Due to their high aspect ratio fractures are often conceptualized as lower-dimensional structures embedded into the surrounding host matrix. This simplification is typically made within the context of numerical simulation, for the inverse estimation of the matrix-diffusion coefficient from break-through curves or for the derivation of analytical solutions describing flow and transport in a fracture–matrix system. It is generally justified by the so called Lauwerier assumption stating that the transversal dispersion inside the fracture is infinitely fast therefore hampering the formation of gradients across the width of the fracture. In this study we want to verify the applicability of such lower-dimensional modeling. To that end we investigate the occurrence of fracture-scale gradients in a simplified fracture–matrix model by virtue of analytical as well as numerical investigations. The relevant processes modeled are advection, dispersion, matrix diffusion and linear decay. In addition, we also investigate the impact on the inverse estimation of matrix-diffusion coefficients through analytical solutions, which assume a lower-dimensional fracture. Results show that a lower-dimensional modeling of fractures will only lead to errors for early periods of the time-dependent solution. Such errors may however, extent to the steady state if fast radioactive decay is considered. The estimation of the matrix-diffusion coefficient too is affected by the assumption of a lower-dimensional fracture. We see errors as big as 20% for the estimation procedure, the value of which depends on the ratio of the matrix-diffusion vs. the transversal dispersion coefficient. Our analysis suggest that a lower-dimensional representation of fractures is justified for many typical conditions and that special attention must only be paid in a confined number of cases.