The use of "dimensional invariants" relating critical size fractions, coordination number, and dimension is investigated for fluid "invasion percolation" on correlated and uncorrelated networks. A new descriptor, the fraction of passable pores, is introduced to unify the treatment of drainage and imbibition (or bond and site percolation) processes, and to calculate new, approximate dimensional invariants. Not only do drainage and imbibition processes in lattices where pore and throat sizes are correlated have similar critical values for the fraction of passable pores for a given coordination number and dimension, but this fraction is also only slightly dependent on coordination number, namely to a power of about 0.17.