Prediction of the solubility of quartz in salt solutions from 25 °C to 900 °C using the 3-parameter Non-Random Two-Liquid (NRTL) model

Abstract

By being able to accurately predict the behavior of silica contained in hot, high pressure water, it is possible to understand and evaluate many important subsurface chemical and geological processes. In this paper, the solubility of quartz is estimated using a 3-parameter Non-Random Two Liquid (NRTL) model, which is commonly used to predict phase equilibrium for a range of chemical processes. Model parameters were fitted to published binary interaction data (e.g. solubility data, vapor–liquid equilibrium data) using a Levenberg–Marquadt algorithm. The model is then extended to ternary systems with dissolved NaOH to predict the solubility of quartz in alkaline hydrothermal media.With no alteration to the NRTL model beyond its basic multi-component form, the model predicted silica solubilities in NaOH–water solutions from 0°C to 900°C, 0.5–3000bar and pH values between 7 and 14 (room temperature/pressure equivalent) with an average error of 62%. As literature reports discrepancies between solubility data by up to an order of magnitude, the predictions seemed reasonable.It was found that the majority of the NRTL model error occurred between 100°C and 200°C because of insensitivity to NaOH concentration. A correction term was added that modeled residual error as a function of sodium hydroxide concentration. The model error was decreased from 62% to 28%. In so doing, the error in calculating the solubility data between 100°C and 200°C was reduced to 25%. While more solubility data is needed to confirm the model accuracy over the broad temperature ranges for which the model was developed, the corrected NRTL model provides a good estimate of solubility from 0.00001mol/kg to 10mol/kg NaOH molality, 0–900°C and 0.1–3000bar.