2WATER CHEMISTRYChemical composition of waters is expressed in terms of major anion and cation contents.Major Cations: Na+, K+, Ca++, Mg++Major Anions: HCO3- (or CO3=), Cl-, SO4=HCO3- dominant in neutral conditionsCO3= dominant in alkaline (pH>8) conditionsH2CO3 dominant in acidic conditionsAlso dissolved silica (SiO2) in neutral formas a major constituentMinor constituents: B, F, Li, Sr, ...
3WATER CHEMISTRYconcentration of chemical constituents are expressed in units ofmg/l (ppm=parts per million)(mg/l is the preferred unit)MolalityMolality = no. of moles / kg of solventNo.of moles = (mg/l*10-3) / formula weight
4WATER CHEMISTRYErrors associated with water analyses are expressed in terms of CBE (Charge Balance Error)CBE (%) = ( z x mc - z x ma ) / (z x mc + z x ma )* 100where,mc is the molality of cationma is the molality of anionz is the chargeIf CBE 5%, the results are appropriate to use in any kind of interpretation
5The constituents encountered in geothermal fluids TRACERSChemically inert, non-reactive, conservative constituents(once added to the fluid phase, remain unchanged allowing their origins to be traced back to their source component - used to infer about the source characteristics)e.g. He, Ar (noble gases), Cl, B, Li, Rb, Cs, N2GEOINDICATORSChemically reactive, non-conservative species(respond to changes in environment - used to infer about the physico-chemical processes during the ascent of water to surface, also used in geothermometry applications)e.g. Na, K, Mg, Ca, SiO2
6WATER CHEMISTRYIn this chapter, the main emphasis will be placed on the use of water chemistry in the determination of :underground (reservoir) temperatures : geothermometersboiling and mixing relations (subsurface physico-chemical processes)
7HYDROTHERMAL REACTIONS The composition of geothermal fluids are controlled by : temperature-dependent reactions between minerals and fluidsThe factors affecting the formation of hydrothermal minerals are:temperaturepressurerock typepermeabilityfluid compositionduration of activity
8At lower temperatures, ZEOLITES and CLAY MINERALS are found. The effect of rock type --- most pronounced at low temperatures & insignificant above 280CAbove 280C and at least as high as 350C, the typical stable mineral assemblages (in active geothermal systems) are independent of rock type and includeALBITE, K-FELDSPAR, CHLORITE, Fe-EPIDOTE, CALCITE, QUARTZ, ILLITE & PYRITEAt lower temperatures, ZEOLITES and CLAY MINERALS are found.At low permeabilities equilibrium between rocks and fluids is seldom achieved.When permeabilities are relatively high and water residence times are long (months to years), water & rock should reach chemical equilibrium.
9At equilibrium, ratios of cations in solution are controlled by temperature-dependent exchange reactions such as:NaAlSi3O8 (albite) + K+ = KAlSi3O8 (K-felds.) + Na+Keq. = Na+ / K+Hydrogen ion activity (pH) is controlled by hydrolysis reactions, such as :3 KAlSi3O8 (K-felds.) + 2 H+ = K Al3Si3O10(OH)2 (K-mica)+ 6SiO K+Keq. = K+ / H+where,Keq. = equilibrium constant,square brackets indicate activities of dissolved species (activity is unity for pure solid phases)
10ESTIMATION OF RESERVOIR TEMPERATURES The evaluation of the reservoir temperatures for geothermal systems is made in terms of GEOTHERMOMETRY APPLICATIONS
12GEOTHERMOMETRY APPLICATIONS One of the major tools for the exploration & developmentof geothermal resources
13GEOTHERMOMETRY estimation of reservoir (subsurface) temperatures using Chemical & isotopic composition of surface discharges fromwells and/ornatural springs/fumaroles
14GEOTHERMOMETERS CHEMICAL GEOTHERMOMETERS ISOTOPIC GEOTHERMOMETERS utilize the chemical compositionsilica and major cation contents of water dischargesgas concentrations or relative abundances of gaseous components in steam dischargesISOTOPIC GEOTHERMOMETERSbased on the isotope exchange reactions between various phases (water, gas, mineral) in geothermal systems
15Focus of the Course CHEMICAL GEOTHERMOMETERS As applied to water dischargesPART I. Basic Principles & TypesPART II. Examples/Problems
16CHEMICAL GEOTHEROMOMETERS PART I. Basic Principles &Types
17BASIC PRINCIPLES Chemical Geothermometers are developed on the basis of temperature dependent chemical equilibrium between the water and the minerals at the deep reservoir conditionsbased on the assumption that the water preserves its chemical composition during its ascent from the reservoir to the surface
18BASIC PRINCIPLESStudies of well discharge chemistry and alteration mineralogythe presence of equilibrium in several geothermal fieldsthe assumption of equilibrium is valid
19BASIC PRINCIPLESAssumption of the preservation of water chemistry may not always holdBecause the water composition may be affected by processes such ascoolingmixing with waters from different reservoirs.
20BASIC PRINCIPLES Cooling during ascent from reservoir to surface: CONDUCTIVEADIABATIC
21BASIC PRINCIPLES CONDUCTIVE Cooling ADIABATIC Cooling Heat loss while travelling through cooler rocksADIABATIC CoolingBoiling because of decreasing hydrostatic head
22BASIC PRINCIPLES Conductive cooling does not by itself change the composition of the waterbut may affect its degree of saturation with respect to several mineralsthus, it may bring about a modification in the chemical composition of the water by mineral dissolution or precipitation
23BASIC PRINCIPLES Adiabatic cooling (Cooling by boiling) causes changes in the composition of ascending waterthese changes includedegassing, and hencethe increase in the solute content as a result of steam loss.
24BASIC PRINCIPLES MIXING affects chemical composition since the solubility of most of the compounds in waters increases with increasing temperature, mixing with cold groundwater results in the dilution of geothermal water
25Geothermometry applications are not simply inserting values into specific geothermometry equations. Interpretation of temperatures obtained from geothermometry equations requires a sound understanding of the chemical processes involved in geothermal systems.The main task of geochemist is to verify or disprove the validity of assumptions made in using specific geothermometers in specific fields.
26TYPES OF CHEMICAL GEOTHERMOMETERS SILICA GEOTHERMOMETERSCATION GEOTHERMOMETERS (Alkali Geothermometers)
27SILICA GEOTHERMOMETERS based on theexperimentally determinedtemperature dependentvariation in the solubility of silica in waterSince silica can occur in various forms in geothermal fields (such as quartz, crystobalite, chalcedony, amorphous silica) different silica geothermometers have been developed by different workers
28SILICA GEOTHERMOMETERS EquationReferenceQuartz-no steam lossT = 1309 / (5.19 – log C)Fournier (1977)Quartz-maximum steam loss at 100 oCT = 1522 / ( log C)QuartzT = C x 10-4 C x 10-7 C log CFournier and Potter (1982)T = C x 10-4 C x 10-7 C log CArnorsson (1985) based on Fournier and Potter (1982)ChalcedonyT = 1032 / ( log C)T = 1112 / ( log C)Arnorsson et al. (1983)Alpha-CristobaliteT = 1000 / ( log C)Opal-CT(Beta-Cristobalite)T = 781 / ( log C)Amorphous silicaT = 731 / ( log C)
29SILICA GEOTHERMOMETERS The followings should be considered :temperature range in which the equations are valideffects of steam separationpossible precipitation of silicabefore sample collection(during the travel of fluid to surface, due to silica oversaturation)after sample collection(due to improper preservation of sample)effects of pH on solubility of silicapossible mixing of hot water with cold water
30SILICA GEOTHERMOMETERS Temperature Rangesilica geothermometers are valid for temperature ranges up to 250 Cabove 250C, the equations depart drastically from the experimentally determined solubility curves
31SILICA GEOTHERMOMETERS Temperature Range Fig.1. Solubility of quartz (curve A) and amorphous silica (curve C) as a function of temperature at the vapour pressure of the solution. Curve B shows the amount of silica that would be in solution after an initially quartz-saturated solution cooled adiabatically to 100 C without any precipitation of silica (from Fournier and Rowe, 1966, and Truesdell and Fournier, 1976).At low T (C) qtz less solubleamorph. silica more solubleSilica solubility is controlled by amorphous silica at low T (C) quartz at high T (C)
32SILICA GEOTHERMOMETERS Effects of Steam Separation Boiling Steam Separationvolume of residual liquidConcentration in liquidTemperature Estimatee.g.T = 1309 / (5.19 – log C)C = SiO2 in ppmincrease in C (SiO2 in water > SiO2 in reservoir)decrease in denominator of the equationincrease in Tfor boiling springsboiling-corrected geothermometers(i.e. Quartz-max. steam loss)
33SILICA GEOTHERMOMETERS Silica Precipitation SiO2 Temperature Estimatee.g.T = 1309 / (5.19 – log C)C = SiO2 in ppmdecrease in C (SiO2 in water < SiO2 in reservoir)increase in denominatordecrease in T
34SILICA GEOTHERMOMETERS Effect of pH Fig. 2. Calculated effect of pH upon the solubility of quartz at various temperatures from 25 C to 300 C , using experimental data of Seward (1974). The dashed curve shows the pH required at various temperatures to achieve a 10% increase in quartz solubility compared to the solubility at pH=7.0 (from Fournier, 1981).pH Dissolved SiO2 (for pH>7.6)Temperature Estimatee.g.T = 1309 / (5.19 – log C)C = SiO2 in ppmincrease in Cdecrease in denominator of the equationincrease in T
35SILICA GEOTHERMOMETERS Effect of Mixing Hot-Water High SiO2 contentCold-Water Low SiO2 content(Temperature Silica solubility )Mixing (of hot-water with cold-water)TemperatureSiO2 Temperature Estimate e.g.T = 1309 / (5.19 – log C)C = SiO2 in ppmdecrease in Cincrease in denominator of the equationdecrease in T
36SILICA GEOTHERMOMETERS Process Reservoir TemperatureSteam Separation OverestimatedSilica Precipitation UnderestimatedIncrease in pH OverestimatedMixing with cold water Underestimated
37CATION GEOTHERMOMETERS (Alkali Geothermometers) based on the partitioning of alkalies between solid and liquid phasese.g. K+ + Na-feldspar = Na+ + K-feldsparmajority of are empirically developed geothermometersNa/K geothermometerNa-K-Ca geothermometerNa-K-Ca-Mg geothermometerOthers (Na-Li, K-Mg, ..)
38CATION GEOTHERMOMETERS Na/K Geothermometer Fig.3. Na/K atomic ratios of well discharges plotted at measured downhole temperatures. Curve A is the least square fit of the data points above 80 C. Curve B is another empirical curve (from Truesdell, 1976). Curves C and D show the approximate locations of the low albite-microcline and high albite-sanidine lines derived from thermodynamic data (from Fournier, 1981).
39CATION GEOTHERMOMETERS Na/K Geothermometer EquationsReferenceNa-KT=[855.6/(0.857+log(Na/K))]Truesdell (1976)T=[833/(0.780+log(Na/K))]Tonani (1980)T=[933/(0.993+log (Na/K))]( oC)Arnorsson et al. (1983)T=[1319/(1.699+log(Na/K))]( oC)T=[1217/(1.483+log(Na/K))]Fournier (1979)T=[1178/(1.470+log (Na/K))]Nieva and Nieva (1987)T=[1390/(1.750+log(Na/K))]Giggenbach (1988)
40CATION GEOTHERMOMETERS Na/K Geothermometer gives good results for reservoir temperatures above 180C.yields erraneous estimates for low temperature waterstemperature-dependent exchange equilibrium between feldspars and geothermal waters is not attained at low temperatures and the Na/K ratio in these waters are governed by leaching rather than chemical equilibriumyields unusually high estimates for waters having high calcium contents
41CATION GEOTHERMOMETERS Na-K-Ca Geothermometer EquationsReferenceNa-K-CaT=[1647/ (log (Na/K)+ (log (Ca/Na)+2.06)+ 2.47)]a) if logCa/Na)+2.06 < 0, use =1/3 and calculate TCb) if logCa/Na)+2.06 > 0, use =4/3 and calculate TCc) if calculated T > 100C in (b), recalculate TC using =1/3Fournier and Truesdell (1973)
42CATION GEOTHERMOMETERS Na-K-Ca Geothermometer Works well for CO2-rich or Ca-rich environments provided that calcite was not deposited after the water left the reservoirin case of calcite precipitationCa 1647T =log (Na/K)+ (log (Ca/Na)+2.06)+ 2.47Decrease in Ca concentration (Ca in water < Ca in reservoir)decrease in denominator of the equationincrease in TFor waters with high Mg contents, Na-K-Ca geothermometer yields erraneous results. For these waters, Mg correction is necessary
43CATION GEOTHERMOMETERS Na-K-Ca-Mg Geothermometer EquationsReferenceNa-K-Ca-MgT = TNa-K-Ca - tMgoCR = (Mg / Mg Ca K) x 100if R from 1.5 to 5tMgoC = log R (log R)2 – (log R)2 / T x 107 log R / T2if R from 5 to 50tMgoC= log R (log R) x105(log R)2/T-1.968x107(log R)3/T2Note: Do not apply a Mg correction if tMg is negative or R<1.5.If R>50, assume a temperature = measured spring temperature.T is Na-K-Ca geothermometer temperature in KelvinFournier and Potter (1979)
44CATION GEOTHERMOMETERS Na-K-Ca-Mg Geothermometer Fig. 4. Graph for estimating the magnesium temperature correction to be subtracted from Na-K-Ca calculated temperature (from Fournier, 1981)R = (Mg/Mg Ca K)x100
45UNDERGROUND MIXING OF HOT AND COLD WATERS Recognition of Mixed WatersMixing of hot ascending waters with cold waters at shallow depths is common.Mixing also occurs deep in hydrothermal systems.The effects of mixing on geothermometers is already discussed in previous section.Where all the waters reaching surface are mixed waters, recognition of mixing can be difficult.The recognition of mixing is especially difficult if water-rock re-equilibration occurred after mixing (complete or partial re-equilibration is more likely if the temperatures after mixing is well above 110 to 150 C, or if mixing takes place in aquifers with long residence times).
46UNDERGROUND MIXING OF HOT AND COLD WATERS Some indications of mixing are as follows:systematic variations of spring compositions and measured temperatures,variations in oxygen or hydrogen isotopes,variations in ratios of relatively *conservative elements that do not precipitate from solution during movement of water through rock (e.g. Cl/B ratios).
47SILICA-ENTHALPY MIXING MODEL Dissolved silica content of mixed waters can be used to determine the temperature of hot-water component .Dissolved silica is plotted against enthalpy of liquid water.Although temperature is the measured property, and enthalphy is a derived property, enthalpy is used as a coordinate rather than temperature. This is because the combined heat contents of two waters are conserved when those waters are mixed, but the combined temperatures are not.The enthalpy values are obtained from steam tables.
48SILICA-ENTHALPY MIXING MODEL Fig. 5. Dissolved silica-enthalpy diagram showing procedure for calculating the initial enthalpy (and hence the reservoir temperature) of a high temperature water that has mixed with a low temperature water (from Fournier, 1981)
49SILICA-ENTHALPY MIXING MODEL A = non-thermal component(cold water)B, D = mixed, warm waterspringsC = hot water component atreservoir conditions(assuming no steamseparation before mixing)E = hot water component at(assuming steam separationbefore mixing)BoilingT = 100 CEnthalpy = 419 J/g(corresponds to D in the graph)Enthalpy values (at corresponding temperatures)are found from Steam Table in Henley et al.(1984)
50SILICA-ENTHALPY MIXING MODEL Steam Fraction did not separate before mixing The sample points are plotted.A straight line is drawn from the point representing the non-thermal component of the mixed water (i.e. the point with the lowest temperature and the lowest silica content = point A in Fig.), through the mixed water warm springs (points B and D in Fig.).The intersection of this line with the qtz solubility curve (point C in Fig.) gives the enthalpy of the hot-water component (at reservoir conditions).From the steam table, the temperature corresponding to this enthalpy value is obtained as the reservoir temperature of the hot-water component.
51SILICA-ENTHALPY MIXING MODEL Steam separation occurs before mixing The enthalpy at the boling temperature (100C) is obtained from the steam tables (which is 419 j/g)A vertical line is drawn from the enthalpy value of 419 j/gFrom the inetrsection point of this line with the mixing line (Line AD), a horizantal line (DE) is drawn.The intersection of line DE with the solubility curve for maximum steam loss (point E) gives the enthalpy of the hot-water component.From the steam tables, the reservoir temperature of the hot-water component is determined.
52SILICA-ENTHALPY MIXING MODEL In order for the silica mixing model to give accurate results, it is vital that no conductive cooling occurred after mixing. If conductive cooling occurred after mixing, then the calculated temperatures will be too high (overestimated temperatures). This is because:the original points before conductive cooling should lie to the right of the line AD (i.e. towards the higher enthalpy values at the same silica concentrations, as conductive cooling will affect only the temperatures, not the silica contents)in this case, the intersection of mixing line with the quartz solubility curve will give lower enthalpy values (i.e lower temperatures) than that obtained in case of conductive cooling.in other words, the temperatures obtained in case of conductive cooling will be higher than the actual reservoir temperatures (i.e. if conductive cooling occurred after mixing, the temperatures will be overestimated)
53SILICA-ENTHALPY MIXING MODEL Another requirement for the use of enthalpy-silica model is that no silica deposition occurred before or after mixing. If silica deposition occurred, the temperatures will be underestimated. This is because:the original points before silica deposition should be towards higher silica contents (at the same enthalpy values)in this case, the intersection point of mixing line with the silica solubility curve will have higher enthalpy values(higher temperatures) than that obtained in case of silica depositionin other words, the temperatures obtained in case of no silica deposition will be higher than that in case of silica deposition (i.e. the temperatures will be underestimated in case of silica deposition)
54CHLORIDE-ENTHALPY MIXING MODEL Fig.6. Enthalpy-chloride diagram for waters from Yellowstone National Park. Small circles indicate Geyser Hill-type waters and smal dots indicate Black Sand-type waters (From Fournier, 1981).
55CHLORIDE-ENTHALPY MIXING MODEL ESTIMATION OF RESERVOIRTEMPERATUREGeyser Hill-type WatersA = maximum Cl contentB = minimum Cl contentC = minimum enthalpy atthe reservoirBlack Sand-type WatersD = maximum Cl contentE = minimum Cl contentF = minimum enthalpy atEnthalpy of steam at 100 C =2676 J/g (Henley et al., 1984)
56CHLORIDE-ENTHALPY MIXING MODEL ORIGIN OF WATERSN = cold water componentC, F = hot water componentsF is more dilute & slightly cooler than CF can not be derived from C by process of mixing between hot and cold water (point N), because any mixture would lie on or close to line CN.C and F are probably both related to a still higher enthalpy water such as point G or H.
57CHLORIDE-ENTHALPY MIXING MODEL ORIGIN OF WATERSwater C could be related to water G by boilingwater C could also be related to water Hby conductive coolingwater F could be related to water G or water H by mixing with cold water N
60ISOTOPES IN GEOTHERMAL EXPLORATION & DEVELOPMENT
61ISOTOPE STUDIES IN GEOTHERMAL SYSTEMS At Exploration, Development and Exploitation StagesMost commonly used isotopesHydrogen (1H, 2H =D, 3H)Oxygen (18O, 16O)Sulphur (32S, 34S)Helium (3He, 4He)
62ISOTOPE STUDIES IN GEOTHERMAL SYSTEMS Geothermal FluidsSourcesSource of fluids (meteoric, magmatic, ..)Physico-chemical processes affecting the fluid comositionWater-rock interactionEvaporationCondensationSource of components in fluids (mantle, crust,..)Ages(time between recharge-discharge, recharge-sampling)Temperatures (Geothermometry Applications)
63Sources of Geothermal Fluids H- & O- IsotopesPhysico-chemical processes affecting the fluid compositionSources of components (elements, compounds) in geothermal fluidsHe-Isotopes (volatile elements)
64Sources of Geothermal Fluids and Physico-Chemical Processes STABLEH- & O-ISOTOPES
66Sources of Geothermal Fluids Stable H- & O-Isotopes (D/H)sample- (D/H)standard D () = x 103(D/H)standard(18O/16O)sample- (18O/16O)standard 18O () = x 103(18O/16O)standardStandard = Standard Mean Ocean Water= SMOW
67Sources of Geothermal Fluids Stable H- & O-Isotopes (D/H)sample- (D/H)SMOW D () = x 103(D/H)SMOW(18O/16O)sample- (18O/16O)SMOW 18O () = x 103(18O/16O)SMOW
68Sources of Geothermal Fluids Stable H- & O-Isotopes Sources of Natural Waters:Meteoric Water (rain, snow)Sea WaterFossil Waters (trapped in sediments in sedimanary basins)Magmatic WatersMetamorphic Waters
69Sources of Geothermal Fluids Stable H- & O-Isotopes
70Sources of Geothermal Fluids Stable H- & O-Isotopes
71Sources of Geothermal Fluids Stable H- & O-Isotopes
72Sources of Geothermal Fluids Stable H- & O-Isotopes
74Physico-Chemical Processes: Stable H- & O-Isotopes Aquifers recharged by precipitation from lower altitutes higher dD - d18O valuesAquifers recharged by precipitation from higher altitutes lower dD - d18O valuesMixing of waters from different aquifers
75Physico-Chemical Processes: Stable H- & O-Isotopes Boiling and vapor separation dD d18O in residual liquidPossible subsurface boiling as a consequence of pressure decrease (due to continuous exploitation from production wells)
76Monitoring Studies in Geothermal Exploitation Any increase in dD - d18O values due to sudden pressure drop in production wellsrecharge from (other) aquifers fed by precipitation from lower altitutessubsurface boiling and vapour separationAquifers recharged by precipitation from lower altitutes higher dD - d18OAquifers recharged by precipitation from higher altitutes lower dD - d18OBoiling and vapor separation dD d18O in residual liquid
77Monitoring Studies in Geothermal Exploitation Monitoring of isotope composition of geothermal fluids during exploitation can lead to determination of, and the development of necessary precautions againstDecrease in enthalpy due to start of recharge from cold, shallow aquifers, orScaling problems developed as a result of subsurface boiling
78(Scaling) Vapour Separation Volume of (residual) liquid Concentration of dissolved components in liquid Liquid will become oversaturatedComponent (calcite, silica, etc.) will precipitateScaling
80Dating of Geothermal Fluids Time elapsed between Recharge-Discharge or Recharge-Sampling points (subsurface residence residence time)3H method3H-3He method
81TRITIUM (3H)3H = radioactive isotope of Hydrogene (with a short half-life)3H formsReaction of 14N isotope (in the atmosphere) with cosmic rays147N + n 31H CNuclear testing3H concentrationTritium Unit (TU)1 TU = 1 atom 3H / 1018 atom H3H 3He + Half-life = yearDecay constant () = y-1
823H – Dating Method3H concentration level in the atmosphere has shown large changesİn between 1950s and 1960s (before and after the nuclear testing)Particularly in the northern hemisphereBefore 1953 : TUIn 1963 : 3000 TU
833H – Dating Method N=N0e-t 3H0 (before 1963) 10 TU 3H-concentration in groundwater < 1.1 TURecharge by precipitations older than nuclear testing3H-concentration in groundwater > 1.1 TURecharge by precipitations younger than nuclear testingN=N0e-t H0 (before 1963) 10 TU3H= 3H0e-t = y-1t = = 40 years 3H 1.1 TU
843H – Dating Method APPARENT AGE 3H= 3H0e-t 3H = measured at sampling point3H0 = measured at recharge point(assumed to be the initial tritium concentration) = y-1t = apparent age
86Geothermometry Applications Isotope Fractionation – Temperature DependentStable isotope compositions utilized in Reservoir Temperature estimationIsotope geothermometersBased on: isotope exchange reactions between phases in natural systems(phases: watre-gas, vapor-gas, water-mineral.....)Assumes: reaction is at equilibrium at reservoir conditions
87Isotope Geothermometers 12CO2 + 13CH4 = 13CO2 + 12CH4 (CO2 gas - methane gas)CH3D + H2O = HDO + CH4 (methane gas – water vapor)HD + H2O = H2 + HDO (H2 gas – water vapor)S16O4 + H218O = S18O4 + H216O (dissolved sulphate-water)1000 ln (SO4 – H2O) = 2.88 x 106/T2 – 4.1(T = degree Kelvin = K )
88Isotope Geothermometers Regarding the relation between mineralization and hydrothermal activitiesMineral Isotope GeothermometersBased on the isotopic equilibrium between the coeval mineral pairsMost commonly used isotopes: S-isotopes
89Suphur (S)- Isotopes (34S/32S)sample- (34S/32S)std. 34S () = x 103(34S/32S)sampleStd.= CD=S-isotope composition of troilite (FeS) phase in Canyon Diablo Meteorite
90S-Isotope Geothermometer 34S = 34S(mineral 1) - 34S(mineral 2)34S = 34S= A (106/T2) + B