Recently, pore network modelling has been attracting attention in the investigation of electrolysis. This study focuses on a 2D pore network model with the purpose to study the drainage of water by oxygen in anodic porous transport layers (PTL). The oxygen gas produced at the anode catalyst layer by the oxidation of water flows counter currently to the educt through the PTL. When it invades the water-filled pores of the PTL, the liquid is drained from the porous medium. For the pore network model presented here, we assume that this process occurs in distinct steps and applies classical rules of invasion percolation with quasi-static drainage. As the invasion occurs in the capillary-dominated regime, it is dictated by the pore structure and the pore size distribution. Viscous and liquid film flows are neglected and gravity forces are disregarded. The curvature of the two-phase interface within the pores, which essentially dictates the invasion process, is computed from the Young Laplace equation. We show and discuss results from Monte Carlo pore network simulations and compare them qualitatively to microfluidic experiments from literature. The invasion patterns of different types of PTLs, i.e., felt, foam, sintered, are compared with pore network simulations. In addition to this, we study the impact of pore size distribution on the phase patterns of oxygen and water inside the pore network. Based on these results, it can be recommended that pore network modeling is a valuable tool to study the correlation between kinetic losses of water electrolysis processes and current density.