# Study of the Applicability of Thermochemical Processes for Solid Recovered Fuel
## 2 Materials and Methods
### Energy Balances
#### 2.3.2 Combustion of SRF from Screening Waste  
An energy balance was carried out to predict the output gas temperature (T; Figure 2). It illustrates the combustion process of SRF. It is noted that 1 kg of dry matter in SRF, characterised by its composition, is introduced into a furnace along with 50% excess air, where combustion occurs. This thermochemical process is associated with theoretical energy losses of 15% of the input energy and yields a series of non-combustible gases, along with 9.4 wt% ash on a dry SRF basis. The analysis was based on experimental [15] and literature data [39]. The following assumptions, simplifications, and stream properties were adopted for the energy balance:  
* The standard reference state was \(T_{0}\) = 25 \({}^{\circ}\)C (298 K) and P\({}_{0}\) = 1.01 \(\times\) 10\({}^{5}\) Pa.
* The characterisation of the input solid stream (SRF) is shown in Table 1 (dry basis). * The calculation basis was a feeding of 1 kg of dry matter in SRF. * Input air excess was of 50%. * Moisture content considered in the SRF stream was varied between 0, 2.5, 5, 7.5, and 10 wt%. * Liquid phases were considered to be ideal solutions. * Thermodynamic properties of liquid and gaseous compounds were obtained from the literature [40]. * Heat losses (\(Q_{losses}\)) were taken into account as 15% of input energy [41]. * Combustion of the SRF was considered complete, with no unburned fuel. Energy assessment  
The enthalpy balance of the system shown in Figure 2 was performed according to Equation (6). \[\Delta h_{input}=Q_{losses}+\Delta h_{output} \tag{6}\]  
where: \(Q_{losses}\): heat losses, which are assumed to be 15% of energy input (MJ). \(\Delta h_{input}\): specific enthalpy input (MJ), which represents the sum of enthalpies of the streams entering the furnace; and \(\Delta h_{output}\) is the specific enthalpy output (MJ), which represents the sum of enthalpies of the streams leaving the furnace. Figure 2: Combustion energy balance diagram. The enthalpy of each stream (\(\Delta h_{input}\), \(\Delta h_{output}\)) was calculated using Equation (7). \[\Delta h=\sum_{i}m_{i}\left(\Delta h^{0}_{f,i}+\int_{T_{0}}^{T}C_{p,i}\times dT\right) \tag{7}\]  
where: \(m_{i}\) is the mass flow of each component (considering 1 kg of dry matter in SRF as the calculation basis). Therefore, the components of the input streams are dry matter in SRF, H\({}_{2}\)O(I) in SFR (corresponding to its moisture), O\({}_{2}\)(g), and N\({}_{2}\)(g) (components of air). The components of the output stream are gas species and ash. The gases include CO\({}_{2}\)(g), H\({}_{2}\)O(g), NO(g), and SO\({}_{2}\)(g), which come from the complete combustion of the dry matter in SRF (see reactions below) and from the evaporation of the moisture content; the exit gas also includes O\({}_{2}\) (coming from the air excess used) and N\({}_{2}\) (inert). m\({}_{i}\) values for the products were calculated by mass balances considering the elemental and ultimate analysis of SRF:  
\( \begin{array}{ll}\text{C(s)}+\text{O}_{2}\text{(g)}\to\text{CO}_{2}\text{(g)}& \Delta\text{H}<0\\ 2\text{H(s)}+\frac{1}{2}\text{O}_{2}\text{(g)}\to\text{H}_{2}\text{O(g)}& \Delta\text{H}<0\\ 2\text{N(s)}+\text{O}_{2}\text{(g)}\to 2\text{NO(g)}&\Delta\text{H}<0\\ \text{S(s)}+\text{O}_{2}\text{(g)}\to\text{SO}_{2}\text{(g)}&\Delta\text{H}<0 \end{array} \)  
\(\Delta h^{0}_{f,i}\): standard enthalpy of formation of each compound at the reference temperature (298 K), (MJ/kg). Data for the gases and H\({}_{2}\)O(I) involved in the process were obtained from the literature [40]. The apparent enthalpy of formation for the dry matter in SRF (feedstock) \(\left(\Delta h_{f,\ dry\ matter\ in\ SRF}\right)\) was calculated from its ultimate analysis and higher heating value according to Equation (8).