Scheme 1 the DBT HDS reaction routes
HDS reaction for DBT is generally considered as a pseudo-first-order, the HDS rate constant kHDS is obtained by the equation as follows:
kHDS =\(\ \frac{F}{m}\ \)ln (\(\frac{1}{1-\tau}\)) (4)
in which F is the feeding rate of DBT reactant with the unit of mol h-1, m is the mass of loading catalyst with the unit of g, and τ is the conversion of DBT reactant.[19]
The formula system according to the reaction mechanism of Scheme 1 is shown in equation 1 to equation 3, in which cn and rn represent the molar concentration of species n (n=Ⅰ,Ⅱ, Ⅲ and Ⅳ) and the reaction rate. ki represent the reaction rate constants for each steps in Scheme 1, which include kDDS, kHYD and kDS. The DBT HDS conversions lower than 35% are applied to calculate the above reaction rate constants.
r= -(kHYD+kDDS) C (5)
r= kDDS C (6)
r= kHYDC-kDSC (7)
r= kDS C (8)
The DBT HDS rate can also be indicated by turnover frequency, TOF (h-1), which is calculated by the following equation:
TOF = (F×τ) / (nMo×fMo) (9)
where nMo is molar quantity of Mo atoms in the catalysts. τ and fMo are in consistent with the above definitions.[12]
Moreover, the Arrhenius and Eyring equations could be used to obtain the activation parameters by draw the figures of ln kHDS vs 1/T, and ln(kHDS/T) vs 1/T.[20,21]
ln kHDS = ln A- (Ea/RT) (10)
ln (kHDS/T) = ln (kB/h) + ( S/R) - ( H/RT) (11)
In the above two equations, Ea is the activation energy with the unit of kJ·mol-1, kB is Boltzmann’s constant of 1.381×10–23 J·K-1, h is Planck’s constant of 6.626×10–34 J·s, ΔS is the activation entropy with the unit of J mol–1·K–1, ΔH is the activation enthalpy with the unit of kJ·mol–1, and R is the ideal gas constant of 8.314 J·K–1·mol–1.