水平气井二项式方程的推导与应用

Derivation and application of quadratic form equation for horizontal gas wells

陈元千 张霞林 齐亚东

中国石油勘探开发研究院，北京 100083

Research Institute of Petroleum Exploration & Development, PetroChina, Beijing 100083, China

由于水平井具有渗流面积大、流动阻力小和负性表皮因子的特点，因此，其产能远远高于垂直井。近20 a来，水平井在我国油气开发中得到了甚为广泛的应用，据悉，长庆气区二叠系气藏的开发，已打水平井800余口。无论是探井或是生产井，当气井出气之后，都需要进行产能测试，确定气井的绝对无阻流量、IPR曲线和合理的气井产量。对于垂直井来说，产能测试的重要方法有二项式和指数式2种。前者是考虑到湍流影响的完善理论方法，后者是考虑湍流影响的修正方法。对于水平气井，目前尚未看到有关二项式和指数式的理论推导，文中基于水平井等效驱动半径的原理，利用拟压力法完成了对水平气井二项式的理论推导，并建立了一点法的无因次IPR方程。通过实例应用表明，文中提供的水平气井多点法的二项式方程和一点法的IPR方程是正确有效的。

Compared to a vertical well, the deliverability of a horizontal well is much higher because the big seepage area, low flow resistance and negative skin factor of horizontal well. For two decades, horizontal wells have been widely applied in the oil and gas field development. It is reported that more than 800 horizontal gas wells have been drilled to develop the Permian gas reservoirs in Changqing gas province. As we known, it′s necessary to test deliverability and determine the AOF (absolute?鄄open?鄄flow) potential, IPR curves and appropriate gas rate after gas showing. For the vertical well, there are mainly two methods to determine the deliverability: quadratic equation and exponential equation. And, the former is a perfect theory method which considers the impact of turbulence, while the latter is a modified method with the consideration of turbulence flow. However, there is no published literature theoretical derivation of quadratic equation or exponential equation relating to the deliverability testing of horizontal gas well. In this paper, based on the principle of equivalent drainage radius, the quadratic deliverability equation of horizontal well is derived and the dimensionless IPR equation for one?鄄point testing is established by using the pseudo?鄄pressure method. Through the practical applications, it has indicated that it is valid both the quadratic equation for multi?鄄points testing and the IPR equation for one?鄄point testing.

10.6056/dkyqt201405014