A large-scale natural-gradient tracer test in a highly heterogeneous aquifer at the Macrodispersion Experiment (MADE) site on the Columbus Air Force Base in Mississippi is simulated using three-dimensional hydraulic conductivity distributions derived from borehole flowmeter test data. Two methods of hydraulic conductivity interpolation, ordinary kriging and conditional geostatistical simulation based on fractional Brownian motion (fBm), are used to construct the hydraulic conductivity distributions needed by the numerical model. Calculated and observed mass distributions are compared to evaluate the effectiveness of the dual-domain mass transfer approach relative to the single-domain advection-dispersion approach. The results show that the classical Fickian advection-dispersion model can reproduce reasonably well the observed tritium plume above a certain concentration limit but fails to reproduce the extensive spreading of the tracer at diluted concentrations as observed in the field. The alternative dual-domain mass transfer model is able to represent the rapid, anomalous spreading significantly better while retaining high concentrations near the injection point. This study demonstrates that the dual-domain mass transfer approach may offer a practical solution to modeling solute transport in highly heterogeneous aquifers where small-scale preferential flow pathways cannot be fully and explicitly represented by the spatial discretization of the numerical model.