Biomass don't have C, it has sugars (C6O6H12, mostly polymerized) and fatty acids (H-(CH2)n-COOH, mostly in oil molecules).
Do you have the chemical composition of the bio-oil? I only found this https://www.music-h2020.eu/publications-reports/MUSIC_D6-1_W... that in page 20 claims 25% of water, so it's a polar solvent like thick sugar syrup, not a non polar solvent like petrol.
That make sense if the graphics are accurate and it's produced from corn stalks (that are mostly cellulose that is polymerized glucose), instead of making it from vegetable oil (that is made of 3 fatty acids and glycerin) and can be transformed in biodiesel by a very different process.
The graphic shows injection after use to make iron. Are you injecting the liquid bio-oil or the CO2 gas after combustion? I very skeptical and expect gas to escape sooner or later.
I think that it's important the "unused carbon" part of the graphic. Here we used to have a big steel mill that had a huge eucalyptus forest to make coke coal (in Spanish) https://es.wikipedia.org/wiki/Aceros_Zapla
C in biomass is converted to C in bio-oil, with relatively small release of CO₂
C in bio-oil is injected deep underground for permanent storage/sequestration
If this process had not happened, the C in the biomass would have been entirely emitted as CO₂ through rotting or burning.