Keywords: mathematical modeling, kinetics, chemical reactors, catalysis, hydrocracking, paraffins The conversion of syngas through the Fischer - Tropsch (FT) process leads to the formation of products, essentially made up of a mixture of n-paraffins, which needs to be subjected to a hydrocracking process in order to improve both yields and cold flow properties of middle distillates. In this regard the development of a kinetic model of hydrocracking of FT products for simulation and optimization purposes is an important step.
An original model sufficiently nimble but able to represent in detail the yields in the various distillation cuts of interest (gasoline, kerosene, gasoil and residue ) and to take into account the variability of the factors (temperature, pressure, H2/wax ratio and WHSV) as considered in the experimental plan has been developed. Experiments were carried out in a continuous down flow trickle bed reactor while the operating conditions of temperature, pressure, H2/wax ratio and WHSV were changed according to a frequently used second order factorial design, the so called Central Composite Design. The range of the operating conditions was: temperature = 343-375 °C; pressure = 35-60 bar; H2/wax= 0.06-0.15 wt/wt; WHSV= 1-3 h-1.
Details of experimental set up procedure for hydroconversion test and methodology to investigate the effect of operating conditions are reported elsewhere.1
The mechanism assumed for hydrocracking and hydroisomerization reactions is represented in Figure 1:
Figure 1. Kinetic scheme
The kinetic expressions for isomerization and cracking are:2
For the physical adsorption on zeolites, Steijns and Froment3 justified the use of the Langmuir isotherm, which was preferred to other equations that could fit as well; the same isotherm has been used though, in our case, the catalyst is amorphous.
Moreover it has been supposed that molecules break giving rise to two chains with the same number of carbon atoms.
The proposed model is able to simulate the behavior of an isothermal plug flow reactor without axial or radial diffusion; this is in accordance with the experimental apparatus, a bench scale trickle bed reactor operated in down flow mode.
No effect due to macrokinetics (i.e. inter- and intra-phase diffusion) has to be taken into account because of the powdered catalyst.
In previous models4,5 the only presence of vapor phase was considered because vapor-liquid equilibrium calculations performed according to different equations of state (RK, SRK, etc.) show that inside the reactor and at the assigned operating conditions vapor phase is prevalent on a molar basis.
In the present model the simplifying assumption has been removed and V-L equilibrium is calculated at each integration step with the SRK equation of state (Figure 2):
Figure 2. Calculation scheme
Since the feed stream consists of n-paraffins in the range C4-C70 the critical properties are not available in literature and an original procedure has been developed for their calculation.6
Moreover the kinetic equations have been written as functions of the fugacity which, at equilibrium, is the same for both liquid and vapor. The whole set of balances that represent the system behavior (the equations for vapor and liquid phase can be summed up) is:
i = 4, 70
i = 3
i = 2
i = 1
i = 36, 70
i = 35
i = 5, 34
i = 4 where:
and:
The comparison between model results and experimental data shows a fairly good agreement. In particular the model is able to better account for the H2/wax ratio. References
(1) Pellegrini, L.; Calemma, V.; Clerici, G.; Benazzi, E. In: Chemical Engineering Transactions; Pierucci S. Eds; Vol. 3, 413; 2003.
(2) Froment, G. F. Kinetics of the hydroisomerization and hydrocracking of paraffins on a platinum containing bifunctional Y-zeolite. Catal. Today 1987, 1, 455.
(3) Steijns, M.; Froment, G. F. Hydroisomerization and Hydrocracking. 3. Kinetic Analysis of Rate Data for n-Decane and n-Dodecane. Ind. Eng. Chem. Prod. Res. Dev. 1981, 20, 660.
(4) Pellegrini, L.; Locatelli, S.; Rasella, S.; Bonomi, S.; Calemma, V. Modeling of Fischer-Tropsch Products Hydrocracking. Chem. Eng. Sci. 2004, 59, 4781.
(5) Pellegrini, L.; Bonomi, S.; Gamba, S.; Calemma, V.; Molinari, D. The “All Components Hydrocracking Model”. Chem. Eng. Sci. 2007, DOI: 10.1016/j.ces.2007.01.076 (in press).
(6) Correra, S.; Calemma, V. Waxy Stream Characterisation to Perform VLE Calculations in Hydrocracking Process. Proceedings of ICHEAP7, Taormina, Italy, 15th-18th May 2005.
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