A numerical method using discontinuous polynomial approximations is formulated for solving a phase-field model of two immiscible fluids with a soluble surfactant. The proposed scheme is shown to decay the total free Helmholtz energy at the discrete level, which is consistent with the continuous model dynamics. The scheme recovers the Langmuir adsorption isotherms at equilibrium. Simulations of spinodal decomposition, flow through a cylinder and flow through a sequence of pore throats show the dynamics of the flow with and without surfactant. Finally the numerical method is used to simulate fluid flows in the pore space of Berea sandstone obtained by micro-CT imaging.

制定了使用不连续多项式近似的数值方法来求解具有可溶性表面活性剂的两种不混溶流体的相场模型。所提出的方案显示在离散水平上衰减总自由亥姆霍兹能量，这与连续模型动力学一致。该方案恢复了平衡时的朗缪尔吸附等温线。对旋节线分解、流经圆柱体和流经一系列孔喉的模拟显示了使用和不使用表面活性剂时的流动动力学。最后采用数值方法对显微CT成像获得的Berea砂岩孔隙空间中的流体流动进行模拟。