A thermodynamically consistent simulation of gas hydrates in porous media using Operator-Based Linearization

Abstract

In this work, we present a kinetic simulation model for gas hydrates in porous media using the Operator-Based Linearization (OBL) technique. The OBL approach introduces algebraic operators that represent the physical terms in the mass and energy balance equations. Operators are calculated only in supporting points comprising the discretized parameter space, and operator values and partial derivatives for linear system assembly are readily obtained through (multi-)linear interpolation. Taking advantage of this setup, the implementation of advanced thermodynamic models for hydrate formation and dissociation under kinetic assumptions is simplified. We test the assumptions for thermodynamic modelling by analysing the Gibbs energy surfaces of the fluid and hydrate phases and demonstrate that, in the limit, the thermodynamic equilibrium for both kinetic and equilibrium reaction models is equivalent. We compare the simulation results with the published experimental results for CH₄-hydrates and extend the assessment to a CO₂-hydrate formation experiment in a semi-batch, constant-pressure configuration. The model reproduces the main pressure–temperature transients and hydrate evolution for both CH₄- and CO₂-systems. We demonstrate applicability at core scale for hydrate formation and, at field scale, for gas production from CH₄-hydrates by thermal stimulation and depressurization. The interaction of thermal-compositional phenomena (phase changes, adiabatic expansion, kinetic rates, and reaction enthalpy) gives rise to highly nonlinear physics that an appropriate OBL discretization resolves. Overall, the patterns of hydrate formation and dissociation are highly sensitive to the kinetic-rate inputs; hence, the appropriate choice of the reaction model remains a key consideration from both physical and numerical perspectives.