Isotopic effects in fracture-dominated reactive fluid–rock systems

A mathematical model is presented that describes the effects of pore fluid aqueous diffusion and reaction rate on the isotopic exchange between fluids and rocks in reactive geo-hydrological systems where flow is primarily through fractures. The model describes a simple system with parallel equidistant fractures, and chemical transport in the matrix slabs between fractures by aqueous diffusion through a stagnant pore fluid. The solid matrix exchanges isotopes with pore fluid by solution–precipitation at a rate characterized by a time constant, R (yr−1), which is an adjustable parameter. The effects of reaction on the isotopes of a particular element in the fracture fluid are shown to depend on the ratio of the diffusive reaction length for that element (L) to the fracture spacing (b). The reaction length depends on the solid–fluid exchange rate within the matrix, the partitioning of the element between the matrix pore fluid and the matrix solid phase, the porosity and density of the matrix, and the aqueous diffusivity. For L/b < 0.3, fluid–rock isotopic exchange is effectively reduced by a factor of 2L/b relative to a standard porous flow (single porosity) model. For L/b > 1, the parallel fracture model is no different from a porous flow model. If isotopic data are available for two or more elements with different L values, it may be possible to use the model with appropriate isotopic measurements to estimate the spacing of the primary fluid-carrying fractures in natural fluid–rock systems. Examples are given using Sr and O isotopic data from mid-ocean ridge (MOR) hydrothermal vent fluids and Sr isotopes in groundwater aquifers hosted by fractured basalt. The available data for MOR systems are consistent with average fracture spacing of 1–4 m. The groundwater data suggest larger effective fracture spacing, in the range 50–500 m. In general, for fractured rock systems, the effects of fracture–matrix diffusive exchange must be considered when comparing isotopic exchange effects for different elements, as well as for estimating water age using radioactive and cosmogenic isotopes.