  The aim of the thesis is to present and analyze two particular problems of
transport in porous media flow. The first of them is related to the process of
saturation of porous building materials. Recently, M. K\"untz and P. Laval\'ee,
using a computer model of this process, have concluded that the anomalous
diffusion assumption is correct. In this thesis I present an alternative
explanation of this results without any refer to anomalous diffusion. The
second part of the thesis covers the numerical analysis of the tortuosity of
the flow -- one of a very interesting physical macroscopic variables
characterizing transport in porous media. (in Polish)
