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Solute transport through fractured media is described by numerically combining advective-dispersive transport, which is dominant in the fractures, and diffusive transport, which is usually dominant in the unfractured matrix. Transport is considered in a manner conceptually similar to ‘double-porosity’ or ‘intra-aggregate’ transport models. A finite element model is developed for simulating nonreactive and reactive solute transport by advection, mechanical dispersion, and diffusion in a unidirectional flow field. The effect of the value of the solute diffusion coefficient in the matrix (termed the matrix diffusion coefficient) is illustrated by solute breakthrough curves and concentration profiles in the fracture as well as in the matrix. The illustrated conditions are similar to the laboratory tracer study on fractured till described in the accompanying paper (Grisak et al.). The effects on solute transport of fracture aperture size, water velocity in the fracture, matrix porosity, matrix distribution coefficient, and dispersivity in the fracture are illustrated with breakthrough curves and concentration profiles. The net effect of large matrix diffusion coefficients and/or large distribution coefficients in the matrix is to reduce significantly the effective solute velocity in the fracture. Reduction in the effective solute velocity can also be seen to be possible in materials with low matrix porosities such as crystalline rocks. The aperture size, matrix porosity, matrix diffusion coefficient, and distribution coefficient, all are important in determining the relative amounts of solute transported in the fracture and stored in the matrix. Implications with regard to aquifer recharge, groundwater chemistry, contaminant transport, tracer tests, and groundwater age dating in fractured media are discussed. The numerical model and the laboratory tracer test data provide considerable insight into the processes controlling solute transport in fractured media.