压裂直井和水平井的探测区域计算公式

Investigation area calculations for fractured vertical well and horizontal well

张洪军,李新春,王瑞刚,王小军,李二党,韩章英

中国石油长庆油田分公司第一采油厂，陕西 延安 716000 西安石油大学石油工程学院，陕西 西安 710065

No.1 Oil Production Plant, Changqing Oilfield Company, PetroChina, Yan′an 716000, China College of Petroleum Engineering, Xi′an Shiyou University, Xi′an 710065, China

为解决压裂直井和水平井探测区域的计算问题，分别建立了压裂直井和水平井的瞬时点源模型。使用Laplace及Fourier等积分变换方法求取了这2种井型的无因次储层压力解，给出了2种井型探测区域外边界随时间变化的曲面方程，并与部分学者的研究成果进行了对比分析。结果表明：随着时间的增大，2种井型探测区域的外边界均趋于圆柱面；当无因次时间分别大于1.674和8.348时，可以采用文献［7］的直井探测半径公式近似计算压裂直井的无因次探测体积，相对误差分别小于5%和1%左右；当无因次时间不小于40时，水平井的压力传播规律与压裂直井完全类似。水平井实例计算结果与试井分析结果一致，进一步验证了该方法的准确性和可靠性。该方法可用于压裂直井和水平井探测区域的精确计算以及气藏瞬态流期间的拟时间计算等，具有一定的理论和实用价值。

In order to solve the calculating problem of investigation area of fractured vertical well and horizontal well, the instantaneous point source models of the above two well types are established respectively. The pressure distribution solutions of the two well types are obtained through applying Laplace and Fourier integral transformation method. The surface equations of the outer boundary changing with time are given, which are also compared with some existing researches. The results show that the outer boundary of the two well types tends to be cylindrical with time increasing. When the dimensionless time is greater than 1.674 and 8.348, the calculation error of investigation volume of fractured vertical well by using the vertical well investigation radius formula from document 7 will be less than 5% and 1%, respectively. When the dimensionless time is greater than 40, the pressure propagation law of horizontal well is exactly the same with that of fractured vertical well. The example results of horizontal well are consistent with the well test analysis results, which further verified the accuracy and reliability of the above method. The results can be used for the accurate value of investigation area for fractured vertical well and horizontal well, as well as the pseudo-time calculation during the transient flow period of gas reservoir, which indicated theoretical and practical values.

10.6056/dkyqt202104019