Packing Nonidealities

Insufficient bed compression, which leads to void volumes at the column inlet, is another source of axial dispersion. Preparative columns should therefore preferably possess a possibility for adjusting the compression of the packed bed. 

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Isotherm measurements of methane at 298 K can be made either by a gravimetric method using a high pressure microbalance [31], or by using a volumetric method [32]. Both of these methods require correction for the nonideality of methane, but both methods result in the same isotherm for any specific adsorbent [20]. The volumetric method can also be used for measurement of total storage. Here it is not necessary to differentiate between the adsorbed phase and that remaining in the gas phase in void space and macropore volume, but simply to evaluate the total amount of methane in the adsorbent filled vessel. To obtain the maximum storage capacity for the adsorbent, it would be necessary to optimally pack the vessel. 

Figure 19.1 Examples of nonideal flow in stirred-tank and packed-bed vessels...

This diffusive flow must be taken into account in the derivation of the material-balance or continuity equation in terms of A. The result is the axial dispersion or dispersed plug flow (DPF) model for nonideal flow. It is a single-parameter model, the parameter being DL or its equivalent as a dimensionless parameter. It was originally developed to describe relatively small departures from PF in pipes and packed beds, that is, for relatively small amounts of backmixing, but, in principle, can be used for any degree of backmixing. 

Packed-bed reactors, 21 333, 352, 354 Packed beds, 25 718 Packed catalytic tubular reactor design with external mass transfer resistance, 25 293-298 nonideal, 25 295... 

The main difficulties of design of catalytic reactors reduce to the following two questions (1) How do we account for the nonisothermal behavior of packed beds and (2) How do we account for the nonideal flow of gas in fluidized beds. 

Another type of nonideal SEC behavior, which will not be covered in this chapter, is related to the use of mixed mobile phases (multiple solvents). Because solute-solvent interactions play a critical role in controlling the hydrodynamic volume of a macromolecule, the use of mixed mobile phases may lead to deviations from ideal behavior. Depending on the solubility parameter differences of the solvents and the solubility parameter of the packing, the mobile phase composition within the pores of the packing may be different from that in the interstitial volume. As a result, the hydrodynamic volume of the polymer may change when it enters the packing leading to unexpected elution results. Preferential solvation of the polymer in mixed solvent systems may also lead to deviations from ideal behavior (11). 

Noeres C, Benvenuti C, Hoffmann A, Gorak A. Reactive distillation nonideal-flow behavior of the liquid phase in structured catalytic packings. Proceedings of International Symposium on Multifunctional Reactors (ISMR-2), Nuremberg, 2001. 

The mass balances [Eqs. (Al) and (A2)] assume plug-flow behavior for both the gas/vapor and liquid phases. However, real flow behavior is much more complex and constitutes a fundamental issue in multiphase reactor design. It has a strong influence on the reactor performance, for example, due to back-mixing of both phases, which is responsible for significant effects on the reaction rates and product selectivity. Possible development of stagnant zones results in secondary undesired reactions. To ensure an optimum model development for CD processes, experimental studies on the nonideal flow behavior in the catalytic packing MULTIPAK are performed (168). 

A far more promising approach is represented by the so-called differential models, such as the axial dispersion model (ADM) (170) as well as the piston-flow model with axial dispersion and mass exchange (PDE) (171). Experimental studies (168) show that the ADM gives an appropriate description of the nonideal flow behavior of the liquid phase in catalytic packings (see Figure 31). Considering... 

A thorough investigation of the influence of the flow nonideality in catalytic packings on the dynamic process behavior of specific CD processes is an objective of some current studies (172). 

Experimental studies were carried out to derive correlations for mass transfer coefficients, reaction kinetics, liquid holdup, and pressure drop for the packing MULTIPAK (35). Suitable correlations for ROMBOPAK 6M are taken from Refs. 90 and 196. The nonideal thermodynamic behavior of the investigated multicomponent system was described by the NRTL model for activity coefficients concerning nonidealities caused by the dimerisation (see Ref. 72). 

The number of equations, M5C + 1), for a large number of trays and components, can be excessive. The global Newton method will suffer from the same problem of requiring initial values near the answer. This problem is aggravated with nonequilibrium models because of difficulties due to nonideal if-values and enthalpies then compounded by the addition of mass transfer coefficients to the thermodynamic properties and by the large number of equations. Taylor et al. (80) found that the number of sections of packing does not have to be great to properly model the column, and so the number of equations can be reduced. Also, since a system is seldom mass-transfer-limited in the vapor phase, the rate equations for the vapor can be eliminated. To force a solution, a combination of this technique with a homotopy method may be required. 

A study of industrial applications by Taylor, Kooijman, and Woodman [ICfiemE. Symp. Ser. Distillation and Absorption 1992, A415— A427 (1992)] concluded that rate-based models are particularly desirable when simulating or designing (1) packed columns, (2) systems with strongly nonideal liquid solutions, (3) systems with trace compo-... 

As we discussed above, efficiency and selectivity are complementary descriptors dependent on the different sets of chromatographic parameters. Efficiency is more dependent on the quality of the column packing, particle size, flow rate, and instrumental optimization, while selectivity is more dependent on the stationary phase properties and the nature of the analytes themselves. However, efficiency is sometimes affected by nonideal interactions of the analyte with the stationary phase (i.e., peak tailing). 

In earlier chapters, tubular reactors of several forms have been described (e.g., laminar flow, plug flow, nonideal flow). One of the most widely used industrial reactors is a tubular reactor that is packed with a solid catalyst. This type of reactor is called fixed-bed reactor since the solid catalyst comprises a bed that is in a fixed position. Later in this chapter, reactors that have moving, solid catalysts will be discussed. 

We first consider nonideal tubular reactors. Tubular reactors may be empty, or they may be packed with some material that acts as a catalyst, heat-transfer medium, or means of promoting interphase contact. Until now when analyzing ideal tubular reactors, it usually has been assumed that the fluid moved through the reactor in piston-like flow (PFR), and every atom spends an identical length of time in the reaction environment. Here, the velocity profile... 

Correlations exist for the amoimt of dispersion that might be expected in common packed-bed reactors, so these systems can be designed using the dispersion model without obtaining or estimating the RTD. This situation is perhaps the only one where an RTD is not necessary for designing a nonideal reactor. 

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