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Licensed Unlicensed Requires Authentication Published by De Gruyter September 6, 2013

Optimization of Trickle-Bed Reactors (TBRs) for Hydrodesulfurization (HDS) and Hydrodearomatization (HDA) of Diesel using Single and Multiple Objectives

Bhadri Srinivas, Srikanth Karthik and B. Sankararao


This article describes the formulation, solution and analysis of two single-objective optimization and one multi-objective optimization (MOO) problems on trickle-bed reactors (TBRs) involving hydrodesulfurization (HDS) and hydrodearomatization (HDA). The model used by Chowdhury et al. (AIChE J 2002;48:26) for TBR involving HDS and HDA is used in this study, to solve these optimization problems. The correctness of algorithm and the numerical procedure used in this study to solve the model equations are validated with the results of Chowdhury et al. (AIChE J 2002;48:26), before the model is used for optimization. Objective functions chosen in our optimization studies are minimization of sulfur concentration and maximization of total conversion of aromatics at the exit of TBR. Decision variables considered are reactor temperature, reactor pressure and liquid hourly space velocity (LHSV). Two single-objective optimization and one MOO problems are formulated and solved using simple genetic algorithm (SGA) and NSGA-II, respectively, to obtain the optimal values of reactor operating conditions. Pareto set for the MOO problem is generated which show that conflicting nature of the objective functions. Specifically, we have shown that the simultaneous minimization of exit sulfur and maximization of aromatics removal conflict each other in hydrotreating.


Assumptions involved in deriving the mathematical model for HDS and HDA reactions in a TBR:

  1. 1.

    The reactor is operated isothermally under isobaric and steady-state conditions;

  2. 2.

    There is no axial diffusion of concentration and temperature, and also their variation along the radial direction within the reactor is neglected;

  3. 3.

    Gas and liquid flows are cocurrent. Gas and liquid velocities are constant throughout the reactor. Constant density of gas and liquid phases along the length of the reactor is assumed;

  4. 4.

    Evaporation of diesel oil occurs instantaneously only at the entrance of the reactor. The evaporation of the reacting components can be neglected due to their high molecular weights;

  5. 5.

    All interfacial concentrations are at equilibrium obeying the Henry’s law;

  6. 6.

    The adsorption coefficient, kad, of the H2S does not depend on temperature.

  7. 7.

    Aromatics consist of three groups, namely, mono-, di- and poly-aromatics. Tri-, tetra- and penta-aromatics belong to the poly-aromatic group. All the poly-aromatics are assumed to behave like tri-aromatic.

Model equations for simultaneous HDS and HDA reactions occurring in a TBR [1]:

Gas phase balances:

The mass balance equations for the gaseous components (H2, H2S) are:


Liquid phase balances:


Rate equations are defined by the following expressions:


Conversions of Ar-S and the mono-, di- and poly-aromatics at any point along the length of the reactor are calculated using the following expressions:



apSpecific surface area, m−1
Ar-SAromatic sulfur compound
CConcentration, kmol m−3
HHenry’s Law constant, MPa m3 kmol−1
ΔHHeat of reaction, kJ kmol−1
kReaction rate constant of desulfurization reaction, (m3)2.16 kg−1 kmol−1.16 s−1
k*Forward pseudo-first-order rate constant of dearomatization reactions, m3 kg−1 s−1
kBackward rate constant of dearomatization reactions, m3 kg−1 s−1
KDynamic equilibrium constant, dimensionless
kadAdsorption equilibrium constant, m3 kmol−1
klMass-transfer coefficient, m s−1
m1Order of desulfurization reaction with respect to aromatic sulfur compounds
m2Order of desulfurization reaction with respect to hydrogen
MMolecular weight of diesel oil, kg kmol−1
PRReaction pressure, MPa
QVolumetric flow rate, m3 s−1
RGas-law constant, kJ kmol−1 K−1
rRate of heterogeneous reaction, kmol kg−1 s−1
TTemperature, K or °C
uSuperficial velocity, m s−1
VVolume, m3
XFractional conversion, dimensionless
zAxial coordinate along the length of the reactor, m
Greek symbols
εVoid fraction, dimensionless
ξFractional volume of catalyst in the reactor, [Vcat/(Vcat + Vinert)], dimensionless
ρDensity of diesel oil feed, kg m−3
ρbBulk density of the catalyst, kg m−3
catof catalyst
Diof di-aromatic
gof gas phase
H2of hydrogen
H2Sof hydrogen sulfide
inertof inert
lof liquid phase
MeABPMean average boiling point
Monoof mono-aromatic
Naphof naphthene
Polyof poly-aromatic
Rof reactor
Totof total aromatic
0initial condition
lliquid phase


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Published Online: 2013-09-06

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