页岩气藏双渗透模型解的结构  

Similar Structure of Solutions for Percolation Model in Dual-Permeability of Shale Gas Reservoirs

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,四川成都610039 [2]北京东润科石油技术股份有限公司,北京100029

出　　处：《西华大学学报（自然科学版）》2017年第1期39-46,共8页Journal of Xihua University:Natural Science Edition

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);西华大学创新基金(YCJJ2016102);西华大学"西华杯"训练项目(LXY2016008)

摘　　要：根据页岩气渗流理论,针对解析吸附、扩散、滑脱以及渗流等复杂的渗流问题,分别从仅考虑基质孔隙滑脱效应、考虑基质微孔隙滑脱效应和气体扩散2种因素以及综合考虑基质微孔隙应力敏感、滑脱效应和气体扩散3种因素共同作用的3个角度出发,建立以考虑解析吸附为前提的页岩气渗流方程;结合3种外边界条件(封闭、定压、无穷大)、初始条件和内边界条件,构成页岩气渗流模型。通过无因次变换和Laplace变换,将该页岩气渗流模型非线性形式转化为常微分方程的定解问题,得到该模型在Laplace空间下的解,并对其进行深入研究与分析,发现该模型的解式之间具有相似结构。这不仅极大地便利了试井分析软件的编制,而且避免了繁琐冗长的计算过程,提高了计算效率,对页岩气产能模型的建立也具有指导意义。As for the shale gas of complex seepage problems about adsorption ＆ desorption, diffusion, slippage, seepage and so on, we established respectively shale gas reservoir seepage equations with the premise on adsorption ＆ desorption according to the shale gas seepage theory. During the establishment, we considered slippage effect in the matrix porosity, the slippage effect and gas diffusion in micro - matrix porosity, synthesis, stress - sensitivity, gas diffusion and so on. The percolation model in dual - permeability of Shale Gas Reservoirs was composed of every kind of shale gas reservoir seepage equations, three kinds of outer boundary conditions （closed, constant pressure, infinity） , initial conditions and boundary conditions. With the dimensionless transform and Laplace trans-form ,the nonlinear model in dual - permeability of Shale gas reservoirs was transformed into a definite solution problem of ordinary dif-ferential equation and solutions of the model in Laplace space were obtained. Then, we analyzed the solutions in depth and found that the solutions of the model had a characteristic of the similar structure. It is great convenience for well test analysis software. It helps to avoid a tedious and complicated calculation process and improve the computational efficiency and, and has a guiding significance on shale gas productivity model.

关 键 词：页岩气 解析吸附 滑脱效应 应力敏感 相似结构 

分 类 号：O29[理学—应用数学] TE3[理学—数学]