边界元法在深部地层井眼稳定中的应用

 为解决石油天然气钻井、地热钻井中深部地层井眼稳定问题,基于连续介质弹性力学建立深部地层井眼稳定平面应变问题的基本微分方程,采用边界元理论推导了井周应力和位移的边界元求解方法;通过建立井眼稳定物理模型、划分边界单元,将求解出的井周应力结果与解析解进行对比;分析了四川某油田深部地层井眼的稳定性情况。结果表明:BEM 求解应力分布与解析解吻合较好,其误差小于0.82%;实例井2500~3500 m 井段井眼稳定性分析结果与实际情况基本一致,实际钻井液密度低于坍塌压力当量密度,导致井眼扩大率普遍达到20%以上,适当提高钻井液密度能够维持井眼稳定,进一步验证了BEM 方法的准确性。该方法为井眼稳定分析提供了一种新的手段和方法。

Application of boundary element method to borehole stability problem in deep formation

To study the borehole stability problem of oil and gas drilling and geothermal drilling in deep formations, a basic differential equation of plane strain problem for borehole stability in deep formation is proposed on the basis of the continuum mechanics of elasticity, and a BEM calculation method of stress and displacement distribution around the wellbore is derived by using the BEM theory. To test the correctness of the BEM method, a physical model and the boundary elements of borehole stability problem are established, then the stress solution around the wellbore is compared with the analytical solution. By analyzing the borehole stability problem of deep formation in a certain oilfield of Sichuan, it is shown that the stress distribution with the BEM method is in good agreement with analytical solution, and its error is less than 0.82%. The borehole stability analysis results are basically in accord with the actual situation at 2500-3500 m in the example well, the actual drilling fluid density is lower than the equivalent density of the collapse pressure, and the hole expanding rate is above 20%. Increasing the density of drilling fluid can maintain wellbore stability, thus the accuracy of the BEM method is further verified. This method provides a new means for wellbore stability analysis.