基于分形理论的煤层气非达西流动分析  

Non-darcy flow analysis of coalbed methane based on the fractal theory

作　　者：张先敏[1] 冯其红[1] 同登科[1] 杨波[2] 

机构地区：[1]中国石油大学(华东),东营257061 [2]新疆油田分公司,克拉玛依834000

出　　处：《应用力学学报》2010年第4期635-639,共5页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(No.40974056);国家973计划专题(No.2009219606);国家油气重大专项基金(No.2009ZX05038-006)

摘　　要：在考虑了煤层的分形特征和启动压力梯度影响的基础上,建立了无限大煤层中气体低速非达西流动的数学模型,并求得了量纲为一的井底压力的Laplace空间解析解,并根据数值求解结果绘制了典型的井底压力动态曲线。研究结果表明:在定产量生产的情况下,分形维数和量纲为一的启动压力梯度对早期井底压力动态无显著影响;在生产的中后期,由于受二者的影响,压力导数曲线上的径向流水平直线段消失;量纲为一的井储系数的影响主要表现在续流阶段,而吸附系数则主要影响煤基质向裂隙扩散的过渡阶段。A mathematical model for low velocity non-Darcy flow of methane in the fractal coalbed methane reservoirs is established with consideration of the fractal structures and starting pressure gradient effects.Analytical solutions for dimensionless bottom-hole pressure in Laplace space are obtained when the constant flow rate is specified in an infinitely large reservoir,and the parameter sensitivity analysis shows that the fractal dimension and starting pressure gradient have no effect on the initial bottom hole pressure behavior,but the derivative curves no longer has a horizontal straight line section of radial flow owing to their effects in the middle-late production stage.It is also found that the main influence of dimensionless wellbore storage factor occurs in the after flow stage while the adsorption factor has an obvious effect on the transition stage.

关 键 词：煤层气 分形维数 启动压力梯度 非达西 LAPLACE变换 

分 类 号：TE323[石油与天然气工程—油气田开发工程]