Chemical enhanced oil recovery (EOR) methods include the injection of aqueous polymer solutions slugs driven by water. Polymer solutions increase water viscosity, decreasing the water phase mobility and improving oil recovery through better sweep efficiency. In this paper, we present the water alternated polymer EOR technique, which is based on the injection of successive polymer slugs alternated by water slugs. The mathematical problem is composed by two conservation equations: one of them is related to the water volume and the other one to the polymer mass. We assume that the polymer may be adsorbed by the rock, and the relation between the concentration in the aqueous solution and the solid is governed by a Langmuir type adsorption isotherm. The water viscosity is a function of the polymer concentration in water. The 2 × 2 system of hyperbolic equations was decoupled by introducing a potential function instead of time as an independent variable. The water alternated polymer injection is represented by a varying boundary condition. The analytical solution presents interactions between waves of different families. It is shown that the polymer slugs always catch up each other along the porous media generating a single slug. As a consequence, the water slugs will disappear. This solution is new and was compared to numerical results with close agreement. It also can be used for the selection of the most suitable enhanced oil recovery technique for a particular oil field.

中文翻译：

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水交替聚合物注射的数学模型

化学强化采油 (EOR) 方法包括注入由水驱动的聚合物水溶液段塞。聚合物溶液会增加水的粘度，降低水相的流动性，并通过更好的波及效率提高采油率。在本文中，我们介绍了水交替聚合物 EOR 技术，该技术基于连续注入聚合物段塞与水段塞交替。数学问题由两个守恒方程组成：一个与水的体积有关，另一个与聚合物的质量有关。我们假设聚合物可能被岩石吸附，并且水溶液中的浓度与固体之间的关系由朗缪尔型吸附等温线控制。水粘度是水中聚合物浓度的函数。通过引入势函数而不是时间作为自变量来解耦 2 × 2 双曲方程组。水交替聚合物注入由变化的边界条件表示。解析解呈现了不同族的波之间的相互作用。结果表明，聚合物段塞总是沿着多孔介质相互追赶，产生单个段塞。结果，水蛞蝓将消失。该解决方案是新的，并且与数值结果进行了比较，结果非常一致。它还可以用于为特定油田选择最合适的强化采油技术。解析解呈现了不同族的波之间的相互作用。结果表明，聚合物段塞总是沿着多孔介质相互追赶，产生单个段塞。结果，水蛞蝓将消失。这个解是新的，并且与数值结果进行了比较，结果非常一致。它还可以用于为特定油田选择最合适的强化采油技术。解析解呈现了不同族的波之间的相互作用。结果表明，聚合物段塞总是沿着多孔介质相互追赶，产生单个段塞。结果，水蛞蝓将消失。该解决方案是新的，并且与数值结果进行了比较，结果非常一致。它还可以用于为特定油田选择最合适的强化采油技术。