Chemical Thermodynamics of Two-Phase Geothermal Systems

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1 Chemical Thermodynamics of Two-Phase Geothermal Systems Stefán Arnórsson P R E P R I N T ICPWS XV Berlin, September 8 11, 2008 Institute of Earth Sciences, University of Iceland, Sturlugata 7, 101 Reykjavík, Iceland stefanar@raunvis.hi.is Chemical thermodynamics is an important tool for quantitative interpretation of geothermal fluid compositions, in particular in constraining the effects on mineral-solution equilibria on these compositions. The field data required for this interpretation include analyzes of vapor and liquid samples and the kind and composition of the minerals with which the fluid is interacting. Thermodynamic data are required on minerals and the aqueous species selected to express mineral dissolution/precipitation reactions as well as dissociation constants for composed aqueous species. Data presently available on minerals generally seem to be of good quality over large temperature and pressure ranges except for non-ideal behavior of solid solutions. On the other hand experimental data on dissociation constants of aqueous species is meager, especially at elevated temperatures and pressures. Interpretation of data on brines is limited by modeling individual aqueous species activities, Many studies indicate that local equilibrium is closely approached between hydrothermal minerals and all major components in aqueous solutions of geothermal systems except for Cl, at least when temperatures are above some 150 C and sometimes at temperatures as low as 50 C. Knowledge about trace element geochemistry in these systems is still limited. Close approach to mineral-solution equilibria in geothermal systems permits use of geothermometers as tools to predict subsurface temperatures in geothermal systems. It also allows predictions to be made regarding scale formation in wells, the effects of mixing of two or more fluids on upon dissolution or precipitation of minerals and lastly it helps in modeling aquifer fluid compositions from wellhead data on excess enthalpy wet-steam well discharges and to estimate the equilibrium vapor fraction in the initial aquifer fluid. Introduction All large systems on Earth are open systems. Assessment of mineral-solution equilibria in such systems, including geothermal systems, is based on the concept of local equilibrium within subsystems of the larger open system. It is often envisaged that local equilibrium in rock-fluid systems between minerals and the through-flowing solution will be closely approached if the time of fluid flow through the system is significantly longer than the time required for the solution to come close to equilibrium with the mineral phases. In natural mineral-fluid systems, however, simultaneous dissolution of primary rock-forming minerals and precipitation of secondary minerals is likely, the dissolution process adding solids to the fluid while precipitation removes them. During the mineralogical transformation of the rock the solution must be under-saturated with respect to the primary minerals but over-saturated with the secondary ones. The field data used for interpreting the state of mineral-solution equilibria includes fluid samples from springs or wells and information on alteration mineralogy from drillings. The fluids sampled can be expected to consist of many components that have travelled different distances through the aquifer, at different velocities and temperatures, to the point or points of inflow into wells or springs. Comparison between fluid compositions and alteration minerals is therefore indirect and based on the selection of a particular temperature and pressure. The use of such data to assess the state of mineral-solution equilibria is most reliable when the rock through which the water has flowed is homogeneous, both compositionally and mineralogically and in the case of geothermal fluids when temperatures are similar over considerable depth range as is the case when temperatures are <100 C and there is good vertical permeability that will level out temperatures by liquid convection. Data interpretation with respect to mineralsolution equilibria, which is based on samples of liquid and vapor collected from wells that discharge a mixture of these fluids (wet-steam wells) poses special problems. First of all the composition of the total well discharge may differ from that of the initial aquifer fluid due to partial separation of the flowing liquid and vapor phases in producing

2 aquifers. Secondly, extensive depressurization boiling of the initial aquifer fluid changes its saturation state with respect to many minerals and may cause them to precipitate or dissolve. These reactions also cause initial aquifer fluid composition to differ from that of the total well discharge. Further, dissolution of casing material and wellhead equipment may cause changes in the fluid composition. Interpretation of fluid compositions with respect to mineral-solution equilibria involves calculation of mineral solubility constants (K) from thermodynamic data and of activity products (Q) from analytical data on the fluid The latter involves aqueous speciation calculations as well as calculation of end-member mineral activities in solid solutions from their analyzed compositions. The basic equation for this interpretation is: For a general reaction Q is given by ΔG r = RTlnK + RTlnQ (1) a[a] + b[b] = c[c] + d[d] (2) Q = [C]c [D] d [A] a [B] b (3) Thermodynamic data on minerals over large temperature and pressure ranges is extensive today. By contrast, for very many aqueous species such data is still meagre, especially at elevated temperatures and pressures. The present contribution emphasizes interpretation of chemical data from wet-steam well discharges applying equilibrium thermodynamics. Boiling in Geothermal Systems Geothermal systems have been classified as vapor-dominated and hot-water (also termed liquiddominated) systems [1]. The mobile fluid phase in vapor-dominated systems is vapor although liquid water may be present as a film on mineral grain surfaces held immobile by capillary forces. In hotwater systems, liquid water is the dominant fluid phase, even in terms of volume. In vapordominated systems pressures vary little with depth but in hot water systems they are essentially determined by the hydrostatic head. When temperatures are above ~100 C in hotwater systems, the rising liquid will begin to boil when the sum of partial pressures of vapor and all dissolved gases equals hydrostatic pressure. Depressurization of the liquid, as it rises further, will lead to successively more vapor formation because the temperature at which liquid water boils decreases with decreasing pressure. Thus, for example, ~19% of liquid water is converted into vapor by adiabatic boiling from 200 to 100 C. The corresponding number is ~40% for adiabatic boiling from 300 to 100 C. Drillhole data show that the fluid below a certain depth in many hot-water geothermal reservoirs is sub-boiling liquid. In other reservoirs the fluid is two-phase (liquid water and vapor), at least down to the deepest levels penetrated by wells. In some systems it is possible that fluid pressure at the deepest level of ground water convection is lower than the critical pressure in which case no supercritical fluid exists. The fluid could be sub-boiling liquid, superheated steam or two-phase. The temperature of geothermal fluids is determined by the rate of fluid throughflow relative to heat flow from the rock to that fluid and the temperature of the heat source. Data from a well drilled in 2007 into the Krafla volcanic geothermal field in NE-Iceland indicate that fluid flow versus heat flow from the magma heat source in the roots of the system is such that super-heated vapor is produced. When this vapor rises, it mixes with liquid water to produce a two-phase reservoir fluid that underlies a sub-boiling liquid reservoir of around 200 C. The two-phase fluid is apparently a mixture of the super-heated vapor and the liquid in the sub-boiling zone, as indicated by the Cl and B contents of the fluid in the upper sub-boiling zone and in the lower two-phase zone [2]. Enthalpy and Composition of Well Discharges When wells drilled into high-temperature hotwater reservoirs are discharged, depressurization leads to extensive boiling of the liquid. If the depth level of first boiling is within the well, the total well discharge composition can be assumed to represent the initial aquifer liquid composition. The same assumption is reasonable if the measured discharge enthalpy is about the same as that of vapor saturated liquid at the aquifer temperature. It is common, however, that the discharge enthalpy of wet-steam wells drilled into hot-water reservoirs is higher than that of the initial aquifer fluid, sometimes dry vapor. Such excess enthalpy may be produced when extensive depressurization 2

3 boiling occurs in the formation. This boiling causes cooling of the fluid and tends therefore to cause conductive flow of heat from the aquifer rock to the flowing fluid, thus enhancing its enthalpy. Due to their different properties, the flowing liquid and vapor may segregate in the aquifer in such a way that the vapor flows into the well but the liquid is partly or totally retained in the formation. It is made immobile by its adsorption onto mineral grain surfaces by capillary forces. Heat transfer from the aquifer rock to the flowing fluid that increases its enthalpy does not change the composition of the total well discharge. It is the same as that of the initial aquifer fluid. Phase segregation on the other hand causes the well discharge composition to differ from that of the initial aquifer fluid. Note on Sampling and Analysis of Wet-Steam Well Discharges Sampling of wet-steam well discharges and subsequent interpretation of the chemical data requires information on well discharge enthalpy, sampling vapor pressure, feed zone temperatures and selection of a model to calculate aquifer fluid compositions [3]. It is not possible to collect representative samples of the total discharge of wetsteam wells. It is necessary to sample the vapor and liquid phases separately using a steam separator and to calculate their proportions in the total discharge from the recorded sampling pressure and measured discharge enthalpy. In liquid water discharged from wet-steam wells, the dissolved silica is all monomeric (with few possible exceptions), because wellhead pressures are adjusted in such a way that the water at the wellhead is maintained amorphous silica under-saturated to avoid scale formation. Upon sample storage, the silica in excess of amorphous silica solubility will polymerize. The polymerization reaction involves extraction of H 4 SiO 4 0 from solution. If ionized silica (H 3 SiO 4 - ) is present in solution in significant concentrations, the formation of polymers will increase the H 3 SiO /H 4 SiO 4 activity ratio and therefore increase the ph of the solution. Formation of silica oligomers, which are stronger acids than monomeric silica [4], will on the other hand cause a decrease of ph. In waters with high initial ph (above ~9 as measured at room temperature), and therefore with a large proportion of ionized silica relative to unionized silica, extraction of H 4 SiO 4 0 from solution by polymerization will dominate changes in water ph whereas below ph of ~8 the formation of oligomers is likely to dominate [5]. Oligomer concentration cannot be determined analytically. Therefore, the only way to obtain a reliable measurement of ph of liquid samples collected from the silica rich fluids (amorphous silica over-saturated at room temperature) of wetsteam wells is to measure it on site before onset of silica polymerization. Sulphur exists as sulphide and sulphate in deep geothermal fluids [6]. Sulphide is easily lost from solution, either by degassing or oxidation into native sulphur, thiosulphate or sulphate. It must therefore either be determined on site or fixed during sampling, for example by its precipitation as ZnS or by complexation with methylene blue [3]. To obtain reliable analysis of sulphate it must be separated from the sulphide on site using ion exchange resins. Modeling of Aquifer Fluid Compositions The temperature of aquifers penetrated by wells drilled into hot-water geothermal reservoirs is often insufficiently high to initiate boiling in the contained fluid when the well is discharged. When this is the case, the depth level of first boiling is within the well. Under these conditions, it is a reasonable approximation to treat the aquifer and well as an isolated system in which case boiling is adiabatic. If the measured enthalpy of a well discharge is about the same as that of vaporsaturated liquid at the aquifer temperature, even if extensive boiling starts in he aquifer, it is considered reasonable to assume that the aquifer fluid composition is the same as that of the total well discharge. Under these conditions, the following expression gives the concentration of chemical component i in the initial aquifer fluid of a wet-steam well X d,v m i d,t = m i d,v X d,v + m i d,l (1 X d,v ) (4) is the vapor fraction in the discharge (by mass). m i denotes concentration of component i. The superscript d stands for discharge and superscripts t, v and i total discharge, vapor and liquid, respectively. The value of X d,v is obtained from X d,v = h d,t h d,l h d,v h d,l (5) h denotes specific enthalpy. The superscripts have the same notation as in equation (4). h d,t must be 3

4 measured whereas h d,v and h d,l are derived from the recorded sampling vapor pressure with the aid of Steam Tables. For excess enthalpy wells, when this enthalpy is formed by conductively adding heat to the flowing fluid equations (1) and (2) can also be used as m i d,t = m i f,t. When phase segregation occurs, the mass flow rate of the total well discharge ( M d,t ) is related to the mass flow rate of the initial aquifer fluid by M d,t = M f,t M e,l (6) If it is assumed that phase segregation occurs at a particular vapor pressure ( P g ) and boiling is taken to be adiabatic before and after such segregation, the concentration of component i in the liquid ( m i g,l ) and vapor ( m i g,v ) phases are related to the total well discharge composition by m i d,t = m i g,v X g,v + m i g,l (1 X g,v ) (7) The value of X g can be obtained from an equation analogous to (5) X g,v = h d,t h g,l h g,v h g,l (8) The composition of the two fluid phases is the same immediately before and after phase segregation since this segregation is taken to occur at a specific pressure. Therefore it follows that m i f,t = m i g,v X e,v + m i g,l (1 X e,v ) (9) where X e,v is the vapor fraction of the fluid just before phase segregation occurred and it is relative to the initial aquifer fluid. Note that X g,v is vapor mass fraction relative to the total well discharge. X e,v can be obtained from X e,v = h f,t h g,l h g,v h g,l (10) if it is assumed that the initial aquifer fluid is represented by liquid only, i.e. h f,t = h f,l. Having selected a value for the initial aquifer temperature, a value for X e,v can be obtained using Steam Tables. If vapor is taken to be present in the initial aquifer fluid, a value for the equilibrium vapor fraction X f,v can be obtained from data on two gases, such as H 2 S and H 2, by assuming that the concentration of these gases in the aquifer liquid are fixed by temperature dependent mineral equilibria. If it is also assumed that the liquid retained in aquifer does not contain significant amount of dissolved gas, we have m s d,t M d,t = m s f,t M f,t (11) The basic equation which relates the equilibrium vapor fraction in the initial aquifer fluid to the concentration of gas s in the aquifer fluid ( m s f,t ), its solubility constant ( K S ) and the equilibrium concentration in the aquifer liquid ( m s f,l ) is given by f m,t f,l s = m s X f,v (12) P tot K s [7]. Combination of equations (11) and (12) yields M d,t M f,t = m s f,l m s d,t X f,v (13) P tot K s Now considering two gases s=1 and s=2, solving two equations like (13) together and isolating X f,v leads to X f,v = A 2 A A 1 A (14) 2 + A 2 A 1 P tot K 2 where A 1 = m 1 d,t /m 1 f,l Now m 1 d,t and m 2 d,t K 1 and A 2 = m 2 d,t /m 2 f,l. are measured quantities and f m,l f 1, m,l 1, K 1 and K 2 are known functions of temperature, evaluated at a chosen temperature, T f so (14) gives X f,v directly. For the conductive heat transfer model, X f,v can also be calculated from equations (11) through (14) and subsequently h f,t from an equation analogous to (10). Examples of Results from Skagafjördur and Nesjavellir, Iceland and Olkaria, Kenya Chemical Geothermometry The quartz and Na/K geothermometers have been extensively used in geothermal studies, both to estimate subsurface temperatures in geothermal system from the silica, sodium and potassium contents of water from springs or shallow drillholes and to evaluate aquifer temperatures in deep wells. The first geothermometer is based on quartz solubility according to data presented by [8] and the second on equilibrium between Na and K-feldspars 4

5 and solution using experimental thermodynamic data given by [9, 10]. Fig. 1 shows estimated quartz equilibrium and Na/K temperatures for producing wells at Olkaria calculated on the assumption that excess well discharge enthalpy is produced by (A) conductive heat transfer from the aquifer rock to the flowing fluid in the zone of depressurization around the wells and (B) by phase segregation. Comparison between the two geothermometers is poor when applying the conductive heat transfer model but good when using the segregation model. By the first model, discrepancy between the two geothermometers increases with increasing discharge enthalpy. Silica concentrations approach zero when the discharge enthalpy approaches that of dry vapor. These results are taken to indicate that Calcite Figs. 2 and 3 show calcite saturation in waters from Skagafjördur in N-Iceland and Olkaria in Kenya. The Skagafjördur samples were collected from springs and shallow wells whereas those from Olkaria are from wells, most of which have excess enthalpy. The Skagafjördur ground and geothermal waters have been divided into two groups, relatively old waters in the Valley of Skagafjördur (with very low or undetectable tritium) and relatively young waters in the interior highlands south of Skagafjördur Valley (tritium levels similar to today s precipitation or slightly lower). The young non-thermal ground waters from the interior highlands are calcite under-saturated but all other waters are very close to saturation. The average deviation from saturation for these waters is only 0.03 logq units. The Olkaria data show much larger scatter than the Skagafjördur data (Figs. 2 and 3) and the results indicate that the aquifer water at Olkaria is on Figure 1. Relationship between quartz equilibrium and Na/K geothermometer temperatures for wetsteam wells at Olkaria, Kenya. The results indicate that the excess enthalpy of well discharges is essentially caused by phase segregation in producing aquifers. Circles: Olkaria East Sector, filled diamond: Central Olkaria, crosses: Olkaria West, diamonds: Olkaria Northeast, triangles: Olkaria Domes, square: Lake Naivasha. Figure 2. Calcite/aragonite saturation in ground waters and up to 90 C geothermal waters from Skagafjördur, Iceland. The solid and broken curves represent the calcite and aragonite solubility constants, respectively. Circles represent waters from the Valley of Skagafjördur and crosses water from the interior highlands to the south of Skagafjördur. 5

6 average somewhat calcite under-saturated. The larger scatter of the Olkaria data is not considered to reflect variable departure from calcite saturation in the aquifer. The relatively large scatter reflects the cumulative effect of many errors in calculating Q for calcite, in particular those associated with modeling the initial aquifer fluid composition and loss of Ca from solution as the liquid boils extensively and deposits calcite. Equilibration between aqueous solution and calcite is rapidly attained at elevated temperature [11]. It is considered that the undisturbed fluid (by extensive boiling) in the aquifer is very close to being calcite saturated. Mineral-Gas Equilibria The concentrations of CO 2 in the aquifer fluid of Olkaria wells are shown in Fig. 4. Three points deserve discussion when inspecting the results depicted in Fig. 4. One is that the solubility constants for the two mineral assemblages considered are very similar over the temperature range C when taking into account the composition of the solid solution minerals in the two assemblages considered (epidote, prehnite and garnet). The second point is that the aquifer fluid is generally very close to equilibrium with the respective mineral assemblages and it is not possible to conclude from the aqueous CO 2 concentrations which assemblage is involved. Prehnite is scarce at Olkaria whereas grossulargarnet is very common. From these data it is considered likely that the garnet-bearing mineral assemblage controls aqueous CO 2 concentrations. If Figure 3. Calcite saturation in aquifer fluids of wells at Olkaria, Kenya. The curve represents the calcite solubility constant and the circles calcite activity product for individual wells. Figure 4. CO 2 concentrations in aquifer fluids at Olkaria in Kenya. Equilibrium constants for two mineral assemblages are shown that potentially could control aqueous CO 2 concentrations. The aquifer fluid concentrations were calculated on the basis of the segregation model taking the equilibrium vapor fraction to be zero. The symbols refer to Figure 1. Figure 5. H 2 S and H 2 concentrations (as log moles/kg) in aquifer fluids at Olkaria in Kenya. Equilibrium constants for four mineral assemblages are shown that potentially could control aqueous H 2 S and H 2 concentrations. The aquifer fluid concentrations were calculated on the basis of the segregation model taking the taking the equilibrium vapor fraction to be zero. The dotted lines indicate H 2 concentrations at equilibrium for selected equilibration vapor fraction values (by weight) as indicated. The symbols refer to Figure 1. 6

7 the conductive heat transfer model had been used, not only low quartz equilibrium temperatures are obtained but also high CO 2 aquifer fluid concentrations, higher than those corresponding to equilibrium and the departure from equilibrium increases with increasing discharge enthalpy. The third point to be mentioned is that aquifer fluids, all from the western part of the Olkaria field, have CO 2 in excess of equilibrium with the mineral assemblages considered. The reason for these high CO 2 concentrations is considered to be high flux of this gas from the magma heat source, too high for equilibrium to be closely approached between fluid CO 2 concentrations and the potentially CO 2 controlling mineral assemblages. This is a reminder of the fact that geothermal systems are open systems, which always needs to be born in mind when interpreting data on the assumption of local equilibrium. Table 1. Initial equilibrium vapor fraction (by weight) in the aquifer of wells at Nesjavellir, Iceland as estimated from the H 2 S and H 2 content of well discharge assuming that the concentrations of the gases dissolved in the liquid are controlled by equilibrium with the mineral assemblage pyrite+pyrrhotite+prehnite+epidote. Well Discharge enthalpy kj/kg Aquifer temp. C Equilibrium vapor fraction, % The concentrations of H 2 S and H 2 in the aquifer fluid at Olkaria seem to be controlled by equilibration with a mineral buffer (Fig. 5). The equilibrium constants for three of the four mineral buffers considered are very similar, especially those two which either include magnetite or epidote plus prehnite. As for CO 2 it is not possible to deduce for indidual samples which buffer may be involved. With few exceptions, however, aquifer fluid H 2 S concentrations closely match those at equilibrium with buffers 1 and 2 (see Fig. 5). The same applies to H 2. Due to its low solubility in water, H 2 concentrations at equilibrium will increase rapidly with increasing equilibrium vapor fraction in the aquifer fluid. The dotted lines in Fig 5 show H 2 concentrations in the aquifer fluid at equilibrium for selected vapor fraction values as indicated. The results indicate that the equilibrium vapor fraction in the aquifer of Olkaria wells is very low, below 0.1% by weight. This contrasts with data from wetsteam wells at Nesjavellir, Iceland (Table 1). In this field calculated equilibrium vapor fraction values are as high as 3.5% by weight although they are mostly below 2% Literature [1] D. E. White, L. J. P. Muffler, and A. H. Truesdell: Vapor-dominated hydrothermal sustems compared with hot-water systems. Econ. Geol., 66: (1971). [2] N. R. Giroud and S. Arnórsson: Unpublished work. [3] S. Arnórsson, J.Ö. Bjarnason, N. Giroud, I. Gunnarsson, and A. Stefánsson: Sampling and analysis of geothermal fluids. Geofluids 6: 1-14 (2006). [4] S. Sjöberg: Silica in aqueous environments. J. Colloid Interface Sci., 196: (1996). [5] I. Gunnarsson: Impact of silica scaling on the efficiency of heat extraction from hightemperature geothermal fluids. Geothermics, 34: (2005). [6] A. Stefánsson. Unpublished work (2008). [7] S. Arnórsson, A. Stefánsson and J. Ö. Bjarnason: Fluid-fluid interaction in Geothermal Systems. Reviews in Mineralogy and Geochemistry, 66: [8] I. Gunnarsson and S. Arnórsson. Amorphous silica solubility and the thermodynamic properties of h in the range of 0 to 3501C at P sat. Geochim. Cosmochim. Acta, 64: (2000). [9] S. Arnórsson, F. D Armore and J. Gerardo- Abaya. Isotopic and chemical techniques in geothermal exploration, development and use.international Atomic Energy Vienna, 351 p. [10] S. Arnórsson and A. Stefánsson. Assessment of feldspar solubility constants in water in the range 0 to 350 C at vapor saturation pressures. Amer. J. Sci., 299:

8 [11] Y. Zhang and R. Dawe. The kinetics of calcite precipitation from high salinity water. Appl. Geochem., 13: (1998). 8