Foam is used in enhanced oil recovery to improve the sweep efficiency by controlling the gas mobility. A common way to describe the foam displacement is by using population balance models, which consider the foam texture as part of the gas phase. Numerical simulation of such equations presents serious difficulties connected to the high non-linearity in the fractional flow. The linear kinetic model is studied mathematically for large initial reservoir water saturation and all possibilities of injection saturation. It was observed that the model contains some structural instabilities, i.e., a small variation in some parameters leads to qualitatively different solutions. One of these solutions presented localized decay in relative gas mobility, indicating that this behavior is due to the equations’ mathematical properties.

泡沫可用于提高采油率，以通过控制气体流动性来提高吹扫效率。描述泡沫位移的一种常用方法是使用人口平衡模型，该模型将泡沫质地视为气相的一部分。这种方程的数值模拟提出了与分流中的高非线性相关的严重困难。对于较大的初始油藏水饱和度和注入饱和度的所有可能性，对线性动力学模型进行了数学研究。据观察，该模型包含一些结构不稳定性，即某些参数的微小变化会导致定性不同的解。这些解决方案之一显示了相对气体迁移率的局部衰减，表明此行为是由于方程的数学性质引起的。