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A multicomponent geothermometer for high-temperature basalt settings

A multicomponent geothermometer for high-temperature basalt settings lars.ystroem@kit.edu Division of Geothermal For successful geothermal reservoir exploration, accurate temperature estimation is Research, Institute of Applied essential. Since reservoir temperature estimation frequently involves high uncertain- Geosciences, Karlsruhe Institute of Technology (KIT ), ties when using conventional solute geothermometers, a new statistical approach is Campus South, Building proposed. The focus of this study is on the development of a new multicomponent 50.40, Adenauerring 20b, geothermometer tool which requires a significantly reduced data set compared to 76131 Karlsruhe, Germany existing approaches. The method is validated against reservoir temperature measure- ments in the Krafla and the Reykjanes geothermal systems. A site-specific basaltic mineral set was selected as the basis to compute the equilibrium temperatures. These high-enthalpy geothermal reservoirs are located in the neo-volcanic zone of Iceland where the fluid temperatures are known to reach up to 350 °C at a depth of 2000 m. During ascent, the fluid composition is prone to changes as well as possible phase segregation due to depressurization and boiling. Therefore, to reduce the uncertainty of temperature estimations, reservoir temperature conditions are numerically recon- structed with sensitivity analyses considering pH, aluminium concentration, and steam loss. The evaluation of the geochemical data and the sensitivity analyses were calcu- lated via a numerical in-house tool called MulT_predict. In all cases, the temperature estimations match with the in situ temperatures measured at Krafla and Reykjanes. The development of this method tends to be a promising and precise tool for reservoir temperature estimation. The developed methodology is a fast and easy-to-handle exploration tool that can be applied to standard geochemical data without the need for a sophisticated gas analysis yet obtaining very accurate results. Keywords: Multicomponent geothermometry, Geochemical exploration, Reservoir temperature estimation, Sensitivity analysis, Krafla geothermal system, Reykjanes geothermal system, MulT_predict Introduction A reliable temperature estimation for a targeted geothermal reservoir, which lays the foundation for the prediction of producible energy, is essential for a successful explo- ration campaign. Conventional solute geothermometers are a commonly used tool for the deduction of reservoir temperature from geochemical composition of geothermal spring samples. These geothermometers were introduced in the 1960s and have been undergoing further development since then (Can 2002; Ellis 1970; Fouillac and Michard 1981; Fournier and Potter 1979; Fournier and Rowe 1966; Fournier and Truesdell 1973; © The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creat iveco mmons .org/licen ses/by/4.0/. Ystroem et al. Geotherm Energy (2020) 8:2 Page 2 of 21 Giggenbach 1988; Sanjuan et al. 2014; Verma and Santoyo 1997). These approaches use the temperature dependence of the saturation of mineral phases (e.g. silica) or certain cation ratios in the fluids. The measured concentrations of these fluid constituents are then directly linked to a reservoir temperature. The fundamental assumption of geother - mometry is the overall chemical equilibrium of the fluid and the reservoir rock. Sec - ondary processes may change the fluid composition and hence, the equilibrium while migrating to the earth surface. These variations can result in large uncertainties for the reservoir temperature determination using solute geothermometers (Nitschke et  al. 2018). The more recently developed multicomponent geothermometry evaluates the equilibria of multiple mineral phases (Spycher et al. 2014). Numerical geochemical spe- ciation codes facilitate this evaluation based on a large number of minerals, which leads to a statistically more robust method. Spycher et al. (2014) proposed a pre-selection of minerals representing the site-specific reservoir rocks to enhance accuracy. Corrections were established to overcome interferences from secondary processes such as dilution, boiling, and mixing of fluids affecting the temperature estimation (Cooper et  al. 2013; Peiffer et  al. 2014; Spycher et  al. 2014). These methods need an additional gas analysis for precise temperature estimations. u Th s, Nitschke et al. (2017) introduced a method to reconstruct in situ conditions of the reservoir temperature by varying sensitive parame- ters, especially pH and aluminium concentration as well as steam loss, to further reduce the uncertainty of equilibrium temperatures. The goals of this study are to refine and to validate the existing specific multicom - ponent approach according to Nitschke et  al. (2017) and to expand it towards a high- precision exploration tool. This study devises a basalt-specific mineral set including secondary mineral phases for global application to basaltic stratigraphy. For the vali- dation, geochemical data and in  situ temperature measurements from basalt-hosted geothermal systems, Krafla and Reykjanes, are used. These are high-enthalpy systems with near-boiling reservoir fluids and, thus, the effect of steam loss between the reser - voir and the liquid sampled at the well-head has to be considered. Krafla hosts dilute meteoric fluids (Arnórsson et  al. 1978), and Reykjanes a more saline reservoir fluid partially originating from seawater (Arnórsson 1978). To validate the method, the tem- perature estimations are compared with direct in situ temperature measurements of the wells published by Guðmundsson and Arnórsson (2002) for Krafla, and Óskarsson et al. (2015) for Reykjanes. The advantage of the validated method is the frugality in terms of input data. High-accuracy temperature estimations can be achieved based on standard fluid analyses and do not require comprehensive high-end fluid and gas analyses, which are required for other solute multicomponent geothermometer approaches. Method and data The basis of the method is a standard fluid analysis comprising major cations and ani - ons as well as aluminium concentration and pH. The water analysis is used to calculate equilibrium conditions between the dissolved constituents in the geothermal fluid and the reservoir rock minerals. For identification of the reservoir temperature conditions, sensitive parameters have to be evaluated statistically. The application relies on the fol - lowing general assumptions: (i) the reservoir and the geothermal fluid are in equilib - rium. Therefore, the ion activity product of a mineral phase equals its thermodynamic Ystroem et al. Geotherm Energy (2020) 8:2 Page 3 of 21 equilibrium constant. (ii) A temperature-dependent reaction between the host rock and the water leads to a specific amount of dissolved solids in the fluid phase. The equilibrium reaction is based on the law of mass action. The state of the dynamic equilibrium between the reactants is expressed in terms of the saturation index SI(1) IAP v v i i SI(T ) = log = log γ x − log (K (T )), (1) i i K (T ) with IAP being the ion activity product and K being the temperature-dependent ther- modynamic equilibrium constant of one mineral phase. IAP is the product of the activity coefficients γ and the mole fractions of the solute mineral phase x considering their sto- i i ichiometric coefficient ν . A positive saturation index indicates an oversaturation and a potential precipitation of the mineral. Though, if the ion activity product is smaller than the equilibrium constant, the saturation index will be negative. In this case, the solution is undersaturated with the potential to dissolve the mineral phase. Therefore, equilib - rium is given at SI = 0. Debye and Hückel (1923) established an equation for non-ideal electrolyte solutions taking into account the electrostatic interaction among the ions by using the activity coefficients γ (2). In order to fit the Debye–Hückel equation to experimental data, Rob - inson and Stokes (2002) extended the original equation by adding a linear concentration term ḂI. Az I log γ =− √ + BI, (2) 1 + (å) B I where A and B are temperature-dependent constants, z is the charge number of the ion, I is the ionic strength, and å is the hydrated ion size. The numerator quantifies the long-range Coulomb forces acting on the ion, whereas the denominator defines the short-range interactions between the ions itself and with the solvent. The extended Debye–Hückel equation (Eq.  2) expands the former validity limit in terms of the ionic strength to I = 1.0 mol/L for mixed electrolytes. Furthermore, there are application lim- its given by specific temperatures and pressures. The latter is negligible at least up to a temperature of 300 °C (Helgeson 1969). In this study, chemical speciation and saturation indices are computed with IPhreeqc 3.4.0-12927 (Parkhurst and Appelo 2013). Ion activity coefficients are based on the extended Debye–Hückel equation. The required constants A, B, and Ḃ are obtained from the commonly used LLNL (Lawrence Livermore National Laboratory) database. Saturation indices are computed for all specified minerals for a given solution. Reed and Spycher (1984) plotted these saturation indices versus temperature to investigate the equilibrium temperature of the geothermal fluid and the reservoir mineral assemblage. For validation of the multicomponent geothermometer, the method is applied on well- studied geothermal sites in Iceland and further developed to obtain an easy-to-handle and convenient high-precision exploration tool. Krafla is a high-temperature geothermal field located in the NE of Iceland. The geo - thermal system is situated in the neo-volcanic zone (Ármannsson et al. 1987). The in situ temperature measurements (Table 1) and the geochemical data of the wells (Appendix 1) Ystroem et al. Geotherm Energy (2020) 8:2 Page 4 of 21 Table 1 In situ measurements of  the  temperature [°C] in  the  wells of  Krafla (K) at  specific depths [m] for  permeable horizons presented in  Guðmundsson and  Arnórsson (2002) (Table 3) K-11 K-24 K-28 1330 m > 240 °C 580 m 190 °C 500 m 230 °C 1600 m > 240 °C 780 m 195 °C 800 m 240 °C 1700 m > 240 °C 920 m 210 °C 2180 m > 300 °C 1150 m 225 °C were published by Guðmundsson and Arnórsson (2002). The upper 1000 m of the stra - tigraphy are built up by alternating layers of basaltic lavas and hyaloclastite. The latter is subglacial erupted basaltic lava, which forms hydrated breccia once it is in contact with water. Below 500  m, the hyaloclastite layers form subhorizontal reservoirs. The follow - ing 1000 m are covering basaltic intrusives, where geothermal fluids of up to 310 °C are evident (Guðmundsson and Arnórsson 2002). A more detailed stratigraphy of the field is given by Ármannsson et  al. (1987). The mineralogical content of Icelandic geother - mal systems and the geochemistry of the fluids are described by Arnórsson et al. (1983). Sampling methods and the geochemical analysis are given in Arnórsson et al. (2006). Results of the analysis The application of this multicomponent geothermometer approach requires the evalua - tion of the equilibrium of each solute mineral phase and, thus, the calculation of satura- tion indices of the considered minerals versus temperature. The saturation indices are calculated from 20 to 300  °C. The calculations of the saturation indices are processed via MATLAB. Therefore, the MulT_predict tool was developed which determines the intersection of the saturation index function for each mineral phase with the equilibrium line (Fig.  1). Thus, the tool calculates all mineral-specific saturation indices functions throughout the temperature range by interacting with IPhreeqc. Only minerals having exactly one intersection with the equilibrium line are taken into account for the temper- ature determination procedure. The resulting intersection temperatures are combined in a box plot. This plot represents a first estimate of the reservoir temperature. Secondary effects perturb the chemical equilibrium of a fluid sample while migrating to the earth surface. The chemistry may change due to boiling, degassing, precipitation of phases, dilution, or mixture with shallow and low-mineralized waters as well as re- equilibration with the surrounding rocks (Cooper et  al. 2013; Fournier 1977; Fournier and Truesdell 1974; Pang and Reed 1998; Reed and Spycher 1984). To determine the most vulnerable sensitive parameters for later sequential sensitiv- ity analysis, a series of variations on system parameters (pH, redox, and steam loss) have been computed. Similarly, the concentrations of aluminium, magnesium, and iron, being major components in the minerals but only trace elements in the fluid, have been examined. The equilibrium temperature distributions for K-28 were exemplarily plotted against these parameters (Fig.  2). It is shown that the most important and vulnerable system parameter is the pH value, which is in good agreement with what is also assumed by Nitschke et al. (2017) as well as Reed and Spycher (1984). Changes have a significant Ystroem et al. Geotherm Energy (2020) 8:2 Page 5 of 21 Fig. 1 Example of the creation of an equilibrium temperature distribution box plot via the saturation indices over the temperature [°C] of the basalt-specific mineral phases for sample K-28. The box plot includes the temperature values of each mineral where SI = 0 (intersection of the saturation index of a mineral phase and the equilibrium line) impact on the solubility of mineral phases. The pH value is prone to phase segregation effects like degassing, boiling, and steam loss. Also, the pH is a temperature-dependent function, which decreases when temperature rises. In addition, regarding Fig.  2, steam loss itself is another vulnerable system parameter. Thus, possible phase segregation due to boiling has to be taken into account. The loss of steam fraction corresponds to a loss of solvent and results in the concentration of the ascending fluid. The effect of steam loss needs to be compensated by adding back the lost water. Equally, the vulner- ability of trace elements is shown in Fig. 2. These constituents are particularly prone to interferences from secondary processes and measurement errors. Simultaneously, they have a high impact on the solubility product and hence, on the saturation index of the majority of reservoir minerals. Clearly, aluminium is the most vulnerable trace ele- ment. Its concentration is a crucial parameter when computing the saturation state of aluminosilicates, which represent the major mineral phases in most geothermal reser- voirs (e.g. basalts, granitoids, sandstone, greywackes, etc.). Such aluminosilicate mineral assemblages contain phases like feldspars, zeolites, micas, and clay minerals. Due to the tendency of complex formation and precipitation processes (Brown 2013), the deter- mination of accurate aluminium concentrations is prone to large errors. Furthermore, the variations of the redox potential as well as magnesium and iron concentration were tested. As it is revealed that these parameters have only marginal effects on the tempera - ture estimations, they are not further discussed in this study. In view of the above, the in situ values of the most vulnerable sensitive parameters, pH, aluminium concentration, and steam loss, have to be reconstructed. For this optimization, a sequential sensitivity analysis for each parameter is used. This sensitivity analysis is executed by the tool. The statistically backed minimization of the temperature spread enables the back-calculation on the in situ geochemical equilibrium between the geothermal fluid and the reservoir mineral assemblage, which is the basic assumption of the method. The tool varies these Ystroem et al. Geotherm Energy (2020) 8:2 Page 6 of 21 Fig. 2 Various sensitivity analyses of several parameters (pH value, boiling, pe value, Al, Fe, and Mg concentration) parameters around the initial measured value such that a minimal temperature spread is found. In an ideal case, the equilibrium temperatures of each mineral phase of the reservoir assemblage converge to one discrete reservoir temperature. Also unknown parameters can be estimated in this manner. Thus, a geochemical foreknowledge of the geothermal system is needed to make an educated guess for the unknown parameter, which then can be estimated towards best-fit conditions. To statistically evaluate the resulting box plots, the mineral set has to remain unchanged throughout all variations. Minerals that do not equilibrate due to over- or undersaturation or have multiple inter- sections with the equilibrium line in any step of the sensitive analyses were discarded Ystroem et al. Geotherm Energy (2020) 8:2 Page 7 of 21 from further statistical processing. Changes within the set of consistent mineral phases during the sensitivity analysis would lead to false conclusions because the temperature estimations would then result from different basic conditions (i.e. different mineral sets). Concerning this, the spread of the overlaying boxes and the median differences of each neighbouring plot are matched to identify the most likely value for the sensi- tive parameter, indicated by the least equilibrium temperature spread. This procedure is done sequentially for the pH value, the aluminium concentration, and the percent- age of steam loss. Afterwards, the best-fit values for all parameters are combined in a final temperature estimation. Nevertheless, the aim of this study is the reconstruction of reservoir temperatures, instead of the encompassing reconstruction of geochemical reservoir conditions. As a generic example, the calculation and optimization will be shown in detail for well K-28 to give an understanding of the procedure. Therefore, the geochemical data (Appendix 1) of the sample is used. The result of this first calculation is shown in Fig.  6a. For the temperature estimation from the non-specific mineral set (Appendix 2) without further optimization, a large temperature spread of 260  °C is obtained. Hence, in this study, a basalt-specific mineral set was devised to enhance the accuracy of this method. The basaltic minerals have been selected according to the mineralogical study of the Krafla reservoir rocks (Arnórsson et al. 1983). This set is extended for secondary mineral phases, occurring in geothermal reservoirs due to hydrothermal alteration processes. It is based on the stability of mineral phases at certain temperature and pressure levels which were described by Giggenbach (1981). The resulting basalt-specific mineral set (Table  2) is used to evaluate the in situ temperatures of the reservoir. After application of the multicomponent geothermometer based on the selected mineral set, the reser- voir temperature estimation could be improved (Fig. 6b), yet the temperature spread still exceeds 100 °C. As a second step, the sensitivity analysis is conducted. Firstly, the pH value is opti- mized. The initial pH of 9.75 is varied in increments of 0.1 towards higher acidity and basicity. The result is shown in Fig.  3 where the minimal spread of the box is reached at pH 7.85. Table 2 Mineral phases contained in  the  basalt-specific mineral set devised and  used in this study Mineral group Associated mineral phases Feldspar Albite (low), microcline, k-feldspar SiO phases Quartz, chalcedony Clays Smectite, clinochlore, illite Carbonate Calcite, aragonite Zeolite Analcime, laumontite, wairakite Sulphate Anhydrite, gypsum Halide Fluorite soro-/inosilicate Epidote, anthophyllite, tremolite, pargasite Fe-phases Pyrite, marcasite, pyrrhotite, goethite Ystroem et al. Geotherm Energy (2020) 8:2 Page 8 of 21 Fig. 3 Sensitivity analysis of pH for sample K-28. The value was varied from 6.75 to 8.15 in increments of 0.1. The figure shows an extract of the data, where the pH value ranges from 7.55 to 8.15 in increments of 0.1. For pH 7.85, the statistical minimum of the boxplot comparison is reached; it is highlighted in a darker blue colour Fig. 4 Sensitivity analysis of aluminium concentration for sample K-28. The value was varied from 0.009 to 0.117 mmol/kg in increments of 0.006 mmol/kg. The figure shows an extract of the data, where the aluminium concentration ranges from 0.021 to 0.057 mmol/kg in increments of 0.006 mmol/kg. The statistical minimum of the boxplot comparison is reached for a concentration of 0.039 mmol/kg highlighted in a darker blue colour Separately, the aluminium concentration is evaluated. The average aluminium concen - tration in the Krafla geothermal fluids is about 1.2 ppm (0.04 mmol/kg) (Guðmundsson and Arnórsson 2002). Therefore, the aluminium concentration is varied in increments of 0.006 mmol/kg. The initial aluminium concentration of the geothermal fluid compo - sition for K-28 is 0.039 mmol/kg. In Fig.  4, an optimal concentration is also reached at 0.039 mmol/kg. Ystroem et al. Geotherm Energy (2020) 8:2 Page 9 of 21 Fig. 5 Sensitivity analysis of steam loss for sample K-28. The value was varied in increments of 1%. The figure shows an extract of the data, where the steam loss ranges from 11 to 17% in increments of 1%. For 14% steam loss, the statistical minimum of the boxplot comparison is reached; it is highlighted in a darker blue colour Fig. 6 Comparison of an unspecific mineral set (a) with the developed basaltic set (b). The boxplot in the third column (c) is the result of the combination of the pH, aluminium concentration, and steam loss sensitivity analysis. All analyses are done separately under static conditions for the remaining parameters, and all best-fit parameters were combined afterwards Lastly, the sensitivity of fluid composition to the magnitude of steam loss is consid - ered. The amount of steam loss is unknown, but has to be back-calculated. Therefore, pure water is virtually added back in increments of 1%. In Fig. 5, the optimum in steam loss is reached at 14%. The final temperature estimation is then computed by combining the best-fit values for pH, aluminium concentration, and steam loss. Figure  6c displays the reduced spread of Ystroem et al. Geotherm Energy (2020) 8:2 Page 10 of 21 the calculated temperature after each optimization step. Simultaneously to the reduced uncertainty, the median of the temperature estimate has ascended. For validation, the concluding reservoir temperature estimations are compared to downhole temperature measurements published by Guðmundsson and Arnórsson (2002) (Table  1). Figure  7 displays the temperature box plots for the wells K-11, K-24, and for K-28 of two consecutive years. The range of the measured in situ temperatures (Table  1) is figured as an orange box. In each case, the estimated temperatures fit very well the measured borehole temperatures after the optimization procedure. Note that even very small temperature ranges are matched by the estimated temperatures (e.g. K-24 and K-28). Discussion The comparison of the optimized temperature estimation and the measured downhole temperatures confirms the functionality of the application. Only for K 24, the median temperature shows a minor overestimation of 1  K above the highest measured inflow temperature, though, the estimations are also located in the measured temperature range. The overall spread of each final plot after the sensitivity analyses does not exceed 7% (K-24), but is on average 3.7% of the absolute median temperature. The uncer - tainty throughout the validation is at maximum 2.6% of the original absolute reservoir Fig. 7 Results of wells K-11, K-24, and K-28 for three stages of the analysis. The first column displays a temperature estimation calculated based on an unspecific mineral set. The box plot in the second column represents the specified basaltic mineral set. The last box plot shows the optimized temperature estimation via the pH, aluminium concentration, and steam loss sensitivity analysis. These box plots can be compared with the range of the measured temperatures in the boreholes, given by the orange box Ystroem et al. Geotherm Energy (2020) 8:2 Page 11 of 21 temperature. Thus, the validated developed tool shows a significant improvement com - pared to uncertainties of conventional solute approaches, following in the discussion. The calculation of the saturation indices relies on the LLNL database which is con - strained to temperatures of 300 °C. Therefore, most of the geochemical modelling tools are also constrained for that p–T range. Icelandic geothermal systems have the poten- tial to exceed these temperatures. To evaluate the validity limits, the investigations were extended to the Reykjanes geothermal system, which is located in the SW of Iceland. Furthermore, as the system is recharged by seawater, also the effects of high salinities can be assessed. Reykjanes is also situated in the neo-volcanic zone and the stratigraphy equals the Krafla structure with alternating layers of basaltic lavas and hyaloclastite in the upper part, followed by basaltic intrusives at greater depth. However, since the geo- thermal system is located on a peninsula, seawater infiltrates the productive horizons of the reservoir. At Krafla, the dissolved solids content is generally up to 1500 ppm. Show - ing sea water concentrations, the salinities at Reykjanes are up to 58 times higher (RN- 23: 87.160  ppm). Óskarsson et  al. (2015) published the geochemical data (Appendix 3) of the fluids from two production wells and the associated temperature logs (Table  3). In the following, the applicability of the numerical scheme will be tested at high-enthalpy geothermal fields with temperatures above 300 °C and elevated salinities. u Th s, the Debye–Hückel coefficients A, B, and Ḃ of Eq. (2) have to be extrapolated towards higher temperatures and implemented into the database. The coefficients A and B were extrapolated by a quadratic fit, whereas Ḃ was extrapolated by a cubic fit. This extrapolation is similar to the scheme proposed by Helgeson (1969). Figure 8 shows the results of polynomial parameter estimation. The obtained values for the coefficients A and B herein are very close to the results computed by Helgeson et  al. (1981). Estima- tions towards the critical temperature of water have to be used with care and, therefore, only exceed up to 350 °C. These modifications of the Debye–Hückel parameters allow technically for the com - putation of saturation indices over an extended temperature range. To gain an overview, the saturation indices of the well RN-12 at Reykjanes were plotted to 350  °C (Fig.  9). The extrapolated coefficients follow the trend of the saturation curves. The results for the reservoir temperature estimation and the comparison against measured values are presented in Fig. 10. Despite the high sodium chloride concentrations, the tool operates thoroughly. Analogous to the methodology presented for the Krafla site, the spread of the temperature box plots is minimized and eventually matches the measured tempera- tures (Table  3). The spread is about 4.7% of the measured absolute reservoir tempera - ture, while the overall temperature accuracy is at 0.5%. Table 3 In situ measurements of  the  temperture [°C] in  the  wells of  Reykjanes (RN) at specific depths [m] presented by Óskarsson et al. (2015) RN-12 RN-23 1000 m 260 °C 900 m 255 °C 1200 m 270 °C 1200 m 280 °C 1300 m 290 °C 1700 m 300 °C 1700 m 310 °C Ystroem et al. Geotherm Energy (2020) 8:2 Page 12 of 21 Fig. 8 Extrapolation of the three parameters A, B, and Ḃ of the extended Debye–Hückel equation for temperatures beyond 300 °C. The values of the solid squares are acquired from the LLNL database in IPhreeqc. The hollowed squares are the results of a polynomial fit Fig. 9 Initial saturation indices of the basalt-specific mineral set of RN-12 with a temperature range of up to 350 °C prior to the sensitivity analyses. Saturation curves approaching the critical point of water have to be used with care To demonstrate the gain of accuracy, the MulT_predict temperature estimations for Krafla and Reykjanes are compared to conventional solute geothermometers. For the comparison, the original data of Krafla and Reykjanes (Appendices 1 , 3) are corrected for Ystroem et al. Geotherm Energy (2020) 8:2 Page 13 of 21 Fig. 10 Results for wells RN-12 and RN-23 for the three stages of the analysis. The first box plot shows a temperature estimation calculated based on an unspecific mineral set. The second column displays the developed basaltic mineral set. The third box plot shows the minimized temperature estimation after the pH, aluminium concentration, and steam loss sensitivity analysis of the specified basaltic mineral set. These box plots can be compared with the range of the measured temperature in the borehole, given by the orange box steam loss via WATCH 2.4 (Bjarnason 2010), requiring additional gas analysis data. After- wards, the solute geothermometers are applied. The table in Appendix 4 comprises quartz geothermometers according to Fournier and Potter (1982), Arnórsson et  al. (1983), and Verma (2000); Na/K geothermometers according to Truesdell (1976), Fournier (1979), Giggenbach (1988), Arnórsson (2000), and Can (2002), as well as Na/K/Ca geothermom- eters according to Fournier and Truesdell (1973), Nieva and Nieva (1987), and Kharaka and Mariner (1989), and K /Mg geothermometer according to Giggenbach (1988). All geothermometers were checked for their applicability in these settings. The results of the conventional geothermometers are visualized in Appendix 5 for Krafla and Appen - dix 6 for Reykjanes together with the results of MulT_predict. In all cases, our applica- tion targeted the measured temperature more precisely with a lower overall spread of the temperature estimation without requiring additional gas analysis data. Compared to MulT_predict (Krafla: 3.7%; Reykjanes: 4.7%), the overall temperature spread of conven - tional solute geothermometers is 10.5% for Krafla and 12.3% for Reykjanes. Conclusion and outlook This application of multicomponent geothermometry is a promising tool for reservoir temperature estimations. This specific approach comprises a devised basalt-specific mineral set and a subsequent sensitivity analysis based on a standard chemical analysis of the fluid composition without the need for a sophisticated gas analysis. The statisti - cally robust temperature estimations of the reservoir are incorporated in a valuable tool Ystroem et al. Geotherm Energy (2020) 8:2 Page 14 of 21 for precise reservoir temperature estimation. Thus, the methodology enhances the usa - bility, the applicability during geothermal exploration as an economically efficient tool for reservoir temperature determination. The emphasis of this study was the validation of this optimized approach of multicom - ponent geothermometry. A basalt-specific mineral assemblage was devised to reduce temperature estimation uncertainties. These estimations were further improved by using a subsequent sensitivity analysis via the herein proposed MulT_predict tool. The opti - mization of pH, aluminium concentration, and steam loss reduces the uncertainty of the temperature estimations significantly. Hence, the back-calculations enable the recon - struction of the in  situ equilibrium temperature conditions between the geothermal fluid and the reservoir mineral assemblage. This equilibrium state corresponds with the underlying geochemical assumptions of geothermometry. The approach presented here would even allow for constraining unknown input parameters. An educated guess of the parameter can be varied to reach the best-fit value. For validation, the calculated reservoir temperatures are compared against measured in  situ reservoir temperatures and classic solute geothermometry. The maximum uncertainty of the temperature estimations is only 2.6% with respect to the in  situ reservoir temperature. The accuracy of the results shows the efficiency and credibility of the method. This multicomponent approach bene - fits from its statistical robustness due to the conjunction of the saturation indices of mul - tiple mineral phases for temperature estimations. Therefore, it can be applied to diverse geothermal sites with different fluid origins. Furthermore, high-temperature systems can be investigated by extrapolation and modification of the Debye–Hückel parameters in the LLNL database, yet resulting in reservoir temperature estimations with small variances. The method is easy to apply because of the simplicity in terms of input data. A standard water analysis is sufficient for obtaining very accurate results, which facilitates the usabil - ity especially at less explored sites where good-quality data is often missing. Overall, the validation of the procedure was successful and improved temperature estimations via multicomponent geothermometry. In future, a broader application over different mineral sets is envisaged to expand the usability of the methodology towards other geological settings. Acknowledgements Thanks to the reviewers and the editor in chief for their constructive suggestions that helped us to improve the manu- script substantially. The study is part of the Helmholtz portfolio project “Geoenergy”. The support from the program “Renewable Energies”, under the topic “Geothermal Energy Systems”, is gratefully acknowledged. We also thank the EnBW Energie Baden-Württemberg AG for supporting geothermal research at KIT. Authors’ contributions LHY: acquisition of data, analysis, interpretation, paper writing. FN: conception of the study, paper writing, paper revision. SH: conception of the study, paper revision. TK: paper revision. All authors read and approved the final manuscript. Funding See section “Acknowledgements”. Availability of data and materials All data on which the current study relies are presented in the text and are cited. Competing interests The authors declare that they have no competing interests. Appendices Appendix 1 See Table 4. Ystroem et al. Geotherm Energy (2020) 8:2 Page 15 of 21 Table 4 Chemical analysis of water samples by Guðmundsson and Arnórsson (2002) from wells at Krafla collected in 1997 and 1998 Sample no. Well Sampling date Pressure [bar] pH value Temperature of pH Element concentration of the sample [mmol/kg] measurement [°C] SiO Na K Ca Mg Cl F SO H S Fe Al CO 2 4 2 2 97-3103 K-28 26.10.1997 6.5 9.75 20.9 7.98 9.66 0.66 0.10 0.0001 0.49 0.048 2.99 1.08 0.00015 0.039 0.70 98-3206 K-11 24.06.1998 1.9 9.65 23.2 10.81 9.70 0.80 0.05 0.0001 1.19 0.105 2.34 1.03 0.00009 0.038 2.15 98-3208 K-24 25.06.1998 2.3 9.73 24.2 6.04 9.48 0.44 0.09 0.0000 0.86 0.040 3.29 0.85 0.00006 0.031 0.41 98-3210 K-28 25.06.1998 5.2 9.55 24.8 7.89 9.86 0.65 0.09 0.0001 0.72 0.042 3.58 1.29 0.00013 0.033 1.23 Ystroem et al. Geotherm Energy (2020) 8:2 Page 16 of 21 Appendix 2 See Table 5. Table 5 The unspecific mineral set, ordered in  groups of  minerals and  their associated phases Mineral group Associated mineral phases Carbonates Calcite, aragonite, dolomite Oxides and hydroxides Spinel, hematite, goethite, diaspore, gibbsite Sulphides and sulphates Pyrite, marcasite, pyrrhotite, anhydrite, gypsum Nesosilicates Forsterite, grossular, andradite, andalusite, sillimanite, kyanite Sorosilicates Gehlenite, lawsonite, epidote, zoisite Inosilicates Wollastonite, diopside, hedenbergite, ferrosilite, enstatite, anthophyllite, tremolite, pargasite Phyllosilicates Talc, muscovite, paragonite, phlogopite, illite, smectite, clinochlore, kaolinite Tectosilicates Quartz, chalcedony, anorthite, albite, sanidine, K-feldspar, microcline, analcime, laumontite, wairakite Ystroem et al. Geotherm Energy (2020) 8:2 Page 17 of 21 Appendix 3 See Table 6. Table 6 Chemical analysis of water samples by Óskarsson (2015) from the Reykjanes field Well Sampling date Pressure [bar] pH value Temperature of pH Element concentration of the sample [mmol/kg] measurement SiO Na K Ca Mg Cl F SO H S Fe Al CO [°C] 2 4 2 2 RN-12 30.10.2012 29.7 5.57 22.3 13.81 465.65 39.74 47.25 0.0382 602.25 0.012 0.18 0.14 0.00553 0.004 1.45 RN-23 21.05.2012 26.3 5.29 21.9 13.03 561.30 49.74 56.25 0.0913 711.54 0.012 0.29 0.02 0.01208 0.006 0.52 Ystroem et al. Geotherm Energy (2020) 8:2 Page 18 of 21 Appendix 4 See Table 7. Table 7 Temperature estimations via conventional solute geothermometers (quartz, Na/K, Na/K/Ca, K /Mg) for the wells at Krafla (K-28, K-11, K-24 and K-28-2) as well as Reykjanes (RN-12 and RN-23) based on back-calculated element concentrations using WATCH 2.4 (Bjarnason 2010) Sample no. Well Solute geothermometer [°C] Quartz Na/K Na/K/Ca K²/Mg Fournier Arnórsson Verma Truesdell Fournier Giggenbach Arnósson Can (2002) Fournier Nieva Kharaka Giggenbach and Potter et al. (2000) (1976) (1979) (1988) (2000) and Truesdall and Nieva and Mariner (1988) (1982) (1983) (1973) (1987) (1989) 97-3103 K-28 197 181 201 204 230 245 211 218 209 173 220 240 98-3206 K-11 250 221 259 227 248 261 232 237 226 194 248 240 98-3208 K-24 213 194 219 163 198 214 169 187 186 187 98-3210 K-28-2 235 210 243 200 227 242 207 215 207 174 219 237 RN-12 301 249 300 231 251 264 236 240 239 195 269 301 RN-23 293 245 295 236 255 267 240 244 244 206 278 288 Ystroem et al. Geotherm Energy (2020) 8:2 Page 19 of 21 Appendix 5 See Fig. 11. Fig. 11 Comparison of conventional qualitative solute geothermometers based on back-calculated element concentrations using WATCH 2.4 (Bjarnason 2010) (cf. Appendix 4) with the end results of MulT_predict (Fig. 7) for the wells at Krafla Ystroem et al. Geotherm Energy (2020) 8:2 Page 20 of 21 Appendix 6 See Fig. 12. Fig. 12 Comparison of conventional qualitative solute geothermometers based on back-calculated element concentrations using WATCH 2.4 (Bjarnason 2010) (cf. Appendix 4) with the end results of MulT_predict (Fig. 10) for the wells at Reykjanes Received: 6 May 2019 Accepted: 15 January 2020 References Ármannsson H, Guðmundsson Á, Steingrímsson BS. Exploration and development of the Krafla geothermal area. Jökull. 1987;37:13–30. Arnórsson S. Major element chemistry of the geothermal sea-water at Reykjanes and Svartsengi, Iceland. Mineral Mag. 1978;42:209–20. https ://doi.org/10.1180/minma g.1978.042.322.07. Arnórsson S. The quartz- and Na/K geothermometers: I. New thermodynamic calibration. In: Proceedings World Geother- mal Congress: Kyushu-Tohoku, Japan. 2000. p. 929–34. Arnórsson S, Grönvold K, Sigurdsson S. Aquifer chemistry of four high-temperature geothermal systems in Iceland. 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Cooper DC, Palmer CD, Smith RW, McLing TL. Multicomponent equilibrium models for testing geothermometry approaches. In: 38th workshop on geothermal reservoir engineering. 2013. Debye P, Hückel E. Zur Theorie der Elektrolyte: 1. Gefrierpunktserniedrigung und verwandte Erscheinungen. Physikalische Zeitschrift. 1923;24:S185–206. Ystroem et al. Geotherm Energy (2020) 8:2 Page 21 of 21 Ellis AJ. Quantitative interpretation of chemical characteristics of hydrothermal systems. Geothermics. 1970;2:516–28. https ://doi.org/10.1016/0375-6505(70)90050 -7. Fouillac C, Michard G. Sodium/lithium ration in water applied to geothermometry of geothermal reservoirs. Geothermics. 1981;10:55–70. Fournier RO. Chemical geothermometers and mixing models for geothermal systems. Geothermics. 1977;5:41–50. https ://doi.org/10.1016/0375-6505(77)90007 -4. Fournier RO. 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A multicomponent geothermometer for high-temperature basalt settings

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Abstract

lars.ystroem@kit.edu Division of Geothermal For successful geothermal reservoir exploration, accurate temperature estimation is Research, Institute of Applied essential. Since reservoir temperature estimation frequently involves high uncertain- Geosciences, Karlsruhe Institute of Technology (KIT ), ties when using conventional solute geothermometers, a new statistical approach is Campus South, Building proposed. The focus of this study is on the development of a new multicomponent 50.40, Adenauerring 20b, geothermometer tool which requires a significantly reduced data set compared to 76131 Karlsruhe, Germany existing approaches. The method is validated against reservoir temperature measure- ments in the Krafla and the Reykjanes geothermal systems. A site-specific basaltic mineral set was selected as the basis to compute the equilibrium temperatures. These high-enthalpy geothermal reservoirs are located in the neo-volcanic zone of Iceland where the fluid temperatures are known to reach up to 350 °C at a depth of 2000 m. During ascent, the fluid composition is prone to changes as well as possible phase segregation due to depressurization and boiling. Therefore, to reduce the uncertainty of temperature estimations, reservoir temperature conditions are numerically recon- structed with sensitivity analyses considering pH, aluminium concentration, and steam loss. The evaluation of the geochemical data and the sensitivity analyses were calcu- lated via a numerical in-house tool called MulT_predict. In all cases, the temperature estimations match with the in situ temperatures measured at Krafla and Reykjanes. The development of this method tends to be a promising and precise tool for reservoir temperature estimation. The developed methodology is a fast and easy-to-handle exploration tool that can be applied to standard geochemical data without the need for a sophisticated gas analysis yet obtaining very accurate results. Keywords: Multicomponent geothermometry, Geochemical exploration, Reservoir temperature estimation, Sensitivity analysis, Krafla geothermal system, Reykjanes geothermal system, MulT_predict Introduction A reliable temperature estimation for a targeted geothermal reservoir, which lays the foundation for the prediction of producible energy, is essential for a successful explo- ration campaign. Conventional solute geothermometers are a commonly used tool for the deduction of reservoir temperature from geochemical composition of geothermal spring samples. These geothermometers were introduced in the 1960s and have been undergoing further development since then (Can 2002; Ellis 1970; Fouillac and Michard 1981; Fournier and Potter 1979; Fournier and Rowe 1966; Fournier and Truesdell 1973; © The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creat iveco mmons .org/licen ses/by/4.0/. Ystroem et al. Geotherm Energy (2020) 8:2 Page 2 of 21 Giggenbach 1988; Sanjuan et al. 2014; Verma and Santoyo 1997). These approaches use the temperature dependence of the saturation of mineral phases (e.g. silica) or certain cation ratios in the fluids. The measured concentrations of these fluid constituents are then directly linked to a reservoir temperature. The fundamental assumption of geother - mometry is the overall chemical equilibrium of the fluid and the reservoir rock. Sec - ondary processes may change the fluid composition and hence, the equilibrium while migrating to the earth surface. These variations can result in large uncertainties for the reservoir temperature determination using solute geothermometers (Nitschke et  al. 2018). The more recently developed multicomponent geothermometry evaluates the equilibria of multiple mineral phases (Spycher et al. 2014). Numerical geochemical spe- ciation codes facilitate this evaluation based on a large number of minerals, which leads to a statistically more robust method. Spycher et al. (2014) proposed a pre-selection of minerals representing the site-specific reservoir rocks to enhance accuracy. Corrections were established to overcome interferences from secondary processes such as dilution, boiling, and mixing of fluids affecting the temperature estimation (Cooper et  al. 2013; Peiffer et  al. 2014; Spycher et  al. 2014). These methods need an additional gas analysis for precise temperature estimations. u Th s, Nitschke et al. (2017) introduced a method to reconstruct in situ conditions of the reservoir temperature by varying sensitive parame- ters, especially pH and aluminium concentration as well as steam loss, to further reduce the uncertainty of equilibrium temperatures. The goals of this study are to refine and to validate the existing specific multicom - ponent approach according to Nitschke et  al. (2017) and to expand it towards a high- precision exploration tool. This study devises a basalt-specific mineral set including secondary mineral phases for global application to basaltic stratigraphy. For the vali- dation, geochemical data and in  situ temperature measurements from basalt-hosted geothermal systems, Krafla and Reykjanes, are used. These are high-enthalpy systems with near-boiling reservoir fluids and, thus, the effect of steam loss between the reser - voir and the liquid sampled at the well-head has to be considered. Krafla hosts dilute meteoric fluids (Arnórsson et  al. 1978), and Reykjanes a more saline reservoir fluid partially originating from seawater (Arnórsson 1978). To validate the method, the tem- perature estimations are compared with direct in situ temperature measurements of the wells published by Guðmundsson and Arnórsson (2002) for Krafla, and Óskarsson et al. (2015) for Reykjanes. The advantage of the validated method is the frugality in terms of input data. High-accuracy temperature estimations can be achieved based on standard fluid analyses and do not require comprehensive high-end fluid and gas analyses, which are required for other solute multicomponent geothermometer approaches. Method and data The basis of the method is a standard fluid analysis comprising major cations and ani - ons as well as aluminium concentration and pH. The water analysis is used to calculate equilibrium conditions between the dissolved constituents in the geothermal fluid and the reservoir rock minerals. For identification of the reservoir temperature conditions, sensitive parameters have to be evaluated statistically. The application relies on the fol - lowing general assumptions: (i) the reservoir and the geothermal fluid are in equilib - rium. Therefore, the ion activity product of a mineral phase equals its thermodynamic Ystroem et al. Geotherm Energy (2020) 8:2 Page 3 of 21 equilibrium constant. (ii) A temperature-dependent reaction between the host rock and the water leads to a specific amount of dissolved solids in the fluid phase. The equilibrium reaction is based on the law of mass action. The state of the dynamic equilibrium between the reactants is expressed in terms of the saturation index SI(1) IAP v v i i SI(T ) = log = log γ x − log (K (T )), (1) i i K (T ) with IAP being the ion activity product and K being the temperature-dependent ther- modynamic equilibrium constant of one mineral phase. IAP is the product of the activity coefficients γ and the mole fractions of the solute mineral phase x considering their sto- i i ichiometric coefficient ν . A positive saturation index indicates an oversaturation and a potential precipitation of the mineral. Though, if the ion activity product is smaller than the equilibrium constant, the saturation index will be negative. In this case, the solution is undersaturated with the potential to dissolve the mineral phase. Therefore, equilib - rium is given at SI = 0. Debye and Hückel (1923) established an equation for non-ideal electrolyte solutions taking into account the electrostatic interaction among the ions by using the activity coefficients γ (2). In order to fit the Debye–Hückel equation to experimental data, Rob - inson and Stokes (2002) extended the original equation by adding a linear concentration term ḂI. Az I log γ =− √ + BI, (2) 1 + (å) B I where A and B are temperature-dependent constants, z is the charge number of the ion, I is the ionic strength, and å is the hydrated ion size. The numerator quantifies the long-range Coulomb forces acting on the ion, whereas the denominator defines the short-range interactions between the ions itself and with the solvent. The extended Debye–Hückel equation (Eq.  2) expands the former validity limit in terms of the ionic strength to I = 1.0 mol/L for mixed electrolytes. Furthermore, there are application lim- its given by specific temperatures and pressures. The latter is negligible at least up to a temperature of 300 °C (Helgeson 1969). In this study, chemical speciation and saturation indices are computed with IPhreeqc 3.4.0-12927 (Parkhurst and Appelo 2013). Ion activity coefficients are based on the extended Debye–Hückel equation. The required constants A, B, and Ḃ are obtained from the commonly used LLNL (Lawrence Livermore National Laboratory) database. Saturation indices are computed for all specified minerals for a given solution. Reed and Spycher (1984) plotted these saturation indices versus temperature to investigate the equilibrium temperature of the geothermal fluid and the reservoir mineral assemblage. For validation of the multicomponent geothermometer, the method is applied on well- studied geothermal sites in Iceland and further developed to obtain an easy-to-handle and convenient high-precision exploration tool. Krafla is a high-temperature geothermal field located in the NE of Iceland. The geo - thermal system is situated in the neo-volcanic zone (Ármannsson et al. 1987). The in situ temperature measurements (Table 1) and the geochemical data of the wells (Appendix 1) Ystroem et al. Geotherm Energy (2020) 8:2 Page 4 of 21 Table 1 In situ measurements of  the  temperature [°C] in  the  wells of  Krafla (K) at  specific depths [m] for  permeable horizons presented in  Guðmundsson and  Arnórsson (2002) (Table 3) K-11 K-24 K-28 1330 m > 240 °C 580 m 190 °C 500 m 230 °C 1600 m > 240 °C 780 m 195 °C 800 m 240 °C 1700 m > 240 °C 920 m 210 °C 2180 m > 300 °C 1150 m 225 °C were published by Guðmundsson and Arnórsson (2002). The upper 1000 m of the stra - tigraphy are built up by alternating layers of basaltic lavas and hyaloclastite. The latter is subglacial erupted basaltic lava, which forms hydrated breccia once it is in contact with water. Below 500  m, the hyaloclastite layers form subhorizontal reservoirs. The follow - ing 1000 m are covering basaltic intrusives, where geothermal fluids of up to 310 °C are evident (Guðmundsson and Arnórsson 2002). A more detailed stratigraphy of the field is given by Ármannsson et  al. (1987). The mineralogical content of Icelandic geother - mal systems and the geochemistry of the fluids are described by Arnórsson et al. (1983). Sampling methods and the geochemical analysis are given in Arnórsson et al. (2006). Results of the analysis The application of this multicomponent geothermometer approach requires the evalua - tion of the equilibrium of each solute mineral phase and, thus, the calculation of satura- tion indices of the considered minerals versus temperature. The saturation indices are calculated from 20 to 300  °C. The calculations of the saturation indices are processed via MATLAB. Therefore, the MulT_predict tool was developed which determines the intersection of the saturation index function for each mineral phase with the equilibrium line (Fig.  1). Thus, the tool calculates all mineral-specific saturation indices functions throughout the temperature range by interacting with IPhreeqc. Only minerals having exactly one intersection with the equilibrium line are taken into account for the temper- ature determination procedure. The resulting intersection temperatures are combined in a box plot. This plot represents a first estimate of the reservoir temperature. Secondary effects perturb the chemical equilibrium of a fluid sample while migrating to the earth surface. The chemistry may change due to boiling, degassing, precipitation of phases, dilution, or mixture with shallow and low-mineralized waters as well as re- equilibration with the surrounding rocks (Cooper et  al. 2013; Fournier 1977; Fournier and Truesdell 1974; Pang and Reed 1998; Reed and Spycher 1984). To determine the most vulnerable sensitive parameters for later sequential sensitiv- ity analysis, a series of variations on system parameters (pH, redox, and steam loss) have been computed. Similarly, the concentrations of aluminium, magnesium, and iron, being major components in the minerals but only trace elements in the fluid, have been examined. The equilibrium temperature distributions for K-28 were exemplarily plotted against these parameters (Fig.  2). It is shown that the most important and vulnerable system parameter is the pH value, which is in good agreement with what is also assumed by Nitschke et al. (2017) as well as Reed and Spycher (1984). Changes have a significant Ystroem et al. Geotherm Energy (2020) 8:2 Page 5 of 21 Fig. 1 Example of the creation of an equilibrium temperature distribution box plot via the saturation indices over the temperature [°C] of the basalt-specific mineral phases for sample K-28. The box plot includes the temperature values of each mineral where SI = 0 (intersection of the saturation index of a mineral phase and the equilibrium line) impact on the solubility of mineral phases. The pH value is prone to phase segregation effects like degassing, boiling, and steam loss. Also, the pH is a temperature-dependent function, which decreases when temperature rises. In addition, regarding Fig.  2, steam loss itself is another vulnerable system parameter. Thus, possible phase segregation due to boiling has to be taken into account. The loss of steam fraction corresponds to a loss of solvent and results in the concentration of the ascending fluid. The effect of steam loss needs to be compensated by adding back the lost water. Equally, the vulner- ability of trace elements is shown in Fig. 2. These constituents are particularly prone to interferences from secondary processes and measurement errors. Simultaneously, they have a high impact on the solubility product and hence, on the saturation index of the majority of reservoir minerals. Clearly, aluminium is the most vulnerable trace ele- ment. Its concentration is a crucial parameter when computing the saturation state of aluminosilicates, which represent the major mineral phases in most geothermal reser- voirs (e.g. basalts, granitoids, sandstone, greywackes, etc.). Such aluminosilicate mineral assemblages contain phases like feldspars, zeolites, micas, and clay minerals. Due to the tendency of complex formation and precipitation processes (Brown 2013), the deter- mination of accurate aluminium concentrations is prone to large errors. Furthermore, the variations of the redox potential as well as magnesium and iron concentration were tested. As it is revealed that these parameters have only marginal effects on the tempera - ture estimations, they are not further discussed in this study. In view of the above, the in situ values of the most vulnerable sensitive parameters, pH, aluminium concentration, and steam loss, have to be reconstructed. For this optimization, a sequential sensitivity analysis for each parameter is used. This sensitivity analysis is executed by the tool. The statistically backed minimization of the temperature spread enables the back-calculation on the in situ geochemical equilibrium between the geothermal fluid and the reservoir mineral assemblage, which is the basic assumption of the method. The tool varies these Ystroem et al. Geotherm Energy (2020) 8:2 Page 6 of 21 Fig. 2 Various sensitivity analyses of several parameters (pH value, boiling, pe value, Al, Fe, and Mg concentration) parameters around the initial measured value such that a minimal temperature spread is found. In an ideal case, the equilibrium temperatures of each mineral phase of the reservoir assemblage converge to one discrete reservoir temperature. Also unknown parameters can be estimated in this manner. Thus, a geochemical foreknowledge of the geothermal system is needed to make an educated guess for the unknown parameter, which then can be estimated towards best-fit conditions. To statistically evaluate the resulting box plots, the mineral set has to remain unchanged throughout all variations. Minerals that do not equilibrate due to over- or undersaturation or have multiple inter- sections with the equilibrium line in any step of the sensitive analyses were discarded Ystroem et al. Geotherm Energy (2020) 8:2 Page 7 of 21 from further statistical processing. Changes within the set of consistent mineral phases during the sensitivity analysis would lead to false conclusions because the temperature estimations would then result from different basic conditions (i.e. different mineral sets). Concerning this, the spread of the overlaying boxes and the median differences of each neighbouring plot are matched to identify the most likely value for the sensi- tive parameter, indicated by the least equilibrium temperature spread. This procedure is done sequentially for the pH value, the aluminium concentration, and the percent- age of steam loss. Afterwards, the best-fit values for all parameters are combined in a final temperature estimation. Nevertheless, the aim of this study is the reconstruction of reservoir temperatures, instead of the encompassing reconstruction of geochemical reservoir conditions. As a generic example, the calculation and optimization will be shown in detail for well K-28 to give an understanding of the procedure. Therefore, the geochemical data (Appendix 1) of the sample is used. The result of this first calculation is shown in Fig.  6a. For the temperature estimation from the non-specific mineral set (Appendix 2) without further optimization, a large temperature spread of 260  °C is obtained. Hence, in this study, a basalt-specific mineral set was devised to enhance the accuracy of this method. The basaltic minerals have been selected according to the mineralogical study of the Krafla reservoir rocks (Arnórsson et al. 1983). This set is extended for secondary mineral phases, occurring in geothermal reservoirs due to hydrothermal alteration processes. It is based on the stability of mineral phases at certain temperature and pressure levels which were described by Giggenbach (1981). The resulting basalt-specific mineral set (Table  2) is used to evaluate the in situ temperatures of the reservoir. After application of the multicomponent geothermometer based on the selected mineral set, the reser- voir temperature estimation could be improved (Fig. 6b), yet the temperature spread still exceeds 100 °C. As a second step, the sensitivity analysis is conducted. Firstly, the pH value is opti- mized. The initial pH of 9.75 is varied in increments of 0.1 towards higher acidity and basicity. The result is shown in Fig.  3 where the minimal spread of the box is reached at pH 7.85. Table 2 Mineral phases contained in  the  basalt-specific mineral set devised and  used in this study Mineral group Associated mineral phases Feldspar Albite (low), microcline, k-feldspar SiO phases Quartz, chalcedony Clays Smectite, clinochlore, illite Carbonate Calcite, aragonite Zeolite Analcime, laumontite, wairakite Sulphate Anhydrite, gypsum Halide Fluorite soro-/inosilicate Epidote, anthophyllite, tremolite, pargasite Fe-phases Pyrite, marcasite, pyrrhotite, goethite Ystroem et al. Geotherm Energy (2020) 8:2 Page 8 of 21 Fig. 3 Sensitivity analysis of pH for sample K-28. The value was varied from 6.75 to 8.15 in increments of 0.1. The figure shows an extract of the data, where the pH value ranges from 7.55 to 8.15 in increments of 0.1. For pH 7.85, the statistical minimum of the boxplot comparison is reached; it is highlighted in a darker blue colour Fig. 4 Sensitivity analysis of aluminium concentration for sample K-28. The value was varied from 0.009 to 0.117 mmol/kg in increments of 0.006 mmol/kg. The figure shows an extract of the data, where the aluminium concentration ranges from 0.021 to 0.057 mmol/kg in increments of 0.006 mmol/kg. The statistical minimum of the boxplot comparison is reached for a concentration of 0.039 mmol/kg highlighted in a darker blue colour Separately, the aluminium concentration is evaluated. The average aluminium concen - tration in the Krafla geothermal fluids is about 1.2 ppm (0.04 mmol/kg) (Guðmundsson and Arnórsson 2002). Therefore, the aluminium concentration is varied in increments of 0.006 mmol/kg. The initial aluminium concentration of the geothermal fluid compo - sition for K-28 is 0.039 mmol/kg. In Fig.  4, an optimal concentration is also reached at 0.039 mmol/kg. Ystroem et al. Geotherm Energy (2020) 8:2 Page 9 of 21 Fig. 5 Sensitivity analysis of steam loss for sample K-28. The value was varied in increments of 1%. The figure shows an extract of the data, where the steam loss ranges from 11 to 17% in increments of 1%. For 14% steam loss, the statistical minimum of the boxplot comparison is reached; it is highlighted in a darker blue colour Fig. 6 Comparison of an unspecific mineral set (a) with the developed basaltic set (b). The boxplot in the third column (c) is the result of the combination of the pH, aluminium concentration, and steam loss sensitivity analysis. All analyses are done separately under static conditions for the remaining parameters, and all best-fit parameters were combined afterwards Lastly, the sensitivity of fluid composition to the magnitude of steam loss is consid - ered. The amount of steam loss is unknown, but has to be back-calculated. Therefore, pure water is virtually added back in increments of 1%. In Fig. 5, the optimum in steam loss is reached at 14%. The final temperature estimation is then computed by combining the best-fit values for pH, aluminium concentration, and steam loss. Figure  6c displays the reduced spread of Ystroem et al. Geotherm Energy (2020) 8:2 Page 10 of 21 the calculated temperature after each optimization step. Simultaneously to the reduced uncertainty, the median of the temperature estimate has ascended. For validation, the concluding reservoir temperature estimations are compared to downhole temperature measurements published by Guðmundsson and Arnórsson (2002) (Table  1). Figure  7 displays the temperature box plots for the wells K-11, K-24, and for K-28 of two consecutive years. The range of the measured in situ temperatures (Table  1) is figured as an orange box. In each case, the estimated temperatures fit very well the measured borehole temperatures after the optimization procedure. Note that even very small temperature ranges are matched by the estimated temperatures (e.g. K-24 and K-28). Discussion The comparison of the optimized temperature estimation and the measured downhole temperatures confirms the functionality of the application. Only for K 24, the median temperature shows a minor overestimation of 1  K above the highest measured inflow temperature, though, the estimations are also located in the measured temperature range. The overall spread of each final plot after the sensitivity analyses does not exceed 7% (K-24), but is on average 3.7% of the absolute median temperature. The uncer - tainty throughout the validation is at maximum 2.6% of the original absolute reservoir Fig. 7 Results of wells K-11, K-24, and K-28 for three stages of the analysis. The first column displays a temperature estimation calculated based on an unspecific mineral set. The box plot in the second column represents the specified basaltic mineral set. The last box plot shows the optimized temperature estimation via the pH, aluminium concentration, and steam loss sensitivity analysis. These box plots can be compared with the range of the measured temperatures in the boreholes, given by the orange box Ystroem et al. Geotherm Energy (2020) 8:2 Page 11 of 21 temperature. Thus, the validated developed tool shows a significant improvement com - pared to uncertainties of conventional solute approaches, following in the discussion. The calculation of the saturation indices relies on the LLNL database which is con - strained to temperatures of 300 °C. Therefore, most of the geochemical modelling tools are also constrained for that p–T range. Icelandic geothermal systems have the poten- tial to exceed these temperatures. To evaluate the validity limits, the investigations were extended to the Reykjanes geothermal system, which is located in the SW of Iceland. Furthermore, as the system is recharged by seawater, also the effects of high salinities can be assessed. Reykjanes is also situated in the neo-volcanic zone and the stratigraphy equals the Krafla structure with alternating layers of basaltic lavas and hyaloclastite in the upper part, followed by basaltic intrusives at greater depth. However, since the geo- thermal system is located on a peninsula, seawater infiltrates the productive horizons of the reservoir. At Krafla, the dissolved solids content is generally up to 1500 ppm. Show - ing sea water concentrations, the salinities at Reykjanes are up to 58 times higher (RN- 23: 87.160  ppm). Óskarsson et  al. (2015) published the geochemical data (Appendix 3) of the fluids from two production wells and the associated temperature logs (Table  3). In the following, the applicability of the numerical scheme will be tested at high-enthalpy geothermal fields with temperatures above 300 °C and elevated salinities. u Th s, the Debye–Hückel coefficients A, B, and Ḃ of Eq. (2) have to be extrapolated towards higher temperatures and implemented into the database. The coefficients A and B were extrapolated by a quadratic fit, whereas Ḃ was extrapolated by a cubic fit. This extrapolation is similar to the scheme proposed by Helgeson (1969). Figure 8 shows the results of polynomial parameter estimation. The obtained values for the coefficients A and B herein are very close to the results computed by Helgeson et  al. (1981). Estima- tions towards the critical temperature of water have to be used with care and, therefore, only exceed up to 350 °C. These modifications of the Debye–Hückel parameters allow technically for the com - putation of saturation indices over an extended temperature range. To gain an overview, the saturation indices of the well RN-12 at Reykjanes were plotted to 350  °C (Fig.  9). The extrapolated coefficients follow the trend of the saturation curves. The results for the reservoir temperature estimation and the comparison against measured values are presented in Fig. 10. Despite the high sodium chloride concentrations, the tool operates thoroughly. Analogous to the methodology presented for the Krafla site, the spread of the temperature box plots is minimized and eventually matches the measured tempera- tures (Table  3). The spread is about 4.7% of the measured absolute reservoir tempera - ture, while the overall temperature accuracy is at 0.5%. Table 3 In situ measurements of  the  temperture [°C] in  the  wells of  Reykjanes (RN) at specific depths [m] presented by Óskarsson et al. (2015) RN-12 RN-23 1000 m 260 °C 900 m 255 °C 1200 m 270 °C 1200 m 280 °C 1300 m 290 °C 1700 m 300 °C 1700 m 310 °C Ystroem et al. Geotherm Energy (2020) 8:2 Page 12 of 21 Fig. 8 Extrapolation of the three parameters A, B, and Ḃ of the extended Debye–Hückel equation for temperatures beyond 300 °C. The values of the solid squares are acquired from the LLNL database in IPhreeqc. The hollowed squares are the results of a polynomial fit Fig. 9 Initial saturation indices of the basalt-specific mineral set of RN-12 with a temperature range of up to 350 °C prior to the sensitivity analyses. Saturation curves approaching the critical point of water have to be used with care To demonstrate the gain of accuracy, the MulT_predict temperature estimations for Krafla and Reykjanes are compared to conventional solute geothermometers. For the comparison, the original data of Krafla and Reykjanes (Appendices 1 , 3) are corrected for Ystroem et al. Geotherm Energy (2020) 8:2 Page 13 of 21 Fig. 10 Results for wells RN-12 and RN-23 for the three stages of the analysis. The first box plot shows a temperature estimation calculated based on an unspecific mineral set. The second column displays the developed basaltic mineral set. The third box plot shows the minimized temperature estimation after the pH, aluminium concentration, and steam loss sensitivity analysis of the specified basaltic mineral set. These box plots can be compared with the range of the measured temperature in the borehole, given by the orange box steam loss via WATCH 2.4 (Bjarnason 2010), requiring additional gas analysis data. After- wards, the solute geothermometers are applied. The table in Appendix 4 comprises quartz geothermometers according to Fournier and Potter (1982), Arnórsson et  al. (1983), and Verma (2000); Na/K geothermometers according to Truesdell (1976), Fournier (1979), Giggenbach (1988), Arnórsson (2000), and Can (2002), as well as Na/K/Ca geothermom- eters according to Fournier and Truesdell (1973), Nieva and Nieva (1987), and Kharaka and Mariner (1989), and K /Mg geothermometer according to Giggenbach (1988). All geothermometers were checked for their applicability in these settings. The results of the conventional geothermometers are visualized in Appendix 5 for Krafla and Appen - dix 6 for Reykjanes together with the results of MulT_predict. In all cases, our applica- tion targeted the measured temperature more precisely with a lower overall spread of the temperature estimation without requiring additional gas analysis data. Compared to MulT_predict (Krafla: 3.7%; Reykjanes: 4.7%), the overall temperature spread of conven - tional solute geothermometers is 10.5% for Krafla and 12.3% for Reykjanes. Conclusion and outlook This application of multicomponent geothermometry is a promising tool for reservoir temperature estimations. This specific approach comprises a devised basalt-specific mineral set and a subsequent sensitivity analysis based on a standard chemical analysis of the fluid composition without the need for a sophisticated gas analysis. The statisti - cally robust temperature estimations of the reservoir are incorporated in a valuable tool Ystroem et al. Geotherm Energy (2020) 8:2 Page 14 of 21 for precise reservoir temperature estimation. Thus, the methodology enhances the usa - bility, the applicability during geothermal exploration as an economically efficient tool for reservoir temperature determination. The emphasis of this study was the validation of this optimized approach of multicom - ponent geothermometry. A basalt-specific mineral assemblage was devised to reduce temperature estimation uncertainties. These estimations were further improved by using a subsequent sensitivity analysis via the herein proposed MulT_predict tool. The opti - mization of pH, aluminium concentration, and steam loss reduces the uncertainty of the temperature estimations significantly. Hence, the back-calculations enable the recon - struction of the in  situ equilibrium temperature conditions between the geothermal fluid and the reservoir mineral assemblage. This equilibrium state corresponds with the underlying geochemical assumptions of geothermometry. The approach presented here would even allow for constraining unknown input parameters. An educated guess of the parameter can be varied to reach the best-fit value. For validation, the calculated reservoir temperatures are compared against measured in  situ reservoir temperatures and classic solute geothermometry. The maximum uncertainty of the temperature estimations is only 2.6% with respect to the in  situ reservoir temperature. The accuracy of the results shows the efficiency and credibility of the method. This multicomponent approach bene - fits from its statistical robustness due to the conjunction of the saturation indices of mul - tiple mineral phases for temperature estimations. Therefore, it can be applied to diverse geothermal sites with different fluid origins. Furthermore, high-temperature systems can be investigated by extrapolation and modification of the Debye–Hückel parameters in the LLNL database, yet resulting in reservoir temperature estimations with small variances. The method is easy to apply because of the simplicity in terms of input data. A standard water analysis is sufficient for obtaining very accurate results, which facilitates the usabil - ity especially at less explored sites where good-quality data is often missing. Overall, the validation of the procedure was successful and improved temperature estimations via multicomponent geothermometry. In future, a broader application over different mineral sets is envisaged to expand the usability of the methodology towards other geological settings. Acknowledgements Thanks to the reviewers and the editor in chief for their constructive suggestions that helped us to improve the manu- script substantially. The study is part of the Helmholtz portfolio project “Geoenergy”. The support from the program “Renewable Energies”, under the topic “Geothermal Energy Systems”, is gratefully acknowledged. We also thank the EnBW Energie Baden-Württemberg AG for supporting geothermal research at KIT. Authors’ contributions LHY: acquisition of data, analysis, interpretation, paper writing. FN: conception of the study, paper writing, paper revision. SH: conception of the study, paper revision. TK: paper revision. All authors read and approved the final manuscript. Funding See section “Acknowledgements”. Availability of data and materials All data on which the current study relies are presented in the text and are cited. Competing interests The authors declare that they have no competing interests. Appendices Appendix 1 See Table 4. Ystroem et al. Geotherm Energy (2020) 8:2 Page 15 of 21 Table 4 Chemical analysis of water samples by Guðmundsson and Arnórsson (2002) from wells at Krafla collected in 1997 and 1998 Sample no. Well Sampling date Pressure [bar] pH value Temperature of pH Element concentration of the sample [mmol/kg] measurement [°C] SiO Na K Ca Mg Cl F SO H S Fe Al CO 2 4 2 2 97-3103 K-28 26.10.1997 6.5 9.75 20.9 7.98 9.66 0.66 0.10 0.0001 0.49 0.048 2.99 1.08 0.00015 0.039 0.70 98-3206 K-11 24.06.1998 1.9 9.65 23.2 10.81 9.70 0.80 0.05 0.0001 1.19 0.105 2.34 1.03 0.00009 0.038 2.15 98-3208 K-24 25.06.1998 2.3 9.73 24.2 6.04 9.48 0.44 0.09 0.0000 0.86 0.040 3.29 0.85 0.00006 0.031 0.41 98-3210 K-28 25.06.1998 5.2 9.55 24.8 7.89 9.86 0.65 0.09 0.0001 0.72 0.042 3.58 1.29 0.00013 0.033 1.23 Ystroem et al. Geotherm Energy (2020) 8:2 Page 16 of 21 Appendix 2 See Table 5. Table 5 The unspecific mineral set, ordered in  groups of  minerals and  their associated phases Mineral group Associated mineral phases Carbonates Calcite, aragonite, dolomite Oxides and hydroxides Spinel, hematite, goethite, diaspore, gibbsite Sulphides and sulphates Pyrite, marcasite, pyrrhotite, anhydrite, gypsum Nesosilicates Forsterite, grossular, andradite, andalusite, sillimanite, kyanite Sorosilicates Gehlenite, lawsonite, epidote, zoisite Inosilicates Wollastonite, diopside, hedenbergite, ferrosilite, enstatite, anthophyllite, tremolite, pargasite Phyllosilicates Talc, muscovite, paragonite, phlogopite, illite, smectite, clinochlore, kaolinite Tectosilicates Quartz, chalcedony, anorthite, albite, sanidine, K-feldspar, microcline, analcime, laumontite, wairakite Ystroem et al. Geotherm Energy (2020) 8:2 Page 17 of 21 Appendix 3 See Table 6. Table 6 Chemical analysis of water samples by Óskarsson (2015) from the Reykjanes field Well Sampling date Pressure [bar] pH value Temperature of pH Element concentration of the sample [mmol/kg] measurement SiO Na K Ca Mg Cl F SO H S Fe Al CO [°C] 2 4 2 2 RN-12 30.10.2012 29.7 5.57 22.3 13.81 465.65 39.74 47.25 0.0382 602.25 0.012 0.18 0.14 0.00553 0.004 1.45 RN-23 21.05.2012 26.3 5.29 21.9 13.03 561.30 49.74 56.25 0.0913 711.54 0.012 0.29 0.02 0.01208 0.006 0.52 Ystroem et al. Geotherm Energy (2020) 8:2 Page 18 of 21 Appendix 4 See Table 7. Table 7 Temperature estimations via conventional solute geothermometers (quartz, Na/K, Na/K/Ca, K /Mg) for the wells at Krafla (K-28, K-11, K-24 and K-28-2) as well as Reykjanes (RN-12 and RN-23) based on back-calculated element concentrations using WATCH 2.4 (Bjarnason 2010) Sample no. Well Solute geothermometer [°C] Quartz Na/K Na/K/Ca K²/Mg Fournier Arnórsson Verma Truesdell Fournier Giggenbach Arnósson Can (2002) Fournier Nieva Kharaka Giggenbach and Potter et al. (2000) (1976) (1979) (1988) (2000) and Truesdall and Nieva and Mariner (1988) (1982) (1983) (1973) (1987) (1989) 97-3103 K-28 197 181 201 204 230 245 211 218 209 173 220 240 98-3206 K-11 250 221 259 227 248 261 232 237 226 194 248 240 98-3208 K-24 213 194 219 163 198 214 169 187 186 187 98-3210 K-28-2 235 210 243 200 227 242 207 215 207 174 219 237 RN-12 301 249 300 231 251 264 236 240 239 195 269 301 RN-23 293 245 295 236 255 267 240 244 244 206 278 288 Ystroem et al. Geotherm Energy (2020) 8:2 Page 19 of 21 Appendix 5 See Fig. 11. Fig. 11 Comparison of conventional qualitative solute geothermometers based on back-calculated element concentrations using WATCH 2.4 (Bjarnason 2010) (cf. Appendix 4) with the end results of MulT_predict (Fig. 7) for the wells at Krafla Ystroem et al. 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