Drilling Fluid Loss Model in Rough Fractures Based on Fractal Theory
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摘要: 当前的漏失模型均未充分考虑裂缝粗糙度对钻井液漏失的影响，对粗糙裂缝的漏失规律认识不清，反演得到的裂缝宽度误差大。为此，基于分形理论建立了二维粗糙裂缝模型，采用赫-巴模式描述了钻井液的非牛顿流变特性，采用指数方程描述了裂缝的非线性变形特征，建立了钻井液漏失模型，并采用中心差分方法对方程进行了数值求解，分析了网格尺寸、分形维数及标准差对钻井液漏失速率及累计漏失量的影响。研究结果表明，模拟网格尺寸足够大时，数值模拟结果的可靠度较高；随着标准差增大，微凸体数量增加、起伏程度提高，漏失速率及累计漏失量显著减小；分形维数对漏失的影响与裂缝面是否接触紧密相关，没有接触时影响较小，接触后随着接触面积增大影响增大。研究表明，建立的漏失模型可为认识漏失机理和反演裂缝宽度提供理论参考。Abstract: Conventional lost-circulation models failed to consider impacts of fracture roughness on losses of drilling fluids.Consequently,patterns of lost circulation in rough fractures were not fully understood,whereas fracture widths derived through inversion were usually characterized by huge errors.In the concerned study,a two-dimensional model for rough fractures was established based on fractal theory.With non-Newtonian rheological behaviors of the drilling fluid were highlighted by using the Herschel-Buckley mode,and with non-linear deformation features highlighted by index equations,a model for losses of drilling fluid could be established.Midpoint displacement method was used to derive numerical solution of the equation to determine the impacts of mesh sizes,number of fractal dimensions and standard deviation on drilling fluid loss rates and cumulative loss.Research results showed when sizes of mesh grids were large enough,numerical simulation might generate results with higher reliability.Loss rates and the cumulative loss might decrease significantly with increases in the standard deviation.The effect of the number of fractal dimensions on fluid loss behavior was related to contact of the two fracture surfaces.Minor effects on the loss could be observed when the contact rate was zero,and the impacts might be enhanced with increases in contact areas.Research results showed the newly established lost-circulation model might provide theoretical references for identification of lost circulation mechanisms and to determine the widths of fractures through inversion.
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Keywords:
- fractured formation /
- roughness /
- fractal dimension /
- Herschel-Buckley fluid /
- fluid loss rate
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