多段压裂水平井负表皮压力动态特征

Negative skin pressure dynamic characteristics of multiple fractured horizontal wells

水平井经多段压裂后,其表皮系数通常为负值。现有的多段压裂水平井渗流模型均利用Duhamel公式考虑表皮系数,然而,Duhamel公式仅能处理正表皮水平井,计算的负表皮渗流特征曲线振荡,无法反映真实的压力动态特性。针对这一问题,通过引入类似于直井的表皮系数做为渗流模型新变量,重新定义了无因次距离、无因次储层厚度等模型参数,建立了均质无限大油藏负表皮多段压裂水平井不稳定渗流新模型;利用正交变换法进行求解,获得了模型在时空间的压力解析表达式;再将实空间的解转换到Laplace空间下考虑井筒储集系数的影响;最后利用Stehfest数值反演绘制了多段压裂水平井负表皮压力动态特征曲线,曲线不再振荡,能够真实反映负表皮渗流特性,成功解决了现有理论模型与实际情况不相符的问题。研究的新模型可同时计算负表皮压力动态特征曲线和正表皮压力动态特征曲线,因此,不仅可用于多段压裂水平井渗流特征分析,还可应用于多段压裂水平井实测压力资料的试井解释。

The skin of a horizontal well after multi-stage fracturing usually has a negative value.All the existing models of multi-ple fractured horizontal wells used the Duhamel formulation to consider skin factor.However,the Duhamel formulation can only deal with positive skin.The negative skin type curves using the Duhamel formulation were oscillating,so that the type curves could not reveal the real pressure dynamic characteristics.To address the problem,we introduced a skin factor that is similar to the vertical well skin as a new variable.The dimensionless model parameters,such as the dimensionless distance and the dimen-sionless formation thickness,were redefined,and then a new model of multiple fractured horizontal wells with negative skin was established for infinite homogenous reservoirs.The model was solved using orthogonal transformation,so the analytical solution expressions in real space were obtained.The solutions in real space were converted to the Laplace space to consider the wellbore storage coefficient.As a result,the pressure dynamic curves of multiple fractured horizontal wells with negative skin were plotted using Stehfest numerical inversion.The curves did not oscillate and could reveal the real flow characteristics of negative skin hori-zontal well.Therefore,the problem that theoretical models did not match the real conditions was solved.Both negative and posi-tive pressure dynamic curves can be calculated using the researched new model,so it not only can be applied to the flow character-istics analysis of multiple fractured horizontal wells,but also can be applied to the well test interpretations of multiple fractured horizontal wells with real testing pressure data.