Retardation Theory for Soluble Gas-Kick Transients: Similarity Laws and Effective Compressibility in Annular Multiphase Flow with Methane Dissolution

Abstract

Gas influx into a drilling annulus remains a central safety concern because small downhole disturbances can transition into rapid surface transients as pressure decreases and methane expands. In synthetic and oil-based drilling fluids, a substantial fraction of methane mass may dissolve at depth, altering both the migration time scale and the mapping from total methane mass to surface indicators such as pit gain and wellhead pressure. Many operational analyses treat dissolution either as a binary switch or as an empirical delay, which obscures the mechanisms by which partitioning modifies compressibility, hydrostatic response, and observability. This paper develops a retardation-based theory for soluble gas-kick transients by deriving a reduced thermo-solutal model in which dissolved inventory acts as a dynamic buffer that slows the propagation of methane mass relative to free-gas holdup. The contribution is a unified set of similarity laws and effective-parameter representations that connect equilibrium solubility, finite-rate mass transfer, annular slip, and circulation into closed-form estimates of arrival time, indicator amplitude, and early-time detectability. The analysis yields an explicit retardation factor that modifies drift-flux transport and an effective mixture compressibility that quantifies how dissolution weakens surface sensitivity to influx during the early stage. A surface-signature inversion is then derived that reconstructs admissible influx histories from pressure and pit-volume observations while accounting for solubility-driven buffering and thermal variation. The resulting theory is intended to support real-time interpretation by providing mechanistic scaling relations, identifiability conditions, and physically constrained inversion operators that remain valid across non-circulating and circulating regimes under high-pressure high-temperature conditions.