The objective of this study is to investigate experimentally and numerically all the processes (i.e., heat-up, drying, pyrolysis, and combustion) experienced by coal or biomass in a packed bed moving on a forward acting grate. As a novelty, the approach considers a packed bed to be composed of a finite number of individual particles, which may have different properties or sizes. Each of these particles undergoes a sequence of processes such as heat-up, drying, pyrolysis, or gasification and oxidation. The latter are described with sufficient accuracy by a set of one-dimensional and transient conservation equations for mass and energy. Thus, the sum of all these processes constitutes conversion of a packed bed. The ensemble of particles has a solid phase and a void space between them. Heat and mass transfer couples the flow within the void spaces to the particles. The state of the gaseous phase is described by differential conservation equations for mass, momentum, and energy of a compressible reacting flow. The predictions of the numerical model are compared to both experiments with single particles and measurements taken inside a combustion chamber close to the bed's surface. The experiments with single particles validated the model for single particles. Good agreement was achieved for the processes of drying, pyrolysis, and gasification for a range of both particle sizes and temperatures. The computed concentrations and temperatures along the surface of the bed were compared to measurements and showed satisfactory agreement.