Kinetically controlled oxygen isotope exchange between fluid and rock in one-dimensional advective flow

The cumulative infiltration of fluid into a permeable and porous solid along a 1-dimensional trajectory leads to systematic alteration of the “aquifer” solid. Model simulations of infiltration into rock of initially uniform oxygen isotope composition provide characteristic profiles of δ 18 O(solid) vs. infiltration distance. Analytic solutions are presented of the governing differential equations. For given initial and input conditions (relative isotope ratios of input water and initial rock compared to equilibrium fractionation) and porosity, the simulated δ 18 O profiles depend upon a single dimensionless quantity N D (Damköhler number), which expresses the variables fluid flux, isotope exchange rate and infiltration distance. The systematics of δ 18 O(solid) vs. distance profiles can be readily adapted to fluid pathways with any given temperature profile and porosity.