多孔介质自吸与加压自吸的自模解

Advances in Geo-Energy Research, 2018, 2(3): 260-268

原文网址: http://www.astp-agr.com/index.php/Index/Index/detail?id=70

  多孔介质内的两相流动主要受控于毛细管力和粘滞力的作用。对于粘滞力主控的流动，Buckley-Leverett（贝克莱——列韦尔特）非混相驱替理论已经被提出超过半个多世纪。但是对于毛管力主要控制下的流动的研究，还主要是基于毛管束模型。而连续介质条件下的解析解，近些年才受到大家的广泛关注。将粘滞力与毛管力同时考虑时，相关研究就更少。

本文呈现了一个多孔介质自吸与加压自吸的自模解，并且提供了相应的简洁算法。类比于Buckley-Leverett驱替理论，通过引入毛细管分流函数和参数变换，得到了这一类非线性偏微分方程的解析解。最后，用一个实例应用证明了该模型对多孔介质非混相流动问题的有效性和准确性。

A self-similar analytical solution of spontaneous and forced imbibition in porous media

Xiukun Wang, James J. Sheng

(Published: 2018-06-21)

CorrespondingAuthor and Email: Xiukun Wang, xiukun.wang@ttu.edu; James J. Sheng, james.sheng@ttu.edu

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Citation: Wang, X., Sheng, J.J. A self-similar analytical solution of spontaneous and forced imbibition in porous media. Advances in Geo-Energy Research, 2018, 2(3): 260-268, doi: 10.26804/ager.2018.03.04.

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ArticleType: Original article

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Abstract：

    Both viscous and capillary forces control the two-phase flow in porous media. The Buckley Leverett solution for viscous flow in porous media has been proposed for over a half century. While the corresponding studies of capillary dominated solutions are mainly based on the capillary tube based models. The continuum solutions are just prevail in recently years. The analytical solution of the combination of both effects is rarely investigated. A self-similar analytical solution of spontaneous and forced imbibition in porous media is proposed in this work and the corresponding concise algorithms are presented. The proposed solution successfully solves this typical non-linear partial differential equation by introducing a transformation variable and the capillary fractional flow function analog to the fractional flow function of Buckley Leverett solution. Finally, the case study is performed, which demonstrates the feasibility and accuracy of this proposed solution to a general two-phase flow condition.

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Keywords: Analytical solution, spontaneous imbibition, forced imbibition, porous media.

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