页岩气压裂水平井不稳定流动模型

水平井多级压裂技术已经成为目前开发页岩气藏的主要手段。针对气体在页岩流动过程中存在的吸附解吸、扩散、滑脱、启动压力梯度和应力敏感等效应,基于三线性渗流方程的基础上,推导出五线性渗流方程,建立了页岩气藏压裂水平井渗流数学模型。运用Laplace变换和Duhamel原理,求解出考虎井筒储集效应和表皮效应的页岩气藏压裂水平井Laplace空间的无因次井底拟压力解。通过Stefest数值反演,绘制了无因次拟压力曲线和拟压力导数曲线。依据特征曲线划分了流动阶段,并分析了不同影响因素对气井压力特征曲线的影响。研究结果表明：压裂水平井泄流范围可划分为五个流动区域,气井的压力特征曲线可划分为六个流动阶段。裂缝导流能力对水平井压力特征曲线的影响主要在过渡阶段、双线性流阶段；吸附系数主要影响过渡段、双线性流段、线性流段以及拟稳定流阶段；视渗透率系数主要影响双线性流动阶段、过渡阶段、窜流扩散阶段、地层线性阶段和拟稳定流阶段；导压系数影响窜流扩散阶段、地层线性流阶段和拟稳定流阶段；压裂改造区宽度主要影响地层线性流和系统拟稳态流动段。模型可以正确认识页岩储层复杂渗流规律,判别页岩气藏压裂水平井流动阶段,为预测单井产能和优化压裂设计参数提供了科学依据。

Unsteady Flow Model of Fractured Horizontal Well in Shale Gas Reservoir

The technology of multi-fractured horizontal well has become one of the most effective and efficient methods to develop shale gas reservoir. Referring to absorption effect, diffusion effect, slippage effect, threshold pressure gradient, and stress sensitivity effect, based on trilinear porous flow equation, a new porous flow mathematical model for fractured horizontal in shale gas reservoir is built. Using the Laplace transform principle and Duhamel principle, the dimensionless down-hole pseudo-pressure solution of the Laplace space, considering wellbore storage effect and skin effect, is solved. Through Stefest numerical inversion, the dimensionless pseudo-pressure curve and derivative curve are plotted. According to the characteristic curve, the flow phase is divided and the influence of different influencing factors on the gas well pressure characteristic curve is analyzed. The result shows that the fractured horizontal well discharge range can be divided into five flow areas, and the gas well pressure characteristic curve can be divided into six flow stages. The influence of fracture conductivity on horizontal well pressure characteristic curve is mainly in transition stage and bilinear flow stage; adsorption coefficient mainly affects transition stage, bilinear flow stage, linear flow stage and quasi-steady flow stage; apparent permeability coefficient is mainly influencing bilinear flow phase, transition phase, turbulent diffusion phase, stratigraphic linear phase and quasi-steady flow phase; the conductance coefficient affects the turbulent diffusion phase, the stratigraphic linear flow phase and the quasi-steady flow phase; the fractured transformation zone mainly affects formation linear flow and system quasi-steady flow stage. The proposed model can correctly understand the complex porous flow law and identify the flow stage of fracturing horizontal well in shale gas reservoir, which provides a scientific basis for predicting single well productivity and optimizing fracture design parameters.