幂律流体偏心环空螺旋流压力梯度的数值计算

Numerical calculation of pressure gradient of helical flow of power-law fluid in eccentric annulus

蔡萌

CAI Meng

大庆油田有限责任公司采油工程研究院，黑龙江大庆　163453

Production and Engineering Research Institute of Daqing Oilfield Co., Ltd. Daqing 163453, China

为合理设计钻井水力参数，对可视为幂律流体的钻井液偏心环空螺旋流动的压力梯度进行了研究。利用待定系数法对幂律流体偏心环空螺旋流的控制方程进行了变换，得到了压力梯度公式。以可视为幂律流体的CMC水溶液为例，利用有限差分法对该流动的压力梯度进行了数值计算，并分析了内管自转速度、环空偏心度和流量对其的影响。结果表明：环空偏心度和流量是其主要的影响因素。通过比较利用轴向速度数值解求得的压力梯度与利用轴向速度解析解求得的压力梯度，发现二者吻合效果较好，进一步说明文中给出的幂律流体偏心环空螺旋流的压力梯度公式和数值计算方法是正确的，可进一步推广应用。

The pressure gradient of helical flow of drilling fluid that can be regarded as power-law fluid in eccentric annulus is studied in this paper to rationally design hydraulic parameters of drilling. The governing equations of helical flow of power-law fluid in eccentric annulus are transformed by the undetermined coefficients method, the pressure gradient formula for this flow is obtained. Taking CMC aqueous solution which can be regarded as a power-law fluid for an example, the pressure gradient of this flow is numerically calculated by using the finite difference method and the influences of the rotation velocity of inner cylinder, the eccentricity and the flow rate on the pressure gradient are analyzed. The results show the eccentricity and the flow rate are main influential factors. Comparing the pressure gradient calculated by the numerical solution of axial velocity given in this paper with that calculated by the analysis solution, they coincide well, which shows that the formula and the numerical calculation method of pressure gradient of helical flow for power-law fluid in eccentric annuls are correct and can be applied further.