QrtzGeotherm: A revised algorithm for quartz solubility geothermometry to estimate geothermal reservoir temperature and vapor fraction with multivariate analytical uncertainty propagation

Abstract

The quartz solubility geothermometry to calculate geothermal reservoir temperature and vapor fraction with multivariate analytical uncertainty propagation is programmed as two classes, SiO2TD and QrtzGeotherm in Visual Basic in Visual Studio 2010 (VB.NET). The class, SiO2TD calculates the total discharge concentration, SiO2TD and its uncertainty, SiO2TDErr from the analytical concentration of silica, SiO2msd and uncertainty, SiO2msdErr of separated water, sampled after N-separations of vapor and liquid. The class, QrtzGeotherm uses the following properties as input parameters: (i) HRes—reservoir enthalpy (kJ/kg), (ii) HResErr—uncertainty in the reservoir enthalpy (kJ/kg), (iii) SiO2TD—total discharge silica concentration (ppm), (iv) SiO2TDErr—uncertainty in the total discharge silica concentration (ppm) (v) GeoEq—number of quartz solubility regression equation, (vi) TempGuess—a guess value of the reservoir temperature (°C). The properties corresponding to the output parameters are (i) TempRes—reservoir temperature (K), (ii) TempResErr—uncertainty in the reservoir temperature (K), (iii) VaporRes—reservoir vapor fraction and (iv) VaporResErr—uncertainty in the reservoir vapor fraction. Similarly, it has a method, SiO2Eqn(EqNo, Temp) to provide the silica solubility as function of temperature corresponding to the regression equation.Four quartz solubility equations along the liquid–vapor saturation curve: (i) a quadratic equation of 1/T and pressure, (ii) a linear equation relating log SiO2to the inverse of absolute temperature (T), (iii) a polynomial of T including logarithmic terms and (iv) temperature as a polynomial of SiO2including logarithmic terms are programmed. A demonstration program, QGeotherm is written VB.NET. Similarly, the applicability of classes SiO2TD and QrtzGeotherm in MS-Excel is illustrated considering Los Azufres geothermal field as an example.