Invasion percolation on correlated and elongated lattices: Implications for the interpretation of residual saturations in rock cores

The invasion percolation model is used to investigate the effect of correla ted heterogeneity on capillary dominated displacements in porous media. The breakthrough and residual saturations are shown to be strongly influenced by the correlations. Correlated heterogeneity leads to lower residual satur ations than those observed in random systems and the scatter commonly obser ved in laboratory core measurements of the residual saturations can be attr ibuted to the presence of such heterogeneity at the pore scale. Invasion pe rcolation computations on elongated lattices, those with a geometry of Ld-1 x nL where n denotes the aspect ratio, show that residual saturations for systems with correlated heterogeneity exhibit a strong dependence on aspect ratio. This effect is not considered by experimentalists who advocate the use of long (high aspect ratio) cores in order to overcome "end-effects" in experiments on shorter cores. A new scaling law is proposed for the residu al saturations in elongated systems with correlated heterogeneity, and is c onfirmed by numerical simulations.