Thermodynamic modeling of solubility and speciation of silica in H2O-SiO2 fluid up to 1300°C and 20 kbar based on the chain reaction formalism

Recent systematic studies of mineral solubilities in water to high pressures up to 50 kbar call for a suitable thermodynamic formalism to allow realistic fitting of the experimental data and the establishment of an internally consistent data base. The very extensive low-pressure (< 5 kbar) experimental data set on the solubility of SiO(2) in H(2)O has in the last few years been extended to 20 kbar and 1300 degrees C, providing an excellent experimental basis for testing new approaches. In addition, solubility experiments with different SiO(2)-buffering phase assemblages and in situ determinations of Raman spectra for H(2)O-SiO(2) fluids have provided both qualitative and quantitative constraints on the stoichiometry and quantities of dissolved silica species. We propose a thermodynamic formalism for modeling both absolute silica solubility and speciation of dissolved silica using a combination of the chain reaction approach and a new Gibbs free energy equation of water based on a homogeneous reaction formalism. For a given SiO(2)-buffer (e.g., quartz) and the coexisting H(2)O-SiO(2) fluid both solubility and speciation of silica can be described by the following two reactions: monomer-forming standard reaction: SiO(2)(s) + 2(H(2)O)L = (SiO(2))center dot(H(2)O)(2) (A) polymer-forming chain reaction: (SiO(2))(n-1)center dot(H(2)O)(n) + (SiO(2))center dot(H(2)O)(2) = (SiO(2))(n)center dot(H(2)O)(n+1) + (H(2)O)(L), (B) where 2 <= n <= infinity, and (H(2)O)(L) stands for "liquid-like" (associated, clustered) water molecules in the aqueous fluid. We show that reactions (A) and (B) lead to the simplified relationships Delta G degrees((Mono),r,PT) = Delta H degrees((mono),r) - T Delta S degrees((mono),r) + Delta Cp((mono),r) [T - 298.15 - Tln(T/298.15)] + Delta V degrees((mono),r)(P - 1), and Delta G degrees((poly),rP,T) = Delta H degrees((poly)j) - T Delta S degrees((poly),r) + Delta V degrees((poly)j) (P - 1) (where the Delta G degrees(r,P,T), are the standard molar Gibbs free energy changes in reactions (A) and (B) as a function of pressure P and temperature T; the Delta H degrees(r), Delta S degrees(r), Delta Cp degrees(r) and Delta V degrees(r) are standard molar enthalpy, entropy, isobaric heat capacity and volume changes, respectively, in reactions (A) and (B) at reference temperature T(o) = 298.15 K and pressure P(o) = 1 bar) that provide excellent descriptions of the available H(2)O-SiO(2) data set in terms of both SiO(2) solubility and silica speciation. Discrepancies between directly determined solubility data and data obtained from in situ Raman spectra are ascribed to (i) possible experimental problems of equilibration and (ii) inherent difficulties of interpreting Raman spectra of dilute H(2)O-SiO(2) solutions. In agreement with recent findings, our model indicates that dissolved silica in quartz-buffered aqueous solutions is considerably polymerized, exceeding 20-25 % at all temperatures above 400 degrees C.