(203j) Shortcoming of Feasibility Analysis Methods for Reactive Distillation Processes

Shortcoming of Feasibility Analysis
Methods for Reactive Distillation Processes

Reactive distillation
process is a highly integrated unit operation and has shown its significant
advantages in chemical industry due to the combination of reaction with distillation
separation (Sharma and Mahajani, 2003). So far, a lot of works have been
carried out for the purpose of both fundamental understanding and industrial
application of the reactive distillation. Generally, the coupled kinetic-thermodynamic
feasibility analysis is the first step to develop a new reactive distillation
process (Almeida-Rivera et al., 2004; Gadewar et al., 2004; Malone and Doherty,
2000). The main reason is that it is considered to be helpful to decide the
theoretical feasibility of the process and provide necessary information for
further conceptual design and experimental verification if the process is
feasible (Subawalla and Fair, 1999; Tang et al., 2005). With regard to the
importance of feasibility analysis, various models with different
simplifications and abstractions of real reactive distillation processes have
been proposed
and developed to acquire as much as possible information, for
example, the
continuous multiphase reactor model, the reactive flash-cascade model
and the singular point equations established by Qi et al. (2004).

An
important aim of this work is to evaluate the
effect of results from feasibility analyses on the design of reactive
distillation processes. For a non-reactive distillation process, it has been
recognized that feasibility analysis methods can give the discharge composition
of distillation column with an infinite separation power. The information on
the maximum separation degree is very helpful to determine the feasibility of
distillation separation and further design the distillation process. However, there is no systematic discussion on whether
feasibility analysis methods can predict the maximum separation degree of a real
reactive distillation process or not.

For this
purpose, a infinity/infinity analysis method for reactive distillation
processes is established in this work to calculate the maximum separation
degree of a reactive distillation process. Eqs. (1-3) for the infinity/infinity
analysis are obtained after mathematic simplifications of the mass and enthalpy
balance equations of a reactive distillation column. With phase equilibrium
equations and relationships between flow rates, they could be employed to calculate
the discharge composition at the top and bottom.

                                                              (1)

 (2≤n≤N-1)    (2)

                                                           (3)

Because
the vapor flow rate V_n in the above equations should keep unchanged
to meet both of the enthalpy balance and overall mass balance equations, the Damköhler
number Da_col,n,j=k_f,jm_cat,n/V_n
can be a constant as the only parameter required in the infinity/infinity
analysis when the catalyst amount m_cat,n on every reactive
tray is the same. It is an important feature of this method developed in this
work, which can provide reasonable comparison with the feasibility analysis
models.

In order
to compare with the infinity/infinity analysis method with single mole-based
parameter, the reactive flash-cascade model presented in Chadda et al.'s work
(2001), which used a mass-based vapor fraction as one of two parameters for the
non-equimolar reaction case, needs to be rebuilt by one only mole-based
parameter. Eqs. (4) and (5) are the fixed-point equations of the rebuilt reactive
flash-cascade
model with Da_s,n,j=k_f,jm_cat,n/V_n and Da_r,n,j=k_f,jm_cat,n/(V_n-1-V_n) (for
convenience the subscript 'n' has been removed).

                                                                    (4)

                                                                     (5)

The condition to determine whether
the reactive flash-cascade model can predict the maximum separation degree of a
real reactive distillation process or not could be further derived by comparison
among Eqs. (1-5). Firstly, assumed that the feasibility analysis method can
predict the maximum separation degree achieved through distillation for a
certain reactive system, it suggests that the possible discharge composition at
the column bottom should meet both of Eq. (1) from the infinity/infinity
analysis method and Eq. (4) from the feasibility analysis method (because the infinity/infinity
analysis method can always give the maximum for any reactive system). The two equations are rewritten
with the new subscript under a fixed Damköhler number,

                                                                          (6)

                                                                     (7)

Because  is always
less than 1 on the basis of the mass balance equations of reactive distillation
column, a relation x_i,N-1=x_i,N=x_i can be obtained from
subtracting Eq. (6) and Eq. (7). It suggests that the compositions on the last
tray and the reboiler from the infinity/infinity analysis for the reactive
system should be the same. According to the relation and the mass balance
equations in the infinity/infinity analysis, another equality x_i,N-2=x_i,N-1=x_i
should also hold true for the compositions from the infinity/infinity analysis.
In this case, Eqs. (1) and (2) from the infinity/infinity analysis method can
be simplified to Eqs. (8) and (9) (the subscript 'N' in these equations has
removed for convenience).

                                                                                        (8)

                                                                                    (9)

Furthermore,
Eq. (10) is derived. The same
equation describing the
characteristics of singular points at column top can also be drawn from Eq. (3) in the infinity/infinity
analysis method
and Eq. (5)
in the feasibility analysis method.

                                                                                                       
 (10)

Eq. (10)
states that it is nearly impossible that the composition point predicted by the
reactive flash-cascade model appears at the bottom or top of the reactive
distillation column with an infinite separation power when it is not a pure
component or a common azeotrope under chemical equilibrium. In
this situation, it is
more likely to appear in the reactive distillation column with a specific separation
power and feeding way. In other words, the reactive flash-cascade model shows a
shortcoming with regard to predicting a too low separation degree.

Although
this conclusion is obtained by the only comparison between the reactive
flash-cascade model and the infinity/infinity analysis method, it still applies
to other feasibility analysis methods, for example, Qi et al.'s method (2004),
where the composition equation of singular points at column bottom has the same
form with Eq. (1). However, the discharge composition of column top need be
calculated by Eq. (11) with the different form from Eq. (2). In Eq. (11), Da_REACL,,j=
k_f,jm_cat/L.

                                                      
(11)

In order to
determine whether Qi et al.'s method has the same shortcoming referred above or
not, the mathematic relationship between the results from the Qi et al.'s model
and reactive flash-cascade model needs to be established at first. In modeling
the rectifying section of reactive flash-cascade, the mass balance equations
can be simplified by two different ways. As the result of the other
simplification, Eq. (12) can also be used to calculate the possible discharge composition
at column top, where Da^*_r,n,j=k_f,jm_cat,n/L_n.
It has the same equation form with Eq. (11), which indicates that the two
equations with the same parameter value could have the same calculated results.

                                                                
(12)

The
relationship between Da_r,n,j in Eq. (5) and Da^*_r,n,j
in Eq. (12) can be determined on the basis of the relation  from the mass balance of
the rectifying section: . This relationship indicates that Qi
et al.'s method can predict the same discharge composition at column top to the
reactive flash-cascade model when the parameters in these two methods meet Eq.
(13).

                                                                  
     (13)

These
analyses suggest that the compositions of singular points predicted by the two
different feasibility analysis models should have the same changing path with
the increase of Da and the difference between results
from the two models is only from the different definitions of the model
parameter Da. Furthermore, it is obviously that Qi et al.'s
method also has the
same shortcoming with regard to predicting the discharge composition point with
a too low separation degree.

Although
the shortcoming of feasibility analysis methods suggests the less help to
determine the feasibility of reactive distillation processes, especially the
feeding ratio of reactants, the inconsistence between the results from the two
types of analysis methods indicates that the separation degree predicted by
feasibility analysis methods is hopeful to be broken through in a real reactive
distillation column by higher reflux ratio or more theoretical plates. For the etherification
of cyclohexene as a ternary reactive system, the feasibility analysis indicates
that the stable singular point of the column top is always the ternary mixture containing
the product (cyclohexyl
formate)
at . However, the rigorous design
work of Katariya et al. (2009) indicated that the product barely
exists in the top discharge under total reflux that means the infinite separation
power.