Insight Into the Heel–Toe Effect of a Long Horizontal Wellbore Based on a Hybrid Numerical Method

Numerical simulation of flow inside a horizontal wellbore with multiple completion stages is presented. Using a hybrid method combining computational fluid dynamics and a lumped parameter model, blocking effect on the toe-end stages observed in long horizontal wells (heel–toe effect) under simplified conditions is explained. A two-dimensional channel geometry was used to model the wellbore, with side inlets representing completion stages. First, using a five-stage well with steady state flow conditions, the existence of three basic flow regimes—trickle flow, partially blocked flow and fully blocked flow—was established. Using these results, the phenomenon of blocking of upstream inlets near the toe by the downstream ones near the heel is explained. The existence of these flow regimes is consistent with well-log data obtained from a horizontal shale gas well with 31 completion stages at two different times during production. Further, to study the dynamic behavior of the completion stages when reservoir fluid flows into the wellbore, a basic reservoir depletion model was created using a pressure boundary condition at the side inlets, varying in time. A lumped-parameter model was used to account for the pressure drop between two inlets separated by large axial distance. Different characteristic time scales, related to the depletion of the reservoirs, were identified. By varying initial conditions, the dynamic behavior of the system with multiple inlets was observed and analyzed. The transition of flow regimes with depletion of reservoirs is consistent with the observed behavior of the horizontal shale gas well.