A single variable aperture fracture plane is the microscopic scale equivalent of a pore in a porous medium, with the advantage that it can be more easily characterized using a deterministic or stochastic description of the fracture aperture. Fracture aperture distributions can be measured in the laboratory for small fractured cores using Computed Tomography (CT) X-ray scanning to a resolution of about 50 &mgr;m. Using the small perturbation analysis developed by Gelhar (1987) based on a stochastic description of the fracture aperture distribution, we predict the breakthrough curve of a dissolved contaminant in an aqueous phase flowing through a single natural fracture, from the knowledge of the geostatistical description of the fracture aperture. The results of the stochastic analysis are compared to experimental results from the actual breakthrough curve of a nonsorbing solute flowing through a single fracture plane in a granite core at different flow rates, with a fracture aperture characterized using CT scanning. The measured effective transmissivity is 13% larger than the estimated value, and the measured dispersivity is 33% larger than the estimated value. Errors introduced by the boundary conditions, the first order approximation and heterogeneities not sampled by the CT scanner may account for the difference. The estimation method may be useful for predicting solute breakthrough at field sites if the required statistics are obtained from hydraulic and tracer tests at similar sites. ¿ American Geophysical Union 1995