Cálculos de las características de fluídos de yacimientos geotermales: GeoSys. Chem and WATCH

Ignacio Salvador Torres-Alvarado¹, Mahendra P. Verma²*, Kizito Opondo³, David Nieva⁴, Füsun Tut Haklidir⁵, Edgar Santoyo¹, Rosa María Barragán², and Víctor Arellano²

¹ Centro de Investigación en Energía, Universidad Nacional Autónoma de México, Priv. Xochicalco s/n, Centro, A.P. 34, 62580 Temixco, Morelos, México.

² Geotermia, Instituto de Investigaciones Eléctricas, Reforma 113, Col. Palmira, 62490 Cuernavaca, Morelos, México. *Mahendra@iie.org.mx

³ Geochemistry Laboratory, Olkaria Geothermal Project, Moi South Lake Road, P.O. Box 785, 20117 Naivasha, Kenya.

⁵Zorlu Energy Group, Zorlu plaza, Avcilar-Istanbul, Turkey.

Manuscript received: April 10, 2012
Corrected manuscript received: August 8, 2012
Manuscript accepted: August 10, 2012

ABSTRACT

A comparative study of the reservoir fluid characteristics calculation of ten production wells of Los Azufres, Los Humeros and Cerro Prieto geothermal fields using two computer codes GeoChem (GeoSys.Chem) and WATCH is presented. GeoSys.Chem estimates the reservoir temperature and vapor fraction through quartz geothermometry and assuming enthalpy conservation, while the average temperature of quartz and Na/K geothermometers is employed in WATCH and vapor fraction is also calculated through enthalpy conservation. Both programs use the conservation of alkalinity (i.e., proton balance) for pH calculations. The difference in temperature (pressure) causes considerable effects on the calculated geothermal reservoirfluid characteristics of high enthalpy wells and negative (or near to zero) vapor fraction for low enthalpy wells. The calculated high concentration of CO₂ in the secondary vapor discharged in the atmosphere at the weir box (up to 11,719 mmole/kg) suggests that the analysis of carbonic species in the geothermal waters is crucial. In the absence ofgood quality analysis of carbonic species it is suggested to consider the CO2 in the vapor sample at the separator and the total dissolved carbonic species concentration in the water sample (i.e., without considering the liberation of CO₂ in the atmospheric vapor at the weir box) for the calculation of geothermal reservoir fluid composition.

Key words: GeoSys.Chem, GeoChem, WATCH, geochemical modeling, geothermal system.

RESUMEN

Se presenta un estudio comparativo del cálculo de las características del fluido de yacimiento de diez pozos productores de los campos geotérmicos Los Azufres, Los Humeros y Cerro Prieto, utilizando dos programas de cómputo, GeoChem (GeoSys.Chem) y WATCH. GeoSys.Chem calcula la temperatura y la fracción de vapor del yacimiento a través de la geotermometría de cuarzo y asumiendo conservación de la entalpía, mientras que la temperatura promedio de geotermómetros de cuarzo y Na/K se emplea en WATCH. WATCH también calcula la fracción de vapor mediante la conservación de la entalpía. Ambos programas utilizan la conservación de alcalinidad (es decir, el balance de protones) para los cálculos de pH. La diferencia en temperatura (presión) provoca efectos considerables en las características del fluido de yacimiento geotérmico calculadas para pozos de alta entalpia, así como fracción de vapor negativa (o cercana a cero) para pozos de baja entalpía. La alta concentración calculada de CO₂ en el vapor secundario liberado en la atmósfera en el vertedero (hasta 11.719 mmol/kg) sugiere que el análisis de las especies carbónicas en las aguas termales es crucial. En la ausencia de análisis de buena calidad de las especies carbónicas, se sugiere tener en cuenta el CO2 de la muestra de vapor en el separador y la concentración total de las especies carbónicas disueltas en la muestra de agua (es decir, sin tener en cuenta la liberación de CO₂ en la atmósfera de vapor en el vertedero) para los cálculos de las composiciones de fluidos en los yacimientos geotérmicos.

Palabras clave: GeoSys.Chem, GeoChem, WATCH, modelado geoquímico, sistema geotérmico.

INTRODUCTION

First step in geochemical modeling of geothermal systems is the calculation of deep geothermal reservoir fluid characteristics from the measured physical-chemical parameters of surface manifestations like springs, fumaroles and drilled wells. Various computer programs have been written for understanding water chemistry in nature as well as in the laboratory, and tracing the reaction mechanisms and processes for water-bodies evolution (Nordstrom et al. 1979; Plummer et al., 1988; Bethke, 1992). Nordstrom et al. (1979) reviewed over 30 chemical modeling programs and concluded that every modeling program had been developed for specific purposes with its own individual capacities and limitations. SOLMNEQ (Kharaka and Barnes, 1973), MINEQ (Westall et al., 1976), WATEQX (van Gaans, 1989) and EQ3NR (Wolery, 1983) deal with chemical speciation using input parameters such as dissolved species concentration, temperature and pH; while WATEQ (Truesdell and Jones, 1974), WATCH (Arnorsson et al., 1982), CHILLER (Reed, 1982), EQQYAC (Barragan and Nieva, 1989) and GeoSys.Chem (Verma, 2012a) may recalculate the pH using charge balance or H+ mass-balance. NETPATH (Plummer et al., 1991) and "The Geochemist's Workbench" (Bethke, 1992, 1994) can also take into account mixing, dilution and evaporation processes. Torres-Alvarado (2002) determined the evolution of chemical equilibrium state of Los Azufres geothermal field using the Geochemist's Workbench.

This article presents a comparative study of the calculation of geothermal reservoir fluid characteristics of ten production wells of Los Azufres, Los Humeros and Cerro Prieto geothermal fields using the computer codes GeoSys.Chem (Verma, 2012a) and WATCH (Arnorsson et al., 1982).

Procedure for the calculation of geothermal reservoir fluid composition

The conceptual diagram of a geothermal system with sampling points of condensed vapor and liquid samples is shown in Figure 1 (after Verma, 2012a). The first step in the geochemical modeling of geothermal systems is the reconstruction of reservoir fluid characteristics [i.e., pressure (P), temperature (T), fraction of liquid (y) and vapor (y_v), and concentration of each chemical species in the liquid (Water₃) and vapor (Vapor₃) phases] from the vapor sample (Vapor₂) collected at the separator and water sample (Water₁) collected in the weir box at atmospheric conditions. There may be n-separations of geothermal reservoir fluids (Verma 2008), however, the last separator is the weir box in order to liberate the separated water at the atmospheric conditions. Figure 1 shows the separation scheme of the studied wells, which was used during the sampling of separated water and condensed vapor. Table 1 presents the analytical datasets of ten wells from Los Azufres, Los Humeros and Cerro Prieto geothermal fields, taken from Henley et al. (1984), Arellano et al. (2003, 2005) and Tello (2005).

Verma (2012a) wrote a demonstration computer program GeoChem using the dynamic link library GeoSys. Chem in Visual Basic in Visual Studio 2010 (VB.NET). The main class is "Fluid", which has three principal properties, Liquid, Vapor, and TD (total discharge) and two methods, TDToFluid and FluidToTD. For the geochemical calculations, the program considers the separation of total discharge fluid into vapor and liquid at a given pressure (or temperature) along the liquid-vapor saturation curve and vice versa. At the separator and weir box, the separation pressure (or temperature) is known. In the geothermal reservoir the total discharge composition of the fluid is the same as the total discharge composition of the fluid at the separator. The reservoir temperature and vapor fraction are estimated by means of quartz solubility geothermometry and conservation of enthalpy (Verma, 2012b).

Algorithm

The distribution of chemical species, alkalinity and enthalpy is expressed as

where A represents chemical species (C), alkalinity (alk) and enthalpy (H), y is the fraction of vapor by weight and sub-indices td, v and l represent the corresponding parameter in the total discharge, vapor and liquid, respectively.

The alkalinity in the liquid phase (alk) is defined according to the following equation

where the α's are the ionization fractions and C_T is the total dissolved concentration of the subscripted constituent, i.e., carbonic acid (car), boric acid (B), silicic acid (Si), hydrogen sulfide (S) and ammonia (N). In case of ammonia, the a's are defined for the corresponding acid (NH₄+). A full discussion on alkalinity is in the book of Stumm and Morgon (1981). The alkalinity in a carbonic system (i.e., bi-proton system) is defined with respect to one of the three equivalence points (EP) (i.e., H₂CO₃EP, HCO₃^-EP, CO₃^2-EP which are represented as H₂CO₃EP, NaHCO₃EP, NA₂CO₃EP, respectively, in order to keep the charge balance in the chemical system). If we define the alkalinity with respect to H₂CO₃EP as defined in Equation (2), it will decrease with the precipitation of CaCO₃or Ca(HCO₃)₂, while it will remain unchanged on the dissolution or removal of CO₂. Similarly, it will not be altered on the removal or addition of H₂S. In the same way, if precipitation or dissolution of NH₄Cl occur, the alkalinity will not change. However, the removal of NH₃ will alter the alkalinity. In all the above processes, the pH of the solution will always change. Thus, the alkalinity is a conservative entity in chemical reactions, but not the pH.

The alkalinity is the acid neutralizing capacity of the solution and is defined with respect to an equivalence point like the definition of gravitational potential. The alkalinity is turned out to be the sum of the concentrations of weak acid-base species in the solution as expressed in Equation (2). The CO₂(or H₂CO₃) concentration is not considered in the equation, and thus the alkalinity will not change on adding or removing CO₂. However, the concentration of NH₃ [i.e., C_TN(α_1N)] in the liquid phase is included in the Equation 2, indicating that the alkalinity is affected by the removal of NH₃. During the separation of the geothermal reservoir fluid into vapor and liquid at lower pressure, NH₃ distributes between the liquid and vapor phases. So, the vapor phase has alkalinity that is equivalent to the concentration of NH₃ in the vapor phase (Verma, 2012a). Likewise, on the precipitation of CaCO3 the alkalinity goes in the solid phase. If we define the alkalinity with respect to Na₂CO₃EP, the addition of removal of CaCO3 will not alter the alkalinity. We have to keep the track of alkalinity of the system during the chemical calculations (e.g., pH calculation).

The pH calculation is performed with the alkalinity conservation approach (i.e., proton balance).

The non-volatile species like Na+, Cl^-, etc., reside only in the liquid phase (i.e., their concentration in the vapor phase is zero); however, the gaseous species like CO₂, H₂S, NH₃, N₂, CH₄, etc., distribute between the liquid and vapor phases. The distribution coefficient D_Coef of a gaseous species is defined as the concentration ratio of the species in the vapor and liquid phases (Giggenbach, 1980).

At high temperature, partition of HCl and B between-vapor and liquid phases occur (Arnórsson and Andrésdóttir, 1995; Giroud, 2008; Bernard et al. 2011). The partition also depends on pH. Giroud (2008) presented experimental data for the distribution of B in vapor and liquid phases. The data are preliminary and limited to define the equation of the distribution coefficient of B, and consequently it is presently not feasible to deal with the distribution of B in the computer code. Additionally, our analytical data set do not have experimental values of B in the vapor phase. Thus the concentrations of HCl and B in the vapor phase are not considered in the present computer codes.

Calculation procedure

Figure 2 shows the stepwise calculation of geothermal reservoir parameters for well 9. Only the carbonic species are shown because of space limits. The calculation procedure is performed according to the following five steps:

Heating the liquid sample up to the weir box separation temperature. The water samples are analyzed at laboratory temperature (say 25°C). The charge unbalance is calculated to verify the analytical data quality. All the major ionic species including H₃SiO₄^- and B(OH)₄^- are considered in the charge unbalance calculations. Actually, all ionic chemical species should be considered in the change unbalance calculation; however, the concentration of trace species does not affect significantly the results. In the present study, the concentration of SiO₂ and B(OH)₃ is high in some water samples, therefore, the ionic species H₃SiO₄^- and B(OH)₄^-contribute significantly to the charge unbalance calculation at high pH. The charge unbalance for all the samples is less than 5% (Table 1).

The alkalinity of water samples at 25°C is calculated from pH and acid-base species for each sample (Table 1).

The alkalinity (3.380 meq/kg for well 9) is a conservative entity when the sample is heated from 25 to 100°C (Stumm and Morgan, 1981). Heating is conducted in a closed system (i.e., without evaporation and steam loss). Similarly, the total concentration of carbonic species (5.540 mmole/kg for well 9) is conserved, but the distribution of carbonic species and pH change in the process of heating.

Verma (2012a) stated the causes for such a high concentration of CO₂ in the vapor phase at the weir box as uncertainty in the analytical method for the measurement of HCO₃^-, non-existence of liquid-vapor equilibrium at the weir box, and uncertainty in the distribution equation for CO₂. However, the incorrect measurement of HCO₃^- is the prime factor (Verma, 2004).

Integration of vapor-liquid to calculate the separated water composition at the separator. The chemical composition of separated water (Water_2Weir) at the separator is calculated by combining the chemical characteristics of water sample (Water^ and secondary vapor (Vapory at the weir box.

Calculation of separated water composition from vapor phase. The gaseous species are analyzed in the vapor sample (Vapor₂). By considering the concentration of non-volatile species and alkalinity of the separated water (Water_2Weir) one can construct the separated water compositions (Water₂) from Vapor₂. There is enormous difference in the carbonic species concentrations of Water₂ and Water_2Weir. The separated water (Water₂) is flushed in the weir box at atmospheric conditions. This also suggests that there is not sufficient CO₂ in the separated water to liberate such a large amount of CO₂ (11,719 mmole/kg) in the atmospheric vapor at the weir box (see step 2). In other words, there are analytical problems in the measurement of carbonic species and/or non-existence of vapor-liquid equilibrium at the separator and weir box.

Calculation of geothermal reservoir fluid compositions. The compositions of geothermal reservoir fluid are calculated by combining the separated water and vapor compositions at the separator. Three types of separated waters are considered: (i) Water₂, (ii) Water that results from the separation, at weir box, of water (i.e., liquid sample) and vapor (without any gaseous species) liberated into the atmosphere, and (iii) Water_2Weir. The steps 5a and 5c (Figure 2) are the extreme cases of the process. In the absence of good quality analysis of carbonic species, the geothermal reservoir fluid compositions are considered as obtained in the step 5b. The results are given in Table 2.

WATCH Computer code

The first step in using the computer code WATCH is the preparation of input data file in a text editor or through an interactive program, WAIN. The chemical speciation in the geothermal reservoir is performed by defining a reference temperature (i.e., the reservoir temperature). The reference temperature may be a fixed temperature value provided by the user or calculated by the program through chemical geothermometers. The average temperature of quartz and Na/K geothermometers is most commonly used for the geochemical calculations. The calculation of the vapor fraction (excess steam) is based on the phase segregation model (open system) proposed by Arnórsson and Stefansson (2005). In the program, it is further assumed that the phase segregation takes place between 180 °C and the initial geothermal reservoir temperature.

The reservoir parameter calculation procedure of WATCH is quite similar to that described for GeoSys.Chem: the chemical composition of secondary steam discharged in the atmosphere at the weir box is calculated from the chemical and physical parameters of the water sample (Waterj). The characteristics of water (Water₂) at the separator are calculated from the water sample (Water^ and the secondary vapor parameters (Vapory. The total discharge fluid characteristics of the well are calculated by combining the properties of the separated water (Water₂) and the vapor sample (Vapor₂). The geothermal fluid characteristics (Water₃ and Vapor₃) are calculated from the total discharged fluid at the separator according to the procedure as described above. The results are given in Table 3.

Table 4 presents the comparison of the calculation procedures of geothermal reservoir fluid characteristics of the computer programs GeoSys.Chem and WATCH. Most of the parameters are calculated in a similar manner by both programs. WATCH does not provide the values at the intermediate points (e.g., the chemical composition of secondary vapor discharged in the atmosphere at the weir box). Thus it is not feasible to present a detailed comparison of both approaches.

Geothermal reservoir temperature and vapor fraction

Figure 3a shows the geothermal reservoir temperatures of the wells. GeoSys.Chem uses the quartz solubility geothermometer, while the average value of quartz and Na/K geothermometers is considered in WATCH.

Initially, the quartz geothermometer was employed by considering only the liquid phase in the reservoir (Henley et al., 1984). This procedure provides geothermal reservoir temperatures lower than 100°C for wells, 3 and 10, which is clearly unrealistic. Similarly, Verma (2012b) showed that there was no enthalpy balance in this approach.

Both programs, GeoSys.Chem and WATCH estimate the geothermal reservoir temperature using the quartz solubility geothermometer and assuming enthalpy conservation. GeoSys.Chem uses the linear quartz solubility equation (Verma, 2003), while WATCH uses the quartz solubility as a polynomial of absolute temperature including logarithmic terms (Gunnarsson and Arnórsson, 2000). However, both the quartz temperatures are close to each other for wells with temperature lower than 300°C. The Na/K temperature is mostly on the extreme side either lower or upper side. Thus, the Na/K temperature departs from the temperature used in GeoSys.Chem and WATCH (Figure 3a).

Verma (2012c) pointed out the limitations of the Na/K cation exchange geothermometer, which is based on the following type of cation exchange reaction

where the capital X represents an anion and z denotes the stoichiometric coefficient. The limitations are the unidi-rectionality of the cation-exchange reaction, the undefined activity of mixed minerals, Na+ = K+ on substituting z=0.5 in Equation (4), the violation of electro-neutrality of the solution, and others.

The enthalpy recalculation results are, in general, consistent for both programs GeoSys.Chem and WATCH.

In case of WATCH, the wells 2 and 4 have higher enthalpy, while the well 3 has lower enthalpy than the corresponding measured enthalpy. Additionally, WATCH provides the reservoir conditions (i.e., pressure and temperature) in the compressed liquid region for wells 1 and 2; however, the vapor fraction value for well 2 is positive, which is unlikely. The enthalpy is calculated by considering the conditions along the saturation curve, thus the vapor fraction value for well 2 is questionable.

Enthalpy-pressure diagram

The enthalpy versus pressure diagram (Figure 4) serves as a mechanism for understanding the evolution of a geothermal reservoir during exploitation (Arellano et al., 2005). The separation boundary between the liquid and vapor phases is formed by the critical isochor and the two-phase region. Most of the wells are in the two-phase region, between the isotherms at 200 and 300 °C. The locations of the well data from GeoSys.Chem and WATCH are close except for wells 3, 5 and 6., which may be a consequence of the different geothermal reservoir temperatures used in the programs.

Behavior of chemical species

The first check on the chemical composition of geothermal reservoir fluids is the ratio of non-volatile species like Na/K. The Na/K ratio calculated by both programs for the geothermal reservoir fluids is the same as that reported for analyzed water samples.

Figure 5a shows the variation of the concentration of CO₂ in the vapor phase in the geothermal reservoir. The values of the CO₂ concentration in the vapor phase of the reservoir fluid in well 2 are 4062 and 627 mmole/kg, for GeoSys.Chem and WATCH, respectively. However, the well has a very small fraction of vapor (<1%). So, a small difference in the algorithm and other parameters like pH may produce significant differences in the value of CO₂.

As discussed earlier, GeoSys.Chem conducts the calculation of geothermal reservoir fluid characteristics by considering three possibilities: (i) Water₂, (ii) water that liberates vapor only (i.e., without any gaseous species) at the weir box in forming Water;, and (iii) Water_2Weir. These cases are identified here as GeoSys.Chem 1, GeoSys.Chem 2, and GeoSys.Chem 3, respectively. In the case GeoSys. Chem 3 there is a maximum concentration of CO₂, since the CO₂ concentration of vapor liberated in the atmosphere at the weir box is considered.

The total concentration of CO₂ in the geothermal reservoir is shown in Figure 5b, where it can be observed that CO₂ concentrations are higher in the case of WATCH than in the case of maximum CO₂ of GoeSys.Chem (GeoSys. Chem 3). This suggests that CO₂ concentrations in the secondary vapor liberated at the weir box are even higher in the case of WATCH. It is well known that the geothermal systems have very little environmental impact and cannot liberate such a large amount of CO₂ (11,719 mmole/kg). We consider that this is an artifact due to analytical errors in the measurement of carbonic species. Thus there is a need to revise the measurement of carbonic species in the vapor and liquid phase of geothermal fluid samples.

CONCLUSIONS

The conclusions of this study on the calculation of deep reservoir fluid characteristics from surface samples of liquid and vapor phases as the first step in geochemical modeling of geothermal systems may be summarized as follows:

Both the programs, GeoSys.Chem and WATCH have similar procedure for the calculation of pH and vapor fraction in the geothermal reservoir fluid.

The assignation of average temperature of SiO₂ and Na/K of geothermometers causes substantial differences in the calculated reservoir fluid properties of high enthalpy and low vapor fraction wells. Additionally, there are conceptual limitations of cation exchange geothermometers (Verma, 2012c). Thus it is recommended to use only SiO₂ geothermometry, although there is high uncertainty in the calculated temperature (Verma, 2012b).

In the absence of good quality analysis of carbonic species it is suggested to consider the CO₂ in the vapor sample at the separator and the total dissolved carbonic species concentration in the water sample (i.e., without considering the liberation of CO₂ in the atmospheric vapor at the weir box) for the geothermal reservoir fluid composition calculations.

The concentration of CO₂ highly influences the geothermal reservoir fluid pH, and pH is a master variable in geochemical modeling (Stumm and Morgan, 1981). Thus it is of prime importance to revise the analytical procedures for the measurement of carbonic species concentration in the vapor and liquid samples.

ACKNOWLEDGMENTS

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