Numerical investigation on preferential imbibition in pore doublet and dual-permeability pore network in the presence of surfactants

The preferential imbibition in non-uniform pore doublet and dual-permeability pore network in the presence of surfactants are modeled using lattice Boltzmann method. This method is first employed to simulate the preferential imbibition in pore doublet and dual-permeability pore network. In both surfactant-laden and clean systems, the critical capillary number Ca_m,c, defined as the capillary number at which the invading fluid simultaneously penetrates the narrower and wider branch channels (the low- and high-permeability regions), monotonically decreases with increasing viscosity ratio (λ). However, the presence of surfactants decreases Ca_m,c at all λ values, indicating that surfactants promote the invading fluid to flow into the wider branch channel (the high-permeability region). The pore doublet model is then used to forecast the imbibition in dual-permeability pore network. In both systems, the pore doublet model can be adopted to forecast the evolution of Ca_m,c with λ in dual-permeability pore network. However, the prediction accuracy in surfactant-laden system is slightly lower than that in clean system. In surfactant-laden system, there is a discrepancy between the instantaneous saturation in pore doublet and that in dual-permeability pore network, which is caused by the temporal variation in the ratio of the effective radii between the high- and low-permeability regions.