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The laboratory and field experiments of [1, 2] showed the possibility of using a high-frequency electromagnetic (EM) field for deep and intense heating of a productive bed by heat sources distributed over the volume. The heat sources occur during interaction of a high-frequency EM radiation with the medium and are caused by conversion of part of energy of the propagating EM waves to heat. When a hydrate-containing rock is heated to the temperature of thermal decomposition of the gas hydrate, the latter can dissociate to the gas and water. Owing to the heat sources distributed over the volume, the phase transition can also occur in the absence of a temperature gradient. In this case, vast zones of phase transition can occur in which the gas hydrate decomposition temperature is attained and the EM field energy is expended on its dissociation.In [3][4][5], the Stefan problem was used as a mathematical model for the mathematical description of processes that occur in a heated medium and are accompanied by phase transitions (melting and decomposition). However, the assumption that phase transitions proceed on a geometrical surface (a front of zero thickness) is applicable only in the case where the width of the phase-transition zone is much smaller than the length of the EM waves radiated into the bed [3]. In addition, the width of the phase-transition zone should be much smaller than the characteristic dimension of the problem, for example, the characteristic length of the zone in which the EM radiation is absorbed by the medium. These conditions are satisfied for small times of heating. It has been shown [5] that, as the productive bed is heated by the EM field, the width of the phase-transition zone increases rapidly and, at some value of the width, the use of the Stefan mathematical model gives a distorted picture of real processes.The expression used in [3][4][5] for the density of heat sources distributed near the EM-wave radiator gives a value that is more than 2 times larger than the real value calculated from the exact solution expressed in terms of Hankel functions.In this connection, it is necessary to use a phase-transition zone of finite width in the mathematical model and obtain new expressions for the distribution of heat sources.1. System of Equations Describing the Thermodynamics of Gas Hydrate Decomposition under the Action of a High-Frequency EM Field. We study the following problem. A hydrate-saturated rock is under a bed pressure at a temperature lower than the decomposition temperature of the gas hydrate at the given pressure. The pore space is initially filled with the gas and the gas hydrate.At the borehole bottom, a sufficiently powerful source of high-frequency EM waves is located opposite to the productive bed. As the EM waves propagate, their energy is converted to heat. Over a fairly large volume of the borehole bottom, the temperature increases, and, near the radiator, it reaches the gas hydrate decomposition temperature that corresponds to the bed pressure. A moving boundary (or an exte...

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