In
this paper, a lattice Boltzmann method is developed to simulate
two-phase flows with soluble surfactants in complex porous media.
This method not only can recover the Langmuir adsorption isotherm
when the bulk surfactant concentration is relatively low but also
allows the surfactant concentration to exceed the critical micelle
concentration. Thanks to its versatility, this method is used to study
the influence of surfactants on steady-state fluid distributions,
specific interfacial lengths (SILs), and relative permeabilities under
different wetting fluid (WF) saturations (S
w) and viscosity ratios (M) of WF to non-WF (NWF).
Regardless of the values of S
w and M, the SIL between two fluids and the SIL between a grain
surface and WF are always higher in a surfactant-laden system than
in a clean system, while the SIL between a grain surface and NWF is
always lower in a surfactant-laden system. For M =
1, we find that the addition of surfactants dramatically increases
the relative permeability (RP) of NWF but slightly decreases the RP
of WF. By adjusting M at S
w = 0.5, the RP of NWF is always higher in a surfactant-laden system
than in a clean system, while the relative magnitude of the WF relative
permeabilities in both systems depends on M: for M < 1, the RP of WF in a surfactant-laden system is higher,
whereas for M ≥ 1, the RP of WF in a clean
system is higher.