We report here a model experimental study oil the influence of pore structure oil the free-imbibition of sessile drops into nanoporous substrates. The work takes advantage of the existence of distinct pore structures oil the two sides or a nanoporous alumina membrane: straight parallel channels versus a denser and tortous network. We show first that the spreading which coexists with the free-imbibition predominates in the early stage well follows oil both sides the power-law scaling with time predicted by the universal Tanner's law. More interestingly, we found also that the imbibition rate scales in a similar way with the time on both sides of the membrane, showing that the pore structure does not affect qualitatively the free-imbibition kinetics. Oil the other hand, our results clearly show that the pore structure has a quantitative impact oil the imbibition rate, which increases markedly from the A side (dense network of short and tortuous pores) to the side B (straight vertical channels). This latter result shows that, as regards the free-imbibition, the topology of the pores has a preeminent impact on their volume, which is here comparable for both sides of the membrane. More unexpectedly, this quantitative impact of the pore structure oil the imbibition rate seems to display a certain sensitivity to the viscosity of the liquid.