During the development of deep-water oil and gas resources, severe engineering problems or even marine geological hazards might be induced by the complex geological characteristics of deep-water weakly consolidated (DWC) formation. To solve these problems, the power-law cementing fluid was used to solidify the DWC formation during the well-cementing operation. However, the transportation process of cementing fluid in DWC formation is still unclear. To guide the solidification operation of DWC formation, a mathematical model for predicting the penetration distance of cementing fluid in DWC formation was proposed based on the generalized Darcy’s law and fractal theory. All the parameters in this model have clear physical meaning and no empirical parameter is involved. The numerical and experimental validation results show that the proposed model calculated penetration distance agrees well with both simulated and experimental results. The model capacity relates to the penetration pressure, the viscosity of cementing fluid, the permeability of formation, the effective radius of the flow path and the fractal dimension of formation. The maximum error of this model is less than 20%, which indicates that the mathematical model is reliable.

中文翻译：

---

深水弱固结地层中幂律固井流体输送的渗透距离建模

在深水油气资源开发过程中，深水弱固结（DWC）地层的复杂地质特征可能引发严重的工程问题甚至海洋地质灾害。为解决这些问题，在固井作业中采用幂律固井液对DWC地层进行固化。然而，DWC地层中固井液的输送过程仍不清楚。为指导DWC地层的凝固作业，基于广义达西定律和分形理论，提出了一种预测DWC地层固井液渗透距离的数学模型。该模型中的所有参数都有明确的物理意义，不涉及经验参数。数值和实验验证结果表明，所提出的模型计算的穿透距离与模拟和实验结果吻合良好。模型容量与渗透压力、固井液粘度、地层渗透率、流道有效半径和地层分形维数有关。该模型的最大误差小于20%，表明该数学模型是可靠的。