幂律钻井液同心环空轴向层流压降的计算

Numerical calculation of pressure drop of axial laminar flow in concentric annulus of
power-law drilling fluid

鲁 港 王立波 王冠军 张 宇

辽河油田分公司勘探开发研究院，辽宁 盘锦 124010 长城钻探工程有限公司钻井二公司，辽宁 盘锦 124010 辽河油田分公司茨榆坨采油厂，辽宁 盘锦 124010

幂律钻井液的同心环空层流压降的精确计算需要求解一个复杂的非线性方程。通过理论推导，将这个复杂的非线性方程转化成另一个等价的非线性方程，证明了该方程满足二分法求解的应用条件。基于二分法，对该方程给出了一个数值迭代算法，该算法具有稳定的迭代收敛性和较快的收敛速度，并且计算过程简单，适合于计算机编程实现。

Precise calculation of the pressure drop of laminar flow in concentric annulus of power-law drilling fluid needs to solve a complicated non-linear equation. Through theoretical derivation, the complicated nonlinear equation has been transformed to another equivalent nonlinear equation, demonstrating that the equation satisfies the applied conditions of dichotomy. Based on dichotomy, a numerical iteration algorithm is given to this nonlinear equation. This algorithm has stable iteration convergence and fast convergence rate, and the calculation process is simple and fit for computer programming realization.