The formation of gas cavities in a liquid-saturated porous medium is studied by means of computer simulations, using a newly developed code for the tracking of moving phase interfaces in 3D porous media. The dependence of the fraction of pore space filled by the gas phase on the volumetric concentration of dissolved gas - a quantity necessary for the calculation of the mean reaction rate and the particle density is determined for porous media of different pore space geometry and several values of physico-chemical parameters such as interfacial tension and contact angle.