Theoretical and numerical analysis of stress shadow effect between echelon fractures in hydraulic fracturing of double vertical wells

The mathematical model containing echelon hydraulic fractures is established after introducing the classical induced stress model into the weight function by combining the weight function stress intensity factor solution, which is verified to be a reliable mathematical model. The mathematical model is used to explore the sensitivity of the stress shadowing effect to echelon fracture spacing and information on the variation of induced stresses when fractures rotate and when non-equal fractures compete for fracture initiation. Detailed mathematical derivation procedures and analytical solution expressions are given for this engineering-scale mathematical model. By establishing typical states of fracture in a mathematical model to define the disturbance factor, we obtained indicators that can determine whether the fractures are mutually suppressed or mutually promoted. The disturbance factor shows that as the fracture spacing changes, there is a peak of disturbance between the fractures, and the phenomenon appears precisely when the shear stresses counteract each other, which is called the optimal spacing that can promote fracture propagation. We also illustrate three typical propagation stages of echelon hydraulic fractures, namely premature and neutral and segistration stages. We figure out how to distinguish the disturbance patterns (promotion/suppression) in different stages and compare them with reliable numerical simulation results to support our conclusion. The hybrid FE-DE method takes into account hydromechanical coupling and leak-off effects and reorientation of 3D non-planar fracture to guarantee high-precision solutions of fracture behavior. The mutual counteraction of shear stress fields is regarded as an important reason affecting the attraction of echelon hydraulic fractures, and the disturbance among fractures is dynamically propagated under the control of shear and principal stresses.