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

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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.

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Acknowledgements

The authors would like to thank the anonymous referees whose comments inspired additional results included in the paper as well as helped to improve the exposition. We also thank our colleague Ralph Showalter who made us aware of the paper [21]. We are grateful to our geoscience collaborators Marta Torres and Wei-Li Hong for motivating discussions. Choah Shin would like to thank Larry Martin and Joyce O’Neill for the generous support with the endowed College of Science at Oregon State fellowship 2019-20. Malgorzata Peszynska would like to thank the NSF DMS IRD plan 2019-21 funding which partially made this research possible. This material is based upon work supported by and while serving at the National Science Foundation. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. This research was also partially supported by NSF DMS-1522734 “Phase transitions in porous media across multiple scales” and DMS-1912938 “Modeling with Constraints and Phase Transitions in Porous Media”.

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    Malgorzata Peszynska & Choah Shin

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This research was partially supported by NSF DMS-1522734 “Phase transitions in porous media across multiple scales” and DMS-1912938 “Modeling with Constraints and Phase Transitions in Porous Media”, NSF IRD plan 2019-20, and Martin-O'Neill COS Fellowship.

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Peszynska, M., Shin, C. Stability of a numerical scheme for methane transport in hydrate zone under equilibrium and non-equilibrium conditions. Comput Geosci 25, 1855–1886 (2021). https://doi.org/10.1007/s10596-021-10053-2

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