## 4 Review of Existing Methods to Track Bio-Fraction of Co-Processed Fuels
### Yield Methods  
Yield methods refers to two distinct approaches resulting in a yield factor which can then be applied to co-processing systems. Each method will be discussed separately. Yield Method A: In this method, the yields of the various products are observed and recorded when an oil refinery runs on pure fossil feedstock. Then, a biomass feedstock is added, and the incremental effect on the final fuels yields is observed and recorded. This extra production of final fuels is considered to be result of the bio-feedstock which entered the co-processing facility, and this extra amount of final fuels is considered of biological origin. The bio-feedstock is then attributed to each product in proportion to the increase in its production. Ecofys [33] provides the following example to illustrate this methodology at work; beginning with \"a baseline scenario where 100 kg of fossil feedstock is processed in a refinery unit, yielding 90 kg of finished fuel, e.g., Diesel, gasoline, kerosene, etc. In the co-processing scenario, 10 kg of renewable feedstock (bio-oil) is added to the process, which increases the total yield to 97 kg. The increase in yield of 7 kg can be fully labelled as \"renewable\". When more bio-feedstock is added for co-processing, the yield factor of 7.2% (i.e., 7/97) can be applied to all outputs to calculate the kg renewable fuel\" [33]. The Californian Air Resources Board (CARB) in their Low Carbon Fuel Standard (LCFS) program, are working on a guidance document for co-processing and had considered this method as a possible approach to tracking bio-carbon. The yield of biofuel in the finished products can be verified with 14C. Once verified, a company co-processing a vegetable oil would simply apply the yield to estimate the bio-content in their co-processed fuels. [PERSON] et al. [31] described tests using a similar \"observed yield\" method, and they noted when it was supplemented with 14C assessment much greater accuracy (than using the observed yield method alone) can be obtained. In the observed yield method A, the fraction of bio-component in the outputs is calculated with Equation (7) below, using based on the ratio between the increase in yield of co-processed fuels in the co-processing scenario due to the addition of the bio-feedstock and the yield obtained in the reference scenario. \[f=\frac{\sum\left(Q_{co-out}^{k}\right)-Q_{f-out}}{\sum(Q_{co-out}^{k})} \tag{7}\]  
where:  
\(Q_{co-out}^{k}\) is the mass of k fuel output from co-processing unit  
\(Q_{f-out}\) is the is the mass flow of total fuel output from refining without co-processing (reference scenario)  
The yield factor of would be then applied to all outputs to calculate the production of the renewable fuels. Yield Method B: again it calculates a yield factor, but instead of applying a factor to the outputs, the factor is applied to the bio-inputs entering the co-processing system which establishes a known level of bio-output per unit of bio-input. It is found (via experimentation and again confirmed by 14C testing), that a set volume of biofuel is produced by a co-processing system for every tonne of (for example) vegetable oil hydrotreated. Ecofys [19] provides a similar example, where in a baseline scenario 100 kg of fossil feedstock is processed in a refinery unit, yielding 40 kg of gasoline and 50 kg of Diesel. Adding 10 kg of renewable feedstock (bio-oil) to the process increases the total gasoline yield to 42 kg and the Diesel yield to 55 kg. In this case, a yield factor of 4.8% (i.e., 2/42) would be applied to calculate the biogenic content of gasoline and a yield factor of 9.1% (i.e., 5/55) to calculate the biogenic content of Diesel. Additionally, once this yield factor is established, it can be applied to every tonne of the same type and standard quality of vegetable oil which is entering the same co-processing unit.