131 Fixed Bed Reactors

In a fixed bed reactor, gas phase reactions are generally carried out using a stationary bed of solid catalyst. In a typical reactor, suitable screens support the bed of catalyst particles, through which the gas phase flows. Gaseous reactants adsorb on the catalyst surface, reactions occur on this surface and reaction products desorb back to the gas phase. Two major types of fixed bed reactor are the conventional axial flow fixed bed reactor and the radial flow fixed bed reactor. These types are shown

FIGURE 13.1 Types of fixed bed reactors. (a) Axial flow fixed bed reactor: Up or down flow, single or multi-stage, with or without inter-stage cooling, single or multi-tubular. (b) Radial flow fixed bed reactor: Radially inward or outward flow, straight or reverse flow (direction of inlet and outlet is same or opposite to each other).

FIGURE 13.1 Types of fixed bed reactors. (a) Axial flow fixed bed reactor: Up or down flow, single or multi-stage, with or without inter-stage cooling, single or multi-tubular. (b) Radial flow fixed bed reactor: Radially inward or outward flow, straight or reverse flow (direction of inlet and outlet is same or opposite to each other).

schematically in Fig. 13.1. These reactors can be operated in various different modes as shown in this figure. The choice of reactor type depends on several issues including intrinsic reaction rate, heat of reaction, influence of external transport resistance on selectivity, molar change during the reaction, and so on. Several commercially important processes such as steam reforming (of methane or naptha), water gas shift reaction, methanol from synthesis gas, oxidation of sulfur dioxide, isomerization of xylenes, ammonia synthesis, alkylation of benzene, hydro de-waxing, reduction of nitrobenzene to aniline, manufacture of tetra-hydrofuran and butanediol from maleic anhydride, butadiene from ethanol, and so on, are carried out in fixed bed reactors.

Reaction engineering models for fixed bed reactors are well developed (Levenspiel, 1972). Generally, fixed bed reactors are modeled as plug flow or axial dispersed plug flow type models. All issues such as by-passing or channeling of gas while flowing through the catalyst bed is usually treated using a lumped parameter approach. Computational fluid dynamic models can make substantial contributions to enhancing our understanding of such complex flow behavior within the catalyst bed. If intrinsic reaction rates are fast, interphase heat and mass transfer characteristics become important design parameters. Accurate prediction of such interphase transport coefficients will require information about local fluid dynamics around catalyst pellets. It is very difficult to obtain such information under operating conditions. Computational flow models can be used to predict local fluid dynamics, from which the desired interphase transport coefficient values can be accurately estimated. These models can also be used to evaluate the influence of internals (bed supports, heat exchanger coils, gas distributors etc.) on flow distribution within the bed. Thus, computational fluid dynamics based models can make substantial contributions to linking actual hardware configuration with reactor performance. To illustrate possible applications of CFD models to fixed bed reactors, here we discuss an example of capacity enhancement of a radial fixed bed reactor (Ranade, 1997). Some recent publications on CFD models for fixed bed reactors are briefly reviewed to point out recent trends and the scope for using CFD models.

13.1.1. Radial Flow Fixed Bed Reactors

Radial flow fixed bed reactors were developed to handle large gas flow rates with minimum pressure drop and are most suitable for processes in which fluids need to be contacted with solid particles at high space velocity (Chang and Calo, 1981). Radial flow fixed bed reactors are used for a variety of processes including catalytic synthesis of ammonia, xylene isomerization and desulphurization.

The fluid dynamics of radial flow reactors (RFR) is very complex and involves severe changes in flow directions. In RFRs, feed enters parallel to the reactor axis either through the center pipe or the annulus and then flows radially through an annular catalyst basket (Fig. 13.1). It has been shown by Chang and Calo (1981) that perfect radial flow always results in the highest conversion. Axial flow through the bed, if present, decreases the conversion efficiency because it mixes fluids of different ages within the bed (similar to backmixing). Flow mal-distribution is, therefore, one of the most important variables controlling the performance of radial flow fixed bed reactors. Obviously, the capacity enhancement exercise for RFR must focus on elimination or minimization of flow mal-distribution. The flow modeling tools and methodology discussed earlier can lead to useful insights and can be used to evaluate various design solutions to minimize flow mal-distribution as discussed below. The discussion is organized in four sub-sections covering the major steps in the application of computational flow modeling to reactor engineering (problem definition, development of a suitable flow model, mapping the model onto a solver and application for process optimization).

Problem definition

The typical radial flow fixed bed reactor configuration shown in Fig. 13.1b is considered here. The reactor configuration is axis symmetric. Details of reactor construction are shown in Fig. 13.2 (only half of the reactor is shown since it is symmetric). The annular catalyst bed is supported by permeable cylindrical screens (inner and outer) and impermeable top and bottom cover plates. The top cover plate also comprises of a shroud as shown in Fig. 13.2. Such a shroud is generally provided to compensate for possible shrinkage in catalyst bed height with time. Reactants are fed to the reactor from the top end. The flow changes direction after hitting the cover plate. The feed enters the catalyst bed from the annular space between the catalyst bed and the reactor shell. The product stream exits through the outlet located at the bottom of the central pipe.

Because of the shroud in the cover plate, the active catalyst bed is limited to the annular zone A shown in Fig. 13.2. The extent of flow mal-distribution within the

Inlet

Inlet

Outlet

Outlet

FIGURE 13.2 Details of considered radial flow fixed bed reactor (from Ranade, 1997).

active catalyst bed is essentially governed by the throughput, configuration details causing severe changes in the flow direction and the resistance offered by the support screens and the catalyst bed. It may be possible to control the resistance of the catalyst bed to some extent, by appropriately selecting the pellet size. However, the design of support screens and the overall configuration are the most important parameters governing fluid dynamics and, thereby, performance of the RFR under consideration. Designs of radial fixed bed reactors generally rely on conventional reaction engineering models (Chang and Calo, 1981). However, to realize the best possible operation and to enhance the performance of these reactors, a detailed knowledge of fluid dynamics and the extent of mal-distribution, is essential. Here we illustrate possible applications of CFD models to capacity enhancement of a typical radial flow fixed bed reactor.

For a radial flow fixed bed reactor, capacity enhancement will involve the following two aspects:

• assessment of fluid dynamics of the existing RFR configuration and identification of the scope for eliminating any flow mal-distribution;

• exploration of the possibility of loading more catalyst by increasing the volume of active catalyst bed. This may be achieved by eliminating the shroud and filling the catalyst up to the top cover plate (zone B in Fig. 13.2) and also by filling the catalyst up to the bottom of the reactor (zone C in Fig. 13.2).

It is, however, necessary to ensure that elimination of the shroud does not lead to flow mal-distribution by proper redesign of the screens. The support screens for the catalyst added in zone C also need to be properly designed to ensure uniform flow through the catalyst bed. It is, therefore, essential to develop a detailed flow model to evaluate these possibilities.

Development of a flow model

In order to understand the possible mal-distribution, it is essential to make an accurate prediction of flow in the upper region of the reactor, where severe changes in flow directions occur. Typical values of throughput for the RFR under consideration indicate that the flow is turbulent (for the specific case modeled here, feed velocity at the inlet was 40 m s-1). The selection of an appropriate turbulence model is, therefore, crucial. Anticipating recirculating flow in the upper region of the reactor with spatial variation of velocity and length scales of turbulence, it will be necessary to use at least a two-equation turbulence model. The standard k-e model of turbulence, which has been tested and found to be useful for a variety of applications, may be used in absence of more specific information.

The next and most important step is to characterize the resistance offered by the porous catalyst bed and support screens. Several correlations relating the pressure drop through porous beds and velocity and bed characteristics are available (Carman, 1937; Ergun, 1952; Mehta and Hawley, 1969). The Ergun equation is one that is widely used to represent the resistance of a catalyst bed, and has the form:

AP = 150^ (1 - P)2 v 1.75p (1 - p) V2 L DUI p3 Dp^p p3

where (AP/L) is the pressure drop per unit length, p is viscosity, Dp is the equivalent pellet diameter, 0p is sphericity, <p is porosity and V is superficial velocity. The knowledge of pellet size, shape and voidage of the bed are thus sufficient to characterize the resistance of the catalyst bed. Equation 13.1 may be written in a compact form containing two parameters namely, permeability, j, and inertial resistance coefficient, C:

For the particular case investigated here, the values of permeability, p and inertial resistance coefficient, C were found to be 10-8 m2 and 104 m-1, respectively. The resistance of the screens can be represented in terms of the contraction and expansion losses. The velocity heads lost during flow through screens can also be expressed in a form similar to that described in Eq. (13.2) by setting p to a very high value (1010) with an appropriate value of C. The additional resistance offered by the fixed bed is usually included as additional body force terms in the governing equations. Compressibility of the gaseous feed may be ignored if the overall pressure drop is not large relative to the operating pressure of the reactor (as was the case in this particular example). The physical properties of the feed were therefore assumed to be constant (viscosity as 10-5 Pa.s and density 1 kg m-3). In this exercise, since the objective was to evaluate possible flow mal-distribution, the development of additional specific sub-models for reactions or heat transfer, was not needed.

Mapping of flow model onto CFD solver

The geometry of the radial flow reactor was modeled and an appropriate grid generated using the 'preBFC' tool (Fluent Inc., USA). Since the reactor configuration is axis symmetric, axis symmetric two-dimensional geometry was considered. The porous media models discussed above were mapped onto a commercial CFD code, FLUENT (Fluent Inc., USA). Preliminary numerical experiments indicated that if the number of grids in the radial direction is more than 40 and in the axial direction is more than 100, the predicted results of pressure drop and flow mal-distribution become insensitive to the actual number of grids. The solution domain and grid used for all subsequent computations (50 grids in the radial direction and 116 grids in the axial direction) is shown in Fig. 13.3.

The standard k-e model was used to simulate the turbulence. In view of the expected pore size distribution of the bed, turbulence generation in the porous catalyst bed was suppressed. Appropriate physical properties were specified in the CFD solver. Standard boundary conditions were used at all the impermeable walls and reactor outlet. The inlet boundary condition was specified using the known throughput of the RFR. It is necessary to specify the turbulence characteristics of the incoming stream at the inlet. These were specified using information about the turbulence in pipe flows. The model equations with the set boundary conditions were solved using the well-known SIMPLE algorithm (Patankar, 1980). To solve flow through porous media, it is always useful to specify a reasonably good initial guess for the pressure drop across the catalyst bed to facilitate speedy convergence. The use of zero as an initial guess for pressure necessitates the use of very low under-relaxation parameters. A few numerical experiments were carried out to select the appropriate solution

Inlet

Symmetry

Inlet

Symmetry

Wall

Outlet

Grid

Wall

Outlet

Grid

FIGURE 13.3 Solution domain and computational grid for radial flow fixed bed reactor (from Ranade, 1997).

parameters. Detailed optimization of the solution parameters (e.g. under-relaxation parameters and number of internal iterations) is difficult and often computationally expensive and is, therefore, not recommended unless several similar simulations need to be carried out.

Application for design and process optimization

Detailed experimental data for the velocity and pressure profiles in the industrial RFR under consideration was, unfortunately, not available for validation of the computational flow model. The available data of overall pressure drop across the bed could, however, be used to validate the flow model, to some extent. The predicted overall pressure drop across the bed (10 kPa) showed good agreement with the available data. In the absence of more data, this agreement was assumed to be adequate and the computational model was used to determine possible mal-distributions and to evaluate different options for capacity enhancement of the RFR under consideration.

The flow model generates detailed predictions of the flow field within the reactor. This allows rigorous scrutiny of the prevailing flow structures. For the case under consideration, details of flow at locations involving severe changes in the flow direction and the extent of mal-distribution within the active catalyst bed are of interest. In the first phase of analysis, the influence of screen resistance on the overall flow patterns and the mal-distribution was studied. The predicted profiles of inward radial velocity at the inner screen across the catalyst bed are shown in Fig. 13.4 for different screen resistance values (sign of radial velocity is negative since the fluid is flowing radially inward). It can be seen that higher screen resistance leads to more uniform flow, which agrees with intuitive expectations. The existing screens (with resistance coefficients C2, of 2 x 105 m-1) seem to be satisfactory since the extent of non-uniformity is less than 10%. Contours of the stream function and a close-up of the flow field near the shroud and top cover plate are shown in Figs 13.5a and 13.6a, respectively. It can be seen that there is significant recirculation at the top end of the catalyst bed. The downward velocity field in the annular region between catalyst bed and reactor shell also exhibits some non-uniformity.

Distance from the inlet, m

FIGURE 13.4 Predicted profiles of radial velocity at different values of screen resistance (from Ranade, 1997). RFR configuration: catalyst in zone A, top cover plate with shroud. Screen resistance coefficient, C/m for + = 0.0, x = 1.E5, □ = 2.E5.

Distance from the inlet, m

FIGURE 13.4 Predicted profiles of radial velocity at different values of screen resistance (from Ranade, 1997). RFR configuration: catalyst in zone A, top cover plate with shroud. Screen resistance coefficient, C/m for + = 0.0, x = 1.E5, □ = 2.E5.

FIGURE 13.5 Predicted contours of stream function. (a) Catalyst in zone A, top cover plate with shroud (C = 2 x I05 m-1). (b) Catalyst in zone A, B and C, top cover plate without shroud (C = 2 x I05 m-1 for all the screens). (c) Catalyst in zone A, B and C, top cover plate without shroud (C = 2 x I05 m-1 for inner screens of A and B and outer screen of A; C = I x I06 m-1 for outer screen of B; C = 5 x I04 m- for inner screen of zone C).

The flow from the catalyst bed into the central pipe is more or less uniform (Fig. 13.4) and indicates that there is not much scope to modify existing screen designs to enhance the capacity of the considered radial flow fixed bed reactor. One must, therefore, explore the second option of removing the shroud and increasing the active catalyst loading by adding catalyst in zones B and C (shown in Fig. 13.2). Fluid dynamics of the proposed RFR with active catalyst filled in zones B and C along with zone A was then simulated. As a first option, support screens for zones B and C were specified similar to the existing support screens for zone A. Contours of the predicted stream function and details of flow near the top cover plate, for this case, are shown in Figs 13.5b and 13.6b, respectively. It can be seen that removal of the shroud leads to increased circulation in the upper region of the RFR. The predicted profile of the radial velocity at the inner edge of the catalyst bed is shown in Fig. 13.7 (the corresponding profile of the base case is also shown in this figure as a reference). It can be seen that removal of the shroud, and filling with catalyst in zones B and C lead to significant non-uniformity of the flow through the catalyst bed.

(a), (b) and (c)).

The high resistance offered by the support screens of zone C leads to very low flow through zone C and a re-circulating zone in the annular space between the catalyst bed and the reactor shell. The non-uniform flow through the catalyst bed also leads to significant re-circulation in the central pipe. Thus, mere removal of the shroud and

Distance from the inlet, m

FIGURE 13.7 Predicted profiles of radial velocity at inner cylindrical screen of reactor (from Ranade, 1997). RFR configuration (as denoted in Fig. 13.5) for + - (a), x - (b), □ - (c).

Distance from the inlet, m

FIGURE 13.7 Predicted profiles of radial velocity at inner cylindrical screen of reactor (from Ranade, 1997). RFR configuration (as denoted in Fig. 13.5) for + - (a), x - (b), □ - (c).

filling with catalyst in zone B and C may not lead to capacity enhancements due to the associated problems of mal-distribution.

The analysis of simulated results, however, may suggest ways to redesign the support screens to improve the flow uniformity. In view of the role of the shroud in the fluid dynamics of RFR, a support screen with significantly higher resistance than the existing support screens may be installed in place of the shroud. To examine this, the resistance of the outer support screen for zone B was set to five times that for zone A. To facilitate more flow through zone C, the resistance of support screens for this zone needs to be reduced. Cover plate (screen) for zone C was, therefore, removed and the resistance of the inner support screen for the zone C was reduced to 5 x 104 m-1. Contours of the predicted streamlines and a close-up of the vector plot near the top cover plate are shown in Figs 13.5c and 13.6c, respectively. The corresponding profile of radial velocity at the inner edge of the catalyst bed is shown in Fig. 13.7. It can be seen that recirculation in the annular space between the catalyst bed and reactor shell has been eliminated by these changes. The size of the recirculating zone in the central pipe has also been considerably reduced. The flow non-uniformity caused by the removal of the shroud is more or less eliminated in this case. The flow through the zone C also has been considerably increased and is now of the same order as flow through zones A and B. Thus, the computational flow model provides quantitative guidelines to enhance the uniformity of the flow (in other words, enhancing the throughput or capacity) of the RFR under consideration.

13.1.2. Brief Review of Modeling of Fixed Bed Reactors

The methodology illustrated by the above example is fairly general and can be applied to any type of fixed bed reactor. For example, Ranade (1994) used a CFD model to optimize the design of a deflector plate in an axial fixed bed reactor. Foumeny and Benyahia (1993) also discuss the application of CFD models to optimizing internals for axial flow fixed bed reactors. It should be noted that the key issue in modeling fixed bed reactors is correct representation of the fixed bed (of solid particles). In most cases, such a fixed bed of solid particles can be modeled as an isotropic or anisotropic porous media. Additional resistance offered by such porous media can then be modeled by introducing an additional momentum sink in the momentum transport equations, as done for the case of RFR. Accuracy of such representation obviously depends on the accuracy of parameters used to represent porous media, namely, permeability, p and inertial coefficient, C. The best option to specify adequately accurate values of these parameters is, of course, experimental data.

However, it is not always possible to carry out experiments to determine values of these parameters, especially under the desired operating conditions of these fixed bed reactors (high pressure, high temperatures). In such cases, it is possible to develop rigorous computational models to characterize resistance of the fixed bed of solid particles. In these CFD models, an array of solid particles is considered. The geometry of these particles is modeled rigorously with an appropriate computational grid to cover the entire void between the solid particles. Rigorous momentum equations can then be solved to understand and to simulate details of fluid dynamics around each solid particle in the array. Such detailed simulations can be very educative about the small-scale phenomena occurring around particles in the bed and can also lead to realistic values of lumped parameters such as p and C under operating conditions. These detailed models can also be used to estimate external heat and mass transfer coefficients for the fixed bed flows. Logtenberg and Dixon (1998) and Logtenberg et al. (1999) developed detailed flow models by considering an array of solid particles. It is possible to solve mass, momentum and energy transport equations by considering intra-particle pores, if the pores are reasonably large. Some particles are specifically designed to generate macropores in addition to micropores, especially for bio-chemical applications involving large molecules. Knowledge of the intraparticle flow field is an important step in deriving predictive models of convective transport in these types of particles. Pfeiffer et al. (1996) simulated intraparticle flow in such macroporous (or gigaporous) particles. In some specialized applications, different types of fixed bed are used. For example, typical catalytic converters used by the automobile industry to reduce harmful emissions employ uniform, honeycomb like structures coated with active catalyst. It is better to use rigorous flow models of these intricate structures rather than representing them as extremely anisotropic porous media. Such detailed computational flow models are useful for understanding basic phenomena and may provide essential information to overall reactor engineering models. Such rigorous flow models may, however, become computationally intractable to use for large scale-industrial reactors. It is, therefore, necessary to develop a hierarchy of CFD models to collect the required information for design and optimization of large-scale industrial reactors.

So far, single-phase gaseous flow through fixed beds of solid particles has been discussed. When liquid flows through a fixed bed, it flows in the form of a film over solid surfaces. The flow, therefore, is entirely different than flow of gas through a fixed bed. In many cases, both, gas and liquid phases may flow through fixed beds. Modeling of these reactors involving flow of liquid over solid surfaces with a gas-liquid interface on the other side of the liquid film is discussed in the following section.

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