Kinetic Modeling of the Reaction Rate for Quartz and Carbon Black Pellet

Abstract

The kinetic modeling for the carbothermal reduction reaction rate in quartz and carbon black pellets is studied at different temperatures, under varying CO partial pressures in ambient atmosphere, varying carbon contents, different quartz particle sizes, and different crucible opening areas. Carbon black is produced by the cracking of natural gas. The activation energy of the SiC-producing step was determined to be 594 kJ/mol. The averaged pre-exponential factor A obtained from 1898 K, 1923 K, and 1948 K (1625 °C, 1650 °C, and 1675 °C) is 2.62E+16 min⁻¹. The reaction rate of the gas-solid interface factor, fix-C content (X_fix-C), temperature (T), and CO partial pressure (X_CO) can be expressed as follows:

$$ \frac{{{\text{d}}\;{\text{pct}}}}{{{\text{d}}t}} = (1 - 0.40 \times X_{{{\text{fix}} - C}}^{ - 0.86} \times {\text{pct}}) \times 2.62 \times 10^{16} \times \exp \left( { - \frac{594000}{RT}} \right) \times (2.6 - 0.015 \times X_{\text{co}} ). $$