Mathematical Modeling of Intrasoil Condensation in Frozen Soils

Abstract

Mass exchange in soils occurs with the absorption of heat during evaporation and, conversely, with the release of heat during condensation. This article is devoted to mathematical modeling of heat and humidity transfer taking into account the condensation and evaporation of subsoil humidity during seasonal thawing of permafrost. Humidity motion can be described using the transfer equation in the humid or potential (Richards equation) forms in saturated and unsaturated soils. Based on the experimental and field data, we carried out verification of the parameters of condensation and evaporation of pore humidity. The numerical realization of the nonlinear heat and humidity transfer problem is carried out by the method of finite differences using the Newton’s method. The adequacy of the proposed model is shown in the case of seasonal thawing of permafrost. As a result of a numerical experiment in the conditions of Central Yakutia, it has been established that the total humidity content of the soil increases with evaporation and condensation of intra-soil. In the spring-summer period there is an intense process of evaporation of intra-soil and a decrease in temperature, and the summer-autumn period shows an increase in the amount of the fall-out of the condensate of water vapor with an increase in the heat content of the soil. At the end of the summer season, as well as the end of September and the beginning of October, there is a “blocking” of the wet thawed layer. The suggested mathematical model more adequately reflects the process of freezing of the “blocking” zone.