Patent US7641717B2.

In the chilled ammonia process, a slurry consisting of a liquid in equilibrium with solid ammonium bicarbonate (NH4HCO3) is produced in an absorber. The slurry releases CO2 at a relatively high pressure after being heated in a desorber. The liquid is cooled and led back to the absorber for a new cycle.

Speciation

The CO2 – NH3 – H2O system was modeled with the Extended UNIQUAC model. (Thomsen K and Rasmussen P, “Modeling of Vapor-liquid-solid equilibrium in gas-aqueous electrolyte systems”, Chemical Engineering Science, 54(1999)1787-1802. An upgraded version of this model valid to higher temperatures and more accurate was published by Victor Darde, Willy J.M. van Well, Erling H. Stenby, Kaj Thomsen, “Modeling of carbon dioxide absorption by aqueous ammonia solutions using the Extended UNIQUAC model”, Ind. Eng. Chem. Res., 49(2010), pp 12663–12674 (24), https://doi.org/10.1021/ie1009519.

The figures show the experimentally measured and the calculated speciation in a 6.226 molal NH3 solution at 40°C. The amount of carbamate formed is indicated in the figure to the left with red triangles (experimental) and a red line (calculated with the Extended UNIQUAC model).

The amounts of NH3, NH4+, and NH2COO are shown in the figure to the left, the amounts of CO2, CO32-, and HCO3 in the same solution are shown to the right. The experimental data were measured by Ute Lichtfers and published in her PhD Dissertation, University of Kaiserslautern, Germany, 2000. The lines were calculated with the Extended UNIQUAC model. There is a good agreement between the experimental data and the corresponding calculated values. It is seen that the amount of carbamate apparently goes through a maximum at approximately 3 mol CO2 per kg water. This maximum occurs at a pH about 9 and at a loading of 0.5 mol CO2 per mol NH3.

Vapor-liquid equilibrium

The figures below show vapor-liquid equilibrium in the CO2-NH3-H2O system at 20°C. Calculated and experimental partial pressure of ammonia shown to the left. Calculated and experimental partial pressure of carbon dioxide shown to the right. The experimental data are from

Precise vapor-liquid equilibrium calculations are important for designing processes such as carbon capture processes using ammonia. The Extended UNIQUAC model was fitted to experimental data in the temperature range from 0 to 110°C and is able to reproduce data with high accuracy in this temperature range and at pressures up to 100 bar. At temperatures above 110°C the accuracy is decreasing.

Sample calculations performed with the Extended UNIQUAC model are shown below. The calculated data are compared with experimental values in order to document the quality of the fit. Partial pressures of NH3 are shown in the figures to the left, partial pressures of CO2 are shown in the figures to the right. The calculations were performed for solutions containing a fixed amount of ammonia while different amounts of carbon dioxide were added. Each ammonia concentration is represented by a branch in the diagram.

It is seen that the partial pressure of ammonia is decreasing by the addition of CO2 while the CO2 partial pressure is increasing. At a loading of approximately 1 mol of CO2 per mole NH3, the partial pressure of CO2 is seen to increase rapidly. This is because ammonia and carbon dioxide react one to one. When the available ammonia is neutralized by carbon dioxide, the vapor pressure of carbon dioxide goes up because the solubility of CO2 in solutions with low pH is not very high.

The figures above show vapor-liquid equilibrium in the CO2-NH3-H2O system at 80°C. Calculated and experimental partial pressure of ammonia shown to the left. Calculated and experimental partial pressure of carbon dioxide shown to the right. The experimental data are from:

Vapor-liquid equilibrium

In the original concept of the chilled ammonia process, solid NH4HCO3 is formed in the absorber. It is therefore important to be able to calculate solid-liquid equilibrium in the system accurately.
The available experimental data for solid-liquid equilibrium in the system are scarce and they are inconsistent. The researchers who reported on solid liquid equilibrium in the system do not agree on what solid phases are formed in the system.

It was found that the experimental data reported by Jänecke, seemed to be most reliable and were given highest weight when determining parameters in the model.

The experimental data plotted in the solid-liquid phase diagram are from:

 

These solids will precipitate from a chilled ammonia solution of sufficient ammonia concentration when carbon dioxide is added (the solution is loaded with carbon dioxide).
Due to constraints caused by Gibbs Phase rule, the two partial pressures remain constant while two solid phases are present simultaneously. In a three component system with four phases, there is only one degree of freedom (see invariant points). If the composition of the gas phase or of the liquid phase is changed, the pressure will change. If the total pressure and the temperature are kept constant, the composition of the gas or of the liquid therefore can not change.

The overall reaction taking place as CO2 is added to the system is: CO2(g) + (NH4)2CO3·H2O(s) ↔ 2NH4HCO3(s).

This is shown in the figure below for a temperature of 10°C, a total pressure of 1 bar and a 27 wt% ammonia in water solution. In the rightmost figure below, the partial pressures of carbon dioxide and ammonia as function of CO2 loading are shown. At low loadings, ammonium carbonate monohydrate is precipitating. The partial pressure of ammonium is decreasing as carbon dioxide is added, and that of carbon dioxide is slightly increasing. As the loading increases, pH of the solution decreases and at a loading slightly above 0.5, ammonium bicarbonate becomes superaturated and starts precipitating. The number of solid phases is therefore two and the total number of phases is four. The system has only one degree of freedom. When carbon dioxide is added, the amount of solid ammonium carbonate is increasing and the amount of solid ammonium carbonate monohydrate is decreasing. At a loading of 0.78, the last ammonium carbonate monohydrate has disappeared. The system now has only one solid phase, one liquid phase and a gas phase. Two degrees of freedom are available and the vapor pressure increases upon further loading with carbon dioxide.

The graph to the left below shows the amounts of solids precipitating from a solution consisting of approximately one kilo water. The precipitated amount of ammonium carbonate monohydrate reaches a maximum at a loading of 0.51. At a loading of 0.78 mol CO2/mol NH3, the last ammonium carbonate monohydrate has disappeared.

The kinetics of this solid-solid transition has not been described in the literature and it is not known if the CO2 absorption or the solid-solid transition is the rate limiting step for the absorption process.

The rightmost figure below shows the partial pressures of carbon dioxide and ammonia during loading of a 27 wt% ammonia solution with carbon dioxide. The figure to the left shows the corresponding amounts of the two solids present in this loading range. These amounts are based on a solution with approximately 1 kg water. The graphs were calculated for 10°C and for a 27 wt% ammonia in water solution. The same scenario is valid in a wide temperature range. When the loaded slurry is heated to 50°C all ammonium bicarbonate seems to dissolve in the solution.

The graphs were calculated using the Extended UNIQUAC model implemented in a DLL fille that is called from Microsoft Excel®. Vapor-liquid-solid equlibrium flash calculations are performed by calling the DLL file through the Visual Basic interface.

The sodium nitrate – sodium sulfate – water system

The figure to the right shows a ternary phase diagram for the NaNO3-Na2SO4-H2O system in the temperature range from -20 to 110°C. The equilibrium compositions were calculated using the Extended UNIQUAC model. Experimental points from several different investigators are marked in the same diagram in order to illustrate the quality of the fit. All points in the diagram represent saturated solutions. The lines in the diagram represent compositions, at which two salts are in equilibrium with the same liquid (and with a gas phase). The intersection between lines are compositions at which three solid salts are in equilibrium with the same liquid (and with a gas phase). These points are invariant points.

The solid phases encountered in this system in the temperature range from -20 to 110°C are:

  • Ice
  • Na2SO4•10H2O (Glauber’s salt)
  • Na2SO4  (Sodium sulfate)
  • NaNO3•Na2SO4•H2O (Darapskite)
  • NaNO3 (Sodium nitrate)
Phase diagram for the sodium nitrate - sodium sulfate water system
Phase diagram for the sodium nitrate – sodium sulfate water system

The vertical blue line marks the eutectic temperature i.e. the lowest temperature at which an aqueous solution can be in equilibrium with ice and salts in this ternary system. At temperatures lower than the eutectic, an equilibrium mixture of water and the two salts will consist of the three separate phases: Na2SO4•10H2O (Glauber’s salt), NaNO3, and Ice.

The ordinate in the diagram above is “Salt fraction”: mol Na2SO4 divided by (mol Na2SO4 + mol NaNO3). The points in the diagram therefore mark compositions on a dry basis. The corresponding water content is not indicated. It could be marked as a third dimension. Alternatively solubility isotherms can be calculated. The temperature is held constant, and all concentrations can be shown in two dimensions.

The 30°C isotherm is marked in the diagram with a vertical brown line with the letters A, B, C, D, and E corresponding to the same points in the solubility isotherm below.

Experimental data from different sources are marked in the diagram. The experimental data come from the following sources:

  • Cornec, E. and Krombach, H., Contribution a l’etude des équilibres entre l’eau, les nitrates, les chlorures et les sulfates de sodium et de potassium, Annales de Chimie, 12(1929)203-295,
  • Chrétien, A., Étude du systéme quaternaire eau, nitrate de sodium, chlorure de sodium, Annales de Chemie, 12(1929)9-155
  • Benrath A., Über das reziproke salzpaar MgSO4-Na2(NO3)2-H2O. I, Z. Anorg. Chem., 170(1928)257-287, https://doi.org/10.1002/zaac.19281700135;
  • Hamid, M. A., Heterogeneous equilibria between the sulphates and nitrates of sodium and potassium and their aqueous solutions. Part II. The quaternary system H2O-Na2SO4-NaNO3-K2SO4-KNO3, J. Chem. Soc., (1926)206-214, https://doi.org/10.1039/JR9262900199.
  • Massink A., Doppelsalzbildung zwischen Nitraten und Sulfaten in wässerigen Lösung, Z. physikalische Chemie, 92(1918)351-380, https://doi.org/10.1515/zpch-1918-9222

Solubility isotherm at 30°C

The 30°C solubility isotherm is shown in the figure below. The solubility isotherm calculated with the Extended UNIQUAC model is shown together with experimental data. The solubility isotherm is marked with the letters A, B, C, D, E, corresponding to the points marked with the same letters in the figure above. The concentration unit in the diagram to the left is weight percent. The green lines in the diagram are tie lines, marking the borders of fields yielding a certain solid salt. Experimental data from two of the sources mentioned above are shown in the figure.

  • The solubility line from A to B mark solutions in equilibrium with glauber’s salt. A mixture with a gross composition in the field marked I, will at equilibrium yield solid glauber’s salt and a saturated liquid with a composition corresponding to a point on the line AB.
  • The solubility line from B to C mark solutions in equilibrium with anhydrous sodium sulfate. A mixture with a gross composition in the field marked II, will at equilibrium yield solid anhydrous sodium sulfate and a saturated liquid corresponding to a point on the line BC
  • Points on the line CD correspond to the composition of saturated solutions in equilbrium with darapskite
  • Points on the line DE mark the composition of saturated solutions in equilibrium with sodium nitrate
  • A solution with a gross composition in the field marked V will at equilibrium yield a saturated liquid of composition B and the two solid phases: glauber’s salt and anhydrous sodium sulfate.
  • A solution with a gross composition in the field marked VI will at equilibrium yield a saturated liquid of composition C and the two solid phases: anhydrous sodium sulfate and darapskite.
  • A solution with a gross composition in the field marked VII will at equilibrium yield a saturated liquid of composition D and the two solid phases: darapskite and sodium nitrate.
Sodium sulfate - sodium nitrate - water phase diagram at 30 °C
Sodium sulfate – sodium nitrate – water phase diagram at 30 °C

Calculation of phase diagrams

The phase diagrams shown on this page can be calculated with extended versions of the software developed by Aqueous Solutions ApS.

The sodium sulfate – magnesium sulfate – water system

In the ternary system consisting of sodium sulfate and magnesium sulfate, the following solid phases appear in the temperature range from -10 to 110°C:

  • Ice
  • Na2SO4·10H2O, glauber’s salt
  • Na2SO4, thenardite
  • MgSO4·12H2O, magnesium sulfate dodecahydrate
  • MgSO4·7H2O, epsom salt
  • MgSO4·6H2O, hexahydrite
  • MgSO4·H2O, kieserite
  • Na2SO4·MgSO4·4H2O, bloedite
  • Na2SO4·MgSO4·2.5H2O, löweite
  • 3Na2SO4·MgSO4, vanthoffite

The temperatures and concentration ranges at which these solids appear are shown in the figure below to the left. All fields in the figure represent saturated solutions. The equilibrium lines and the experimental data in the diagram represent compositions and temperatures at which two solid phases are in equilibrium with the same solution. The water content of the solutions are not shown. It can be thought of as a third dimension in the diagram

The 85°C isotherm of this system is shown below to the right. Because the temperature is fixed, the composition of all three components of this ternary system can be displayed in a two-dimensional diagram. The green lines in the figure below are tie lines indicating phases and compositions in equilibrium with each other.

Phase diagram for the sodium sulfate - magnesium sulfate - water system over a temperature range
Phase diagram for the sodium sulfate – magnesium sulfate – water system over a temperature range
85 °C solubility isotherm in the sodium sulfate - magnesium sulfate - water system
85 °C solubility isotherm in the sodium sulfate – magnesium sulfate – water system

The magnesium sulfate – potassium sulfate – water system

The figure to the right shows a phase diagram for the MgSO4-K2SO4-H2O system in the temperature range from -10 to 120°C. The equilibrium compositions were calculated using the Extended UNIQUAC model. Experimental points from several different investigators are marked in the same diagram in order to illustrate the quality of the fit.

All points in the diagram represent saturated solutions. The lines in the diagram represent compositions, at which two salts are in equilibrium with the same liquid (and with a gas phase).

 The intersection between lines are compositions at which three solid salts are in equilibrium with the same liquid (and with a gas phase). These points are invariant points.

The solid phases encountered in this system in the temperature range from -10 to 120°C are:

  • H2O (s) Ice
  • K2SO4 (potassium sulfate)
  • MgSO4·12H2O (magnesium sulfate dodecahydrate)
  • MgSO4·7H2O (epsom salt)
  • MgSO4·6H2O (hexahydrite)
  • MgSO4·H2O (kieserite)
  • K2SO4·MgSO4·6H2O (schoenite)
  • K2SO4·MgSO4·4H2O (leonite)
  • K2SO4·2MgSO4 (langbeinite)
As a result of thermodynamic modeling of salt solutions phase diagrams like this can be calculated
Phase diagram for the magnesium sulfate – potassium sulfate – water system from -10 to 120 °C

The vertical blue line marks the eutectic temperature i.e. the lowest temperature at which an aqueous solution can be in equilibrium with ice and salts in this ternary system. At temperatures lower than the eutectic, an equilibrium mixture of water and the two salts will consist of separate phases of MgSO4·12H2O, K2SO4, schoenite, and Ice.

The ordinate in the diagram above is “Salt fraction”: mol K2SO4 divided by (mol K2SO4 + mol MgSO4). The points in the diagram therefore mark compositions on a dry basis. The corresponding water content is not marked. It could be marked as a third dimension. Alternatively solubility isotherms can be calculated.

Solubility isotherm at 75°C

The 75°C solubility isotherm is shown in the figure to the right. The solubility isotherm calculated with the Extended UNIQUAC model is shown together with experimental data. The concentration unit in this triagonal diagram is weight percent. The green lines in the diagram are tie lines, marking the borders of fields yielding a certain solid salt.

The 75°C isotherm for this system consists of four branches, appearing from left to right:

  • K2SO4 (potassium sulfate)
  • K2SO4·MgSO4·4H2O (leonite)  
  • K2SO4·2MgSO4 (langbeinite)  
  • MgSO4·H2O (kieserite)  
75 °C solubility isotherm in the magnesium sulfate - potassium sulfate - water system
75 °C solubility isotherm in the magnesium sulfate – potassium sulfate – water system

The sodium chloride – sodium nitrate system

The figure to the right shows a ternary phase diagram for the NaCl-NaNO3-H2O system in the temperature range from -30 to 110°C. The equilibrium compositions were calculated using the Extended UNIQUAC model. Experimental points are marked in the diagram in order to illustrate the quality of the fit.

All points in the diagram represent saturated solutions. The lines in the diagram represent compositions, at which two salts are in equilibrium with the same liquid (and with a gas phase). The intersection between lines are compositions at which three solid salts are in equilibrium with the same liquid (and with a gas phase). These points are invariant points.

The solid phases encountered in this system in the temperature range from -30 to 110°C are:

  • H2O (s) Ice
  • NaNO3 (sodium nitrate)
  • NaCl•2H2O (hydrohalite)
  • NaCl (sodium chloride, halite)

The vertical blue line marks the eutectic temperature i.e. the lowest temperature at which an aqueous solution can be in equilibrium with ice and salts in this ternary system (-25.5°C). At temperatures lower than the eutectic, an equilibrium mixture of water and the two salts will consist of separate phases of hydrohalite, sodium nitrate, and Ice.

Phase diagram for the sodium chloride - sodium nitrate system as a function of temperature
Phase diagram for the sodium chloride – sodium nitrate system as a function of temperature

Solubility isotherm at -10°C

The -10°C solubility isotherm is shown in the figure below. The solubility isotherm calculated with the Extended UNIQUAC model is shown together with experimental data. The concentration unit used in the figure is weight percent. The green lines in the diagram are tie lines, marking the borders of fields yielding a certain solid salt.

The phase diagram shows that ice will form in dilute solutions (above the upper equilibrium line). The lower equilibrium line consists of two branches. The left branch represents solutions saturated with hydrohalite (NaCl·2H2O). The right branch represents solutions saturated with sodium nitrate (NaNO3).

Solubility isotherm for the sodium chloride - sodium nitrate system at -10 °C
Solubility isotherm for the sodium chloride – sodium nitrate system at -10 °C

The phosphoric acid – sodium hydroxide – water system

A large number of different solid phases can form in the P2O5 – Na2O – H2O system. Many of the solid phases reported in the literature are mapped in the triangular diagram to the right. 

The red dots in the diagram correspond to the compositions of the various solid phases. The three corners of the diagram represent P2O5, H2O, and Na2O. All the solids mapped in the diagram can be formed by a combination of two or three of the components P2O5, H2O, and Na2O.

All the solids mapped in the diagram below appear at specific concentration and temperature ranges in the P2O5 – Na2O – H2O system.

Composition of solids that can form in the phosphoric acid - sodium hydroxide system
Composition of solids that can form in the phosphoric acid – sodium hydroxide system

The phase diagram for the system at 25°C is shown below. The abscissa in the diagram is the Na2O fraction. The ordinate is the number of moles of water per mole of salt. The dashed blue lines are tie-lines connecting the saturated liquid with the corresponding solid. Only the tie-lines marking the transition to another stable solid phase are shown.

Phosphoric acid is very soluble in water. In the left side of the diagram it can be seen that four to five moles of water are required to dissolve one mole of phosphoric acid at 25°C. The phosphates of sodium become gradually less soluble towards the basic side. The least soluble sodium phosphate compound is the basic salt Trisodium Phosphate Dodecahydrate or Sodium Orthophosphate Dodecahydrate, 4(Na3PO4·12H2O)·NaOH. It requires up to 60 moles of water per mole of salt to dissolve.

Solubility isotherm for the phosphoric acid - sodium hydroxide - water system at 25 °C
Solubility isotherm for the phosphoric acid – sodium hydroxide – water system at 25 °C

The 60°C diagram for the same system is shown below. The solubility of sodium phosphate salts increase significantly with temperature. At 60°C, less than 20 moles of water are required to dissolve one mole of Sodium Orthophosphate Dodecahydrate.

To the left in the diagram, at zero Na2O content, the solution consists of water and pure phosphoric acid, H3PO4. The melting point of pure H3PO4 is approximately 40°C. The solid-liquid equilibrium line therefore does not start in the 60°C phase diagram until there is enough sodium content for NaH2PO4·H3PO4 to form.

Solubility isotherm for the phosphoric acid - sodium hydroxide - water system at 60 °C
Solubility isotherm for the phosphoric acid – sodium hydroxide – water system at 60 °C

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