Transient immiscible and miscible displacement experiments performed on artificial glass-etched pore networks are used to determine the capillary and relative permeability curves as well as the hydrodynamic dispersion coefficients. The transient responses of the total and axial distribution of the wetting phase (WP) saturation and the pressure drop across the pore network are introduced into an inverse modeling scheme to estimate the imbibition capillary pressure and relative permeability curves of pore networks by varying the capillary number, the contact angle, and the shear-thinning rheology of the nonwetting phase (NWP). The temporal evolution of the spatial distribution of the solute concentration profiles over selected areas of the pore network is fitted to analytical one-dimensional solute dispersion models to estimate the longitudinal dispersion coefficient as a function of the Peclet number, in single- and dual-pore networks. Under an unfavorable viscosity ratio the growth pattern is a two-dimensional fractal object, its description with the one-dimensional macroscopic two-phase flow equations is questionable, a high uncertainty is introduced into the capillary pressure curve, whereas average relative permeability functions are estimated. The relative permeability of the NWP may be a decreasing or increasing function of the capillary number over the viscous or capillary fingering pattern, respectively. The relative permeability of the WP is an increasing function of the capillary number and increases weakly with the NWP shear-thinning rheology strengthening. The longitudinal dispersion coefficient varies nonlinearly with Peclet number following power laws with exponents ranging from 1 to 2 and depending on the relative contribution fraction of the macrodispersion (associated with the spatial variation of pore sizes) and Taylor dispersion (associated with the flow channeling) to the entire process.