Convergent flow tracer tests constitute a convenient way of characterizing hydraulic parameters in an aquifer. Interpretation of tracer breakthrough curves from convergent flow tests normally is made under the assumption of radial symmetry. Nevertheless, these curves may display directional dependence; that is when tracers are injected at several points located at the same distance, both arrival times and estimated dispersivities may be significantly different. This result is why some authors attribute a tensorial nature to porosity or, equivalently, talk about directional porosity when trying to explain the variations in computed porosity depending on the relative orientation of pumping and injection wells. Our main ponit is that this directional effect is nothing but an artifact of an inappropriate selection of a conceptual model, where anisotropy (local of statistical) in hydraulic conductivity is not properly characterized. To illustrate this point, we first consider the situation of a simple homogeneous and anisotropic model of the medium. We prove analytically that this model leads to arrival time being proportional to the square root of directional hydraulic conductivity. Using a stochastic approach, we determine the same directional behavior of arrival time for a locally isotropic hydraulic conductivity field with statistical anisotropy caused by an anisotropic correlation structure. A statistical anisotropic covariance model for hydraulic conductivity is consistent with field evidence.