Russian Journal of Earth Sciences Russian Journal of Earth Sciences Russian Journal of Earth Sciences 1681-1208 95899 10.2205/2025ES001031 ksezmc ОРИГИНАЛЬНЫЕ СТАТЬИ ORIGINAL ARTICLES ОРИГИНАЛЬНЫЕ СТАТЬИ Mathematical Model of Degradation of Frozen Hydrate-Bearing Saline Rocks Under Thermal Influence from Above and Below Mathematical Model of Degradation of Frozen Hydrate-Bearing Saline Rocks under Thermal Influence from Above and Below https://orcid.org/0000-0002-2468-1272 Рамазанов Мукамай Магомедович Ramazanov Mukamay Magomedovich mukamay-ipg@mail.ru

доктор физико-математических наук;

doctor of physical and mathematical sciences;

 https://orcid.org/0000-0002-8033-8452 Лобковский Леопольд Исаевич Lobkovsky Leopold Isaevich llobkovsky@mail.ru https://orcid.org/0000-0002-4224-1246 Булгакова Наталья Сергеевна Bulgakova Natal'ya Sergeevna ipgnatali@mail.ru

кандидат технических наук;

candidate of technical sciences;

 https://orcid.org/0009-0003-3942-7749 Гаджимагомедова Салихат Рамазановна Gadzhimagomedova Salikhat Ramazanovna salikhat.g@gmail.com Институт проблем геотермии и возобновляемой энергетики - филиал Объединенного института высоких температур РАН Россия Institute for Geothermal Research and Renewable Energy (Branch of the Joint Institute for High Temperatures, Russian Academy of Sciences) Russian Federation Институт динамики геосфер РАН Россия Institute of Geosphere Dynamics of the Russian Academy of Sciences Russian Federation Институт океанологии им. П.П. Ширшова РАН P.P.Shirshov Institute of Oceanology of the Russian Academy of Science Томский государственный университет Tomsk State University Институт проблем геотермии и возобновляемой энергетики - филиал Объединенного института высоких температур РАН Махачкала Россия Institute for Geothermal Research and Renewable Energy (Branch of the Joint Institute for High Temperatures, Russian Academy of Sciences) Makhachkala Russian Federation Дагестанский государственный институт народного хозяйства Россия Dagestan State Institute of National Economy Russian Federation Институт проблем геотермии и возобновляемой энергетики – филиал Объединенного института высоких температур Российской академии наук Махачкала Россия Institute for Geothermal Research and Renewable Energy (Branch of Joint Institute for High Temperatures, Russian Academy of Sciences) Makhachkala Russian Federation Дагестанский государственный институт народного хозяйства Россия Dagestan State Institute of National Economy Russian Federation 17 11 2025 17 11 2025 25 5 ES5021 20 03 2025 09 06 2025 https://rjes.ru/en/nauka/article/95899/view

A mathematical model has been formulated to describe the degradation of saline permafrost containing ice, gas hydrate accumulations, and free gas, as a result of climate warming and the influence of heat flow from below, considering the effects of osmosis. The degradation rates of hydrate-bearing permafrost from above and below, along with the corresponding rates of methane release into the surrounding permeable fractured-porous medium and gas migration channels or faults, have been studied. To investigate degradation from above, several temperature values at the upper boundary of the frozen layer were considered, including both positive and negative values in degrees Celsius. This allowed for the separate assessment of the contributions of heat and salinity to the degradation rates, as well as to evaluate the role of osmotic forces. To investigate degradation from below, several values of heat flow caused by the geothermal gradient were considered. As an application of the model, the results of calculations for the degradation rates of the frozen hydrate-bearing layer, following the onset of ocean transgression on the Arctic shelf approximately 10 thousand years ago, are presented.

A mathematical model has been formulated to describe the degradation of saline permafrost containing ice, gas hydrate accumulations, and free gas, as a result of climate warming and the influence of heat flow from below, considering the effects of osmosis. The degradation rates of hydrate-bearing permafrost from above and below, along with the corresponding rates of methane release into the surrounding permeable fractured-porous medium and gas migration channels or faults, have been studied. To investigate degradation from above, several temperature values at the upper boundary of the frozen layer were considered, including both positive and negative values in degrees Celsius. This allowed for the separate assessment of the contributions of heat and salinity to the degradation rates, as well as to evaluate the role of osmotic forces. To investigate degradation from below, several values of heat flow caused by the geothermal gradient were considered. As an application of the model, the results of calculations for the degradation rates of the frozen hydrate-bearing layer, following the onset of ocean transgression on the Arctic shelf approximately 10 thousand years ago, are presented.

 permafrost gas hydrate ice melting degradation solutions osmosis mathematical model permafrost gas hydrate ice melting degradation solutions osmosis mathematical model The research was funded by the Ministry of Science and Higher Education of the Russian Federation (state assignment No. 075-00269-25-00) and the Russian Science Foundation (grant No. 22-67-00025). The research was funded by the Ministry of Science and Higher Education of the Russian Federation (state assignment No. 075-00269-25-00) and the Russian Science Foundation (grant No. 22-67-00025).

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