Hydrodynamic control of tracer retention in heterogeneous rock fractures

We investigate the statistical properties of a Lagrangian random variable β [T/L], which has been shown to quantify hydrodynamic impact on retention [ Cvetkovic et al. , 1999], using Monte Carlo simulations of flow and transport in a single fracture. The “local cubic law” of water flow is generalized to a power law Q ∼ b n , where Q is the flow rate, b is the half aperture, and n ≤ 3. Simulations of flow and particle transport are carried out assuming “local cubic law” ( n = 3) and “local quadratic law” ( n = 2), and for two typical flow configurations: uniform flow and radially converging flow. We find that β is related to τ as β ∼ τ m , where m is dependent on the power n and the configuration of flow and transport. Simulation results for uniform flow indicate that for a small source section; as the source section increases, we have the convergence to β ∼ τ. For radially converging flow, we find β ∼ τ for a small source section and a convergence to β = const for an increasing source section. Simulation results for both flow configurations are consistent with the results for a homogeneous fracture. The results for a homogeneous fracture provide reasonable bounds for simulated β. The correlation between β and Q is relatively weak for all cases studied.