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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。
Drilling fluid properties and annulus geometry have a significant impact on fluctuating pressures. In this paper, the governing equations of the eccentric steady-state fluctuating pressure of non-Newtonian fluid under bipolar coordinates are established. By using the integral method and the finite difference method, the numerical model of elliptic variable coefficient inhomogeneous partial differential equations is deduced. As an example, the excited pressure gradient and the eccentric annulus velocity distribution under the casing operation were calculated. The results of model calculation show that as the eccentricity increases, the fluctuating pressure decreases, the eccentric annulus width increases, and the velocity distribution in the narrow gap increases. Fluctuating pressures when the column is fully lying on the underside of the borehole are about half the center of the column. In the paper, numerical model calculation results are also compared with empirical model and approximate model calculation results.