Stability of a numerical scheme for methane transport in hydrate zone under equilibrium and non-equilibrium conditions

TL;DR

This paper presents a novel numerical stability analysis for a simplified methane hydrate transport model under equilibrium and non-equilibrium conditions, demonstrating convergence and stability of the proposed scheme.

Contribution

It is the first analysis of a gas transport model with hydrate formation/dissociation, focusing on stability and convergence of the numerical scheme under fixed pressure conditions.

Findings

Proved weak stability of the upwind scheme for the regularized conservation law.

Confirmed convergence through numerical simulations.

Illustrated model applicability for various hydrate transport scenarios.

Abstract

In this paper we carry out numerical analysis for a family of simplified gas transport models with hydrate formation and dissociation in subsurface, in equilibrium and non-equilibrium conditions. These models are adequate for simulation of hydrate phase change at basin and at shorter time scales, but the analysis does not account directly for the related effects of evolving hydraulic properties. To our knowledge this is the first analysis of such a model. It is carried out for the transport steps while keeping the pressure solution fixed. We frame the transport model as conservation law with a non-smooth space-dependent flux function; the kinetic model approximates this equilibrium. We prove weak stability of the upwind scheme applied to the regularized conservation law. We illustrate the model, confirm convergence with numerical simulations, and illustrate its use for some relevant equilibrium and non-equilibrium scenarios.