基于应力敏感的天然裂缝性页岩气藏双孔模型解的结构  

Similar Structure of the Solution to the Dual-Porosity Model for Naturally Fractured Shale Gas Reservoirs Based on Stress Sensitivity

作　　者：李顺初[1] 任丽[1] 郑鹏社[1] 桂钦民 

机构地区：[1]西华大学理学院应用数学研究所,成都610039 [2]北京东润科石油技术股份有限公司,北京100029

出　　处：《应用数学和力学》2017年第2期233-242,共10页Applied Mathematics and Mechanics

基　　金：四川省科技厅2015年第一批科技计划项目(基本科研-重点研发)(2015JY0245);四川省教育厅自然科学重点项目(12ZA164);四川省教育厅自然科学重点项目(15ZA0135)

摘　　要：针对天然裂缝性页岩气藏,研究了3种外边界条件(无穷大、定压、封闭)及内边界条件下的定产量生产问题,并建立了考虑应力敏感性和解析吸附的不稳定渗流的试井分析模型.先对此模型作线性化处理;然后通过摄动法以及利用Laplace变换,求得线性化后的无因次储层压力的Laplace空间精确解;最后根据解的相似结构理论,给出了求解该模型解结构的步骤,并且定义了3种外边界条件下的相似核函数,发现了此模型在3种外边界条件下精确解之间的相似结构.这项研究不仅为编制试井分析软件提供便利,提高计算效率,而且对页岩气藏渗流理论的研究具有重要意义,也为页岩气藏渗流模型的求解提供了一种新的方法.For naturally fractured shale gas reservoirs,the problem about fixed output was addressed in 3 outer boundary conditions（infinite boundary-constant pressure and closed boundary） and inner boundary conditions-to build a well test analysis model for unsteady seepage flow in view of stress sensitivity and desorption ＆ adsorption.Firstly-the model was linearized.Secondly-the perturbation method and the Laplace transform were used to get the exact solution of dimensionless reservoir pressure in the Laplace space with the linearized model.Finally-according to the similar structure theorythe steps leading to the similar structure of the solution to this model were presented.In addition-the kernel functions in the 3 outer boundary conditions were defined and it was found that a similar structure existed among the exact solutions of this model in the 3 outer boundary conditions.The work not only facilitates the development of well test analysis software with higher calculation efficiency-but also helps a lot in the investigation of shale gas seepage mechanisms-making a new method for the solution of the shale gas seepage model.

关 键 词：应力敏感性 裂缝性页岩气藏 解析吸附 相似核函数 相似构造 

分 类 号：O29[理学—应用数学] TE3[理学—数学]