Regime-Switching Bayesian Digital Twins for Two-Phase Wellbore Hydraulics and Early Kick Recognition Under Partial Observability

Abstract

Multiphase flow in wellbores and near-wellbore conduits remains a central uncertainty driver in drilling automation and managed-pressure operations, especially when the available measurements are sparse, delayed, and dominated by surface instrumentation. In practice, operators must infer downhole pressure, holdup, and evolving flow patterns from noisy standpipe pressure, choke states, pump schedules, and occasional density estimates, while simultaneously maintaining the bottom-hole pressure within narrow operational limits. This paper presents a probabilistic digital-twin framework that treats two-phase hydraulics as a stochastic hybrid dynamical system whose continuous states follow reduced-order two-fluid physics, while an unobserved discrete regime process governs closure behavior, transient mixing, and slip. The proposed model couples a regime-switching state-space formulation with Bayesian inference to provide time-resolved posterior distributions over pressure and gas fraction along the wellbore, and to produce calibrated probabilities of abnormal gas influx. The main technical contribution is an inference-and-control stack that fuses physics-consistent propagation with sequential probabilistic learning of regime-dependent closures, enabling coherent uncertainty quantification and risk-aware decisions. The approach is designed to work with heterogeneous data sources and to remain well-posed when only surface pressure is continuously available. Simulation studies across vertical and deviated segments demonstrate that regime uncertainty can be separated from influx uncertainty when the model explicitly represents closure switching and measurement delays, reducing false alarms while preserving rapid detection in low signal-to-noise scenarios.