A Semianalytical Mathematical Model and Seepage Characteristics of Off-Center Fractured Vertical Wells with Multiwing Asymmetrical Fractures

The complexity of formation conditions leads to multiwing asymmetric fractures after large-scale fracturing. According to a well pattern model and reservoir characteristics, a testing well is away from the center of the reservoir, and the existing well-test mathematical model cannot meet the field data analysis demand. Therefore, the mathematical model for the fractured wells with multiwing asymmetrical fractures is established. The model solution of the Laplace domain is obtained by the Laplace transform, nonuniform fracture discretization, and pressure drop superposition principle. The model is compared with the numerical model in this paper, and the result shows that the presented semianalytical model and the calculation method are correct. The eight main flow stages are divided according to pressure derivative characteristics and the seepage process of off-center fractured vertical wells with multiwing asymmetrical fractures. The larger off-center distance will lead to higher pressures and derivative curves. Larger fracture asymmetry factors are higher pressures and derivative curves during bilinear and linear flow regimes. The field data show that the model is applicable and that the model can give the guidance of fractured well formation evaluation.