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Stable-isotope exchange fronts, Damköhler numbers, and fluid to rock ratios |
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| Authors: | Peter Blattner Keith R Lassey |
| Institution: | 1 New Zealand Geological Survey, Lower Hutt, New Zealand 2 Institute of Nuclear Sciences, Lower Hutt, New Zealand |
| Abstract: | The advection of extraneous fluid into permeable solid rock along a one-dimensional path is a fundamental scenario of geochemistry. Model solutions are presented for advection with “instantaneous” as well as with kinetically restricted equilibration. An initial step input of a stable-isotope δ-value leads to the propagation of a “geochemical” or isotope front. For pure advection and instantaneous isotope exchange between fluid and solid, fronts are sharp and their positions and velocities determined by the carrier porosity Ψ (e.g., oxygen porosity) of the aquifer. For limited exchange rates the dimensionless “Damköhler number” ND = (κ/q)L, where κ is an exchange rate constant, q the interstitial fluid velocity, and L the total theoretical infiltration distance, determines the isotope front shape, i.e. the degree of degradation of the original sharp fronts. The effects of temperature (Δ) variations and, for the first time, of variations in initial rock composition, are shown and a model calculation for a one-dimensional system with two isotopic elements of distinct Ψ (O and Sr) is given. Dispersion in the fluid is considered, and for an idealised geothermal system the combined effects of (1) dispersion in the fluid and (2) limited exchange rates, characterised by their respective Péclet and Damköhler numbers, are also calculated. Fluid/rock ratios need to be treated differently in one-dimensional and zero-dimensional models and in general it is preferable in flow models to replace them with information on porosity, infiltration distance and Damköhler numbers. |
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