## 2 Materials and Methods
### Numerical Particle Model  
A numerical model of the particle and its surrounding is used to simulate the release behaviour of the K species from different biomass sources based on their chemical composition given in Table 1.  
The particle model considers heat and mass transfer inside and outside of the particle, where gradients of species and temperature are resolved using an adaptive mesh. Particle shrinkage, evolution of porosity and multi-component diffusion are taken into account. Formation and subsequent reactions of the volatiles in the gas phase are also considered in the model. Since the focus of this paper is on the release of K, a global gas phase chemistry is used to model homogeneous volatile combustion [6; 35]. A detailed description of the model, the governing equations and validations can be found in [17]. Recently, we developed a sub-model for the K release from biomass, where the interaction between K/S/Cl composition in the particle ash is taken into account [30]. This sub-model is explained in more detail in the following section. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Unit** & **Softwood** & **Salix** & **Miscanthus** & **Wheat Straw** \\ \hline Particle mass & kg & \(5.00\times 10^{-4}\) & \(5.00\times 10^{-4}\) & \(5.00\times 10^{-4}\) & \(5.00\times 10^{-4}\) \\ Particle volume & m\({}^{3}\) & \(4.02\times 10^{-7}\) & \(4.52\times 10^{-7}\) & \(4.02\times 10^{-7}\) & \(5.03\times 10^{-7}\) \\ Particle density & kg/m\({}^{3}\) & 1243.4 & 1105.2 & 1243.4 & 994.7 \\ \hline \hline \multicolumn{6}{c}{Calorimetric and proximate analysis} \\ \hline LHV & MJ/kg dry & 18.9 & 18.7 & 17.9 & 16.6 \\ Moisture & wt-\% rec. & 6.1 & 8.9 & 8.2 & 10.0 \\ Ash content & wt-\% dry & 0.42 & 0.98 & 3.22 & 9.05 \\ \hline \hline \multicolumn{6}{c}{Ultimate analysis} \\ \hline C & wt-\% dry & 50.07 & 49.43 & 47.58 & 44.28 \\ H & wt-\% dry & 6.2 & 6.13 & 5.8 & 5.62 \\ N & wt-\% dry & 0.04 & 0.28 & 0.24 & 0.88 \\ O & wt-\% dry & 43.3 & 43.2 & 43.1 & 40.0 \\ \hline \hline \multicolumn{6}{c}{Main ash-forming elements} \\ \hline K & mg/kg dry & 499 & 1460 & 2780 & 14600 \\ Na & mg/kg dry & 29.9 & 21.1 & 87.1 & 214 \\ Ca & mg/kg dry & 904 & 2310 & 1110 & 5110 \\ Mg & mg/kg dry & 136 & 254 & 480 & 1130 \\ Fe & mg/kg dry & 46.7 & 59.2 & 191 & 546 \\ Zn & mg/kg dry & 10.9 & 30.7 & 11.5 & 22.7 \\ Al & mg/kg dry & 76.6 & 49.5 & 233 & 701 \\ Si & mg/kg dry & 308 & 285 & 10,100 & 22,100 \\ P & mg/kg dry & 47.5 & 493 & 298 & 882 \\ S & mg/kg dry & 56.3 & 234 & 343 & 1390 \\ Cl & mg/kg dry & 23 & 40.1 & 239 & 3510 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Physical and chemical properties, including fuel analysis, of softwood, Salix, Miscanthus and wheat straw biomass particles. Sub-Model for the Release of K/S/Cl from Biomass  
The presence of organic and inorganic compounds in biomass, specifically potassium, sulphur and chlorine, poses a significant challenge in biomass thermochemical conversion systems. To understand the release behaviour of these species, a sub-model is added to the particle conversion model, where the temporal release of these species during biomass combustion is calculated. However, the release of K from biomass is highly dependent on other elements in the structure of biomass. Chlorine and sulphur, for instance, can significantly facilitate K release, while the presence of silicate and aluminium can lead to formation of stable compounds that stay in the ash structure. The current model takes into account the interaction between K, Cl and S through a set of elementary reactions. Potassium can be found in organic and inorganic form in the biomass structure. Inorganic potassium in the form of K\({}^{+}\) can form crystallized salts as the particle starts to dry.