## 4 Review of Existing Methods to Track Bio-Fraction of Co-Processed Fuels
### Energy (or Mass) Balance plus Equal Allocation Method  
The energy balance approach records the energy content in (a) the biomass feedstocks and (b) the fossil feedstocks entering the co-processing facility. The energy content of both feedstocks is calculated using the mass of feedstock and its heating value. The energy in the biomass feedstock is then expressed as a percentage of the total energy content of all feedstocks (i.e., bio and fossil) entering the co-processing facility. This calculated \"bio-percentage\" is then applied to the outputs, i.e., the fuels which result from co-processing, to give an estimation of the bio-content in the final fuel products. In the case of equal allocation, this bio-fraction of the energy content in the input fuels is shared equally across the different fractions resulting from the co-processing produced, e.g., if 10% of the total energy in the feedstocks entering the co-processor is bio in origin, and if the co-process produced diesel, kerosene and propane gases, then this method estimates that the products contain 10% bio-content by energy. In the energy balance method, the fraction of bio-component in the inputs is calculated with Equation (1) below using based on energetic weighted ratios of bio-based and fossil inputs. \[f=\frac{\sum\left(Q_{b-in}^{i}\cdot LHV_{b-in}^{i}\right)}{\sum\left(Q_{b-in} ^{i}\cdot LHV_{in}^{i}+Q_{f-in}^{j}\cdot LHV_{f-in}^{j}\right)} \tag{1}\]  
where:  
\(f\)--bio yield factor  
\(Q_{b-in}^{i}\)--mass flow of \(i\) biomass feedstock entering co-processing unit \begin{table}
\begin{tabular}{l l} \hline \multirow{2}{*}{Mass balance method} & Total mass balance \\ \cline{2-3}  & Carbon mass balance \\ \hline Energy balance & Energy balance \\ \hline \multirow{2}{*}{Radiocarbon testing} & Accelerator Mass Spectrometry (AMS) \\ \cline{2-3}  & Liquid Scintillation Counting \\ \hline \multirow{2}{*}{Isotope Ratio, optical and inline techniques} & Isotope Ratio Mass Spectrometer (IRMS) \\ \cline{2-3}  & Nuclear Magnetic Resonance spectroscopy (NMR) \\ \hline \end{tabular}
\end{table} 
Table 2: Methods to determine the bio-content in co-processing. \(LHV_{b-in}^{i}\)--low heating value of \(i\) biomass feedstock entering co-processing unit  
\(Q_{f-in}^{j}\)--mass flow of \(j\) fossil feedstock entering co-processing unit  
\(LHV_{f-in}^{j}\)--low heating value of \(j\) fossil feedstock entering co-processing unit  
The amount of renewable fuel is determined by Equation (2) below  
\[Q_{ren}=f\cdot Q_{f}=\frac{\sum(Q_{bin}^{i}\cdot LHV_{bin}^{i})}{\sum(Q_{in}^{ i}\cdot LHV_{in}^{i})}\cdot Q_{f} \tag{2}\]  
The mass balance approach is a straight forward method, somewhat similar to the energy balance, albeit it relies on the mass flows of the biomass feedstock and fossil fuels. The mass of biomass feedstock going into co-processing is recorded, and expressed as a percentage of the total mass of feedstocks going into the co-processer. The products are then considered to have this percentage (by mass) of bio-content. Water input with the feedstock would need to be excluded. In this method, the bio-content of the co-processed fuel is determined with the mass balance ratio given by Equation (3) below. \[f=\frac{\sum Q_{b-in}^{i}}{\sum Q_{b-in}^{i}+Q_{f-in}^{j}} \tag{3}\]  
where:  
\(f\)--bio yield factor  
\(Q_{b-in}^{i}\)--mass flow of \(i\) biomass feedstock entering co-processing unit  
\(Q_{f-in}^{j}\)--mass flow of \(j\) fossil feedstock entering co-processing unit  
The amount of the renewable (bio) fuel output is calculated with Equation (2) below. \[Q_{ren}=f\cdot Q_{f}=\frac{\sum Q_{b-in}^{i}}{\sum\Bigl{(}Q_{b-in}^{i}+Q_{f-in }^{j}\Bigr{)}}\cdot Q_{f} \tag{4}\]  
where:  
\(Q_{ren}\)--the amount of the renewable (bio) fuel produced  
\(Q_{f}\)--mass flow of the fuel produced  
A further modification to this is the carbon mass balance and the so-called total mass balance methods, which are described by [33; 34].