Passivity-Constrained Digital Twins for Dissolution-Buffered Gas Kicks in Managed Pressure Drilling

Abstract

Drilling in narrow pressure windows increasingly depends on managed pressure drilling, where choke and pump actuation continuously reshape annular boundary conditions. These operational advantages complicate early kick interpretation because surface measurements reflect both physical disturbances and deliberate control transients. In oil-based and synthetic-based systems, additional ambiguity arises when invading gas dissolves into the liquid phase and induces swelling, changing volumetric returns and effective density without an immediately dominant free-gas holdup. This paper develops a passivity-constrained digital-twin architecture for real-time diagnosis and safety monitoring of dissolution-buffered gas kicks. The technical contribution is an energy-based state-space formulation of annular hydraulics with explicit dissolved-gas inventory and swelling-modified constitutive relations, cast into a port-Hamiltonian structure with provable dissipation under friction and bounded thermodynamic exchange. This structure is leveraged to construct structure-preserving discretizations and passivity-based observers whose error dynamics admit incremental energy bounds even under time-varying boundary actuation and sensor bias. A certificate layer maps the digital-twin energy balance into conservative online bounds on bottomhole-pressure deviation and on surface gas-handling risk proxies over short horizons, enabling decision thresholds that remain valid under closure uncertainty. Numerical studies show that passivity constraints stabilize estimation during aggressive choke maneuvers, prevent unphysical state excursions near phase appearance, and improve discrimination between swelling-driven pit gain and free-gas expansion when measurements are sparse. The resulting framework provides a tractable pathway to integrate dissolution physics into safety-critical monitoring without requiring full multiphase simulators in the real-time loop