基于双曲线对五点法井网流线轨迹拟合研究

Curve fitting of five-spot well pattern streamline traces based on hyperbolic equation

李根

Li Gen

中海石油（中国）有限公司天津分公司，天津 300452

Tianjin Branch of CNOOC Ltd., Tianjin 300452, China

以五点法井网流线轨迹的解析解为基础，对MATLAB绘制的流线轨迹进行分析得出，流线呈双曲线的几何特征。以双曲线方程作为目标函数，对解析解的流线轨迹进行拟合，建立了以流线与主流线夹角为自变量的流线拟合式。流线特征在夹角接近45°的位置对夹角变化最为敏感，因此在该位置取样进行了加密处理，增大了拟合的可靠性，尤其对存在启动压力的油田，此位置一般靠近死油区，加密处理很有意义。文中求出的拟合式能够良好地拟合解析解轨迹“两端直、中间弯”的特点，与解析解曲线的重合度很高。将得到的流线方程与传统的三角形简化流线形式进行了对比，结论表明，以双曲线为基础的拟合式从流线形态、长度、波及面积和流管阻力上均优于三角形简化形式，使得对流线的简化处理和流线模拟计算更准确。

Based on the analytical solution of the streamline traces of the five-spot well pattern, the streamline traces were plotted by MATLAB and analyzed, it is found that the streamline forms show the geometric traits of hyperbola. Using the hyperbolic equation as the objective function, the streamline traces of the analytical solution were fitted, the general curve-fitting formulas with the angle between the streamline and the main streamline as the independent variable were established. For the geometric traits are very sensitive to the angle when the angle is close to 45°, so it is neccesary to infill the sampling in this area to increase the fitting′s reliability. In the oilfield with start-up pressure gradient, the 45° area is near the inert area, so the infilling work is meaningful. The general fitting formulas gained by this paper can reflect the "bent-ends, straight-middle" features of the streamlines satisfactorily, and have an ideal coincidence with the reality. Compared with the traditional simplified triangle method, the gained formulas have the advantages of shape, length, square, and stream tube resistance. All the privilages make the simplification and simulation of the streamlines more reliable.

10.6056/dkyqt201601019