Abstract
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.
Appendix
Assumptions involved in deriving the mathematical model for HDS and HDA reactions in a TBR:
- 1.
The reactor is operated isothermally under isobaric and steady-state conditions;
- 2.
There is no axial diffusion of concentration and temperature, and also their variation along the radial direction within the reactor is neglected;
- 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.
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.
All interfacial concentrations are at equilibrium obeying the Henry’s law;
- 6.
The adsorption coefficient, kad, of the H2S does not depend on temperature.
- 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:
Nomenclature
| ap | Specific surface area, m−1 |
| Ar-S | Aromatic sulfur compound |
| C | Concentration, kmol m−3 |
| H | Henry’s Law constant, MPa m3 kmol−1 |
| ΔH | Heat of reaction, kJ kmol−1 |
| k | Reaction 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 |
| k– | Backward rate constant of dearomatization reactions, m3 kg−1 s−1 |
| K | Dynamic equilibrium constant, dimensionless |
| kad | Adsorption equilibrium constant, m3 kmol−1 |
| kl | Mass-transfer coefficient, m s−1 |
| m1 | Order of desulfurization reaction with respect to aromatic sulfur compounds |
| m2 | Order of desulfurization reaction with respect to hydrogen |
| M | Molecular weight of diesel oil, kg kmol−1 |
| PR | Reaction pressure, MPa |
| Q | Volumetric flow rate, m3 s−1 |
| R | Gas-law constant, kJ kmol−1 K−1 |
| r | Rate of heterogeneous reaction, kmol kg−1 s−1 |
| T | Temperature, K or °C |
| u | Superficial velocity, m s−1 |
| V | Volume, m3 |
| X | Fractional conversion, dimensionless |
| z | Axial coordinate along the length of the reactor, m |
| Greek symbols | |
| ε | Void fraction, dimensionless |
| ξ | Fractional volume of catalyst in the reactor, [Vcat/(Vcat + Vinert)], dimensionless |
| ρ | Density of diesel oil feed, kg m−3 |
| ρb | Bulk density of the catalyst, kg m−3 |
| Subscripts | |
| cat | of catalyst |
| Di | of di-aromatic |
| g | of gas phase |
| H2 | of hydrogen |
| H2S | of hydrogen sulfide |
| inert | of inert |
| l | of liquid phase |
| MeABP | Mean average boiling point |
| Mono | of mono-aromatic |
| Naph | of naphthene |
| NTP | at NTP |
| Poly | of poly-aromatic |
| R | of reactor |
| Tot | of total aromatic |
| 0 | initial condition |
| Superscript | |
| l | liquid phase |
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