In this study, we consider the complex problem of how to model steady regimes in CFB boilers, taking into account classical and oxy-fuel combustion. In accordance with the population balance technique and the theory for difference equations, we propose a novel mathematical description which is coherent and includes a set of original expressions and parameters describing behaviour of the CFB boiler as a complex system. We then discuss and illustrate how our internal-partial models and the governing model operate under oxy-fuel and classical combustion conditions. In global scale we compared simulation results with experimental data for operating the pilot scale 0.1 MWth test rig within the oxy-fuel combustion. The presented computational results can be used to realistically model mass fluxes in steady regimes in CFB industrial installations. (C) 2013 Elsevier B.V. All rights reserved.