Hydrodynamic control of tracer retention in heterogeneous rock fractures

We investigate the statistical properties of a Lagrangian random variable beta[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 Qsimilar tob(n), where Q is the flow rate, b is the half aperture, and nless than or equal to3. 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 beta is related to tau as betasimilar totau(m), where m is dependent on the power n and the configuration of flow and transport. Simulation results for uniform flow indicate that betasimilar totau(n/n-1) for a small source section; as the source section increases, we have the convergence to betasimilar totau. For radially converging flow, we find betasimilar totau for a small source section and a convergence to beta=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 beta. The correlation between beta and Q is relatively weak for all cases studied.