Entropy-Stable Differentiable Simulation for Dissolution-Affected Gas Influx in Drilling Annuli with Adjoint-Based Calibration

• Rizal Mendoza

  Central Mindanao University, University Town, Musuan, Maramag 8710, Philippines

  Author

• Alvin Bautista

  West Visayas State University, Luna Street, La Paz, Iloilo City 5000, Philippines

  Author

Drilling hydraulics operated near narrow pressure margins require models that are simultaneously fast, numerically robust, and physically consistent under strong compressibility and transient actuation. Managed pressure drilling amplifies this requirement because choke and pump actions can generate pressure waves and flow reversals that interact with multiphase transport and with thermodynamic gas dissolution into oil-based or synthetic-based fluids. Dissolution-driven swelling modifies the effective liquid volume and density, reshaping pit-volume and pressure signatures and complicating interpretation of early influx events. This paper develops a thermodynamically consistent, entropy-stable, and differentiable annular simulator that couples one-dimensional transient transport with a bounded dissolution and swelling closure. The technical contribution is a discrete formulation that enforces positivity of phase fractions and densities, satisfies a provable discrete entropy inequality under time-dependent boundary actuation, and remains differentiable end-to-end through implicit source updates. Differentiability enables continuous-adjoint calibration of uncertain friction, slip, sensor bias, and dissolution-kinetic parameters from streaming surface measurements, while entropy stability prevents unphysical oscillations that can corrupt gradient-based inversion. The simulator uses an invariant-region-preserving flux with well-balanced hydrostatics, an IMEX operator split for dissolution, and an implicit-function-theorem treatment of stiff thermodynamic updates to provide stable gradients. Numerical studies show that entropy-stable discretization reduces spurious pit-gain transients and prevents gradient blow-up under aggressive choke maneuvers, yielding tighter parameter posteriors and more reliable early-event classification when swelling competes with free-gas expansion.

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