A 3-dimensional simulation of fluid displacement in a disordered porous solid is performed. The solid heterogeneities are characterized by two pore size distributions in the context of the dual site-bond model (DSBM). It is shown how invasion patterns and relevant quantities in invasion percolation are affected by the disordered porous matrix confirming and also contrasting previous results in 2-dimensional networks. Deeper understanding of the problem is achieved by allowing the presence of anisotropy in the porous space.