基于均匀化理论的页岩基质流固耦合尺度升级

Upscaling of hydro-mechanical coupling in shale matrix based on homogenization theory

关键词:  页岩气  流固耦合  等效连续介质  均匀化理论  尺度升级

Key words:  shale gas  hydro-mechanical coupling  equivalent continuous medium  homogenization theory  upscaling

摘要:

页岩基质通常由微尺度的有机质和无机质组成,由于这两种介质的力学性质差异较大,且气体在两者中的赋存方式和流动机制均不相同,要准确刻画气体在页岩基质中的流固耦合过程,需针对两种介质建立不同的微尺度模型,但由于计算效率问题,微尺度模型无法直接用于宏观模拟。基于均匀化理论建立一种页岩基质流固耦合尺度升级方法,将微尺度上有机质和无机质各自特征有效地表征到宏观模拟中。首先,将页岩基质看成是由有机质和无机质组成的非均质多孔弹性介质,考虑真实气体在这两种介质中不同的赋存方式和流动机制,建立微尺度流固耦合模型;然后,采用均匀化理论进行尺度升级,推导得到页岩基质的宏观等效流固耦合模型,并给出相关等效参数的定义和计算方式;最后,通过数值算例验证方法的正确性,并分析有机质力学性质、体积分数和分布对页岩气藏宏观流固耦合数值模拟的影响。结果表明:有机质弹性模量越小、无机质连通性越好,累积产气量越高,而有机质体积分数越高,早期的累积产气量越低,后期的累积产气量越高。

Abstract:

In shale gas reservoirs, gas is mainly stored in shale matrix. Therefore, to establish a hydro-mechanical coupling (HM) model in shale is important for the macroscopic HM simulation of shale gas production. At microscopic scale, shale matrix is usually composed of organic and inorganic matters. The mechanical properties of these two media are quite different, and so that both gas storage type and transport mechanisms are different in the two media. Thus it is necessary to develop different microscale models to accurately describe the HM process of gas in shale matrix. However, the microscale models cannot be straightly applied to macroscale simulation due to huge calculation time and data storage requirement. In this study, an efficient upscaling method based on the homogenization theory was proposed for the HM process in shale matrix, which can accurately represent the microscale characteristics of the organic and inorganic matters in macroscale simulations. Firstly, the shale matrix is assumed as a heterogeneous porous elastic medium composed of organic and inorganic matters, and the microscale HM models were developed according to different storage type and transport mechanism of real gas in these two media. Then, the microscale HM models were homogenized to obtain the equivalent macroscopic HM models for the shale matrix, along with the definition and calculation method of equivalent parameters in the micro and macro models. Lastly, the accuracy and application of the proposed method were verified via several case studies, and the influence of the mechanical properties, the content and distribution of organic matters on the macro HM simulation in shale gas production were also analyzed. The results indicate that the cumulative gas production increases with the decrease of the elastic modulus of the organic matter, and it correlates positively with the connectivity of the inorganic matter. Besides, at early period, gas production decreases with the increase of the total organic content, but it will increase at late period of the process.