Invasion percolation with long-range correlations: First-order phase transition and nonuniversal scaling properties

We present the results of extensive Monte Carlo simulations of the invasion percolation model with trapping (TIP) with long-range correlations, a prob lem which is relevant to multiphase flow in held-scale porous media, such a s oil reservoirs and groundwater aquifers, as well as flow in rock fracture s. The correlations are generated by a fractional Brownian motion character ized by a Hurst exponent H. We employ a highly efficient algorithm for simu lating TIP, and a novel method for identifying the backbone of TIP clusters . Both site and bond TIP are studied. Our study indicates that the backbone of bond TIP is loopless and completely different from that of site TIP. We obtain precise estimates for the fractal dimensions of the sample-spanning cluster (SSC), the minimal path, and the backbone of site and bond TIP. an d analyze the size distribution of the trapped clusters, in order to identi fy all the possible universality classes of TIP with long-range correlation s. For site TIP with H>1/2 the SSC and its backbone are compact, indicating a first-order phase transition at the percolation threshold, while the min imal paths are essentially straigth lines. For H<1/2 the SSC, its backbone, and the minimal paths are all fractal with fractal dimensions that depend on the Hurst exponent H. The fractal dimension of the loopless backbone for bond TIP is much less than that of site TIP for any H.