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The Solubilities and Thermodynamic Equilibrium of Anhydrite and Gypsum

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Abstract

Anhydritic claystones consist of a clay matrix with finely distributed anhydrite. Their swelling has led to severe damage and high repair costs in several tunnels. Gypsum growth combined with water uptake by the clay minerals is the main cause of the swelling process. Identifying the conditions under which gypsum rather than anhydrite represents the stable phase is crucial for understanding rock swelling. As existing studies on the anhydrite–gypsum–water equilibrium appear to be contradictory and do not provide all of the information required, we revisit this classic problem here by formulating and studying a thermodynamic model. In contrast to earlier research, our model is not limited to the anhydrite–gypsum equilibrium, but allows for the determination of the equilibrium concentrations of the individual anhydrite dissolution and gypsum precipitation reactions that underlie the sulphate transformation. The results of the paper are, therefore, also valuable for the formulation of comprehensive sulphate–water interaction models that consider diffusive and advective ion transport simultaneously with the chemical dissolution and precipitation reactions. Furthermore, in addition to the influencing factors that have been considered by previous studies (i.e., fluid and solid pressures, concentration of foreign ions, temperature), we consistently incorporate the effect of the surface energy of the sulphate crystals into the thermodynamic equations and discuss the effect of the clay minerals on the equilibrium conditions. The surface energy effects, which are important particularly in the case of claystones with extremely small pores, increase the solubility of gypsum, thus shifting the thermodynamic equilibrium in favour of anhydrite. Clay minerals also favour anhydrite because they lower the activity of the water. The predictions from the model are compared with experimental results and with predictions from other models in the literature. Finally, a comprehensive equilibrium diagram is presented in terms of pore water pressure, solid pressure, temperature, water activity and pore size.

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Abbreviations

A :

Parameter of Davies equation

A i :

Total interfacial area of species i

C :

Concentration

c 0 :

Concentration at standard state

c eq,A :

Anhydrite equilibrium concentration

c eq,G :

Gypsum equilibrium concentration

c i :

Concentration of constituent i

g :

Gravitational acceleration

G :

Gibbs free energy

I :

Ionic strength

K G :

Ion activity product of gypsum

K eq,A :

Equilibrium solubility product of anhydrite

K eq,G :

Equilibrium solubility product of gypsum

\( n_{{{\text{Ca}}^{2 + } }} \) :

Number of moles of Ca2+

n G :

Number of moles of gypsum

n W :

Number of moles of water

n i :

Number of moles of constituent i

\( n_{{{\text{SO}}_{4}^{2 - } }} \) :

Number of moles of SO 2–4

p A :

Anhydrite pressure

P atm :

Atmospheric pressure

p G :

Gypsum pressure

P i :

Pressure of constituent i

p S :

Solid pressure

p V :

Vapour pressure of a solution

p V,0 :

Vapour pressure of pure water

p W :

Pore water pressure

Q :

Heat

R :

Universal gas constant

r p :

Pore radius

r i :

Radius of particle i

r A :

Radius of anhydrite particles

r G :

Radius of gypsum particles

\( S_{{{\text{Ca}}^{2 + } }}^{0} \) :

Molar entropy of Ca2+ at standard state

S 0A :

Molar entropy of anhydrite at standard state

S 0G :

Molar entropy of gypsum at standard state

S 0W :

Molar entropy of water at standard state

S i :

Molar entropy of constituent i

S i :

Molar entropy of constituent i at standard state

\( S_{{{\text{SO}}_{4}^{2 - } }}^{0} \) :

Molar entropy of SO 2−4 at standard state

T :

Temperature

T 0 :

Temperature at standard state

T eq :

Equilibrium temperature

T 0eq :

Equilibrium temperature under atmospheric pressure

U :

Internal energy

V :

Volume

\( V_{{{\text{Ca}}^{2 + } }}^{0} \) :

Molar volume of Ca2+ at standard state

V 0A :

Molar volume of anhydrite at standard state

V 0G :

Molar volume of gypsum at standard state

V 0W :

Molar volume of water at standard state

V i :

Molar volume of constituent i

V W :

Molar volume of water

V 0 i :

Molar volume of constituent i at standard state

\( V_{{{\text{SO}}_{4}^{2 - } }}^{0} \) :

Molar volume of SO 2−4 at standard state

H :

Depth below surface

z i :

Ion valence of constituent i

\( \alpha_{{{\text{Ca}}^{2 + } }} \) :

Activity of Ca2+

α G :

Activity of gypsum

α W :

Water activity

α i :

Activity of constituent i

\( \alpha_{{{\text{SO}}_{4}^{2 - } }} \) :

Activity of SO 2−4

γ ± :

Mean activity coefficient

γ A :

Surface free energy of the anhydrite–water interface

\( \gamma_{{{\text{Ca}}^{2 + } }} \) :

Activity coefficient of Ca2+

γ G :

Surface free energy of the gypsum–water interface

γ i :

Surface free energy of the interface of constituent i with water

γ i :

Activity coefficient of constituent i

\( \gamma_{{{\text{SO}}_{4}^{2 - } }} \) :

Activity coefficient of SO 2−4

\( \Delta_{\text{f}} G_{{{\text{Ca}}^{2 + } }}^{0} \) :

Standard Gibbs energy of formation of Ca2+

Δf G 0A :

Standard Gibbs energy of formation of anhydrite

Δf G 0G :

Standard Gibbs energy of formation of gypsum

Δf G 0W :

Standard Gibbs energy of formation of water

Δf G 0 i :

Standard Gibbs energy of formation of constituent i

\( \Delta_{\text{f}} G_{{{\text{SO}}_{4}^{2 - } }}^{0} \) :

Standard Gibbs energy of formation of SO 2–4

Δr,A G 0 :

Standard Gibbs energy of anhydrite dissolution

Δr,G G 0 :

Standard Gibbs energy of gypsum dissolution

Δr,GA G 0 :

Standard Gibbs energy of anhydrite hydration

Δr,A S 0 :

Standard entropy of anhydrite dissolution

Δr,G S 0 :

Standard entropy of gypsum dissolution

Δr,GA S 0 :

Standard entropy of anhydrite hydration

Δr,A V 0 :

Standard volume of anhydrite dissolution

Δr,G V 0 :

Standard volume of gypsum dissolution

Δr,GA V 0 :

Standard volume of anhydrite hydration

ε :

Dielectric constant (Davies equation)

λ W :

Ater activity coefficient

\( \mu_{{{\text{Ca}}^{2 + } }} \) :

Chemical potential of formation of Ca2+

μ A :

Chemical potential of formation of anhydrite

μ G :

Chemical potential of formation of gypsum

μ W :

Chemical potential of formation of water

μ i :

Chemical potential of constituent i

\( \mu_{{{\text{SO}}_{4}^{2 - } }} \) :

Chemical potential of formation of SO 2–4

ρ R :

Rock density

ρ W :

Water density

x W :

Mole fraction of water

Ψ :

Potential

Ψ m :

Matric potential

Ψ π :

Osmotic potential

Ψ a :

Adsorptive component of the matric potential

Ψ c :

Capillary component of the matric potential

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Acknowledgments

This paper evolved within the framework of the research project ‘Modelling of anhydritic swelling claystones’ which is being carried out at the ETH Zurich, financed by the Swiss National Science Foundation (SNF) with Project Nr. 200021-126717/1 and the Swiss Federal Roads Office (FEDRO) with Project Nr. FGU 2010-007. The Authors would like to acknowledge Prof. Dr. Robert Flatt, ETH Zurich, for his valuable suggestions concerning the importance of pore size and liquid–crystal interfacial effects.

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    K. Serafeimidis & G. Anagnostou

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Serafeimidis, K., Anagnostou, G. The Solubilities and Thermodynamic Equilibrium of Anhydrite and Gypsum. Rock Mech Rock Eng 48, 15–31 (2015). https://doi.org/10.1007/s00603-014-0557-1

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