Scale-Up of Kinetic Data

A useful method to handle this problem is to measure kf at various liquid rates, and if possible, at two reactor scales, and fitting the data to the following empirical equation (Bondi, 1971)  

Equation 8.19 provides a relationship in which the apparent rate coefficient approaches that of particle kinetics as superficial liquid mass velocity (G ) goes to infinity, with fitting parameters A and B. For a number of systems, the value of exponent B typically falls between 0.5 and 0.7, more commonly 2/3. The particle rate constant is approximated in the form of II kf by extrapolation to infinite superficial liquid mass velocity (intercept on the y-axis). For this case, the procedure was applied using the information from the LHSV bench-scale experiments and from a semi-industrial scale test ( 10 BPD plant). 

Deactivation of heavy oil hydroprocessing catalysts is driven by two factors coking and metals buildup. It is well documented that coke formation is responsible for the rapid initial activity decay, which occurs during the first hours of operation (generally the first 100 h) and then apparently reaches equilibrium, whereas metals are accumulated during the whole cycle in a linear fashion (Furimsky and Massoth, 1999 Sie, 2001). The contribution of these two processes to the global catalyst deactivation rate can be expressed as follows  

The effect of these two processes on catalyst activity is modeled according to the following empirical expression (Alvarez et al., 2011)  

The first term of Equation 8.21 is a hyperbolic function that represents the rapid initial activity decline as a function of time t with fitting parameters and for reaction j. As stated in the list of assumptions, it is considered that this happens during the first 100 h of operation, and after this time period the initial deactivation period is over, which means that the value of this function is constant for the rest of the operation cycle. 

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