The vector of development of solid-fuel energy is currently directed towards expanding the range of renewable fuels used. Along with the direct combustion of fuel, the processes of controlled thermal transformation of the raw biomass in an oxygen-free surrounding to obtain a new fuel based on it (liquid, solid, gaseous) are widely spread. A significant part of research in this sphere is related to the study of the formal kinetics of such processes, at the same time, the hardware design of the process is no less important, but less studied. Thus, development of mathematical models of pyrolysis equipment operation is relevant. A decisive difference approximation of these processes in the framework of an axisymmetric formulation of the problem is chosen as a mathematical basis for modeling physical and chemical transformations and transfer processes in the radial direction of a cylindrical pyrolysis reactor. The material constants of the processes are borrowed from the well-known literature references The authors studied the modes of reactor operation not covered by a full-scale experiment, using the previously proposed and verified one-dimensional mathematical model of a cylindrical pyrolysis reactor. The issues of the influence of the dimensionless kinetic function of the process (reaction model) on the thermal transformation of the material in the apparatus are considered. The significant influence of the chosen reaction model on the kinetic nature of the process is pointed out. The mutual influence of drying and pyrolysis the presence of which is due to the energy effects of the processes is considered. A significant spatial heterogeneity of the process is defined and the possibility of the existence of a non-trivial effect of advanced heating of the internal zones of the apparatus in comparison with the peripheral ones is specified. The paper shows that a computational experiment can help to detect non-trivial effects and identify the variability of the process implementation even within the framework of a single design and technological solution of the pyrolysis process. According to the authors, the results of the obtained numerical experiments indicate that mathematical modeling can be the basis of making technological solution. However, further research is also needed to determine reliably the material constants of the process.