不对称垂直裂缝压力动态特征

针对压裂过程中出现的不对称垂直裂缝问题，基于渗流力学原理，根据点源函数和Green函数基本理论建立三种不同外边界条件下不对称有限导流垂直裂缝试井解释数学模型.采用Laplace积分变换和Stehfest数值反演获得典型特征曲线.研究表明：典型特征曲线分为四个流动阶段，井储阶段、压力导数曲线斜率为1/4的双线性流阶段、压力导数曲线斜率为1/2的线性流阶段及0.5水平线的径向流阶段；不对称因子主要影响双线性流阶段结束的时间，不对称因子越大，双线性流阶段结束的越早；裂缝的导流能力越大，不对称因子对特征曲线的影响越不明显；不对称因子越大，裂缝流量分布越不对称.为不对称有限导流垂直裂缝的试井分析提供理论依据.

Transient Pressure for a Fractured Well with Asymmetric Fracture

Asymmetric vertical cracks in process of pressure was studied. Based on principle of seepage mechanics, well-test mathematical model, which is asymmetric finite-conductivity vertical fracture with three different outer boundary conditions, was established according to point source function and Green function. Typical curves were obtained with Laplace integral transformation and Stehfest numerical inversion. It shows that typical curve is divided into four flow stages, stage of wellbore storage,1/4-slope bilinear flow, 1/2-slope linear flow and 0.5-value horizontal line radial flow. Asymmetric factors affect mainly end time of bilinear flow stage. The greater the asymmetry factor is, the sooner the bilinear flow stage ends is. The greater the conductivity capability of fracture is, the more unobvious characteristic of pressure derivative curve of bilinear flow stage are. The bigger asymmetric factor is,the more uneven rate distribution of asymmetric fracture is. The model provides theoretical basis for well test analysis of asymmetric finite-conductivity vertical fracture.