For the traditional problem of gas flow to a well in the center of circular reservoir, the influence of initial reservoir conditions on dynamics of gas moisture content distribution has been determined. Investigations have been performed in the framework of mathematical model of non-isothermal real gas flow through porous media where heat conductivity was considered to be negligible in comparison with convective heat transfer. It is closed by empirical correlation of compressibility coefficient with pressure and temperature, checked in previous publications. Functional dependence of moisture content in gas on pressure and temperature is based on empirical modification of Bukacek relation. Numerical experiment was performed in the following way. At first step, axisymmetric problem of non-isothermal flow of real gas in porous media was solved for a given value of pressure at the borehole bottom, which gives the values of pressure and temperature as functions of time and radial coordinate. Conditions at the outer boundary of the reservoir correspond to water drive regime of gas production. At the second step, the calculated functions of time and coordinate were used to find the analogous function for moisture content. The results of experiment show that if reservoir temperature essentially exceeds gas – hydrate equilibrium temperature than moisture content in gas distribution is practically reflects the one of gas temperature. In the opposite case, gas will contain water vapor only near bottom hole and at the rest of reservoir it will be almost zero. In both cases, pressure manifests its role through the rate of gas production, which in turn influences convective heat transfer and gas cooling due to throttle effect.
The necessity of accounting for real gas properties, thermal interaction with permafrost rocks and the possibility of formation (dissociation) of gas hydrates in these objects for adequate description of the operation of gas wells and main gas pipelines in the regions of the Far North by appropriate mathematical models is shown. Mathematical models that take into account the non-isothermal gas flow within the framework of pipe hydraulics, the change of the area of tube cross-section due to the formation of hydrates and the dependence of the heat transfer coefficient between gas and hydrate layer on the varying flow area over time are proposed. The corresponding conjugate problem of heat exchange between the imperfect gas in the well and the environment (rocks) is reduced to solving differential equations describing the non-isothermal flow of gas in the pipes and the heat transfer equations in rocks with the corresponding conjugation conditions. In the quasi-stationary mathematical model of hydrate formation (dissociation), the dependence of the gas-hydrate transition temperature on the pressure of gas is taken into account. Established that the formation of hydrates in wells, even at low reservoir temperatures and a thick layer of permafrost, takes a fairly long period of time, which allows to quickly prevent the creation of emergency situations in gas supply systems. Some decisions taken in the design of the first section of the main gas pipeline «Power of Siberia» have been analyzed by methods of mathematical modeling. In particular, it is shown that if the gas is not dried sufficiently, the outlet pressure may drop below the allowable limit in about 6-7 hours. At the same time, for completely dry gas, it is possible to reduce the cost of thermal insulation of the pipeline at least two fold.
