Tracer experiments in fractured rocks: Matrix diffusion and the validity of models

Several published tracer tests are reexamined using the single fracture dispersion model (SFDM), i.e., a solution to the transport equation in which fractured rock is represented by a single fracture and the tracer is allowed to diffuse into the matrix. The model has three fitting parameters, i.e., the mean time of flow, dispersivity, and a diffusion parameter which combines such physical parameters as matrix porosity, coefficient of matrix diffusion, and adjusted fracture aperture. The model is easily calibrated yielding as good, or better, fits as did the models applied in original works, which were based on an assumption of negligible matrix diffusion and were characterized by larger numbers of fitting parameters. The SFDM better describes the short-term transport in investigated systems and/or their parameters than models applied so far. Validation of the model was obtained by showing that the values of its physical parameters either agree with those known from other methods or are within expected ranges. Another validation was achieved for tests performed in the same pair of wells with two tracers characterized by distinctly different coefficients of molecular diffusion. In spite of distinct differences in the shapes of the experimental curves, the SFDM yielded the same values of the fracture aperture, matrix porosity, and intrinsic dispersivity. The ratio of the diffusion coefficients in the matrix was close to that known from the diffusion coefficients in free water.