Numerical Model for Evaluating Well Kick and Lost Circulation During Managed Pressure Drilling

Based on the rapidly varying casing pressure method and multiphase flow theory, we have constructed a transient mathematical model for managed pressure drilling (MPD) that combines kick with mud loss in a single fracture. The finite difference method was used to iteratively solve this model. The model calculated values agree well with the experimental results, which confirms the reliability of the model. Casing pressure, casing shoe pressure, pit gain, outlet flow, and choke opening during the entire well control process are analyzed. Experimental results show that equality of inlet flow and outlet flow may not imply influx stoppage when a kick is coupled with mud loss. In addition, the loss rate at the casing shoe initially increases linearly over time and then decreases exponentially, ultimately becoming constant. After completion of well control, drilling can be safely continued until loss is negligible. This study may provide a theoretical basis for better control of wells with complicated kick and circulation loss in managed pressure drilling (MPD).