Motion of a passive component in a periodic incompressible steady flow is studied in the presence of intrinsic diffusivity of a medium. It is rigorously proven that for large distance and time the transport can be described as an effective anisotropic diffusion. Analytical properties of the effective diffusivity D_n* for a given direction n as a function of complex P² (P is the Peclet number) are discussed. It is shown that the function D_n*(P²) is meromorphic and both poles and zeroes of D_n*(P²) are real and negative. It is proven that D_n* < D(1 + const P²) for any real P. New algorithm based on the continued fractions is given to compute D_n*(P²).