Kenig ey chemical product and process modeling advanced modeling of reactive separation units with structured packings vol2 iss1

Chemical Product and Process
Modeling
Volume 2, Issue 1

2007

Article 5

Advanced Modeling of Reactive Separation
Units with Structured Packings
E. Y. Kenig∗

∗

Univ Dortmund,

Copyright c 2007 The Berkeley Electronic Press. All rights reserved.


Advanced Modeling of Reactive Separation
Units with Structured Packings
E. Y. Kenig

Abstract
Reactive separations combining mass transfer with simultaneous chemical reactions within
a single column unit provide an important synergistic effect and bring about several advantages.
The influence of column internals in reactive separations increases significantly, because these internals have to enhance both separation and reaction and maintain a sound balance between them.
To solve this problem, a novel generation of column internals with enhanced mass transfer performance and low pressure drop has been created. Among them, corrugated packings of the regular
type or structured packings have gained a wide acceptance.
This paper gives a state-of-the-art review of the structured packings modeling methods, focusing on two innovative and particularly promising approaches. The first of them is based on the
application of CFD, whereas the second one employs the idea of hydrodynamic analogy between

complex and simple flow patterns. Both approaches are illustrated with several case studies.
KEYWORDS: reactive separations, structured packings, mass transfer, CFD, hydrodynamic analogies


Kenig: Modeling of Reactive Separation Units with Structured Packings

INTRODUCTION
Manufacturing of chemical products from selected feed stocks is based on a
variety of chemical reactions. The reaction extend is often limited by the chemical
equilibrium between the reactants and products, thus reducing the conversion and
selectivity towards the main product. The process must then include the
separation of the equilibrium mixture and recycling of the reactants.
Conventionally, each unit separation operation is performed in individual
items of equipment, which, when arranged together in sequence, make up the
complete process plant. As reaction and separation stages are carried out in
discrete equipment units, their equipment and energy costs are added up.
However, in recent decades, a combination of separation and reaction inside a
single unit has become more and more popular. The potential for capital cost
savings is obvious; besides, there are often many other process advantages that
accrue from such combinations (Noble, 2001). Therefore, many new processes
called reactive separations (RS) have been invented based on this integration
principle (see, e.g., Doherty and Buzad, 1992; Zarzycki and Chacuk, 1993; Agar,
1999; Bart, 2001; Noeres et al., 2003; Stankiewicz and Moulijn, 2003;
Sundmacher et al., 2005; Schmidt-Traub and Górak, 2006).
Among the most important examples of RS processes are reactive
distillation, reactive absorption, reactive stripping and reactive extraction. For
instance, in reactive distillation, reaction and distillation take place within the
same zone of a distillation column. Reactants are converted to products with
simultaneous separation of the products and recycle of unused reactants. The
reactive distillation process can be both efficient in size and cost of capital

equipment and in energy used to achieve a complete conversion of reactants.
Since reactor costs are often less than 10% of the capital investment, the
combination of a relatively cheap reactor with a distillation column offers great
potential for overall savings. Among suitable reactive distillation processes are
etherifications, nitrations, esterifications, transesterifications, condensations and
alcylations (Doherty and Buzad, 1992).
As a rule, RS occur in moving systems, and thus the process
hydrodynamics plays an important part. Besides, these processes are based on the
contact of at least two phases, and therefore, the interfacial transport phenomena
have to be considered. Further common features are multicomponent interactions
of mixture components, a tricky interplay of mass transport and chemical
reactions, complex process chemistry and thermodynamics.
For all these reasons, the design of RS columns is more sophisticated than
that of traditional operations. Above all, the influence of column internals
increases significantly. These internals have to enhance both separation and
reaction and maintain a sound balance between them. This represents a

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Chemical Product and Process Modeling, Vol. 2 [2007], Iss. 1, Art. 5

challenging task, since effective separation requires a large contact area, whereas
effective reaction strives for a significant amount of catalyst.
To solve this problem, a novel generation of column internals, corrugated
packings of the regular type, also referred as structured packings (SP), has been
created. These packings provide enhanced mass transfer performance with
relatively low pressure drop and, consequently, have gained a wide acceptance.

Since the early 1980s, when corrugated sheet metal SP appeared on the market,
great advances toward the process intensification have been made. Being initially
developed for separation of thermally unstable components in vacuum distillation,
structured packings have permanently been gaining in popularity and cover a
large field of applications in chemical, petrochemical and refining industries due
to their more effective performance characteristics (Shilkin et al., 2006).
For heterogeneously catalyzed processes containing solid catalyst phase
(e.g. in catalytic distillation and catalytic stripping), SP represent complex
geometric structures made from gauze wire or metal sheets and containing
catalyst pellets (see Fig. 1). In this case, both mass transfer area and catalyst
volume/surface become important parameters influencing the process
performance. For homogeneously catalyzed and auto-catalyzed processes (e.g.
reactive absorption, reactive distillation, reactive extraction), the packing function
is to provide both sufficient residence time and mass transfer area (Fig. 2). In
some RS processes, reactive and non-reactive SP are combined within the same
column (Sundmacher, and Kienle, 2002; Noeres et al., 2003). In this paper, both
SP types are considered.
Over the years, serious efforts have been made regarding the choice of an
appropriate packing material as well as the optimization of the corrugated sheet
geometry (McNulty and Hsieh, 1982; Chen et al., 1983; Olujic et al., 2001). This
can be achieved only if transport and reaction phenomena in the packings are
properly understood, and, hence, the development of sound predictive models is
required. The modeling accuracy strongly depends on the appropriate description
of phase interactions. Basically, it is well known that the most accurate methods
of (reactive) separation processes are based on the continuous mechanics, and
thus the methods of computational fluid dynamics (CFD) represent a promising
application (Davidson, 2001). In recent years, there have been significant
academic and industrial efforts to exploit CFD for the design, scale-up and
optimal operation of various types of chemical process equipment. However, the
simulation of large-scale RS columns still appears too difficult, mostly due to

superposition of different scales and largely undetermined position of the phase
interface.
For the separation processes taking place in geometrically simple flows,
e.g. flat films, cylindrical jets, spherical drops, physical boundaries of the
contacting phases can be spatially localized. In this case, the partial differential

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Kenig: Modeling of Reactive Separation Units with Structured Packings

equations of convective mass and heat transfer offer the most rigorous way to
capture the transport phenomena. However, even for the regular geometry
provided by corrugated sheet SP, the exact localization of phase interfaces
represents a difficult problem, due to intricate inter-phase interactions. Therefore,
most often, the modeling of (reactive) separation processes is accomplished with
the traditional stage concept (Taylor and Krishna, 1993), either using the
equilibrium or rate-based stage models.

Fig. 1. Catalytic structured packings KATAPAK®-S (left) and KATAPAK®-SP11 (right) by Sulzer Chemtech Ltd.

Fig. 2. Structured packings metal Mellapak by Sulzer Chemtech Ltd (left),
Montz-Pak A3-500 by Julius Montz GmbH (middle) and plastic Mellapak by
Sulzer Chemtech Ltd (right).

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Chemical Product and Process Modeling, Vol. 2 [2007], Iss. 1, Art. 5

STAGE CONCEPT
Large industrial RS units are usually modeled by a proper sub-division of a
column unit into smaller elements. These elements (the so-called stages) are
linked by mass and energy balance equations. The stages are related to real trays
for tray columns, and to packing segments for packed columns. They can be
described using different theoretical concepts, with a wide range of
physicochemical assumptions and accuracy (Noeres et al., 2003).

EQUILIBRIUM STAGE MODEL
The equilibrium stage model was largely used for the description of separation
processes during the last century. Since 1893, after the first equilibrium stage
model was put forward by Sorel (1893), numerous publications have appeared in
the literature, discussing different aspects of its further development and
application (Henley and Seader, 1981). Equilibrium stage model assumes that the
streams leaving a stage are at thermodynamic equilibrium. This idealization is
usually far from real process conditions, and therefore, process equipment is
designed using the “height equivalent to a theoretical plate” (HETP), a gross
parameter comprising the influence of packing type, size and material.
The limitations of the equilibrium stage model have long been recognized.
For a multicomponent mixture, the same HETP is assumed for all components,
this value being constant through the packing height. The latter is in contradiction
with the experimental evidence and may lead to a severe underdesign (Taylor and
Krishna, 1993). Moreover, this model is not able to consider the packing
geometry characteristics, which play a key role in actual mass and heat transfer.
Therefore, for kinetically controlled processes, it is very difficult to use the
equilibrium stage model without significant loss of accuracy.

RATE-BASED STAGE MODEL
The so-called rate-based stage model presents a different way to the modeling of
separation processes, by directly considering actual mass and heat transfer rates
(Seader, 1989; Taylor and Krishna, 1993). A number of models fall into the
general framework of the rate-based stage. In most cases, the film (Lewis and
Whitman, 1924) or penetration and surface renewal (Higbie, 1935; Danckwerts,
1951) models find application, whereas the necessary model parameters are
estimated by means of correlations. In this respect, the film model appears
advantageous due to numerous correlation data available in the literature (see,
e.g., Billet and Schultes, 1999).

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Kenig: Modeling of Reactive Separation Units with Structured Packings

According to the film model, all the resistance to mass transfer is
concentrated in two thin films adjacent to the phase interface. The film
thicknesses represent model parameters which can be estimated using the mass
transfer correlations (Sherwood et al., 1975; Taylor and Krishna, 1993). It is also
postulated that the mass transfer occurs within these films solely by molecular
diffusion and that outside the films, in the bulk fluid, the level of mixing is so
high that all compositions gradients disappear. Mass transfer takes place through
the films in the direction normal to the phase interface, whereas both molecular
diffusion and convection parallel to the interface are neglected. Contrary to the
equilibrium stage model, thermodynamic equilibrium is assumed here only at the
phase interface. The mass balances are fulfilled for each phase separately and
related by means of component diffusion fluxes (Taylor and Krishna, 1993). For
multicomponent separations, which are most commonly encountered in industrial

practice, multicomponent diffusion in the film phases is described by the
Maxwell-Stefan equations which can be derived on the basis of the kinetic gas
theory (Hirschfelder at al., 1964).

MODEL PARAMETERS AND VIRTUAL EXPERIMENTS
The rate-based stage model parameters describing the mass transfer and
hydrodynamic behavior comprise mass transfer coefficients, specific contact area,
liquid hold-up, residence time distribution characteristics and pressure drop.
Usually they have to be determined by extensive and expensive experimental
estimation procedures and correlated with process variables and specific internals
properties.
In the nature of things, experiments are performed in equipment units
filled with particular column internals. Let us now imagine that we are able to
gain the relevant correlation by purely theoretical way, just by simulating the
phenomena on and in packings. In this case, we would be able to investigate the
column internals even prior to their manufacturing. Such simulations can be
considered as “virtual experiments” replacing corresponding real experiments for
the parameter estimation. Virtual experiments can open the way towards virtual
prototyping and manufacturing of column internals and enable computer aided
optimization of both internals and overall processes.
The development of CFD-based virtual experiments for SP in RS
processes was one of the main goals of a large European project INTINT
(Intelligent Column Internals for Reactive Separations, Project No. GRD1
CT1999 10596) funded within the 5th Framework Programme GROWTH of the
European Union. In this project, universities collaborated with large chemical and
petrochemical companies, manufacturers of column internals and developers of
the CFD code (see Special Issue of Chemical Engineering and Processing

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Chemical Product and Process Modeling, Vol. 2 [2007], Iss. 1, Art. 5

“Intelligent Column Internals for Reactive Separations“, Chem. Eng. Process. vol.
44, issue 6). A new methodology for the packing optimization was suggested
which combines certain CFD procedures with rate-based model simulations
accomplished with the help of the software tools developed in INTINT (see, e.g.,
Kloeker et al., 2003; Egorov et al., 2005). The INTINT results revealed both
advantages and limitations of the suggested approach and were in general
encouraging.

CFD APPLICATIONS TO THE PARAMETER ESTIMATION
In this section, some examples are given in which the CFD simulations are used
as virtual experiments in order to estimate hydrodynamic and transport
characteristics of SP. First, pressure drop in non-catalytic SP in a pre-load regime
is considered based on Sulzer BX packing analysis (Egorov et al., 2005).
Afterwards, a detailed study of flow characteristics (Egorov et al., 2005) and
liquid-solid mass transfer (Kloeker et al., 2005) in catalytic SP are highlighted
using Sulzer Katapak“-S as an example. Any other periodic structure of a packing
can be analyzed in a similar way. The results are obtained using a general-purpose
CFD package CFX by ANSYS“.

PRESSURE DROP
Counter-current gas/vapor-liquid film flows in SP above the load conditions are
extremely complicated. For this reason, it appears improbable that the CFD-based
virtual experiments replace real experiments entirely in the near future. However,
even single-phase CFD simulations can improve predictivity of pressure drop
models, since all correlations “pressure drop – gas load” used in practice contain

some dry pressure drop correlation as a basic element. Replacing this correlation
by the rigorous CFD analysis helps to avoid heuristic assumptions on possible
correlation structure, which are inevitable both in conventional mechanistic
models (Rocha et al., 1993) and in more sophisticated considerations (Olujic,
1997).
The importance of the appropriate representation of the underlying
geometry of the internals is well understood, with special attention paid on the
effect of the corrugation angle. In this example, CFD calculations of dry pressure
drop in corrugated sheet packings are performed for the widely used Sulzer-BX
internals, with the standard corrugation angle of 60°. These internals can be
applied for homogeneously catalyzed RS processes, besides they are used in noncatalytic sections of reactive distillation columns. The computational domain
contains a single periodical sub-volume (one crossover, shown in Fig. 3). The
influence of the apparatus wall is not considered and the flow is treated as

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Kenig: Modeling of Reactive Separation Units with Structured Packings

established, with the periodic boundary conditions satisfied on the open
boundaries.
a

b

Fig. 3. Schematic representation of a
corrugated sheet packing adapted from (Olujic, 1997) (left) and a packing
crossover (right).

Fig. 4. Flow structure in the free shear layer. Color shows velocity values.

The Reynolds number of the gas flow is usually in the transitional or
turbulent flow regime. Therefore, a proper choice of the turbulence model is
required, with a grid accurate enough for resolving details of the mixing layers
and the generation of turbulence there.
Numerical experiments revealed strong pressure drop sensitivity to the
corrugation angle value. Besides, the complicated flow structure, shown in Fig. 4,

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Chemical Product and Process Modeling, Vol. 2 [2007], Iss. 1, Art. 5

clearly demonstrates that a high resolution degree of the vortex scales responsible
for the turbulence generation is crucial. Correlations between the pressure drop
and the gas load determined here with a grid of 96000 control volumes inside a
crossover are compared with the correspondent experimental data available from
Sulzer
Chemtech
(see
/>eprise/SulzerChemtech/Sites/design_tools/designtools.html). This comparison is
presented in Fig. 5, and a good agreement can be recognized.

DETAILED FLOW ANALYSIS IN A SINGLE CROSS-OVER
Recently, a number of studies, both theoretical and experimental, has been
dedicated to the catalytic packing Katapak“-S (s. Figs. 1 and 6) manufactured by
Sulzer Chemtech Ltd. This packing consists of open channels for gas flow and

closed channels in which the granular catalyst is immobilized. At operation
conditions below the load point, the liquid flows through the bags filled with the
catalyst (Moritz and Hasse, 1999). CFD-based studies of different authors (van
Gulijk, 1998; Higler et al., 1999; van Baten et al., 2001; van Baten and Krishna,
2002) treat the catalyst bed in closed channels as a quasi-homogeneous medium.
They analyze residence time distribution and mass transport between the gas and
liquid phases (Higler et al., 1999; van Baten et al., 2001; van Baten and Krishna,
2002).

10
Dry Pressure Drop in Sulzer-BX Packing
Air/Water Column ID 250 mm
1
' p [mbar/m]

0.1
Experiments by Sulzer Chemtech
CFD, k-epsilon model, wall functions
0.01
0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0.5

F-factor [Pa ]

Fig. 5. Calculated and measured dry pressure drop.

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Kenig: Modeling of Reactive Separation Units with Structured Packings

Furthermore, a CFD based description of single-phase and multi-phase
flows in column internals is given in (Yin et al., 2000; Yin et al., 2002) for
random packings, in (Petre et al., 2003; Larachi et al., 2003) for structured
packings and in (Trubac et al., 2001) for a structured catalytic packing.
The quasi-homogeneous approach allows only the calculation of average
hydraulic characteristics, since the whole packing space is treated as filled in with
the homogeneous fluid flowing with the smoothly distributed velocity field. A
detailed CFD analysis of the mixing processes in the open cross-flow geometry of
the Katapak“-S and similar catalytic internals demands an accurate grid

resolution of the individual catalytic grains. This requires significant computer
memory resources and therefore can be performed for some limited piece of
packing only.

Fig. 6. KATAPAK“-S laboratory packing (left) and schematic representation of
empty and catalyst-filled channels in this packing (right) adapted from van Baten
and Krishna (2002).
In this example, one periodic element (a cross-over) of the laboratory scale
version of Katapak“-S was selected for the detailed CFD simulation with CFX-5.
This solver uses the finite volume discretization method in combination with
hybrid unstructured grids. Around 1,100 spherical particles of 1 mm diameter
were included in the computational domain. As the liquid flows through the
catalyst-filled channels at operating conditions below the load point (cf. Moritz
and Hasse, 1999), permeability of the channel walls made of the wire mesh is not
taken into account by this particular model. The catalyst-filled channels are
considered fully wetted by the liquid creeping down, whereas the empty channels
are completely occupied by the counter-current gas. It means that the bypass flow

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Chemical Product and Process Modeling, Vol. 2 [2007], Iss. 1, Art. 5

of liquid outside the packed bags and the voids within the packed bags are
neglected.
A geometry generation procedure for the randomly packed spheres was
developed. An adaptive grid technique available in CFX-5 was applied in order to
automatically resolve the surface of each grain thus avoiding unnecessary fine

grid far from the surfaces. Several grid adaptation steps were performed until the
resulting superficial velocity reached its asymptotic value. Simulations were
carried out using pure water as the liquid component. The calculated superficial
flow velocity at load point of 2.2 mm/s agrees well with the experimental results
of Moritz and Hasse (1999).

Fig. 7. Direct simulation of liquid flow through the catalytic packing with the
grid-resolved catalyst structure: channeling effect.

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Kenig: Modeling of Reactive Separation Units with Structured Packings

The residence time distribution can be estimated by analyzing the local
velocity field. Here the performed calculations highlighted an important feature of
this flow, namely the effect of the liquid channeling near the packed bag
boundary. The velocity distribution over the wire mesh surface presented in Fig. 7
is characterized by the local velocity values along the shown “channels” up to 170
mm/s, whereas the average superficial velocities inside the packed bag are only 45 mm/s. This channeling effect is especially pronounced for the selected small
size of the packing, because the same diameter of the catalyst grains is normally
used for both laboratory and industrial scale internals. It means that for the proper
scale-up, additional investigations of the different packing sizes should be
performed rather than applying residence time distributions obtained in the
laboratory to the industrial internals.

INVESTIGATION OF A CATALYTIC BED: HYDRODYNAMICS AND MASS
TRANSFER BETWEEN SOLID PARTICLES AND LIQUID PHASE
This study is based on the analysis of catalyst bags in Katapak“-S (see Egorov et

al., 2002; Kloeker et al., 2005). For the description of mass transport phenomena
at the catalyst particle surface, the particles have to be resolved directly. To
simulate the mass transport in the chosen system with sufficient accuracy, it is
necessary to apply a high density grid, especially near the particle surface.
Regarding a high number of grid cells necessary in order to resolve each particle,
one has to restrict the computational domain by a few particles in order to avoid
prohibitively expensive calculations. The number of variables increases also with
each additional component, and hence, the requirements regarding computer
capacity grow.
Therefore, in this example, the number of particles was reduced to a
reasonable value and, in the first instance, instead of the random packing shown
in the previous section, a regular arrangement consisting of spherical particles was
assumed. Similar to the arrangement of atoms in ideal crystals, two densest
particle beds were chosen. For the body-centered cubic (bcc) arrangement of
catalyst particles, the void fraction is equal to 32%, for the face-centered cubic
(fcc) arrangement, it is 26%.
The elementary cell represents a cube which can be arbitrary expanded
and, due to the symmetry, mirrored. The symmetry can be used here, as, for a
regular spherical particle bed system, with the boundary effects neglected, the
fluid flow does exhibit a periodic behavior. However, the influence of mass
transport or chemical reactions destroys this periodicity. The applied geometries
are demonstrated in Fig. 8 showing in each case a computational domain

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Chemical Product and Process Modeling, Vol. 2 [2007], Iss. 1, Art. 5

consisting of the two periodic elementary cells. The considered particles are not
porous.

(a)

(b)

Fig. 8. Body-centered-cubic (left) and face-centered-cubic (right) particle
arrangements.
The application of unstructured grids in CFX-5 allows a good
discretization of complex geometries. Close to the particle surface, a particularly
high grid density is generated based on the application of a local grid refinement.
The number of the grid elements in one elementary cell is over 200,000 for the
bcc-geometry and about 380,000 for the fcc-geometry, since in the latter case
there are twice as many particles per elementary cell.

HYDRODYNAMIC STUDY
As a first step, the hydrodynamics in the studied geometry is analyzed using
periodic boundary conditions, except for the main flow direction. In the CFD
simulations, water at 20°C is used as a model fluid. The results are illustrated in
Fig. 9 with an example given for a bcc-packing with a 6.4 mm particle diameter.
In this example, the velocity specified at the inlet is 5 mm/s resulting in a
superficial velocity of 2.05 mm/s, this yields the Reynolds number Re=13.1.
The velocity field is represented in Fig. 9 by the velocity magnitude
distribution. Local acceleration of liquid in the narrow flow passages is clearly
seen there. Particle trailing zones and leading zones before the following particles
overlap forming stagnant zones where the transport phenomena are limited.
Circulation flows between the particles can be clearly recognized. All these
observations are in a good agreement with the results of other studies (see
Logtenberg and Dixon, 1998; Dixon and Nijemeisland, 2001). Experimental

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Kenig: Modeling of Reactive Separation Units with Structured Packings

investigations dealing with regular packed bed show a similar velocity
distribution.

Fig. 9. Velocity distribution for the flow through a body-centered-cubic particle
arrangement: overall velocity with stagnant zones between the particles in the
main flow direction.

MASS TRANSFER
For the reactive separation unit design, the knowledge on local mass transfer
phenomena is crucial. In this example, CFD is used to determine the liquid-solid
mass transfer coefficient correlations which can be used for the design of reactors
and (reactive) separation units. Deciding advantages of CFD are that it makes
possible to minimize or even avoid using real experiments, to investigate any
arbitrary (and even still not truly existing) geometries and to de-couple
phenomena. In real experiments, for example, an isolated study of external mass
transport in the case of porous particles is not possible.
Real experiments for the determination of external mass transfer
coefficients are used as an example for virtual experiments with CFD. Here
experimental studies (Williamson et al., 1963; Wilson and Geankopolis, 1966) on
the flow of two liquids, namely water and a propylene glycol–water mixture,
through a packed bed of spherical particles made from solid benzoic acid are

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Chemical Product and Process Modeling, Vol. 2 [2007], Iss. 1, Art. 5

applied. The particles have a diameter of about 6.4 mm, whereas the internal
diameter of a glass cylinder is equal to 67 mm. Benzoic acid is barely solvable in
water, whereas the 2.6% diameter reduction in each experiment (Wilson and
Geankopolis, 1966) is negligible. In simulations, the saturation concentration of
benzoic acid is used as a boundary condition at the particle surface. The
simulations are performed for both, bcc and fcc, arrangements, with different flow
velocities. Based on average entrance and exit concentration and using the
average logarithmic concentration difference ('c)ln, similar to Wilson and
Geankopolis (1966), it is possible to determine the mass transfer coefficient
kls

L(cout  cin )
am X ('c)ln

(1)

where am is specific contact surface, cin and cout are inlet and outlet average
concentrations, L is mass flow rate, X bed length, and ('c)ln

'cin  'cout
is
§ 'cin Ã
ln ă
á

â 'cout ạ

logarithmic concentration difference.
To characterize the mass transport, Wilson and Geankopolis (1966) used
the J-factor according to Chilton-Colburn (Bird et al., 2003) which is defined as
follows

J

kls Đ Q Ã
ă á
L âDạ

2/3

(2)

where D is diffusion coefficient and Q is kinematic viscosity.
Figure 10 shows the concentration of benzoic acid in two cutting planes. A
significant local increase of benzoic acid concentrations is clearly seen, especially
in the particle trailing regions (Fig. 10a), as these areas are characterized by lower
velocities (cf. Fig. 9). Dissolving effects are also displayed. Figure 10b
demonstrates a cutting plane spanned over between the diagonal of the entrance
plane and the side edge of an elementary cell in the main flow direction, whereas
an increase of the benzoic acid concentration in this direction is visible. At the
contact points of the particles, the saturation concentration is reached.

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Kenig: Modeling of Reactive Separation Units with Structured Packings

(a)

(b)

Fig. 10. Benzoic acid concentration for a body-centered-cubic particle
arrangement; sections along the main flow direction. Saturation at surfaces and in
contact points, enrichment in the main flow direction
The analysis of cutting planes normal to the main direction allows
identification of local benzoic acid concentration (Kloeker et al., 2004). The
velocity between the particles is relatively low, as shown in the hydrodynamic
studies. This zone is thus almost stagnant, and diffusion becomes dominant
resulting in a high concentration. Oppositely, for areas further away from the
centre, the concentrations are low due to higher velocity.
With the help of relevant post-processing and using the average entrance
and exit concentrations, the mass transfer coefficient and J-factor can be
determined via Eqns. (1),(2). In Fig. 11, the simulation results for different
particle arrangements and particle size are compared with the experimental data
taken from (Williamson et al., 1963; Wilson and Geankopolis, 1966). For the
experimental set “Wilson (1966), a”, the void fraction is estimated as 43.6 %,
whereas for the experimental set “Wilson (1966), b", it is 40.1 % (Wilson and
Geankopolis, 1966). In the experiments by Williamson (1963), the void fraction is
equal to 43.1 % or 44.1 %, respectively. The J-factor decreases with increasing

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Chemical Product and Process Modeling, Vol. 2 [2007], Iss. 1, Art. 5

Reynolds number, because the mass transfer coefficient increases more slowly
than the liquid load.

Fig. 11. J-factor as function of Reynolds number: experiments vs. simulations.
The comparison of simulation and measured data shows that the CFD
calculations can match experimental results qualitatively. For the geometries
studied, the theoretical value of the J-factor is higher that its experimental value.
The deviations can be largely attributed to the regular bed assumption used in the
CFD simulations, e.g. lower void fraction of the regular arrangements resulting in
a more intensified and uniform mixing and thus in a better mass and heat transport
as well as neglecting of column wall effects (Kloeker et al., 2004). The mass
transfer coefficients determined with CFD can be used in the design of reactors
and unit operations, in which the boundary effects are negligible, that is, at high
apparatus-to–particle-diameter-ratios.

A CLOSER LOOK ON THE TWO-FILM THEORY
The methods described above are directly related to the application of the ratebased stage modeling and, more specifically, the two-film theory. As already
mentioned, this theory is widely used; however, some problems arise when it is
applied to complex processes. A critical analysis shows that the difficulties are

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Kenig: Modeling of Reactive Separation Units with Structured Packings

mainly connected with the estimation of the film thickness. First, it is determined

from the mass transfer correlations which directly depend on the diffusion
coefficients (cf. Sherwood et al., 1975; Billet and Schultes, 1999).
Multicomponent mixtures are characterized by several diffusion coefficients
related to different component binary pairs, and, therefore, the film thickness is
different for each component (Kenig, 1997). This leads to a formal contradiction,
as, according to the film theory, the film thickness should be unique. Thus, in
engineering practice, this important model parameter has to be estimated as an
average of component film thicknesses.
Another difficulty is related to the mass transfer by convection, as, by
definition, the films are stagnant and hence, there should be no mass transport
mechanism, except for molecular diffusion in the direction normal to the interface
(Kenig, 2000). Nevertheless, convection in films is directly accounted for in
correlations. Moreover, in case of reactive systems, the film thickness should
depend on the reaction rate, which is beyond the two-film theory consideration.
The film theory, once developed for equimolar binary mass transfer in
non-reactive systems (Lewis and Whitman, 1924), was free from contradictions.
Nowadays, it is widely applied for much more complicated processes, and
therefore, additional assumptions have to be made. These assumptions are in
some conflict with physical backgrounds, and thus, application of this theory
becomes problematic (Kenig, 2000).

THE IDEA OF HYDRODYNAMIC ANALOGY
As already mentioned, the main reason for the application of simplified models,
such as the film model, is the extremely complex hydrodynamics in the most
industrial RS columns. It is hardly possible to localize the phase boundaries and
specify the boundary conditions there. Consequently, the rigorous equations of
continuum mechanics cannot usually be directly applied to the modeling of
(reactive) separation columns.
However, there exists a way to employ the rigorous equations of
continuum mechanics even for the cases, in which real phase boundaries cannot

be exactly localized. This way is associated with the idea of hydrodynamic
analogy between complex and simpler flow phenomena. More precisely, some
particular similarities are meant between complex flow patterns encountered in
industrial separations and geometrically simpler flows like planar films,
cylindrical jets, spherical drops, etc., as well as their combinations (Kenig, 1997).
These similarities are used in the hydrodynamic analogy approach by which the
complex hydrodynamics established in a real column is replaced with an
appropriate combination of simpler flow patterns. Such a replacement occurs on
the basis of experimental observations which are very important for the successful

Published by The Berkeley Electronic Press, 2007

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Chemical Product and Process Modeling, Vol. 2 [2007], Iss. 1, Art. 5

application of the proposed modeling approach. The simplified hydrodynamics in
the developed hydrodynamic analogy enables the use of rigorous equations of
heat and mass transfer to describe phenomena in RS units as well as in some other
applications in which a certain flow regularity exists (see Kholpanov et al., 1988;
Boyadzhiev, 1990; Kenig et al., 1990; Tschernjaew et al., 1996; Kenig, 1997).

HYDRODYNAMIC ANALOGY FOR STRUCTURED PACKING
To build up a hydrodynamic analogy for columns equipped with SP, substantial
features of the fluid flow have to be revealed and captured. Let us consider an
example of a gas/vapor-liquid (reactive) separation unit filled with a non-catalytic
structured packing (Shilkin and Kenig, 2005a).
Generally, corrugated sheet structured packings are installed into a column
as a bed of certain height and diameter. It is composed of a number of stacked

elements (segments). The segments are perpendicular to each other to produce the
mixing effects for both gas and liquid at each transition from one packing
segment to another (Olujic et al., 1999). Each packing segment consists of a
number of corrugated sheets, manufactured from gauze, metal, ceramics or
plastics and additionally mechanically or chemically treated to improve their
wetting characteristics. A typical geometry of such corrugated sheets is sketched
in Fig. 12.
According to experimental study of liquid flow over adjacent corrugated
sheets under influence of gravity (Stoter, 1993), liquid generally tends to move in
form of laminar films at the minimal angle with the column axis, Į. Based on
geometry and spatial arrangement of corrugated sheets and taking into account
previous studies (Rocha et al., 1993; Olujic, 1997), let us assume that fluid flow
over/through structured packing can be mirrored by a flow in a bundle of inclined
round channels, with dimensions derived directly from the corrugation geometry.
The channel inner surface is irrigated by the liquid flowing downwards, whereas
the rest of the volume is occupied by a counter-current gas flow. Furthermore,
turbulence is accounted for in the gas phase, while liquid phase is presumed to be
laminar. Both flows are considered to be fully developed, being ideally mixed at
regular intervals. The latter assumption is necessary to take into account the
mixing effects caused by abrupt change in the both liquid and gas flow direction
due to corrugation geometry. For the gas flow, such flow redirection occurs by
transition into the neighboring channel when it reaches the column wall (see
Fig. 12,a).
The length of the undisturbed flow for the gas phase is assumed to be
equal to the average channel length. For the liquid flow, this packing specific
model parameter is equal to the liquid flow path between two corrugation ridges.
The interval length for both phases as well as the number of channels can be

/>
18

Kenig: Modeling of Reactive Separation Units with Structured Packings

derived directly from the packing geometry (Shilkin and Kenig, 2005b; Shilkin et
al., 2006).

Fig. 12. Schematic of the experimentally observed (Stoter, 1993) fluid flow
over/through structured packing (a) and the flow pattern in a single channel (b)

GOVERNING EQUATIONS
The hydrodynamics is then described by the system of Navier-Stokes equations in
the film-flow approximation (Shilkin et al., 2006):

1 w Đ
wuL
ă rP L
r wr â
wr
wPL
0
wr

à wPL
 U L g sin D
á
ạ wx

wuG Ã wPG
1 w Đ

 UG g sin D
ă rP G
á
wr ạ wx
r wr â
wPG
0
wr

0
(3)

0, P G

PGlam  Pturb
G
(4)

where g is gravity, r radial coordinate, P pressure, u velocity, x axial coordinate,
D gravity flow angle, P dynamic viscosity, U density.
In this work, gas-phase turbulent viscosity is estimated using the following
empirical correlation (Gersten and Herwig, 1992; Schlichting and Gersten, 1997)

Published by The Berkeley Electronic Press, 2007

19


Chemical Product and Process Modeling, Vol. 2 [2007], Iss. 1, Art. 5

Pturb
G  r
UG Rh uW

Here, uW

N
1  r 2 1   A  1
r 2
2A