非牛顿幂律流体压力特征非线性解

Nonlinear Solution to Pressure Characteristics of Non-Newtonisn Power Law Fluid

由于非线性项的限制，对于非牛顿幂律流体不稳态压力的解析解只能经一定简化得来。针对这一情况，提出了一种准确描述非牛顿幂律流体非线性渗流的数值解。以均质地层中一口注入井为例，经过差分计算得出无限大地层的典型曲线，并与解析解作了比较。同时考虑井筒存储和表皮系数的影响，计算并绘制了Gringarten图版。经分析认为非线性幂律指数n影响着非牛顿幂律流体的非线性压力特征。n值越大，无限大地层的数值解与解析解越接近，绘制的Gringarten曲线的上翘幅度越小。

Because of the limitation of nonlinear term, the analytic solution to non-steady pressure of non-Newtonian power law fluid can only be derived through certain simplification. To this condition,a numerical solution to accurately describe the nonlinear porous flow of non-Newtonian power law fluid is presented. With an injection well in homogeneous formation as an example,the type curve for infinite formation is calculated with differential and compared to the analytic solution,the effect of wellbore storage and skin factor is also considered to calculate and draw up Gringarten type curves. The analysis indicates that nonlinear power law exponent n affects nonlinear pressure characteristics of non-Newtonian power law fluid. The bigger n value, the closer the numerical solution to analytic solution of infinite formation, the smaller the raise magnitude of Gringarten type curves.