A pore network model is proposed to simulate the complex process of in situ foam generation, destruction, and propagation as a drainage process. Motivated by the need to account for viscous flow effects, which arise from the viscous drag of moving bubbles, the statistical physical method of the modified invasion percolation with memory algorithm is extended. The model is capable of capturing the flow characteristics of (weak) continuous gas and (strong) discontinuous gas foams based on a minimum number of input parameters, that is, pore throat size distribution, regeneration probability, network dimensionality, and size. The dependence of the flowing foam fraction on the applied pressure gradient is predicted. The steady-state relative permeabilities during the simultaneous flow of a liquid and a gas, with lamella generation, destruction, and mobilization by flow displacement, are computed. The proposed model adequately portrays literature results with the decrease in the gas relative permeability upon introduction of foams in agreement with the reported results for similar porous media. The results find application in optimizing the current population balance models and guide foam-based enhanced oil recovery projects.