The Culebra dolomite Member of the Rustler Formation, New Mexico, is considered the most likely potential pathway for radionuclide transport beyond the regulatory boundary of the WIPP, the world's first operational facility for geologic disposal of nuclear waste. Previous studies have confirmed that pore-scale heterogeneity in the Culebra leads to the presence of multiple simultaneous diffusive mass transfer rates; the rate distributions can span orders of magnitude, and are present within sampling volumes ranging from ~0.00001 to ~100 cubic metres. However, the effects of such multirate matrix diffusion processes upon contaminant transport over large temporal and spatial scales, of uncertainty in mass transfer parameters, and of the relative significance of variability in mass transfer and flow parameters, have not previously been ascertained. In this heuristic study, deterministic and stochastic simulations of one-dimensional advective-dispersive transport invoking a variety of mass transfer regimes are completed at the regional scale, using parameters believed reasonable for the Culebra. In general, single-rate nonequilibrium mass transfer causes increases in tailing and dispersion, a decrease in maximum plume concentration, and faster initial solute arrival relative to equilibrium processes. We find here that a distribution of matrix diffusion rates can greatly accentuate most of these phenomena and, in particular, may result in rate-limited mass transfer under conditions for which single-rate diffusion approaches equilibrium, with significant potential consequences to aquifer remediation design and waste repository risk assessment. These effects generally persist under statistically-described uncertainty in flow and mass transfer parameters. It is also demonstrated that, in a multirate model, a hypothesized scaling of mean effective diffusion rate with experimental duration could simultaneously result in both extreme tailing and, perhaps of particular interest to the potential impacts of a nuclear waste repository breach, initial solute arrival times approaching those found for nonreactive transport.