THE INFLUENCE OF VARIABLE FLUID RESIDENCE TIME DISTRIBUTIONS ON STABLE ISOTOPE FRACTIONATION

Hydrogeochemical processes governing groundwater quantity and quality are often inferred from fluid samples that are the flux-weighted average of a heterogeneous system. This connection has been demonstrated for solutes subject to transport and equilibrium constraints, in which the steady state concentration – discharge relationship is cast in terms of the choice of expression for residence time distribution (Maher, 2011). Here, we examine the extent to which the spatial structure of the permeability field, which governs the fluid residence time distribution, exerts a principle control on the partitioning of stable isotopes between reactant and product species during heterogeneous reactions in groundwater systems.

We demonstrate this relationship using numerical simulations of δ⁵³Cr fractionation due to abiotic CrO₄^2- reduction by Fe²⁺, implemented in the reactive transport code CrunchFlow. The chemically homogeneous redox reaction generates Cr³⁺ with an isotope ratio distinct from the reactant pool, and in turn this product species precipitates as a mineral phase Cr(OH)_3(s) through a non-fractionating reaction. The corresponding chromate δ⁵³Cr enrichment across a homogeneous domain varies from a maximum value set by the kinetic fractionation factor (α_k) at high mean fluid residence times, to a value <α_k as fluid velocity increases, demonstrating a transition from reaction-limited to transport-limited regimes. For physically heterogeneous flow fields, the transition in isotopic fractionation from a reaction-limited to a transport-limited regime becomes variable, and falls between the upper and lower bounds set by the homogeneous simulations at slow and fast precipitation rates, respectively. Our results show that while no variation occurs in the steady-state isotopic profile of the reactant species (δ⁵³Cr of CrO₄^2-), the combined effects of the precipitation rate and the heterogeneous structure of the porous media lead to a wide range in the steady state isotopic composition of the product species (δ⁵³Cr of Cr³⁺) both in the fluid and mineral phase.