Correlation effects play an important role in the description of turbulent transport. The present paper considers the influence of drift flow and time-dependence effects on the passive scalar behavior in the framework of the percolation approach. The renormalization method of a small parameter in continuum percolation models is reviewed. The modification is suggested of the renormalization condition of the small parameter of the percolation model in accordance with the additional external influences superimposed on the system. This approach makes it possible to consider simultaneously both parameters: the characteristic drift velocity $U_{\rm d}$ and the characteristic perturbation frequency $\omega $. The effective diffusion coefficient $D_{\rm eff} \,{\propto}\, \omega ^{1/7}$ satisfactorily describes the low-frequency region $\omega $, where the long-range correlation effects play a significant role. The character of the dependence of $D_{\rm eff}$ on the drift flow amplitude $U_{\rm d}$ in different regimes is analyzed.