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.