基于分形理论, 用裂缝宽度分维和迂曲分维表征裂缝线密度和裂缝性储层等效渗透率。将储层水平井井筒周围流体流动状态划分为内外两个区域:内部渗流区为垂直于水平井段的平面径向流和水平井两端的球面向心流, 外部渗流区为平面椭圆渗流区。基于质量和动量守恒方程, 建立二区耦合稳态渗流数学模型, 推导出裂缝性稠油油藏水平井产能公式。计算结果表明, 缝宽分维越大, 裂缝线密度越大, 基质-裂缝等效渗透率越大;迂曲分维越大, 等效渗透率越低;水平井长度的增加, 会提高裂缝性稠油储层水平井的产能;幂律指数大于0.75 时, 对产能的影响逐渐增大, 且随着幂律指数的增大, 产能逐渐增大;启动压力越大, 水平井产能越低, 且随着启动压力梯度的增加, 产能降低的幅度也在增加。
Based on the dual fractal dimension in the fractal theory, the linear density of fractures and the equivalent permeability are characterized by the fractal dimensions of the fracture width and the tortuosity. The seepage field around the horizontal well bore is divided into two regions: the inner seepage region and the outer elliptical nonlinear seepage region. A mathematical model for the two-region coupling steady flow is established based on the conservation law of mass and the motion equation, and the productivity equation is obtained. It is shown that the larger the fractal dimension of the fracture width, the greater the linear density of the fractures, and the larger the equivalent permeability. The greater the tortuosity fractal dimension, the lower the equivalent permeability. Increasing the horizontal well length can have a great impact on the productivity improvement. As the power- law exponent increases, the influence on the productivity of the horizontal well grows, when the power-law exponent n is greater than 0.75. The increase of the threshold pressure gradient leads to a larger decrease rate of the productivity.
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