Mathematical modeling of gas hydrates dissociation in porous media with water-ice phase transformations using differential constrains

• Published in: Mathematics
• Main Authors: Alekseeva, Natalia, Podryga, Viktoriia, Rahimly, Parvin, Coffin, Richard, Pecher, Ingo
• Format: Article in Journal/Newspaper
• Language: English
• Published: 2022
• Subjects: nonlinear partial differential equations; differential constraints; gas hydrates; multi-component fluid dynamic; permafrost formation; Ice; permafrost
• Online Access: https://hdl.handle.net/1969.6/94054; https://doi.org/10.3390/math10193470

2D numerical modeling algorithms of multi-component, multi-phase filtration processes of mass transfer in frost-susceptible rocks using nonlinear partial differential equations are a valuable tool for problems of subsurface hydrodynamics considering the presence of free gas, free water, gas hydrates, ice formation and phase transitions. In this work, a previously developed one-dimensional numerical modeling approach is modified and 2D algorithms are formulated through means of the support-operators method (SOM) and presented for the entire area of the process extension. The SOM is used to generalize the method of finite difference for spatially irregular grids case. The approach is useful for objects where a lithological heterogeneity of rocks has a big influence on formation and accumulation of gas hydrates and therefore it allows to achieve a sufficiently good spatial approximation for numerical modeling of objects related to gas hydrates dissociation in porous media. The modeling approach presented here consistently applies the method of physical process splitting which allows to split the system into dissipative equation and hyperbolic unit. The governing variables were determined in flow areas of the hydrate equilibrium zone by applying the Gibbs phase rule. The problem of interaction of a vertical fault and horizontal formation containing gas hydrates was investigated and test calculations were done for understanding of influence of thermal effect of the fault on the formation fluid dynamic. The work of Rahimly P. (mathematical model, analysis) was supported by the Russian Science Foundation (project № 22-71-10109). The work of Podryga V. (numerical calculations) was carried out within the framework of the state assignment of KIAM RAS.