## 3 Model Description
### Procedure of Dynamic Simulations  
The long-term steady-state test run with lignite lasted 57 h so that short-term fluctuations are compensated and the data is very reliable. Therefore, the test point is suitable to tune the APROS model to the corresponding solid fuel and the bed properties. The objective of the tuning process was to achieve a high agreement between the simulation results of the steady-state test and the experimental data, especially concerning the pressure and temperature profile. Mainly nine parameters were tuned, such as the number of calculation nodes, the heat transfer coefficient calculation method, or the global split coefficient between core and annulus and vice versa. Details of the tuning process and the tuned parameters are presented in Section 4.1.  
After the model was tuned, validation of the model was done with the experimental data of the part-load tests. Therefore, no additional parameters were adjusted or tuned and only the boundary conditions were modified. The mass flow of solids (fuel and sand) and the air mass flow was modified with pre-defined setpoints according to the experimental data. Figure 3 shows a graphical visualization  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & \multirow{2}{*}{
\begin{tabular}{c} **Density \(\rho\)** \\ **[kg/m\({}^{3}\)]** \\ \end{tabular} } & \multicolumn{3}{c}{**Heat Capacity C\({}_{\text{p(T)}}\) = A + B\(\cdot\)T + C\(\cdot\)T\({}^{2}\) + D\(\cdot\)T\({}^{3}\) + E\(\cdot\)T\({}^{4}\) [kj/kg/K]**} \\ \cline{2-7}  & & **A** & **B** & **C** & **D** & **E** \\ \hline Sand & 2650 & 0.723 & \(1.26\times 10^{-3}\) & \(-6.9\times 10^{-7}\) & \(2.67\times 10^{-10}\) & \(-3.8\times 10^{-14}\) \\ \hline Solid fuel & 1300 & 2.5 & 0 & 0 & 0 & 0 \\ \hline Char & 1350 & 0.739 & \(2.09\times 10^{-3}\) & \(-3.6\times 10^{-6}\) & 0 & 0 \\ \hline Ash & 2400 & 745.6 & 1.041 & \(-0.6\times 10^{-3}\) & 0 & 0 \\ \hline Lime & 3350 & 0.84 & 0 & 0 & 0 & 0 \\ \hline Limestone & 2700 & 0.4091 & \(2.1\times 10^{-3}\) & \(-2\times 10^{-6}\) & \(7\times 10^{-10}\) & 0 \\ \hline Calcium sulphate & 800 & 1.09 & 0 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Density and heat capacity of solid particles in the riser.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & \multirow{2}{*}{\(\lambda_{\text{(800\ ^{o}C)}}\)} & \multicolumn{3}{c}{**Thermal Conductivity [W/m/K]**} \\ \cline{2-5}  & & & \multicolumn{3}{c}{\(\lambda_{\text{(T)}}\) = A + B\(\cdot\)T + C\(\cdot\)T\({}^{2}\) + D\(\cdot\)T\({}^{3}\)**} \\ \cline{2-5}  & & **A** & **B** & **C** & **D** \\ \hline Dense refractory & \multirow{2}{*}{1.657} & \multirow{2}{*}{3.1} & \multirow{2}{*}{0} & \multirow{2}{*}{\(-7\)} & \multirow{2}{*}{0} \\ concrete & & & & & \\ \hline Calcium silicate & 0.2874 & 0.09 & \(1\times 10^{-4}\) & \(4\times 10^{-7}\) & \(-2\times 10^{-10}\) \\ \hline Microporous & 0.05352 & 0.016 & \(2\times 10^{-5}\) & \(2\times 10^{-8}\) & \(4\times 10^{-11}\) \\ \hline \hline \end{tabular}
\end{table}
Table 8: Thermal conductivity of furnace insulation.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Material**} & \multirow{2}{*}{
\begin{tabular}{c} **Density \(\rho\)** \\ **[kg/m\({}^{3}\)]** \\ \end{tabular} } & \multicolumn{2}{c}{**Heat Capacity C\({}_{\text{p(T)}}\) = A + B\(\cdot\)T [kj/kg/K]**} \\ \cline{2-5}  & & **A** & **B** \\ \hline Dense refractory & \multirow{2}{*}{2450} & \multirow{2}{*}{0.8} & \multirow{2}{*}{0} \\ concrete & & & & \\ \hline Calcium silicate & 260 & 0.08 & \(0.5\times 10^{-3}\) \\ \hline Microporous & 230 & 1 & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Density and heat capacity of solid particles in the riser.  
of the set points in the experiment and the simulation. As in the experiment, the load was increased from 63% to 88% to 100% followed by a load reduction from 100% to 89% and 68%. For details regarding the boundary conditions during the part-load simulations, see Table 5.