Calculate the amount \((\mathrm{kg})\) of \(\mathrm{H}_{2}\) needed per \(\mathrm{kg}\) product for complete deoxygenation of pyrolysis oil and discuss the economics of the process based on this number.

Pyrolysis oil typically has a composition containing oxygen, carbon, and hydrogen. For this exercise, we will assume that all oxygen in pyrolysis oil is present as C-OH (hydroxyl) groups. The overall reaction for complete deoxygenation can be simplified as: Oxygen in the form of C-OH + H2 -> H2O + Carbon residue Since we are dealing with pyrolysis oil, empirical formulae can be used to represent its composition. A common empirical formula is CH1.8O0.27, representing the oxygen content of 27% in the oil. We will now balance the equation: CH1.8O0.27 + H2 -> 0.27H2O + CH1.53 The balanced equation has a stoichiometric ratio of 1 mole pyrolysis oil to 0.27 moles of H2.

To convert the stoichiometric ratio into a mass ratio, we need the molar mass of pyrolysis oil and hydrogen. Molar mass of H2 = 2 g/mol (since there are 2 hydrogen atoms per H2 molecule) Molar mass of CH1.8O0.27 (pyrolysis oil) = (12.01 × 1) + (1.01 × 1.8) + (16 × 0.27) = 12.01 + 1.818 + 4.32 = 18.148 g/mol

Using the balanced equation from Step 1 and the molar masses from Step 2: mass of H2 per 1 mol pyrolysis oil = 0.27 mol × (2 g/mol) = 0.54 g mass of pyrolysis oil = 18.148 g Thus, the mass ratio of hydrogen to pyrolysis oil is: 0.54 g H2 / 18.148 g pyrolysis oil

To calculate the amount of H2 needed per kg of product, we will use the mass ratio calculated in step 3: (0.54 g H2 / 18.148 g pyrolysis oil) * (1 kg pyrolysis oil / 1000 g) = (0.54 / 18.148) kg H2 = 0.02976 kg H2 Therefore, 0.02976 kg of hydrogen is needed per kg of product for complete deoxygenation of pyrolysis oil.

Based on our calculations, 0.02976 kg of hydrogen is needed per kg of product to completely deoxygenate pyrolysis oil. The cost of hydrogen production varies depending on the method used, but it is generally in the range of \(1.50 - \)6.00 per kg of hydrogen. Thus, the hydrogen cost for deoxygenating 1 kg of pyrolysis oil could range from \(0.04464 to \)0.17856. This cost should be compared with the price of the final product and other costs involved in the production process to determine the economic viability of this deoxygenation process. It is important to consider that the cost of hydrogen production may decrease in the future as renewable hydrogen production technologies are developed and commercialized, which may improve the economics of this process.