Title: Modeling of non-monotone two-phase flow in porous media
Abstract:This talk includes two parts. In the first part, saturation overshoot and pressure overshoot are studied by incorporating dynamic capillary pressure, capillary pressure hysteresis and hysteretic dynamic coefficient with a traditional fractional flow equation in one-dimensional space. Using the method of lines, the discretizations are constructed by applying the Castillo-Grone's mimetic operators in the space direction and a semi-implicit integrator in the time direction. Computed profiles capture both the saturation overshoot and pressure overshoot phenomena. In the second part, the effects of the dynamic capillary coefficient, the infiltrating flux rate and the initial and boundary values are systematically studied using a traveling wave ansatz and efficient numerical methods. The traveling wave solutions may exhibit monotonic, non-monotonic or plateau-shaped behaviour. Special attention is paid to the non-monotonic profiles. The traveling wave results are confirmed by numerically solving the partial differential equation using an accurate adaptive moving mesh solver. Comparisons between the computed solutions using the Brooks-Corey model and the laboratory measurements of saturation overshoot verify the effectiveness of our approach.