Saturation Index (chemical calculations)
Mineral dissolution and precipitation depend on the degree of saturation of the geothermal water. If it is undersaturated, minerals will dissolve; if supersaturated, minerals can precipitate. Whether this occurs to any great extend depends on several aspects, but it is critically related to how saturated the water is with respect to a mineral.
For a given mineral composed of ions X and Y, the solution is saturated when the actual ion activity product (IAP) equals that dictated by the solubility product (Ksp). Typically, the degree of saturation is given as the ratio of these two parameters to obtain the saturation state (W):
where Ksp refers to the solubility product, which gives the equilibrium activities of the ions that form the solid (i.e., (X)Eq and (Y)Eq) and IAP, to the product of the actual activities ((X)Ac and (Y)Ac). This notation means that the solution is undersaturated at W < 1, saturated at W = 1, and supersaturated at W > 1. The degree of saturation can also be given on a logarithmic scale as the saturation index,
log(W). In his case, the solution is undersaturated at log(W) < 0, saturated at log(W) = 0, and supersaturated at log(W) > 0.
If data exist on the composition, temperature and pressure of the waters, geochemical speciation codes allow calculation of W or SI, meaning that one can determine if dissolution and precipitation can take place, i.e., if either of the reactions are thermodynamically favourable. It is important to note that such calculations are not straight forward. If solutions have been sampled at the surface, for example, their composition could have been affected by reactions occurring during passage in the production well. Moreover, correct definition of solubility products of solids and gases for concentrated solutions is not easy to attain. Thus, it would be important to choose a database capable of correctly describing the thermodynamic state of the system.
Nevertheless, if carefully done such geochemical calculations can provide valuable information on the risks that mineral dissolution and precipitation could pose for the geothermal operation. The geochemical calculations can also give the charge balance for the determined composition of the water. Given that solutions must be charge neutral, deviations from charge neutrality allows one to gauge the quality for the data. Usually, a charge imbalance of ± 5% is accepted for data of reasonable quality (Appelo and Postma, 2005).
To provide an example of the use of these tools, we have performed geochemical calculations using the solution compositions given in our database using the modelling code PHREEQC version 3.4 (Parkhurst and Appelo, 2013). The software features a variety of databases that employ different schemes for activity corrections and contains different thermodynamic data (e.g., reaction constants and their temperature and pressure dependence). From the benchmarking of the databases conducted in WP2 so far, the Pitzer database, that is currently distributed with the software (Appelo, 2015), performs well for a range of phases and water compositions. Thus, we have used this database in our calculations. Our tests so far as well as published work (Appelo, 2015), indicate that it is able to correctly predict the solubility of the two most important phases in this context, calcite and barite, in NaCl solutions at a variety of pressures (P), temperatures (T), and concentrations (C).
The charge balance of the solutions is given in Table 1 along with the degree of saturation assuming 25 °C and 15 bar pressure. The saturation calculated at downhole conditions is given in Table 2. For many of the waters, the phases are undersaturated (i.e., log(W) < 0). Barite, however, is typically supersaturated, with SI reaching almost 2 for a couple of sites (assuming a temperature of 25°C and 15 bar pressure; (Figure 1A). Of the sites that features the highest saturation, evidence for barite precipitation exists downhole at Groß Schönebeck, and at the surface at GeneSys Horstberg, and to minor extend, for stagnant surface waters at Margretheholm (PERFORM database, Regenspurg et al., 2015, Schulz, 2009). In addition, anonymous sites of the Upper Rhine Graben are reported to be plagued by barite scales (Haas-Nüesch et al., 2018). For these sites, calculations yield log(W) > 1 for at least some solutions, meaning that the solutions are highly supersaturated with respect to barite. Caution should be displayed when interpreting the results, because of uncertainties in the calculations and because precipitation may have affected the composition of the solution both prior and during sampling. Nevertheless, the data suggests that sites producing solutions with log(W) > 1 should be aware that an elevated risk exists for barite scaling (marked by grey area in Figure 1A). At lower supersaturation, slow nucleation kinetics of barite most likely means that significant barite scale will not form.
For most sites illustrated in Figure 1B, the calculations with down hole temperature and pressure yield log(W) close to 0 for barite and/or calcite, suggesting that the formation waters are at equilibrium with one or both of the phases. Exceptions from equilibrium include the dataset from Den Haag, where the formation water is predicted to be substantially supersaturated with respect to barite, and one of the datasets from Thisted Varmeforsyning and from Honselersdijk, where formation waters are indicated to be significantly undersaturated with respect to calcite. Why these datasets are outlying is currently unknown, but we note that the gas concentrations in the two datasets from Thisted Varmeforsyning and from Honselersdijk differ from the other dataset(s) from the sites.
Figure 1. A (left): Saturation (log(W)) for barite at 25 °C and 15 atm.
B (right): Downhole saturation for barite and calcite.
Appelo, C.A.J. and Postma, D., 2005: Geochemistry, Groundwater and Pollution, 2nd Edition. Balkema, Rotterdam, 634p.
Appelo, C. A. J., 2015: Principles, caveats and improvements in databases for calculating hydrogeochemical reactions in saline waters from 0 to 200 °C and 1 to 1000 atm. Appl. Geochem.; 55, pp. 62-71.
Haas-Nüesch, R., Heberling, F., Schild, D., Rothe, J., Dardenne, K., Jähnichen, S., Eiche, E., Marquardt, C., Volker Metz, and Schäfer, T., 2018: Mineralogical characterization of scaling formed in geothermal sites in the Upper Rhine Graben before and after the application of sulphate inhibitors. Geothermics; 71, pp. 264–273.
Parkhurst, D. L. P. and Appelo, C. A. J., 2013: Description of input and examples for PHREEQC. Version 3 – A computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations. U.S. Geological Survey, Techniques Methods, book 6, chapter A43, pp. 1-497.
Regenspurg, S., Feldbusch, E., Byrne, J., Deon, F., Driba, D.L., Henninges, J., Kappler, A., Naumann, R. Reinsch, T. and Schubert, C., 2015: Mineral precipitation during production of geothermal fluid from a Permian Rotliegend reservoir. Geothermics; 54, pp. 122–135.
Schulz R., 2009: GeneSys Horstberg II – Methoden und Konzepte zur Erdwärmegewinnung aus gering permeablen Sedimentgesteinen – Zwischenbericht. Leibniz-Institut für Angewandte Geophysik, Hannover, Institut für Geowissenschaftliche Gemeinschaftsaufgaben, 8p.