Safety-Certified Robust Model Predictive Control for Managed Pressure Drilling Under Soluble Gas-Kick Transients

Abstract

Deepwater and extended-reach drilling increasingly relies on managed pressure drilling to maintain bottomhole pressure within narrow operational windows while accommodating uncertain formation responses and complex annular hydraulics. Gas influx events remain difficult to handle because the observable surface signatures can be delayed or distorted by compressibility, slip, thermal gradients, and dissolution into non-aqueous drilling fluids. This paper develops a control-centric framework for gas-kick mitigation that treats the wellbore--riser system as a constrained dynamical plant and synthesizes a safety-certified robust model predictive controller for real-time choke and pump management. The core technical contribution is a compact, control-oriented thermo-solutal drift-flux model whose parameters are structured to support uncertainty sets and whose state representation explicitly tracks both free and dissolved gas inventories. The controller minimizes deviation from a pressure trajectory consistent with pore and fracture bounds while enforcing state and input constraints on wellhead pressure, choke actuation rate, circulating flow, and pit-volume growth. Robustness is addressed via tube-based tightening and stochastic disturbance models that capture sensor error, unmodeled friction, and uncertain mass transfer. Safety certification is provided by embedding control barrier constraints that guarantee forward invariance of a conservative safe set even when the predictive model is imperfect. Numerical studies across circulation regimes show that the proposed design can reduce peak pressure excursions and mitigate rapid riser unloading tendencies under plausible uncertainty magnitudes, while maintaining feasible control actions compatible with typical surface equipment limits. The framework is intended to unify mechanistic kick physics with modern constrained control in a manner suitable for automation and supervisory decision support.