Mathematical Model of the Decomposition of Unstable Gas Hydrate Accumulations in the Cryolithozone

Abstract

We present a generalization of the mathematical model of gas discharge from frozen rocks containing gas-saturated ice and gas hydrates in a metastable state (due to the self-preservation effect) caused by the drop in external stress associated with various geodynamic factors. These factors can be attributed, for example, to a decrease in hydrostatic pressure on a gas-bearing formation due to glacier melting, causing an isostatic rise, or to the formation of linear depressions in the bottom topography on the shelf due to iceberg ploughing. A change in external pressure can also be associated with seismic and tectonic deformation waves propagating in the lithosphere as a result of ongoing strong earthquakes. Starting from the existing hydrate destruction model, operating at the scale of individual granules, we consider a low-permeable hydrate and ice-saturated horizontal reservoir. Generalization is associated with the introduction of a finite threshold for the external pressure drop, which causes the destruction of the gas hydrate and gas-saturated microcavities of supramolecular size. This makes it possible to take into account the effect of anomalously high pressures occurring in the released gas as a result of partial hydrate dissociation. Numerical and approximate analytical solutions to the problem were found in the self-similar formulation. A parametric study of the solution was carried out, and regularities of the hydrate decomposition process were revealed.