## 1 Introduction  
Climate change due to high CO\({}_{2}\) emissions has led to a substantial increase in the proportion of electricity generated from renewable sources around the world in the last two decades [1]. Wind and solar energy account for a large share of these renewables. These two energy sources have the disadvantage that they are not suitable to provide baseload and, depending on the conditions, the electricity generated can fluctuate strongly and rapidly. There is a demand for highly flexible technologies to ensure the energy supply with low CO\({}_{2}\) emissions at the same time. Circulating fluidized bed (CFB) combustion can be a key element in the future energy supply, as it can combust a high spectrum of solid fuels of different origins such as biomass and waste-derived fuels [2; 3; 4; 5]. The technology comes with a high combustion efficiency [6] and with low emissions of SO\({}_{2}\) and NOx[7; 8]. CFB boilers can operate over a wide range of thermal loads and are therefore capable of compensating a fluctuating electricity demand. The high fuel flexibility is made possible by a large mass of inert particles in the reactor, which can compensate for fluctuations in the fuel composition. However, the high thermal inertia of this material has a negative impact on the load following capability and especially the cold start-up of CFB combustors [6]. During transients from medium to high load, ramp rates of up to 7% MCR/min (MCR:maximum continuous rating) are claimed to be possible [9]. However, modern large-scale CFB boilers, such as the Polish CFBC unit at Lagisza have load following capabilities of up to 4% MCR/min, which is similar to pulverized coal power plants [6]. The need for even faster load change rates increases with the rising share of renewable energies. Therefore, there is a demand to investigate novel concepts to accelerate load ramps in CFB combustion. For example, thermal energy storage systems can be used to rapidly extract a large amount of energy from the furnace [10]. Another option is to apply smart control strategies for the water/steam side and the fuel and air mass flow [11; 12; 13]. To examine novel concepts, experimental investigations are necessary but often very expensive, especially on a large scale. Computational fluid dynamics (CFD) simulations, on the other hand, are complicated and require a lot of computing time, even though they are often the only way to study CFB combustion inside a furnace in detail [14; 15; 16; 17]. One-dimensional dynamic process models offer the advantage of low computing time and an appropriate accuracy to evaluate new approaches before they are tested in an industrial-scale boiler [18; 19]. The commercial software APROS is used extensively in industry and research for the dynamic process modeling of thermal power plants [12; 20; 21]. So-called 1.5-dimensional core-annulus models take into account the mass and heat flow from the core to the annulus and vice versa. Particles and particle clusters stream upwards in the core region of the furnace, while they stream downwards in the annulus, due to the low gas velocities near the wall. This internal circulation of solids in the furnace is up to 2 times higher than the external circulation via cyclone and loop seal [22]. The convective heat transfer to the walls of the furnace is mainly determined by the mass flow from the core to the annulus and from the annulus to the core, so it is important to take this mechanism into account. However, the only way to prove the suitability of process models for dynamic investigations is by validation with experimental data. Suitable models must be able to show all typical characteristics of the CFB combustion: the load change duration/behavior, the combustion chemistry, the hydrodynamic conditions (particle distribution, temperature development), and the heat transfer. The present study presents a sophisticated 1.5D-model of a CFB combustor based on the core-annulus approach for the CFB furnace.