## 3 Model Description
### APROS Model  
The core of the APROS model of the pilot plant is the circulating fluidized bed reactor. Figure 4 shows the process diagram of the net of the CFB furnace including air supply, solid handling, cooling lances, insulation and the solid recirculation system. The core of the model is the fluidized bed module of the APROS simulation software. It is based on a 1.5 D core annulus approach. This allows the modelling of a typical circulating fluidized bed flow pattern, in which the particles flow upwards in the core region and downwards in the annulus near to the wall. The fluidized bed module is separated into 20 calculation nodes. Ten types of materials are considered in the riser (three fluids: air, flue gas, water and seven solids: solid fuel, sand, limestone, calcium sulfate, lime, char, ash). The solid recirculation to the riser (in the experiment by the cyclone, standpipe, and loop seal) is modelled with a solid split block (cyclone) and a heat structure module (standpipe and loop seal). In the experiments, the air is injected into the loop seal to maintain fluidization of the solids. This air mainly flows to the standpipe, heats up, mixes with the flue gas and leaves the reactor through the cyclone. To reproduce this behavior, the loop seal air is mixed with the flue gas after the cyclone at a temperature of 300 \({}^{\circ}\)C. The heat that is required to increase the temperature of the air from 25 \({}^{\circ}\)C to 300 \({}^{\circ}\)C is taken into account, by withdrawing exactly this amount of heat from the recirculating solids. Solid fuel is injected to the riser at 0.481 m, while the fuel is separated into three components before injection: water/moisture, lime, and the rest of the fuel (dry fuel without lime). Water is separated from the fuel to avoid numerical instabilities according to the user manual of APROS. Line is supplied separately to take into account the desulfurization reaction (\(CaO+SO_{2}+1/2O_{2}\to CaSO_{4}\)). The individual mass flow rates of the three components are calculated based on the ultimate and proximate analyses of the fuel, see Table 3.  
In the model, the mass flow of the bottom ash is calculated by solving the solids mass balance. A major part of the incoming solid fuel is converted to gas by drying, devolatilization, and combustion reactions. Contrary, a small part of the gas is converted back to a solid state (e.g., by desulphurization reaction). After the chemical reactions, the solid materials ash, sand, lime, calcium sulfate, and unburned carbon leave the reactor either as fly ash or as bottom ash. The bottom ash mass flow is adjusted in such a way to maintain a constant inventory of a pre-defined set point of 130 kg. The air is supplied to the reactor by three main lines: primary air, secondary air (injection at two different heights), and burner air. The air supply is modeled in a separate net, which is not shown here. The air streams enter the riser at the same height and at the same temperature as in the experiment. The primary air pre-heating is modeled by the implementation of a PI controller that either increases or decreases the heat supply to the air stream to match the temperature set point. Each of the combustion air streams is modeled by a fan, which speed is controlled by a PI controller to supply the specified mass flow rate (with the setpoint coming from the experimental data). The piping of the air supply is modeled with the APROS module \"pipe\". The geometrical and material data for this piping is taken from the pilot plant. Figure 4: Circulating fluidized bed (CFB) combustor net. The blue gas path (from the heat exchanger to stack) is modeled in detail in another net. The blue gas flows to the two-path blue gas cooler, the filter, the ID fan, and the stack. Geometrical and material data for both paths of the heat exchanger and the piping of the blue gas lines are taken from the pilot plant design and implemented in the model. The fabric filter is not presented by a standard APROS library component.