Compositional simulation is typically used to study subsurface displacement processes that involve complex physics. Such processes are highly nonlinear and they occur at the interplay of phase thermodynamics (phase stability and split) and rock/fluid interaction (relative permeability). To better characterize the convergence failures of compositional nonlinear solvers, we study the analytical and discrete forms of the component flux functions for the transport problem. We focus on isothermal, two-hydrocarbon phase models in the presence of viscous forces. Our analysis shows that the component flux function exhibits both kinks and inflection points, as described in the literature. We study the kinks due to the crossing of phase boundaries and we show their impact on residual terms. We, then, investigate the location, direction, and evolution of the inflection loci inside the two-phase region. Our findings suggest that these inflection loci may exhibit complex features, as a result of which an a priori determination of such loci is computationally prohibitive. We propose a nonlinear solver that detects phase boundaries and guides the Newton update to avoid crossing these boundaries. Our numerical results show that this phase change detection solver has superior performance in comparison with standard Newton solvers for a wide range of cases.

成分模拟通常用于研究涉及复杂物理学的地下位移过程。这样的过程是高度非线性的，它们发生在相热力学（相稳定性和分裂）和岩石/流体相互作用（相对渗透率）的相互作用中。为了更好地刻画复合非线性求解器的收敛失效，我们研究了输运问题的分量通量函数的解析形式和离散形式。在粘性力存在的情况下，我们专注于等温的两烃相模型。我们的分析表明，分量通量函数同时表现出扭结和拐点，如文献所述。我们研究了由于相界线的交叉而引起的扭结，并显示了它们对残差项的影响。然后，我们调查位置，方向，两相区域内拐点的变化和演化。我们的发现表明，这些拐点位点可能表现出复杂的特征，因此，对这些位点的先验确定在计算上是令人望而却步的。我们提出了一种非线性求解器，该算法可检测相边界并指导牛顿更新以避免跨越这些边界。我们的数值结果表明，在很多情况下，这种相变检测求解器与标准的牛顿求解器相比具有出色的性能。我们提出了一种非线性求解器，它可以检测相边界并引导牛顿更新以避免跨越这些边界。我们的数值结果表明，在很多情况下，这种相变检测求解器与标准的牛顿求解器相比具有出色的性能。我们提出了一种非线性求解器，它可以检测相边界并引导牛顿更新以避免跨越这些边界。我们的数值结果表明，在很多情况下，这种相变检测求解器与标准的牛顿求解器相比具有出色的性能。