Abstract
Drilling operations routinely operate within narrow pressure margins where small transient disturbances can produce disproportionate safety consequences. Gas influx events are especially challenging because the surface observables used for monitoring, including wellhead pressure and pit-volume change, are shaped by nonlinear multiphase transport, compressibility, slip, thermal gradients, and, in synthetic or oil-based drilling fluids, methane dissolution that can temporarily conceal gas mass. This paper develops a certified digital-twin methodology aimed at alarm integrity rather than point prediction. The core contribution is a multi-fidelity modeling and analysis stack that produces real-time outer bounds on safety-critical indicators under bounded uncertainty in influx, hydraulics, and thermodynamic partitioning between free and dissolved gas. A physics-consistent one-dimensional annular model is formulated as a constrained dynamical system with explicit dissolved-gas inventory and smooth phase-partition closure. Uncertainty is propagated through reachability analysis that computes guaranteed enclosures of indicator trajectories, enabling quantified false-alarm and missed-detection risk without assuming perfect calibration. To achieve field-feasible runtime, the method couples conservative interval-based propagation for stiff thermodynamic components with reduced-order linear surrogates learned from local linearizations, while preserving certification by bounding surrogate residuals. The resulting digital twin supplies time-varying alarm thresholds, integrity metrics, and decision support signals that adapt to operating conditions and uncertainty magnitude. Computational studies across circulation regimes illustrate how dissolution can widen certified uncertainty bands early in an event while tightening later as exsolution becomes observable, and how certified bounds can prevent both overconfident early dismissal and unnecessary shutdowns triggered by benign transients.