## 2 Materials and Methods
### Life Cycle Assessment
#### 2.6.2 Inventory Analysis
A high mass of the waste product relative to the primary product could have the adverse effect that the manufacturer starts claiming that the environmental impact of their primary product is low. Economic allocation which additionally considers the differences in economic value between primary product and by-product normally overcomes this issue. Yet, one must remain aware of the fact that economic allocation coefficients calculated as such may not be very constant because of the temporal and geographical variability of the economic value. To overcome this issue for this paper, multiple recent economic allocation coefficients were used to assign part of the carbon footprint of coal-fired electricity production to the fly ash. Table 3 gives an overview of these economic allocation coefficients (C\({}_{\text{e}}\)). Equation (6) shows the underlying formula for calculation of this C\({}_{\text{e}}\) value:  
\[\text{C}_{\text{e}}=\ \frac{\left(\text{p}\cdot\text{m}\right)_{\text{by-product}}} {\left(\text{p}\cdot\text{m}\right)_{\text{primary product}}+\left(\text{p} \cdot\text{m}\right)_{\text{by-product}}} \tag{6}\]  
with (p \(\cdot\) m) the price per unit of the materials (p) multiplied by the mass of materials produced during the process (m), the by-product being the fly ash and the primary product being coal-fired electricity. Note that in order to have a mass value for the electricity in Equation (6) the amount of hard coal burned (around 0.367 kg) to produce 1 kWh of electricity was used as input cf. [PERSON] et al. [7]. Each of the economic allocation coefficients listed in Table 3 were once applied to the following ecoinvent LCI for coal fired electricity production: Electricity, high voltage {DE} electricity production, hard coal | Cut-off, U. As such, 5 different LCIs representing economic allocation for the fly ash were obtained. Since the fly ash used in this research originated from a coal-fired power plant in Germany, the LCI based on a C\({}_{\text{e}}\) value of 0.50% is probably the most representative one for further carbon footprint calculations in this regard. However, additional consideration of similar calculations done with the LCIs based on the other C\({}_{\text{e}}\) values will give an indication on to what extent the outcome of carbon footprint calculations for fly ash can vary. According to [PERSON] et al. [7] the basic treatment of the fly ash after its capture from the flue gases by the electrostatic precipitators should be fully assigned to the fly ash. This basic treatment comprises basic drying and storage. [PERSON] et al. proposed an LCI for this. The same LCI was used in this study after updating all input data to the most recent version of the ecoinvent database. A detailed overview of the LCI can be found in Appendix A (Table A1). Thus, a full LCI for fly ash comprises the sum of the LCI covering its basic treatment (drying + storage) and the LCI that deals with the economic allocation of coal fired electricity production. In total, five versions of this fully LCI were compiled considering the five considered C\({}_{\text{e}}\) values from literature (Table 3). Apart from that, also an LCI only addressing the basic treatment was drafted. This was done for the following reason: Despite the fact \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Source** & **C\({}_{\text{e}}\) (\%)** & **Country** & **Year** \\ \hline [PERSON] et al. [8] & 0.50 & Germany & 2020 \\ [PERSON] et al. [8] & 0.25 & China & 2020 \\ [PERSON] et al. [8] & 0.11 & United Kingdom & 2020 \\ [PERSON] et al. [9] & 0.98 & United States & 2019 \\ [PERSON] et al. [10] & 4.30 & Canada & 2017 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Overview of the considered economic allocation coefficients (C\({}_{\text{e}}\)) for fly ash from literature. that fly ash clearly meets the criteria of being a by-product, it is generally not yet well accepted to include an allocated impact for the fly ash. For example, environmental product declarations (EPDs) of commercially available composite cements rarely account for it.