Koopman-Lifted Observability and Optimal Excitation for Dissolution-Buffered Gas Influx Identification in Managed Pressure Drilling

Abstract

Drilling operations conducted within narrow pressure windows increasingly rely on managed pressure drilling to regulate annular pressure through choke and pump actuation. Yet, early gas influx identification remains challenging because surface measurements are aggregated, boundary actuation is persistent, and fluid properties evolve with pressure and temperature. In oil-based and synthetic-based systems, a substantial fraction of invading gas may dissolve and induce liquid swelling, altering pit-volume and pressure signatures without immediate formation of a dominant free-gas phase. This paper develops an operator-theoretic identification framework that targets the underlying information limitation directly: the separation of influx, dissolution, and frictional transients is fundamentally an observability problem under constrained excitation. The technical contribution is a Koopman-lifted, control-affine surrogate of dissolution-aware annular hydraulics that enables tractable computation of observability and Fisher-information surrogates in a lifted space while preserving bounded thermodynamic state augmentation. A receding-horizon excitation design is then posed to maximize a risk-weighted information metric subject to bottomhole-pressure constraints and actuator rate limits, yielding control perturbations that are intentionally informative yet operationally admissible. The resulting method produces calibrated posterior contraction rates for influx-rate and depth proxies without assuming that any single sensor signature is uniquely attributable to free gas. Numerical studies show that modest, structured choke perturbations can increase identifiability of dissolution kinetics and influx magnitude in regimes where pit gain alone is ambiguous, and that Koopman-lifted information metrics remain stable under property-model uncertainty and sensor bias, supporting real-time deployment as an observability-aware layer alongside conventional control.