A two-temperature mathematical model of steady filtration combustion of a solid fuel in open systems is proposed. Air or a mixture of air with water vapors is considered as a gaseous oxidizer. The model takes into account that the heat capacities of the phases depend on temperature and composition and that the reactor length is finite and allows obtaining the composition of gaseous combustion products. Calculated results on gasification of a mixture of carbon with an inert component are presented. It is demonstrated that thermodynamic calculations are important for obtaining the upper estimate of gasification efficiency. Even a sufficiently long reactor becomes "short" in the regime of transient combustion waves, which results in more intense entrainment of heat by combustion products and, as a consequence, in lower efficiency of the process. a solid fuel, heat wave, porous medium.Filtration combustion (FC) is understood as propagation of waves of exothermal transformation in a porous medium with gas filtration [1][2][3][4]. The mechanism of propagation of the reaction zone in such systems normally includes heating of initial substances ahead of the combustion front and local chemical interaction of reagents with heat release. A specific element determining the special features of combustion in such systems is filtration of the gas, which acts not only as a participant of the chemical reaction but also as a heat-carrying agent forming the thermal structure of the combustion wave. Propagation of a wave of exothermal transformation in a mixture of a solid fuel with an inert component, the oxidizer being filtered through this mixture, leads to the so-called "superadiabatic" heating [5,6]. This phenomenon occurs because the heat released is not entrained by reaction products but is concentrated in the combustion region, which allows a significant increase in temperature in this region. The simplicity of implementation of superadiabatic heating is the advantage of the FC process over other processes of combustion. The FC principle is encountered in natural (underground flames and smoldering), technological (coal gasification and self-propagating high-temperature synthesis), and industrial (ore agglomeration and waste processing) processes [7,8]. It should be noted, however, that the FC process has not been adequately studied despite the increasing interest in it.The schematic of filtration combustion of a solid fuel in open systems is shown in Fig. 1. As almost all fuels contain chemically inert admixtures (e.g., ash) from the very beginning, the porous medium ahead of the reaction zone in the general case is a mixture of the solid fuel and the inert material. The substance formed behind the combustion front is a porous residue containing the dead matter and solid combustion products. The heat released during the reaction is transferred to nonreacted layers of the substance with a lower temperature and initiates their own heat release, which results in self-sustaining propagation of the reaction wave. Owing to heterog...

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