For a packed bed

Phase Diagram (Zenz and Othmer) Zenz and Othmer (op. cit.) have graphically represented (Fig. 17-2) all gas-solid svstems in which the gas is flowing counter to gravity as a function o pressure drop per unit of height versus velocity. Note that line OAB in Fig. 17-2 is the pressure-drop versus gas-velocity curve for a packed bed and BD the cui ve for a fluid bed. Zenz indicates an instability between D and H because with no sohds flow all the particles will be entrained from the bed however, if sohds are added to replace those entrained, system JJ prevails. The area DHJJ will be discussed further. 

A similar equation would be used for a packed column except the constant (jr/16) would be replaced by the D Arcy constant for a packed bed. 

Glaser and Lichtenstein (G3) measured the liquid residence-time distribution for cocurrent downward flow of gas and liquid in columns of -in., 2-in., and 1-ft diameter packed with porous or nonporous -pg-in. or -in. cylindrical packings. The fluid media were an aqueous calcium chloride solution and air in one series of experiments and kerosene and hydrogen in another. Pulses of radioactive tracer (carbon-12, phosphorous-32, or rubi-dium-86) were injected outside the column, and the effluent concentration measured by Geiger counter. Axial dispersion was characterized by variability (defined as the standard deviation of residence time divided by the average residence time), and corrections for end effects were included in the analysis. The experiments indicate no effect of bed diameter upon variability. For a packed bed of porous particles, variability was found to consist of three components (1) Variability due to bulk flow through the bed... 

The shape of the breakthrough curve for a packed bed is steeper than that for the fluidized bed and the breakthrough curves obtained from semi-fluidized bed lies between those obtained from the packed and fluidized beds. 

Model for a Packed-Bed Catalytic Reactor with Periodic Reversal of... 

Fig. 17. Comparison of the variation of the time-average S02 conversion and the maximum bed temperature predicted for stationary cycling condition by an unsteady-state and a steady-state kinetic model for a packed-bed S02 converter operating with periodic flow reversal...

Normalized tracer response data for a packed bed hydrodesulfurizer are tabulated.The time will be found at which 75% of the tracer has left the vessel. The fraction of the tracer that has exited the vessel is represented by the integral of the last column. Interpolating, E(tr) - 0.75 when tr = 1.05. 

For a packed bed consisting of spherical particles, equation 9.23 can be written in the form... 

For a packed bed, substituting the equivalent diameter de from equation 9.20 into equation 1.65 gives... 

For a packed-bed membrane reactor (PBMR) the membrane is permselective and removes the product as it is formed, forcing the reaction to the right. In this case, the membrane is not active and a conventional catalyst is used. Tavolaro et al. [45] demonstrated this concept in their work on CO2 hydrogenation to methanol using a LTA zeolite membrane. The tubular membrane was packed with bimetallic Cu/ZnO where CO2 and H2 react to form EtOH and H2O. These condensable products were removed by LTA membrane which increased the reaction yield when compared to a conventional packed bed reactor operating under the same conditions [45]. 

In order to illustrate this approach, we next consider the optimization of an ammonia synthesis reactor. Formulation of the reactor optimization problem includes the discretized modeling equations for a packed bed reactor, along with the set of knot placement constraints. The following case study illustrates how a differential-algebraic problem can be optimized efficiently using (27). In addition, suitable accuracy of the ODE model can be obtained at the optimum by directly enforcing error restrictions and adaptively adding elements. Finally, bounds on the continuous state profiles can be enforced directly in the optimization problem. 

Amundson (A5) discussed the analytical solution of the heat dispersion equations for a packed bed chemical reactor. The form of the differential equations is, of course, similar to the mass dispersion equations for certain cases. A wealth of analytical methods and results are presented for various types of boundary conditions. 

There is no radial velocity, and the axial velocity across the radius of the packed bed is uniform. Schwartz and Smith (1953) found that the velocity across the diameter of a packed bed is not uniform for radial aspect ratios (tube-to-particle diameter) less than about 30, due to the significant effect of the increased void space near the wall where the particles are locally ordered. This result has been verified by Hoiberg et al. (1971) for a packed bed reactor with radial aspect ratio about 50. They considered a radial velocity variation suggested by experimental observations with a sharp peak about 15% greater than the mean fluid velocity situated close to the wall. Simulations using their model showed results virtually identical to those obtained with a uniform velocity profile.3... 

In designing a control system for a packed bed reactor, to make the most effective use of modern control theory it is necessary to reduce the size of the model from that we have been using. In this section, we consider how this reduction is carried out. 

Repeat problems 2 and 3 above for a packed bed absorption tower. 

Develop a model for a packed-bed immobilized fermentor and the MATLAB code for the design of the unit. 

Solution For a packed bed with monodispersed spheres in a large container, the volume fraction for solids is about 0.45. Thus, for particles under the bed height of 1 m, the average pressure caused by gravity is... 

Equation (4.16) can be reduced to Eq. (4.15) as dj becomes infinitely large. For a packed bed of monodispersed spheres arranged in a cubic particle array, the mean thickness of the shell of gas surrounding the particle can be approximated by... 

The molar balance equation for a packed bed-flow catalytic reactor is given by [126]... 

From the literature it is not possible to deduce a kinetic scheme suitable for modeling the reaction, since the majority of publications (10-39) do not present an unequivocal picture. Also the fundamental difficulties of estimating from independent measurements heat transfer parameters for a packed-bed reactor are well known (5,6,7). 

Is this expectation really realistic In sharp contrast to a packed bed, a monolithic reactor has no flow in the radial direction there is no flow from one charmel to an adjacenf one. When the initial distribution of liquid in fhe radial direction is nonhomogeneous, this distribution will propagate down the reactor unchanged. In a packed-bed reactor, there is always some radial flow. Therefore, in a design of a monolith reactor, the inlet design is more critical than that for a packed-bed reactor. In scale-up of a monolifh reacfor, fhe reacfor inlef system has to be designed such that the distribution of fhe liquid af fhe enhance of fhe reactor is ideal. 

A relatively large number of models can be written down for a packed-bed reactor, depending on what is accounted for in the model. These models, however, basically fall into two categories pseudohomogeneous models and heterogeneous models. The various models are described in standard reaction engineering texts — such as those of Carberry ( ), Froment and Bischoff ( ), and Smith ( ), to cite just a few — and in review articles (cf., and so details of their equations will not be reported here. We will, instead, only make some qualitative remarks about the models. 

Pea d,u/Da) is about 10 with turbulent flow Re = d,up)/]x greater than 2100) (not shown). Thus, all real reactors will have some effects of dispersion. The question is, how much Consider again Equation (8.4.7) but now define PCa d uj where d is an effective diameter and could be either dp for a packed bed or for an open tube. Equation (8.4.7) can be then written as ... 

Figure 10.2 Schematic diagram of a plug-flow macroscopic model for a packed-bed membrane shell-and-tube reactor...

The pressure drop occurring in the tube region is given by the Ergun equation. Equation (10-34c), for a packed bed ... 

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