Thermodynamic calculations for the salt crystallisation damage in porous built heritage using PHREEQC

Abstract

This work considers the crystallisation mechanisms of the most common and aggressive salts that generate stress in porous building stones as a result of changing ambient conditions. These mechanisms include the salt crystallisation that result from decreasing relative humidity and changes in temperature and, in hydrated salts, the dissolution of the lower hydrated form and the subsequent precipitation of the hydrated salt. We propose a new methodology for thermodynamic calculations using PHREEQC that includes these crystallisation mechanisms. This approach permits the calculation of the equilibrium relative humidity and the parameterization of the critical relative humidity and crystallisation pressures for the dissolution–precipitation transitions. The influence of other salts on the effectives of salt crystallisation and chemical weathering is also assessed. We review the sodium and magnesium sulphate and sodium chloride systems, in both single and multicomponent solutions, and they are compared to the sodium carbonate and calcium carbonate systems. The variation of crystallisation pressure, the formation of new minerals and the chemical dissolution by the presence of other salts is also evaluated. Results for hydrated salt systems show that high crystallisation pressures are possible as lower hydrated salts dissolve and more hydrated salts precipitate. High stresses may be also produced by decreasing temperature, although it requires that porous materials are wet for long periods of time. The presence of other salts changes the temperature and relative humidity of salt transitions that generates stress rather than reducing the pressure of crystallisation, if any salt has previously precipitated. Several practical conclusions derive from proposed methodology and provide conservators and architects with information on the potential weathering activity of soluble salts. Furthermore, the model calculations might be coupled with projections of future climate to give as improved understanding of the likely changes in the frequency of phase transitions in salts within porous stone.

Appendix 1: PHREEQC input files calculations

PHREEQC is used for calculating a variety of reactions and processes in natural waters and laboratory experiments. A full description of many alternatives for input and the mathematical background can be found in the manual of the programme by Parkhurst and Appelo (1999, 2013), Appelo and Postman (2005) and at the link: http://www.xs4all.nl/~appt/.

The aim of this Appendix is to show how the calculations were carried out (for the PHREEQC users) and to present this widely used geochemical code to the researchers in the heritage conservation as a new tool to model salt weathering. Of course, there are other ways to structure the input file for modelling salt crystallisation. Here, we try to build up the input an easy and intuitive way. The number of calculations can be increased using the REACTION keyword, by adding or removing chemical, minerals or water; and REACTION_TEMPERATURE, which changing the temperature of the solution. Results can be delivered in a spreadsheet-type format (e.g. EXCEL) using the keyword SELECTED_OUTPUT keyword.

Calculation of pressure crystallisation by dissolution of the lower hydrated form and the precipitation of the hydrated salt

Examples of these transitions are thenardite (Na₂SO₄) → mirabilite (Na₂SO₄·10H₂O); thenardite (Na₂SO₄) → heptahydrite (Na₂SO₄·7H₂O); hexahydrite (MgSO₄·6H₂O) → epsomite (MgSO₄·7H₂O) and are recorded in Table 4. This calculation considers that water dissolves the lower hydrated form until equilibrium is reached (ϕ = 0). The resulting solution is then supersaturated in the hydrated salt at a given temperature. The temperature interval in which hydrated phase is more stable than lower hydrated form is reported in Tables 4.

PHREEQC calculates the saturation index and pressure crystallisation using the Current’s equation (Eq. 1). This thermodynamic calculation can be carried out considering the following:

Dissolution–precipitation in pure water

This calculation only considers the simple transformation by dissolution–precipitation at a given temperature or changing the temperature of solution using the REACTION_TEMPERATURE keyword. For example, the dissolution of thenardite and mirabilite precipitation at 20 °C can be calculated as:

The output of this simple calculation provides interesting results: composition of solution (or pore water); pH; ionic conductivity (evaluation ionic diffusion); density (necessary to fluid transport studies); ionic strength; distribution of species and the saturation index. The resulting solution is saturated in mirabilite and heptahydrite. Using the Corren’s equation (Eq. 1), crystallisation pressure of mirabilite precipitation after thenardite dissolution at 20 °C is then estimated as follows:

$$P_{\text{c}} = \frac{RT \cdot \ln10}{{v_{\text{c}} }}\phi = \frac{8.3145 \cdot (20 + 273.15) \cdot \ln10}{220}0.53 = 13.56\,{\text{MPa}}.$$

(A1)

The calculation at different temperatures through the REACTION_TEMPERATURE keyword can be preformed using the following input file:

This example calculates the saturation index of mirabilite at 7 temperatures from 0 to 30 °C at constant intervals. This keyword also permits the user to specify temperatures or as steps, as done below. In this example, we calculate the equilibrium from 0 to 30 °C in 7 steps (0 30 in 7 steps).

The output file contains a large quantity of results. PHREEQC can select some of parameters using the SELECTED_OUPUT keyword in a text or EXCEL file. These parameters include the saturation index, pH, activities, temperature, etc. In the previous example, the excel file contains the saturation index for mirabilite, heptahydrite and thenardite and solution temperature.

Pressure crystallisation is calculated using Corren’s equation, the saturation index and a fitted linear function of temperature. Table 4 gives linear expressions for different mineral transitions using the our methodology.

Presence of other salts

The presence of other salts is a common situation buildings. Their influence on mineral transitions and the crystallisation pressure is easy to be evaluated using PHREEQC. The chemical composition of solution is changed, in isothermal conditions, using a given chemical composition of solution or through REACTION keyword. For example, the presence of 1 mol Kg⁻¹ NaCl in the hexahydrite → epsomite transition at 20 °C can be computed as follows:

The input file for calculating this transition by adding 0, 0.1, 0.5, 1, 3, 4 and 5 mol of NaCl at 20 °C presents the following structure:

In this example, the EXCEL output file contains temperature, Cl⁻ concentration and the saturation index of epsomite, hexahydrite, halite and mirabilite, although a widely options can be selected for the user at the SELECTED_OUTPUT data block. The presence of other ions in solution generates a multicomponent saline solution and, consequently, other minerals can precipitate and generate stress. Figures 3 and 6 are produced using this method.

Chemical dissolution of the host rock

The dissolution of calcite in the presence of saline solutions increases the concentration of calcium and bicarbonate–carbonate ions. As commented in the previous section, the presence of ions can precipitate other minerals. The input file might include the following information:

This example displays the mirabilite precipitation after thenardite dissolution at 20 °C. As the equilibrium is imposed (thermodynamic approach), thenardite dissolves in pure water with the rock-forming calcite in equilibrium with the atmospheric CO₂ (open system). The resulting solution is supersaturated in mirabilite and is slightly substantiated in gypsum, which might precipitate after some evaporation.

Precipitation from the solution

Equilibrium or deliquescence relative humidity

The equilibrium or deliquescence relative humidity, RH_eq, of a salt is the relative humidity in which crystallises in an aqueous solution and varies with the temperature and by the presence of other ions in the solution. RH_eq can be obtained by calculating water activity as described above. The input file is similar to other described in “Appendix 1.” Water activity is displayed in the “description of solution” in the output file. For example, RH_eq for halite at 20 °C can be calculated using the following input file:

In this example, halite solubility is 6.088 mol kg⁻¹ and the activity of water is 0.755 and therefore RH_eq = 75.5 %. The influence of temperature and other ions can be evaluated using the previous input file or through the REACTION_TEMPERATURE or REACTION keywords. For example:

The EXCEL file contains the log a _w for temperatures in the range of 0–60 °C.

Mineral precipitation by varying temperature and/or concentration

At high values of equilibrium relative humidity (higher than RH _eq ) salts can also be precipitated from an aqueous solution by decreasing the temperature.

Mineral precipitation from a saturated solution is produced by decreasing temperatures and/or increase concentration. This pathway can be carried out through a simple speciation by calculating a multiple of speciation. A simple speciation includes the chemical composition and temperature of the solution as follows:

This example calculates the saturation index of minerals of MgSO₄ system (epsomite; hexahydrite; Kieserite; Pentahydrite and Starkeyite) in a 4 mol kg⁻¹ MgSO₄ solution at 20 °C. Pressure crystallisation is calculated using Eq. (1).

However, multiple calculations are recommended since a multiple set of saturation indexes (and crystallisation pressures) are obtained. Moreover, the mineral stability zones can be graphically displayed as in Figs. 2 and 5. The input file requires either the REACTION_TEMPERATURE or REACTION keywords in order to save time in the calculation. Thus, the REACTION_TEMPERATURE keyword is used for an each concentration as follows:

whereas the REACTION keyword is considered for each temperature:

Saturation index each mineral is obtained and pressure crystallisation is calculated using Eq. (1).

Precipitation from saline pore water

The analysis of chemical composition of soluble salts within stones is a frequent procedure for conservators and architects. Salt analysis permits to estimate the theoretical mineral precipitation sequence, which has not been considered in the present paper. We here include a sort reference that can illustrate this interesting task.

A simple speciation can be carried out defining the chemical composition, pH and temperature of solution. Calculation of the saturation indexes of minerals provides a good idea of the precipitation sequence that may occur in the stone.

This approach can be improved by the simulation of evaporation, which is accomplished by removing water from the chemical system. Thus, water can be removed by an irreversible reactant with a negative reaction coefficient in the REACTION keyword input. An interesting example that can illustrate this simulation is accessed in the User’s Guide to PHREEQC:

http://wwwbrr.cr.usgs.gov/projects/GWC_coupled/phreeqc.v1/html/phqc_55.html.