Precise pore-level knowledge of effective thermal and electrical conductivities guarantees proper thermophysical and petrophysical characterization of the multiphase saturated porous media. High resolution advancing imaging techniques and developing modeling approaches are capable of simulating pore-scale phenomena in micro- and nano-scales. In this paper, a numerical framework is presented to predict relative electrical and thermal conductivity curves of two-phase saturated pore-level structures. Displacement scenarios are first performed applying a geometrical filling process. A set of rules to construct the fluid interfaces under capillary-driven transport are implemented. Subsequently effective thermal and electrical conductivity curves, quantifying the relationship between conductivity and saturation, are determined using steady state diffusion equation. The media under consideration include three-dimensional binary images of oil/water-wet sandstone and carbonate formations and the fluid systems contain steam-oil and water-oil equilibriums. The result packages, including thermal diffusivity and conductivity, electrical conductivity, formation factor, apparent diffusion coefficient, and saturation exponent, are generated and discussed considering rock types and fluid configurations.