基于分形理论的固井水泥浆体系设计

为了有效解决复杂工况下油井水泥混合料配比设计面临的难题,引入分形几何理论建立了颗粒群分形级配模型,结合激光粒度测试得到的材料粒径分布状况及分形维数的合理筛选(D=2.561),假定在小于1.68、1.68～56.23、大于56.23μm三个粒径范围内分别填充微硅、水泥和漂珠,设计出密度为1.40g/cm3的低密三元级配体系,并参照塔里木深井固井技术指标对体系水泥石力学性能(抗压、抗折和界面胶结强度)和浆体性能进行了测试.结果表明,三元体系紧密堆积效果显著,水泥石强度明显高于同密度的微硅或漂珠类二元体系,浆体失水量和析水率较低,稳定性好,稠化和流变性能均满足固井施工要求.实验结果验证了应用分形级配理论辅助设计固井水泥浆体系的可行性.

Design of well-cementing slurry system based on fractal theory

The fractal theory is used in the establishment of the fractal grading model for the proportion design of the well-cementing slurry materials.The grain-size distributions of the slurry materials are measured by a laser grain-size test machine,and an appropriate fractal dimension is screened(D=2.561).Suppose that the grain sizes of micro-silica,cement and floating beads distribute respectively in <1.68 μm,1.68～56.23 μm and >56.23 μm,and a ternary low-density cement slurry system of 1.40 g/cm3 is designed.Then the mechanical property(compression strength,bending strength and interfacial cementing strength) of the cement stone and the properties of the slurry in the proposed system are tested.The results show that the particles in the system closely pile,the mechanical property of the cement stone in the ternary system is obviously higher than that in the binary systems of micro-silica or floating beads with the same density.The performance of the cement slurry of the ternary system can meet the requirements of cementing operations due to its lower water loss and syneresis rate,favorable stability,and desired thickening property and rheological property.These experimental results validate the feasibility of the fractal grading theory in assisting the design of well cementing slurry system.