We investigate the statistical properties of a Lagrangian random variable ¿ , 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 ~ bn, 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 ¿ is related to τ as ¿ ~ τm, where m is dependent on the power n and the configuration of flow and transport. Simulation results for uniform flow indicate that $beta sim tau^{frac{n}{n-1}}$ for a small source section; as the source section increases, we have the convergence to ¿ ~ τ. For radially converging flow, we find ¿ ~ τ for a small source section and a convergence to ¿ = 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 ¿. The correlation between ¿ and Q is relatively weak for all cases studied.