### Abstract

The kinetics of the dissolution of carbon dioxide in water and subsequent chemical reactions through to the formation of calcium carbonate, a system of reactions integral to carbon sequestration and anthropogenic ocean acidification, is mathematically modelled using the mass action law. This group of reactions is expressed as a system of five coupled nonlinear ordinary differential equations, with 14 independent parameters. The evolution of this system to equilibrium at 25 degrees C and 1 atm, following an instantaneous injection of gaseous carbon dioxide, is simulated. An asymptotic analysis captures the leading-order behaviour of the system over six disparate time scales, yielding expressions for all species in each time scale. These approximations show excellent agreement with simulations of the full system, and give remarkably simple formulae for the equilibrium concentrations.

Original language | English |
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Pages (from-to) | 1265-1290 |

Number of pages | 26 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 466 |

Issue number | 2117 |

DOIs | |

Publication status | Published - 8 May 2010 |

### Keywords

- TRANSPORT
- carbon sequestration
- asymptotic analysis
- IMPACT
- SYSTEM
- ocean acidification
- calcium carbonate
- carbon dioxide dissolution
- OCEANS
- reaction kinetics
- CO2 SEQUESTRATION

## Cite this

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*,

*466*(2117), 1265-1290. https://doi.org/10.1098/rspa.2009.0349