Fixed bed reactor model

By pseudo-homogeneous models, fixed bed reactors are described without considering the existence of two different phases at least, but imposing balance equations for one single pseudo-phase and calculating chemical-physical properties and transport coefficients by applying empirical expressions. 

For the reasons stated earlier, it is important that we determine which regime controls the operating behavior of our model fixed-bed reactor. If we do not know which regime controls our model process, then our scaled prototype will most likely not behave similarly to it. Such an outcome can necessitate expensive modifications to our newly commissioned prototype, an outcome guaranteed to displease corporate management. 

For the prototype fixed-bed reactor to operate similarly to the model fixed-bed reactor, the following must hold... 

Thus geometric similarity between the prototype fixed-bed reactor and the model fixed-bed reactor is not strictly held. The question is can we accept this fact in our prototype design If we are downscaling a fixed-bed reactor, the fluid flow velocity profile will be flat across the... 

In this case chemical similarity does not hold between the prototype fixed-bed reactor and the model fixed-bed reactor. But, that does not mean we should abandon dimensional analysis. In fact, the opposite is true we should use dimensional analysis to determine the extent of the chemical dissimilarity between two fixed-bed reactors. We do that by estimating ko for the prototype fixed-bed reactor and for the model fixed-bed reactor from Fig. 3.9 in the chapter entitled Control Regime. We then insert the experimentally determined value into the above dimensionless ratios and compare each pair of dimensionless ratios. If heat required or released is our major concern, then we will want... 

Ren, X.H. (2003) NMR studies of molecular transport in model fixed-bed reactors. Doctoral thesis. University of Technology Aachen. 

Steps 1 through 9 constitute a model for heterogeneous catalysis in a fixed-bed reactor. There are many variations, particularly for Steps 4 through 6. For example, the Eley-Rideal mechanism described in Problem 10.4 envisions an adsorbed molecule reacting directly with a molecule in the gas phase. Other models contemplate a mixture of surface sites that can have different catalytic activity. For example, the platinum and the alumina used for hydrocarbon reforming may catalyze different reactions. Alternative models lead to rate expressions that differ in the details, but the functional forms for the rate expressions are usually similar. 

Sandelin, F., Salmi, T., and Murzin, D. (2006) Dynamic modelling of catalyst deactivation in fixed bed reactors skeletal isomerization of 1-pentene on ferrierite. Ind. Eng. Chem. Res., 45, 558-566. 

Traditionally, an average Sherwood number has been determined for different catalytic fixed-bed reactors assuming constant concentration or constant flux on the catalyst surface. In reality, the boundary condition on the surface has neither a constant concentration nor a constant flux. In addition, the Sh-number will vary locally around the catalyst particles and in time since mass transfer depends on both flow and concentration boundary layers. When external mass transfer becomes important at a high reaction rate, the concentration on the particle surface varies and affects both the reaction rate and selectivity, and consequently, the traditional models fail to predict this outcome. 

In continuous flow systems, the expenditure in mechanical energy necessary to run a process is directly proportional to the pressure drop over the system. Hence the pressure drop is an important figure determining the operating costs of a device. After having verified the chemical equivalence of the two reactor types introduced above, the question arises of whether using a micro-channel reactor instead of a fixed-bed reactor allows a decrease in the pressure drop. In order to estimate the pressure drop in the fixed-bed reactor, the Carman-Kozeney hydraulic diameter model (see, e.g., [116]) was used ... 

When a number of competing reactions are involved in a process, and/or when the desired product is obtained at an intermediate stage of a reaction, it is important to keep the residence-time distribution in a reactor as narrow as possible. Usually, a broadening of the residence-time distribution results in a decrease in selectivity for the desired product. Hence, in addition to the pressure drop, the width of the residence-time distribution is an important figure characterizing the performance of a reactor. In order to estimate the axial dispersion in the fixed-bed reactor, the model of Doraiswamy and Sharma was used [117]. This model proposes a relationship between the dispersive Peclet number ... 

GP 9] [R 16] By finite-element reactor modeling, it was shown that for conversions as large as 34%, concentration differences within the mini wide fixed-bed reactor of only less than 10% are found [78], Thus, the reactor approximates a continuous-stirred tank reactor (CSTR). This means that the mini wide fixed-bed reactor yields differential kinetics even at large conversions, larger than for reactors used so far (< 10% conversion). 

Fixed-bed reactors are used for testing commercial catalysts of larger particle sizes and to collect data for scale-up (validation of mathematical models, studying the influence of transport processes on overall reactor performance, etc.). Catalyst particles with a size ranging from 1 to 10 mm are tested using reactors of 20 to 100 mm ID. The reactor diameter can be decreased if the catalyst is diluted by fine inert particles the ratio of the reactor diameter to the size of catalyst particles then can be decreased to 3 1 (instead of the 10 to 20 recommended for fixed-bed catalytic reactors). This leads to a lower consumption of reactants. Very important for proper operation of fixed-bed reactors, both in cocurrent and countercurrent mode, is a uniform distribution of both phases over the entire cross-section of the reactor. If this is not the case, reactor performance will be significantly falsified by flow maldistribution. 

Esterification over Amberlyst BD20 was evaluated by processing a model mixture in a fixed-bed reactor. The model reaction mixture was prepared by dissolving 10 wt.% of pure stearic acid (> 97%, Fluka, Germany) in a low-acid vegetable oil (0.04 %) bought in the supermarket. Methanol (> 99.5%) was used without any preliminary treatment. 

J. N. Papageorgiou, G. F. Froment 1995, (Simulation models accounting for radial voidage profiles in fixed-bed reactors), Chem. Eng. Sci. 50, 3043. 

Fig. 5.1.10 (a) MR measured propagators and (b) corresponding calculated RTDs for flow in a model packed bed reactor composed of 241 -pm monodisperse beads in a 5-mm id circular column for a fixed observation time of 300 ms and as a function of biofilm fouling. As the porous media becomes biofouled, a high veloc-... 

Fig. 5.2.2 (a) The upper section of a typical the superficial flow direction (down the col-model trickle-bed reactor used in MRI studies, umn, z) have been measured 2D slice sections (b) MR image of water flowing within a fixed through the 3D image are shown with slices bed of spherical glass beads the beads have no taken in the xy, yz and xz planes indicated. 

Yuen et al. [24] first demonstrated the nature of the information that can be obtained regarding chemical mapping within a fixed-bed reactor, using the liquid phase esterification of methanol and acetic acid catalyzed within a fixed bed of H+ ion-exchange resin (Amberlyst 15, particle size 600-850-pm) catalyst as the model... 

Xiao, W.-D., and Yuan, W.-K., Modelling and simulation for adiabatic fixed-bed reactor with flow reversal. Chem. Eng. Sci. 49(21), 3631-3641 (1994). 

The units of rv are moles converted/(volume-time), and rv is identical with the rates employed in homogeneous reactor design. Consequently, the design equations developed earlier for homogeneous reactors can be employed in these terms to obtain estimates of fixed bed reactor performance. Two-dimensional, pseudo homogeneous models can also be developed to allow for radial dispersion of mass and energy. 

This equation may be used as an appropriate form of the law of energy conservation in various pseudo homogeneous models of fixed bed reactors. Radial transport by effective thermal conduction is an essential element of two-dimensional reactor models but, for one-dimensional models, the last term must be replaced by one involving heat losses to the walls. 

Pseudo homogeneous models of fixed bed reactors are widely employed in reactor design calculations. Such models assume that the fluid within the volume element associated with a single catalyst pellet or group of pellets can be characterized by a given bulk temperature, pressure, and composition and that these quantities vary continuously with position in the reactor. In most industrial scale equipment, the reactor volume is so large compared to the volume of an individual pellet and the fraction of the void volume associated therewith that the assumption of continuity is reasonable. 

Equations 12.7.28 and 12.7.29 provide a two-dimensional pseudo homogeneous model of a fixed bed reactor. The one-dimensional model is obtained by omitting the radial dispersion terms in the mass balance equation and replacing the radial heat transfer term by one that accounts for thermal losses through the tube wall. Thus the material balance becomes... 

The One-Dimensional Pseudo Homogeneous Model of Fixed Bed Reactors. The design of tubular fixed bed catalytic reactors has generally been based on a one-dimensional model that assumes that species concentrations and fluid temperature vary only in the axial direction. Heat transfer between the reacting fluid and the reactor walls is considered by presuming that all of the resistance is contained within a very thin boundary layer next to the wall and by using a heat transfer coefficient based on the temperature difference between the fluid and the wall. Per unit area of the tube... 

Equations 12.7.48 and 12.7.39 provide the simplest one-dimensional mathematical model of tubular fixed bed reactor behavior. They neglect longitudinal dispersion of both matter and energy and, in essence, are completely equivalent to the plug flow model for homogeneous reactors that was examined in some detail in Chapters 8 to 10. Various simplifications in these equations will occur for different constraints on the energy transfer to or from the reactor. Normally, equations 12.7.48 and 12.7.39... 

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