## 3 Results and Discussion  
The use of SRK, PR, or PSRK EoS gave slightly different, but qualitatively the same, numerical results, so the relevant results are provided using PSRK EoS only. As the first main result, the stream leaving the system from the RGibbs block has the same composition, enthalpy, and any other property in all arrangements and regardless of the decomposition carried out in the RYield. Therefore, it is not necessary to exactly specify all the chemical species present in the feed stream to perform the method based on the minimization of the total Gibbs free energy of the system, and only the mass composition of the elements constitutive of the biomass (mainly, C, H, O, N, Cl, and S) is required. This result can be explained by the way the method works. The key lies in how the stream leaving the RGibbs block is calculated: An expression of the total Gibbs free energy of the system is implemented, accounting for the number of moles of reactants, products, and inert compounds (i.e., all species present) in all phases, so the number of moles of each species in each phase subject to the stoichiometric constraints is varied until a solution is found that minimizes the total Gibbs energy of the system to achieve chemical equilibrium between reactants and products. This is typically accomplished using the Lagrange multipliers method. It might seem that because the formation free energy and fugacity coefficients of all the compounds, present in both the feed and the product of the reactor, are required to compute their chemical potentials in the minimization of the Gibbs free energy method, the feed entering the RGibbs block would change the composition of the stream leaving the reactor. However, this is not the case, and by using the elemental analysis as the input, the result is the same if the mass of chemical elements in the feed is conserved. The composition of the stream leaving the RGibbs block is always the following for all arrangements (kg/h): H\({}_{2}\), 99.0; CO, 221.3; CO\({}_{2}\), 1025.4; CH\({}_{4}\), 21.7; N\({}_{2}\), 7.5; NH\({}_{3}\), 0.5; H\({}_{2}\)O, 8589.6. In the ash separator, 35 kg/h of ash is removed from the biomass entering the reactor. This method is a nonstoichiometric approach in which no reactions are provided and no equilibrium constants are used. Because only equality constraints (conservation of the atoms of the elements present in the feed) are involved in the minimization problem, the solution can be obtained by adding as many Lagrange multipliers as there are elements present in the feed. They represent the element potentials [43; 44; 45] in such a way that the chemical potential of a component is just the sum of the products of the element potentials multiplied by the number of element moles present in its chemical formula. Thus, each atom of a given element adds the same amount to the Gibbs free energy of the system, regardless of the molecule or phase in which it is present. Therefore, the only unknown variables of the problem are these multipliers, along with the total number of moles in each phase at the given temperature (T) and pressure (P), irrespective of the number of chemical species present. Chemical reactions make the system components not independent, and, by the Gibbs phase rule, a minimum number of components leads to a minimum number of independent reactions. The former corresponds to the number of elements present in the feed along with the dominant species in equilibrium. More components involve more reactions, but the number of degrees of freedom is the same, thus explaining the result obtained in the simulation. Table 1 illustrates the validation of the model used in the simulation, as described in the previous section, when the biomass is glycerol with the same concentration used in this paper and using an Ni-based catalyst with a space velocity of 5 h\({}^{-1}\) at 800 \({}^{\circ}\)C. Note that the experimental data match the equilibrium very well.