Electro-osmosis phenomena are studied in a two-dimensional (2D) model disordered porous medium. The flow passages are represented by a network of spatially distributed rectangular channels with random orientations. The channels may represent microfractures in fractured porous media or in a network of interconnected microfractures, pores in a porous medium, or fibers in a fibrous porous material. The linearized equations of electrokinetics are solved numerically in a single channel, and in the 2D network of the channels. The macroscopic electrical conductivity σ and electro-osmotic coupling coefficient β are computed as functions of the electrical surface potential ζ and such geometrical parameters of the network as the channels' number density and widths, as well as the porosity of the medium. Despite the complexity of the phenomena and the model of porous media that is used, both σ and β appear to depend on the characteristics of the phenomena and porous media through very simple relations.