论文标题
毛细血管滞后和重力分离在两相流经多孔培养基中
Capillary Hysteresis and Gravity Segregation in Two Phase Flow Through Porous Media
论文作者
论文摘要
当考虑到相之间的压力差（毛细管压力）之间的历史依赖性时，我们研究了一维均匀的多孔柱中两个流体相的重力驱动流动。在双曲线极限中，此类系统的溶液具有非单调通量函数满足Buckley-Leverett方程。但是，在多种情况下，滞后案例的溶液不会在双曲线极限下收敛到经典溶液。特别是，除了经典的组件（例如冲击，稀疏波和恒定状态）之外，静态冲击是可能的。我们获得了固定冲击的可接纳性标准，并概述了所有可接受的冲击。根据毛细管压力功能，通量函数和Riemann数据，确定了两种情况，该溶液由固定冲击组成。在第一种情况下，冲击仍处于初始条件不连续的点。在第二种情况下，该溶液在至少一个半限制的一半中被及时冷冻。使用数值结果验证了预测。
We study the gravity-driven flow of two fluid phases in a one-dimensional homogeneous porous column when history dependence of the pressure difference between the phases (capillary pressure) is taken into account. In the hyperbolic limit, solutions of such systems satisfy the Buckley-Leverett equation with a non-monotone flux function. However, solutions for the hysteretic case do not converge to the classical solutions in the hyperbolic limit in a wide range of situations. In particular, with Riemann data as initial condition, stationary shocks become possible in addition to classical components such as shocks, rarefaction waves, and constant states. We derive an admissibility criterion for the stationary shocks and outline all admissible shocks. Depending on the capillary pressure functions, flux function, and the Riemann data, two cases are identified a priori for which the solution consists of a stationary shock. In the first case, the shock remains at the point where the initial condition is discontinuous. In the second case, the solution is frozen in time in at least one semi-infinite half. The predictions are verified using numerical results.
