Flow in monolithic channels

A major simplification in the modeling of monolithic channels is to decouple fluid mechanics from the problem by assuming a well-defined velocity profile. In this respect, the laminar flow assumption is likely to be valid since the timescale for viscous diffusion over a transverse length a is much smaller than the one for convection through a channel with length L  

The condition expressed by Equation 8.2 is usually fulfilled and channel flow occurs in the laminar range. This allows the problem to be treated analytically and the solutions presented in this chapter rely on this assumption. Accounting for the simultaneous development of the velocity profile compared with concentration/temperature fields requires numerical evaluation, and the importance of this effect is measured by Prandtl s number for heat transfer or by Schmidt s number for mass transfer  

The knowledge of this entrance length is important for the design of inlet sections or to define the validity of simplified models derived on the basis of fully developed laminar flow conditions. In practice, an inlet presection in the channel (with an uncoated/inert wall) can be used to allow for flow development before the fluid reaches the catalytically active region. A similarity between the entrance length of velocity and concentration/temperature profiles can be found, particularly when the wall temperature can be assumed to be uniform or severe external mass transfer control [42]. In Lopes et al. [43], the thickness of this region is discussed for the mass transfer problem with a finite wall reaction. 

Pressure drop is important to quantify the process energy requirements and can even be the limiting factor in the design and performance of a monolith reactor. It is related to Darcy s friction factor (four times higher than the Fanning factor) by [41] 

When Pr— cso and Sccso, the flow field develops much faster than the temperature or concentration profiles, respectively. Thus, mass transfer in a monolith channel should occur in fully developed laminar flow in liquid-phase processes. In the opposing limit (Pr— 0 and Sc— 0), plug flow can be used as an 

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The up-scaling from microreactor to small monoliths principally deals with the change of geometry (from powdered to honeycomb catalyst) and fluid dynamics (from turbulent flow in packed-bed to laminar flow in monolith channels). In this respect, it involves therefore moving closer to the conditions prevailing in the real full-scale monolithic converter, while still operating, however, under well controlled laboratory conditions, involving, e.g. the use of synthetic gas mixtures. 

Development of models that descnbe the flow in monolith channels in catalytic converters has received great attention [68,69]. See also Ref. 58 and references therein. As with channel interaction, the models applicable to monolith combustion catalysts are similar to those for catalytic converters... 

The most important processes in monolith channel convection of exhaust gas, heat and mass transfer between the flowing gas and the washcoat, internal diffusion, catalytic reactions in the washcoat, heat and mass accumulation and heat conduction—are schematically depicted in Fig. 7. 

Catalytic combustion in a monolith channel provides an illustration of boundary-layer flow in a channel [322], Figure 17.18 shows a typical monolith structure and the particular single-channel geometry used in this example. Since every channel within the monolith structure behaves essentially alike, only one channel needs to be analyzed. Also a cylindrical channel is used to approximate the actual shape of the channels. 

N. Reinecke, D. Mewes, Oscillatory transient two-phase flows in single channels with reference to monolithic catalyst supports, Int. J. Multiphase Flow 25 (6-7) (1999) 1373-1393. 

Fig. 8.10. Top view of different monolith types and the corresponding MRI-visualization of the liquid flow in one channel.

Magnetic resonance imaging permitted direct observation of the liquid hold-up in monolith channels in a noninvasive manner. As shown in Fig. 8.14, the film thickness - and therefore the wetting of the channel wall and the liquid hold-up -increase nonlinearly with the flow rate. This is in agreement with a hydrodynamic model, based on the Navier-Stokes equations for laminar flow and full-slip assumption at the gas-liquid interface. Even at superficial velocities of 4 cm s-1, the liquid occupies not more than 15 % of the free channel cross-sectional area. This relates to about 10 % of the total reactor volume. Van Baten, Ellenberger and Krishna [21] measured the liquid hold-up of katapak-S . Due to the capillary forces, the liquid almost completely fills the volume between the catalyst particles in the tea bags (about 20 % of the total reactor volume) even at liquid flow rates of 0.2 cm s-1 (Fig. 8.15). The formation of films and rivulets in the open channels of the structure cause the further slight increase of the hold-up. 

Fig. 8.14. Liquid hold-up in monolith channels comparison of modeling result with data obtained from MRI-experiments for liquid flow visualization.

More recent studies of gas-phase imaging with more direct relevance to chemical processing and reaction engineering have involved the examination of thermally polarized gas (and liquid) flow in monolithic catalysts. Koptyug et al. (2000a) have obtained quantitative, spatially resolved velocity maps for the flow of thermally polarized acetylene, propane, butane and water flowing through the channels of alumina monoliths with an in-plane spatial resolution of 400 pm. The monoliths had a channel cross-section of 4.0 mm2 and a wall channel... 

The most extensively investigated mode of flow in monoliths is cocurrent downflow. It can be realized in two ways, either with a controlled flow of gas or with a free recirculafion in bofh cases, fhe gas flow through the channels is caused by entrainment by the liquid at the entrance of fhe monolith (Figure 16). 

Besides ceramic monoliths, metallic monoliths are available (64). In comparison with ceramic monoliths, metallic monoliths can be produced in more advanced structures, for example, to create turbulence in the flow in the channels (65). Several structured catalyst supports, such as solid foams or Sulzer packings, are usually made from metal. The surface area of the metal itself will be usually too low for practical applications. 

Models may be one-, two-, or three-dimensional Of course, more advanced models describe the flow in the channels more accurately, but this is not required in all types of investigations. Section 2 in Chapter 8 provides an in-depth discussion of relevant flow phenomena that have to be taken into account when modeling monoliths. One-dimensional models can provide interesting information on mass and heat transfer effects in the washcoat [54]. However, if the development of a laminar flow in the monolith channels IS to be simulated, a two-dimensional model is needed. This is the case if multimonolith combustors are investigated [67]. This specific design, discussed in detail in Section IV.A, has a number of monoliths in senes, which enables vanation of monolith materials and cell density. Moreover, it leads to improved mass transfer by induced turbulence at the entrance of each monolith segment. 

The route from reactant to product molecule in a monolith reactor comprises reactant transport from the bulk gas flow in a channel toward the channel wall, simultaneous diffusion and reaction inside the porous washcoat on the channel wall, and product transport from the wall back to the bulk flow of the gas phase. 

In this chapter, after a general description of possible flow patterns in monolith channels, the main features and properties of monoliths will be discussed. Following this, the monolith reactor will be compared to some other conventional reactors that are widely used. Next, applications of monolith reactors in catalytic gas-liquid processes will be summarized. Finally, some ideas concerning the future needs in this field will be presented. 

In this chapter, first, the existing correlations for three-phase monolith reactors will be reviewed. It should be emphasized that most of these correlations were derived from a limited number of experiments, and care must be taken in applying them outside the ranges studied. Furthermore, most of the theoretical work concerns Taylor flow in cylindrical channels (see Chapter 9). However, for other geometries and flow patterns we have to rely on empirical or semiempirical correlations. Next, the modeling of the monolith reactors will be presented. On this basis, comparisons will be made between three basic types of continuous three-phase reactor monolith reactor (MR), trickle-bed reactor (TBR), and slurry reactor (SR). Finally, for MRs, factors important in the reactor design will be discussed. 

Monolithic catalytic converters continue to receive attention in the literature because of their applications in air pollution control and clean energy production. They differ from packed-bed reactors in their configuration as there are many parallel channels coated with a layer of catalyst. The flow in the channels is typically laminar. Because of its large void fraction, it is expected that the temperature transients will exhibit a significant impact on the performance of the monolith, particularly with respect to thermal stability. 

Instead of polarized noble gases, thermally polarized NMR microimaging was used to study of liquid and gas flow in monolithic catalysts. Two-dimensional spatial maps of flow velocity distributions for acetylene, propane, and butane flowing along the transport channels of shaped monolithic alumina catalysts were obtained at 7 T by NMR, with true in-plane resolution of 400 xm and reasonable detection times. The flow maps reveal the highly nonuniform spatial distribution of shear rates within the monolith channels of square cross-section, the kind of information essential for evaluation and improvement of the efficiency of mass transfer in shaped catalysts. The water flow imaging, for comparison, demonstrates the transformation of a transient flow pattern observed closer to the inflow edge of a monolith into a fully developed one further downstream. 

Investigations on Taylor flow in noncircular channels originated from flows in porous materials, for instance, in enhanced oil recovery. They are also relevant to microstructured reactors and to the many monolithic systems which in many cases have noncircular reaction channels. 

A common feature of monolithic reactors and microreactors are therefore the gas flow in small channels which creates different reactor properties when compared to conventional fixed-bed... 

In monolith reactors, the distribution of fluid into the channels is typically at least somewhat uneven [9] this is why it is very important to predict the flow distribution and include it in the quantitative modeling. Experimental techniques can also be used to study the flow distribution in monolith channels this method is introduced in Figure 9.9 [10]. CFD calculations make it possible to obtain the flow characteristics of the experimental system. In this case, the calculations were performed using the software CFX.4.4 [7]. The flow profiles in the gas and liquid phases were described by the turbulent k-e method (320,000 calculation elements), and to evaluate the distribution of gas bubbles, the multiple size group method was applied. The results from the CFD calculations gave the flow velocities for gas... 

FIGURE 9.9 Experimental setup to study the gas and liquid flow distributions in monolith channels. 

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