多翼裂缝压裂偏心井半解析模型及其渗流特征

A Semi-Analytical Model and Seepage Characteristics of Multi-Wing Fracture Off-Center Wells

考虑压裂多翼裂缝偏心井的实际情况,建立了多翼裂缝偏心井的数学模型.采用Laplace变换和压降叠加原理得到Laplace空间多翼裂缝压裂偏心井井底压力的半解析解.采用非均匀流量法,对井底压力的半解析解进行离散.结合Stehfest数值反演获得实空间井底压力的数值解和产量分布.借助SAPHIR试井分析软件建立了储层的数值试井模型并进行了数值离散计算.将计算结果与该文的半解析模型计算结果进行了对比,验证了该文模型的正确性.结果表明,多翼裂缝压裂偏心井井底压力变化可划分为8个主要流动阶段.最后讨论了裂缝的无因次导流能力、裂缝的不对称因子和井的偏心距对井底压力变化和产量分布特征的影响.

In view of the actual situation of multi-wing fracture off-center wells,the mathematical model for the wells was established.Based on the Laplace transform and the pressure drop superposition principle,the semi-analytical solution of the bottom hole pressure in the multi-wing fracture off-center well in the Laplace space,was obtained.The semi-analytical solution was discretized with the non-uniform flow method.Combined with Stehfest numerical inversion,the numerical solution of the real space bottom hole pressure and the production distribution were obtained.The numerical well test model for the reservoir was established with the SAPHIR well test analysis software,and the numerical discrete calculation was carried out.The numerical results were compared with the calculation results of the semi-analytical model,which verifies the correctness of the semi-analytical model.The results show that,the bottom hole pressure variation of the multi-wing fracture off-center well can be divided into 8 main flow stages.Finally,the effects of the dimensionless conductivity,the fracture asymmetry factor and the off-center distance on the bottom hole pressure variation and production distribution characteristics,were discussed.