A hydrodynamic model for analyzing the closure stresses in the wellbore strengthening problem

Abstract The problem of creating unwanted fractures while drilling ultradeep wells is mitigated with the application of wellbore strengthening techniques. Despite the numerous applications, an open question remains about the efficiency of the loss of circulation materials (LCM) and its implications on the closure stress distribution change during plugging. This work investigates the effects on the stress field before and after plugging along the fracture extension axis by introducing a hydrodynamic plug. With the hydrodynamic plug, fluid flow is constrained by pressure conditions at specific locations in the fracture simulating the LCM. Three different scenarios were considered. First, the efficiency of the bridge is simulated by varying the pressure drop. Second, the location of the bridge inside the fracture and finally a nearly packed fracture. The models are fully coupled and were solved with the finite element method in impermeable and permeable hard rocks. We find that for high‐efficiency bridges, narrower fracture profiles are predicted, which causes the induced closure stresses to increase significantly. On the other hand, when the bridge is close and near the wellbore area, the fracture profiles are maintained wide and narrow when it is nearest to the tip. The predicted fracture geometry induces higher closure stresses when the plug is near the well and slightly reduces when it is near the tip. Finally, the pressure profile resulting from the packed fracture significantly affects the fracture dimensions, resulting in narrower fracture, however resulting in a smooth variation of induced closure stresses with high magnitude comparable to the stresses at the state of propagation. The diffusion occurring in the permeable case creates back‐stresses that appear to have an additive contribution to the induced closure stresses. This underlines the significance of diffusion on the induced coupled closure stresses for large fractures while performing wellbore strengthening methodologies.