# Modeling and Kinetic Study of an Ebullated Bed Reactor in the H-Oil process

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## Abstract

The present work was devoted to investigate the kinetic behavior of an industrial-scale ebullated bed reactor, licensed by Axens Co., in Lukoil refinery at Bourgas, Bulgaria. Another objective of the present work is to formulate a steady state mathematical model to predict the profile of products along the reactor, and to investigate effects of the operating variables [e.g., operating temperature, weight hour space velocity (WHSV), and reaction time] on the kinetic parameters, and performance of the industrial ebullated bed reactor. A five-lump kinetic model was utilized to describe the catalytic hydrocracking of heavy oil and to formulate the reaction rate equations of the main components of heavy oil. The formulated model was validated by comparing its outcome with experimental measurements of fractions of VR, VGO, and N at the effluent of industrial reactor against residence time. Results revealed an opposite relationship of the effectiveness factor with both temperature and WHSV. Results showed that the activation and deactivation energies were approximately equal, indicating that catalyst deactivation has no appreciable effect on the hydrocracking reactions in the ebullated bed reactor. The hydrocracking reactions of vacuum residue to lower molecular weight components are preferentially obtained in the following descending order: VGO; middle distillates; naphtha; gases. WHSV has a negative effect on the yield of the industrial reactor while the trend was different with the operating temperature. Outcomes of the formulated model were compared with the data reported in the literature.

## Keywords

Ebullated bed reactor Reaction pathways Mathematical model Heavy oil Hydroprocessing H-oil unit## Abbreviations

- \(C_\mathrm{s,i}\)
Concentration of component i on catalyst surface, kg kg-cat\(^{-1}\)

- \(C_\mathrm{b,i}\)
Concentration of component i in the bulk, kg \(\hbox {m}^{-3}\)

- \(D_\mathrm{c}\)
Reactor diameter, m

- \(D_{\mathrm{e}}\)
Effective diffusivity, \(\hbox {m}^{2 }\,\hbox {s}^{-1}\)

- \(E_\mathrm{A}\)
Apparent activation energy, kJ \( \hbox {mol}^{-1}\)

- \(g_{\mathrm{i},0}\)
Content of fraction i in the feed flow rate, kg \(\hbox {s}^{-1}\).

- \(g_\mathrm{i}\)
Content of the fraction i (gases, naphtha, middle distillates, or vacuum gas oil) in the product, \(\hbox {kg}\,\mathrm{s}^{-1}\)

- \(g_{\mathrm{T,o}}\)
Total amount of reactants entering the reactor, kg \(\hbox {s}^{-1}\)

- \(k_\mathrm{c}\)
Fluid-particle mass transfer coefficient, m \(\hbox {s}^{-1}\)

- \(k_\mathrm{d}\)
Deactivation rate constant, \(\hbox {s}^{-1}\)

- \(k_\mathrm{o}\)
Overall constant of hydrocracking reaction, \(\hbox {s}^{-1}\)

- \(k_\mathrm{i}\)
Reaction rate constant of i pathway, \(\hbox {s}^{-1}\)

*I*Deactivation rate order

- \(m^{\bullet }\)
Initial mass flow rate, kg \(\hbox {h}^{-1}\)

*n*Order of reaction rate

- \(r_\mathrm{s}\)
Radius of particle, m

- \(r_\mathrm{i}\)
Reaction rate of the fraction i (gases, naphtha, middle distillates or vacuum gas oil) \(\hbox {kg}_{\mathrm{reacted}}\,\hbox {kg}^{-1}_{\mathrm{cat}}\) s

*R*Universal gas constant (= 1.987), kcal mol\(^{-1}\) K

*t*Time, h

*T*Temperature, K

*W*Weight of catalyst used, kg

*Y*Total conversion

- \(w_\mathrm{i}\)
Composition of component i in product

- \(w_{i,o}\)
Initial composition of component i in feed

## Greek letters

- \(\lambda \)
Catalyst deactivation function

- \(\xi \)
Catalyst effectiveness factor

- \(\varepsilon \)
Thiele modulus

- \(\sigma \)
Gas–liquid surface tension, kg \(\hbox {s}^{-2}\)

- \(\gamma _{0}\)
Specific gravity

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## Notes

### Acknowledgements

The authors gratefully acknowledge the Petroleum Research and Development Center, Ministry of Oil, Iraq, in sponsoring the work (Grant Number {3721/15-8-2013}). Thanks are also due to the representatives of Axens Co., for their valuable assistance on the field of Lukoil refinery.

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