油藏数值模拟的精确井模型开发

Advances in Geo-Energy Research, 2019, 3(3): 242-249

原文网址: https://www.yandy-ager.com/index.php/ager/article/view/136

        Peaceman井模型将井流量、井底压力和井网格压力三者联系进来，通过定义等效半径能准确计算出井流量，该模型是油藏数值模拟的标准算法。本文指出，在网格长宽比很大的情况下，尽管Peaceman井模型能准确计算井流量，但对井附近区域的压力场计算存在显著误差。

       基于均匀介质中的点源解析解，中国科学技术大学张生生、刘志峰、王晓宏等人提出了两种改进算法：点源补偿法和模式竞争法。在点源补偿法里，不直接求解原始泊松方程，而是求解严格满足拉普拉斯方程的辅助压力变量，从而提高计算精度。在模式竞争法里，线性流模式和点源诱导的径向流模式相互竞争，竞争结果，网格间传导率取相应的最小值。数值结果表明，这两种方法不仅能准确计算出井流量，而且能准确计算出井附近压力场。

Development of accurate well models for numerical reservoir simulation

Shengsheng Zhang, Zhifeng Liu, Anfeng Shi, Xiaohong Wang

(Published: 2019-06-06)

Corresponding Author and Email:

Zhifeng Liu, lzf13@ustc.edu.cn;

ORCID: https://orcid.org/0000-0002-9309-7029

Citation: Zhang, S., Liu, Z., Shi, A., Wang, X. Development of accurate well models for numerical reservoir simulation. Advances in Geo-Energy Research, 2019, 3(3): 250-257, doi: 10.26804/ager.2019.03.03.

ArticleType: Original article

Abstract：

    The Peaceman well model has been an industrial standard in numerical reservoir simulation. With the help of defined equivalent radius, the bottom-hole inflow or outflow flux is calculated as being proportional to the difference between the bottom-hole pressure and the well-grid block pressure. We show in this paper that, although the bottom-hole flux is calculated accurately in the Peaceman well model, some significant errors of pressure arise near the well for a large value of the length-to-width ratio of the mesh. We propose two alternative methods, the source term compensation method and the pattern competition method, both of which are based on an analytic solution induced by the source term for the homogeneous case. In the source term compensation method, the auxiliary pressure, which strictly satisfies the Laplace equation, is defined and solved instead of the original pressure variable only satisfying the Poisson equation. In the pattern competition method, different flow patterns including the linear flow pattern and radial flow pattern are considered. Each flow pattern corresponds to an specific value of the transmissibility of the two adjacent grid blocks. The smallest transmissibility will outcompete, and be used for solving the discrete pressure equations. Numerical results show that not only the bottom-hole flux but also the pressure fields can be calculated accurately using both of proposed methods.

Keywords: Peaceman well model, equivalent radius, bottom-hole pressure, source term compensation method, pattern competition method.

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