Abstract: Drilling fluid properties and annular geometry have great impact on surge pressure.This paper presents the governing equations of steady surge pressure of non-Newtonian fluid in an eccentric annulus under bi-polar coordinates.A numerical model for this elliptic,non-linear,non-homogeneous partial differential equations with variable coefficients worked out by box-integration and finite-difference methods.Take the Power-law fluid as an example,the paper calculates the surge pressure gradient and velocity distribution in eccentric annuli produced by-running pipe in the wellbore.Numerical results show that with the increase of eccentricity,surge pressure decreases.The velocity distribution differs greatly in the wider and the narrower section of the annulus.The surge pressure as the inner pipe fully lies in the lower side of the wellbore is only half of that as the inner pipe is coaxial with the wellbore.Moreover,the paper also compares the numerical solution with that of approximation method and empirical method.

Key words: non-Newtonian fluid, eccentric, surge pressure, annulus numerical model

摘要： 钻井液性能和环空几何形状对波动压力影响很大.本文建立了双极坐标下非牛顿流体偏心环空稳态波动压力的控制方程,利用盒式积分法和有限差分法推导了椭圆型变系数非齐次偏微分方程的数值模型,以幂律流体为例计算了下套管作业时所产生的激动压力梯度和偏心环空速度分布.模型计算结果表明:随偏心度增加,波动压力减小,偏心环空宽、窄间隙内速度分布差异增大.管柱完全平躺于井眼下侧时的波动压力大约只有管柱居中时的一半.文中还把数值模型计算结果与经验模型和近似模型计算结果进行了对比.

关键词: 非牛顿流体, 波动压力, 偏心, 环形空间, 数值模拟