| Title | An heuristic equation correlating silica polimerization induction times to temperature and silica concentration in geothermal brines |
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| Authors | Alessandro Lenzi |
| Year | 2026 |
| Conference | World Geothermal Congress |
| Keywords | |
| Abstract | Oversaturation is a common phenomenon in various compounds, from physical states like supercooled or superheated water to solubility oversaturation, such as CO₂ or silica in water. In geothermal systems, silica oversaturation is particularly notable. As geothermal brine cools, silica can remain dissolved beyond equilibrium levels, eventually leading to polymerization. This process typically includes a delay known as the "polymerization induction period." Despite being off-equilibrium, silica oversaturation follows a regular pattern. Several models have been proposed to describe this behavior. In this study, we build on the early empirical work of Rothbaum and Rohde to develop a heuristic expression that fits experimental data and can be refined with further observations. The correlation is given by: \ln{\left(It\right)}=-0.0049\left(\left[\mathrm{SiO}2\right]-\left[\mathrm{SiO}2\right]eq\right)+3.6106 By incorporating Fournier et al.’s general expression for silica equilibrium, we derive a more comprehensive formula: \log{\left(tp\right)}=3.6106-0.0049\left(\left[\mathrm{SiO}2\right]_0-{10}^{\left(4.52-731/T\left(K\right)\right)}\right)\ This expression aligns with polymerization models where initial tetrameric silica rings form, as described by Iacopini et al., followed by oligomer coalescence governed by standard kinetics. The resulting correlation not only fits observed induction times but also provides a theoretical framework for understanding silica polymerization, offering a more robust heuristic model than previous empirical-only approaches. |