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262264 Study On Multi-Scale of Composition in a Reactive Distillation Column for Gasoline Desulfurization

Study on Multi-scale of Composition in a Reactive Distillation column for Gasoline Desulfurization

Yonghong Li^{1,2}, Benshuai Guo^{2}

(1) National Engineering Research Center for Distillation Technology, Tianjin, China

(2) School of Chemical Engineering and Technology, Tianjin University, Tianjin, China,

**1 Introduction**

Reactive distillation (RD) is one of the important methods of process intensification in chemical engineering, as it has great potential to lower process costs and reduce environmental emissions. The RD residue curve maps are highly useful tools to visualize and elucidate conceptual designs of reactive distillation processes [1]. However, present computation of reactive residue curve assumes the homogeneous composition in the liquid phase, which would neglect the multi-scale structure of the reactive distillation system. As traditional mean filed (MF) models cannot always accurately capture the complex dynamics possibly resulting in lack of understanding of the interactions underpinning the system [2], a multi-scale model is required to analyze the reactive distillation system. The objective of this work is to study the muti-structure of a reactive distillation process with heterogeneous catalyst.

**2 Muti-scale analysis**

**2.1 ****Macro-scale analysis**

Considering a simple reactive batch
distillation process, assuming that only one reaction occurs in the liquid
system, the equations for computation of the reactive residue curves are written as^{ }[3]

_{
}*i *=1,2,3, ......

The mole fractions of component *i* in the liquid phases and in vapor phases should be obtained with respect to "warped" time *¦"* by solving the above Equations.

**2.2 ****Micro-scale analysis**

Considering an lighter reactant molecule in the solution of the reactive distillation system, it has two paths to undergo°ª°ªbe transferred to the gas phase or participate the reaction. The two control mechanisms in the micro-scale suggest that the reactive distillation couldn't be described thoroughly in the view of macro-scale, for it neglects the competition of the reaction and distillation in the micro-scale. Therefore, a meso-scale description is needed to relate the micro-scale and macro-scale.

**2.3 ****Meso-scale analysis**

According to the different paths of
micro-scale molecules, the homogenous liquid phase (*x _{i}*) in the macro-scale is divided into two
phases (reaction phase

*x*

^{R}

*and distillation phase*

_{i}*x*

^{D}

*) in the meso-scale. Here the concept phase is different from that in the thermodynamics, and it refers to the set of molecules with different behaviors.*

_{i}**3 The multi-scale model**

For a batch distillation system with one heterogeneous reaction, the multi-scale model proposed in our work can be described as follows:

¢Ù Equation of mass balance in the system

_{
}

¢Ú Equation of phase equilibrium

_{
}

¢Û Equation of mass balance in the liquid phase

_{
}

where *¦Å *is the mole ratio of the distillation phase.

¢Ü Equation of reaction kinetics

_{
}

The distribution of the distillation
phase and reaction phase is determined by their time and space. For the entire
system, the reaction and distillation have equal time (*t*_{D}=*t*_{R}).
The space of distillation and reaction (*V*_{D}
and *V*_{R}) can be described
by the multiple of the film thickness *¦Ä*
and surface area *a* respectively. The
film thickness of the reaction space and distillation space can be assumed to
be equal, as they are both decided by the flow conditions of the liquid.
Therefore, the distribution of the reaction phase and distillation phase can be
determined by the surface area of reaction space and distillation space.

_{
}

It is hard to derive this relation
theoretically, so we use the adsorption of component *i* in the liquid phase on a heterogeneous catalyst for reference. As
adsorption is a step of heterogeneous reaction, it is reasonable to use the
relation of *¦È _{i}*
with

*C*to describe the relation of concentration between the reaction phase and distillation phase.

_{i}_{
}

However, the sum up of *x*^{R'}* _{i}* computed by equation (6) is not equal to 1, for the presence
of unoccupied activity sites on the catalyst. Therefore, the mole fraction of
reaction phase computed from equation (6) has to be normalized.

Based on the above analysis of reactive distillation with heterogeneous catalyst, a general conclusion could be derived: for a system with two control mechanisms, a multi-scale model is needed to give a detail description. Both the competition in the micro-scale and the compromising in the macro-scale should be included in the multi-scale model, and the bridge between the micro-scale and the macro-scale could be established by a meso-scale description.

Therefore, the key of multi-scale modeling for a system with two control mechanisms is to establish a meso-scale description, which on one hand needs to represent the competition between different mechanisms in the micro-scale, and on the other hand needs to be related with the composition in the macro-scale.

**4 Analysis of particle-fluid system**

Circulating fluidized beds have been used in a variety of industrial plants. As a typical example of complex system, extensive research has been carried out both experimentally and theoretically. Li [4] proposed an energy-minimization multi-scale (EMMS) model for CFB, based on the division of the flow system into dense phase and dilute phase.

Considering the heterogeneous structure of CFB, Li divided the flow system in to a gas-rich dilute phase and a solid-rich dense phase, and attributed the poor performance of predicting to the false assumption of the mean field of drag coefficient. He defined different drag coefficients for the dense phase, dilute phase and inter phase and established the stability conditions for particle-fluid system.Here we would like to illustrate the complexity of the particle-fluid system from the view of control mechanisms. In the macro-scale, the flows of particle and fluid are compromised. However, considering an element of one particle and little fluid in the micro-scale, there are two different control mechanisms-the behaviors of the element could be controlled by either the particle or the fluid, which would have a competition between each other, and this competition is not represented in the conventional macro-scale equations for describing the dynamics of CFB.

Therefore, meso-scale description is needed to bridge the gap of macro-scale and micro-scale. The competition of different control mechanisms leads to the two phases (dense phase and dilute phase) in the meso-scale, and the compromising of particle and fluid in the macro-scale could be derived from the equations of mass balance. Besides, the stability conditions are the expression of the control mechanisms, one dominated or compromising with each other.

**5 Conclusion**

There is a contradiction between macro-scale description of reaction distillation and the competition of the molecular motion in micro-scale. To establishe a multi-scale model for a system of gasoline desulfurization in a RD column, the liquid phase should be divided into reaction phase and distillation phase in the meso-scale according to the control mechanisms of the molecular motion in the micro-scale.

**Acknowledgments**

We aregratefultotheFundof National NaturalScience Foundation ofChina (No. 20976129) and the Program of Universities' InnovativeResearchTerms (No. IRT0936) for financial support.

**References**

[1] C.Thiel, K. Sundmacher, U. Hoffmann. Chem. Eng. J. 66 (1997) 181-191.

[2] H. Bostjan, T. Constantinos. AIDIC Conference Series (2009) 167-176

[3] A.S. Granados-Aguilar, T. Viveros-Garc¨ªa, E.S. P¨¦rez-Cisnero. Chem. Eng. J. 143 (2008) 210-219.

[4] J. Li, W. Ge, J. Zhang, M. Kwauk. Multi-Scale Comromise and Multi-Level Correlation in Complex Systems--Challenges and opportunities for Chemical Engineering. Keynote speech at the 7th World Congress of Chemical Engineering, Glasgow, Scotland, 2005,10-14.

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