A versatile class of superellipsoids which smoothly interpolate from octahedron via ellipsoid to cuboid is introduced. By approximating the shapes of pore elements in the particulate networks by these superellipsoids with different shapes or sizes, we investigate the percolation performance of 3D disordered particulate media consisting of the binary penetrable superellipsoidal pores. To derive the critical percolation threshold of these continuum systems, a finite-size scaling method is applied here. By combining the finite-size scaling theory with different cubic models of bidisperse superellipsoids, the impact of polydispersity of particle shape and size on the value of phi(c) for different particulate networks is independently studied. Based on the obtained dataset, the relationship between the percolation thresholds and the pore-structure characteristics is further analyzed and quantified by the generalized formulas. The comparisons reveal the proposed empirical formulas can provide an effectively approximate estimate of for phi(c) a series of 3D binary superellipsoid dispersions. (C) 2019 Elsevier B.V. All rights reserved.