In this paper, the heterogeneous combustion of porous metal-containing media is studied taking into account the phase transitions of metal in condensed and gas phases. Such process takes place when applying a novel promising method for the extraction of rare metals from various combustible materials, such as coal and petroleum wastes, by means of filtration combustion. A novel mathematical model, based on the conservation laws, is developed for investigating the physicochemical and gas-dynamic processes during the propagation of combustion waves in porous media with admixtures of metals. Using numerical experiments, the possibilities of metal mass transfer and accumulation of condensed metal in a narrow zone of the porous reactor are shown. The effect of the gas velocity at the reactor inlet and initial metal concentration on combustion of porous metal-containing media is studied. It is revealed that by changing the gas velocity at the reactor inlet, it is possible to control the process of metal transfer and accumulation during the extraction of rare metals from various combustible media. It is shown that the investigated method of rare metals extraction can be very effective for combustible media with a low initial metal concentration.

在本文中，考虑了金属在冷凝和气相中的相变，研究了含金属多孔介质的非均质燃烧。当采用一种新颖的有前途的方法通过过滤燃烧从各种可燃材料（例如煤和石油废料）中提取稀有金属时，就会发生这种过程。建立了一种基于守恒律的新型数学模型，用于研究燃烧波在金属混合物与多孔介质中传播过程中的物理化学和气体动力学过程。使用数值实验，显示了金属质量转移和冷凝金属在多孔反应器狭窄区域中积累的可能性。研究了反应器入口处的气体速度和初始金属浓度对多孔含金属介质燃烧的影响。据揭示，通过改变反应器入口处的气体速度，可以控制在从各种可燃介质中提取稀有金属的过程中金属的转移和积累过程。结果表明，所研究的稀有金属提取方法对于初始金属浓度低的可燃介质可能非常有效。