Numerical Simulation of Cross-Layer Hydraulic Fracture Propagation in Interbedded Sandstone Reservoirs of the Lianggaoshan Formation

Vertical cross-layer propagation of hydraulic fractures is critical for the efficient stimulation of interbedded sandstone reservoirs in the Lianggaoshan Formation. To investigate the vertical fracture propagation mechanisms and controlling factors in this complex lithological setting, a three-dimensional (3D) numerical model was established using the continuum–discontinuum element method (CDEM) based on the typical “mudstone–sandstone–mudstone” geological structure of the Lianggaoshan Formation. The effects of geological parameters, including interlayer stress contrast, vertical stress contrast, elastic modulus ratio, and reservoir thickness, as well as engineering parameters, including fluid viscosity and injection rate, were systematically evaluated. The results show that interlayer stress contrast is the primary factor restricting vertical fracture growth. As the interlayer stress contrast increases from 2 MPa to 8 MPa, the fracture morphology gradually changes from effective cross-layer propagation to complete containment within the sandstone layer, while the injection pressure at 300 s increases from 55.91 MPa to 58.90 MPa and the fracture width increases from 4.58 mm to 5.05 mm. In contrast, vertical stress contrast has a limited influence under the horizontal-stratification conditions investigated. Increasing fluid viscosity and injection rate can enhance intra-fracture net pressure and promote interface breakthrough. When the fluid viscosity increases from 5 mPa·s to 50 mPa·s, the breakdown pressure increases from 61.05 MPa to 69.59 MPa and the fracture width increases from 4.79 mm to 6.37 mm. When the injection rate increases from 0.6 m3/min to 3.6 m3/min, the breakdown pressure increases from 58.57 MPa to 63.35 MPa and the fracture width increases from 4.28 mm to 5.17 mm. Based on the Effective Vertical Propagation Index (EVI), three vertical propagation modes were identified: restricted vertical propagation, partially effective cross-layer propagation, and effective vertical propagation. Gray Relational Analysis (GRA) revealed the following sensitivity ranking: interlayer stress contrast > injection rate > fluid viscosity > elastic modulus ratio > reservoir thickness > vertical stress contrast. For reservoirs with a typical 4 MPa stress barrier, effective vertical breakthrough can be achieved when the fluid viscosity exceeds 25 mPa·s or the injection rate reaches 3.6 m3/min. These findings provide quantitative guidance for optimizing fracturing parameters in interbedded sandstone reservoirs.