A pore scale description of calcium isotope exchange and equilibration with calcite

The distribution of stable isotope ratios between dissolved and solid phases are commonly used to assess processes of mineral formation, alteration and dissolution in a variety of low temperature systems. In order to model this partitioning, a description of isotopic exchange occurring at the fluid-solid surface is required. The use of continuum scale reactive transport models to describe heterogeneous isotopic fractionation is thus hindered by the ability to discretize isotopic gradients within a solid phase. Here we present a multi-component pore scale model for the partitioning of calcium isotopes between dissolved Ca²⁺ and calcite using a lattice Boltzmann method capable of describing the isotopic composition of an evolving mineral surface distinct from the bulk calcite composition.

A key feature of our model is the ability to simultaneously track isotopic exchange at the fluid-solid surface as well as the isotopic composition of both bulk fluid and bulk calcite. This is significant in that the surface exchange dictates the evolution of isotopic compositions through time, while the bulk isotope ratios represent the actual measured values of samples collected in the field. Using this approach, we reexamine the distribution of calcium isotope ratios in pore fluids and carbonates reported for deep-sea core profiles with particular emphasis on interpretation of the equilibrium fractionation factor. Based on simulations of an initially supersaturated fluid surrounding a calcite crystal at a range of porosities, we show that the fluid can achieve both chemical and isotopic equilibrium with the solid surface while maintaining the appearance of disequilibrium with the bulk solid. The extent to which the final equilibrated calcium isotope ratio of the bulk fluid and bulk solid agree is therefore a function of the depth into the mineral surface that is exchangeable with the fluid.