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

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.