Two-Dimensional Mathematical Modeling of Gas Hydrate Dissociation with a Nonlinear Forchheimer-Type Filtration Law

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.