The purpose of this paper is to present a one-dimensional model that simulates the thermo-physical processes for methane hydrate decomposition in porous media. The mathematical model consists of equations for the conservation of energy, gas, and liquid as well as the thermodynamic equilibrium equation for temperature and pressure $\left(P-T\right)$ in the hydrate stability region. The developed model is solved numerically by using the implicit finite difference technique on the grid system, which correctly describes the appearance of phase, latency, and boundary conditions. The Newton–Raphson method was employed to solve a system of nonlinear algebraic equations after defining and preparing the Jacobean matrix. Additionally, the proposed model describes the decomposition of methane hydrate by thermal catalysis of the components that make up the medium through multiple phases in porous media. In addition, the effect of thermodynamic processes during the hydrate decomposition on the pore saturation rate with hydrates a7nd water during different time periods was studied in a one-dimensional model. Finally, in a one-dimensional model over various time intervals, $t=1,\hspace{0.17em}10,\hspace{0.17em}50\hspace{0.17em}\mathrm{s}$, the pressure and temperature distributions during the decomposition of methane hydrates are introduced and investigated. The obtained results include more accurate solutions and are consistent with previous models based on the analysis of simulations and system stability.

In the work, the method of splitting by physical processes is consistently applied to the problems of underground hydromechanics associated with gas hydrates and taking into account the presence of ice and the ice-water phase transition, as well as the presence of salt. The systems are reduced to the block form, with the separation of the dissipative and hyperbolic parts. It was shown by the method of characteristics that the usual approximation of the upwind coefficients should be modified here. Using the Gibbs phase rule, a choice was made of the determining variables in the flow zones that differ from each other in the number of phases and components. A general mathematical model has been built for the entire area of the process.

В настоящее время исследование газогидратных месторождений является весьма актуальным. Изучение содержащих газогидраты осадочных бассейнов затруднено наличием в них сложной геометрии регионов (пропластков, сдвиговых и низкопроницаемых зон и т.д.). Площадные и профильные расчеты обладают пространственной стратиграфической неструктурированностью областей, их произвольным расположением и переменной эффективной толщиной пластов. В данной работе рассматривается задача двумерной фильтрации в зоне трехфазного гидратного равновесия (газ, гидрат, вода) с учетом возможной слабой проницаемости пород. Для решения этой задачи применяется оригинальная фильтрационная модель с неклассической формой закона движения. На основе метода опорных операторов разработаны эффективные вычислительные алгоритмы, выделяющие гиперболическую (для переноса водо- и гидратонаыщенностей) и пьезопроводно-диссипативную части задачи. Выполнена их программная реализация на сетках нерегулярной структуры, позволяющих моделировать процессы диссоциации газовых гидратов в осадочных бассейнах сложного геометрического и литологического строения. Проведены численные расчеты для модельной области с параметрами, соответствующими реальному осадочному бассейну в Южно-Китайском море. Currently, the investigation of gas hydrate deposits is very relevant. The study of sedimentary basins containing gas hydrates is complicated by the presence of complex geometric regions in them (interlayers, shear and low-permeability zones, etc.). Areal and profile calculations have spatial stratigraphic unstructured areas, their arbitrary location and variable effective thickness of layers. This work focuses on the study of the problem of two-dimensional filtration in a zone of three-phase hydrate equilibrium (gas, hydrate, water), taking into account the possible low permeability of rocks. To solve this problem, an original filtration model with a non-classical form of the law of motion is used. Based on the support operator method, the effective computational algorithms that distinguish the hyperbolic (for the transfer of water and hydrate saturation) and piezoconductive-dissipative parts of the problem have been developed. Their program implementation on grids of irregular structure, which make it possible to model the processes of dissociation of gas hydrates in sedimentary basins of complex geometric and lithological structure were realized. Numerical calculations for a model domain with parameters corresponding to a real sedimentary basin in the South China Sea were realized.

The work provides a description of the spatial filtration problem in a three-phase hydrate equilibrium zone. A mathematical model is presented for studying two-dimensional fluid flows taking into account the solid hydrate phase and the irregular structure of formations. A non-classical form of the motion law is used, applicable at low permeability and low pressure drops. Efficient computational algorithms based on the support operator method are proposed that make it possible to separate the hyperbolic and dissipative subsystems of the problem. The algorithms are implemented on meshes of irregular structure to model the two-dimensional multiphase processes of gas hydrate dissociation. Testing is carried out on model piezoconductive processes with saturation transfer, where it is shown that depression processes are less expressed when using a nonlinear law of motion.

The work considers the problem of gas hydrate dissociation in a porous medium using the two-term Forchheimer law, corresponding to high flow rates of reservoir fluids. Such rates can arise during the decomposition of gas hydrates, since a large amount of gas is released. Intensive emissions of gases from the earth’s interior are observed on the ocean floor. They are also associated with a large number of subvertical geological structures under the ocean floor, coming to the surface in the form of local ring funnels (pockmarks). Many similar objects have also been found on land. Particular interest in this problem is caused by climate threats associated with the release of greenhouse gases. The movement of gas released from the hydrate to the breakthrough channel is similar to the gas inflow to the well (without hydrate), which is usually described by a two-term filtration law. In this work, a mathematical model of gas hydrate dissociation with a nonlinear Forchheimer-type law of motion is developed. The system is split in two blocks by physical processes, taking into account the quadratic correction to the velocity in the filtration law. The first block is responsible for the convective transfer of saturation parameters in the model, water, gas and hydrate saturations are taken into account. The second block corresponds to the equation of dissipative piezoconductivity with a different number of thermodynamic degrees of freedom, taking into account heat and mass transfer in a porous medium. The performed splitting allows using explicit-implicit difference schemes when solving problems and avoiding strong refinement of the step in time and space. For numerical modeling, the support operator method is used, which makes it possible to discretize partial differential equations on irregular grids, which allows taking into account the complex geometry and lithology of the reservoir. A difference scheme based on the support operator method is developed, which, due to the mutually consistent approximation of vector analysis operations (divergence and gradient), allows to take into account the various flux laws between adjacent grid cells, including quadratic corrections to the velocity. Based on the developed numerical algorithms and their program implementations, calculations of gas hydrate dissociation are performed both in a reservoir of simple geometric structure and in a heterogeneous reservoir of complex configuration. The results obtained correspond to the physics of the processes under consideration.

The work is devoted to the application of irregular computational grids to problems of underground fluid dynamics in the presence of gas hydrates taking into account gravity. Discretization of filtration equations is carried out using the support operator method. The obtained algorithms are tested on the problem of gravitational differentiation of gas and water in a porous medium taking into account gas hydrates. One of the criteria used in testing is the horizontality of the gas-water contact in the stationary case. The calculations are divided into two stages. At the first stage, a regular rectangular grid is used, which makes it possible to check compliance with this criterion. At the second stage, calculations are carried out on an irregular grid for a system of heterogeneous layers of complex geometric structure corresponding to real geological structures. The results obtained correspond to the physics of the process. The approach can be used to study the migration of deep gas released during the dissociation of gas hydrates to the earth's surface.