(91f) 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 Guo²

(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_i and distillation phase x^D_i)
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.

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

           (1)

¢Ú Equation of phase equilibrium

                             
(2)

¢Û Equation of mass balance in the
liquid phase

                  
  (3)

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

¢Ü Equation of reaction kinetics

                            
(4)

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.

                          
(5)

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

                      
(6)

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.