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

Kenig Abstract Reactive separations combining mass transfer with simultaneous chemical reactions within a single column unit provide an important synergistic effect and bring about sever

Advanced Modeling of Reactive Separation

Units with Structured Packings

E Y Kenig∗

∗ Univ Dortmund, e.kenig@bci.uni-dortmund.de

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 in- ternals 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 mance and low pressure drop has been created Among them, corrugated packings of the regular type or structured packings have gained a wide acceptance.

perfor-This paper gives a state-of-the-art review of the structured packings modeling methods, ing 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.

focus-KEYWORDS: reactive separations, structured packings, mass transfer, CFD, hydrodynamic

analo-gies

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

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

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®

-SP-11 (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)

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)

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)

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

“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

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

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 non-catalytic 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

a b

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

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,

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

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)

Dry Pressure Drop in Sulzer-BX Packing Air/Water Column ID 250 mm

0.01 0.1 1 10

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

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

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 4-

5 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

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

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

(b) (a)

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

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

ln

( )

'

out in ls

m

L c c k

where a is specific contact surface, m c and in c are inlet and outlet average out

concentrations, L is mass flow rate, X bed length, and ( )ln

c c c

c c

is

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

2 / 3Q

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