Longitudinal dispersion coefficients in given realizations of the transport computed by two currently used approximations of the first-order in velocity variance are compared with accurate global random walk simulations. The comparisons are performed for the same ensemble of realizations of the Darcy velocity field, approximated by a quasiperiodic random field, for lognormal hydraulic conductivity with small variance and finite correlation lengths. The results show that at finite times of about one dispersion timescale, the mean coefficient is underestimated by ≈20%, and the fluctuations are overestimated by ≈80%. At larger times the errors decrease monotonously, and the first-order approximations yield fairly good predictions for the mean and the fluctuations of the dispersion coefficient.