Fluid dynamics dynamic holdup

Figure 4-1 Effect of fluid dynamics on holdup (after Henry and Gilbert ).

The effectiveness of a fixed-bed operation depends mainly on its hydraulic performance. Even if the physicochemical phenomena are well understood and their application in practice is simple, the operation will probably fail if the hydraulic behavior of the reactor is not adequate. One must be able to recognize the competitive effects of kinetics and fluid dynamics mixing, dead spaces, and bypasses that can completely alter the performance of the reactor when compared to the ideal presentation (Donati and Paludetto, 1997). The main factor of failure in liquid-phase operations is liquid maldistribution, which could be related to low liquid holdup in downflow operation, or other design problems. These effects could be critical not only in full-scale but also in pilot- or even in laboratory-scale reactors. 

The holdup of a phase is usually defined as the volume of the phase per unit reactor volume. However, for a fixed-bed reactor, the gas and liquid holdups are often defined on the basis of void volume of the reactor. In a fixed-bed reactor, the liquid and sometimes gas holdups are divided into two parts dynamic holdup, which depends largely on the gas and liquid flow rates and the properties of the fluids and the packing material, and static holdup, which depends to a major extent on the nature of the packing (e.g., porosity of the packing) and the fluids properties. The relationships between the holdups of various phases and the system variables for a variety of three-phase reactors are discussed in Chaps. 6 through 9. 

In addition to the basic continuous column model assumptions of equilibrium stages and adiabatic operation, dynamics-related assumptions are made for the batch model. Distefano (1968) assumed constant volume of liquid holdup, negligible vapor holdup, and negligible fluid dynamic lag. Although different solution strategies may be employed, the fundamental model equations are the same. 

Starting from total reflux conditions, the distillate rate is incremented from zero to D, thereby lowering the reflux rate to Lq - D. Since negligible fluid dynamic lags are assumed, all the liquid rates are instantly lowered to Lj - D. The vapor rates are maintained at Vj. These flow rates and the steady-state total reflux mole fractions are used to calculate the mole fraction derivatives by Equations 17.29 through 17.31. The molar holdups in these equations are calculated from the assumed constant volume holdups multiplied by calculated molar densities. 

Circulation of liquid across the heating surface is caused by the action of the boiling liquid (natural circulation). The circulation rate through the evaporator is many times the feed rate. The downcomers are therefore required to permit the liquid to flow freely from the top tubesheet to the bottom tubesheet. The downcomer flow area is, generally, approximately equal to the tubular cross-sectional area. Downcomers should be sized to minimize holdup above the tubesheet in order to improve heat transfer, fluid dynamics, and minimize foaming. For these reasons, several smaller downcomers scattered about the tube nest are often the better design. 

The time-averaged velocities and gas holdups in the compartments, as well as the fluid interactions between the zones, are first calculated by computational fluid dynamics (CFD). Then, balance equations for heat and mass transfer and for chemical reactions are evaluated and solved using appropriate software. First results from a simulation of a cumene oxidation reactor on an industrial scale were impressive, as they matched real temperature and concentration fields. 

The simulation results show that in addition to precise microkinetics, knowledge of the fluid dynamics, especially the liquid holdup, is an essential prerequisite for modeling a trickle-bed reactor. The advantage of a simulation program is not so much the calculation of the conversion for a concrete situation rather, it is the splitting of a complex problem into individual steps, which allows parameter smdies to be carried out [10]. 

Even though the transition regime may offer a maximum for the gas holdup and interfacial area, it is not desired for industrial processes due to its unstable and erratic nature. The instability has made the exact identification of the transition point nearly impossible. Although computational fluid dynamics and other methods are capable of predicting the other flow regimes, these methods usually have a difficult time predicting the transition point or the hydrodynamic behavior near it (Olmos et al., 2003). Hence, even if the operator wanted to work with the transition regime, it would be nearly impossible to achieve consistent results. 

Furthermore, very often a first-order irreversible reaction with respect to the liquid reactant has been assumed (for a second order rate equations see [63]). Depending on the lumping of fluid-dynamics either into axial dispersion, liquid holdup or partial wetting of the catalyst these oversimplifications result in the relations shown in Fig. 19 for the chemical conversion. 

It is still common practice to estimate the fluid dynamic properties from empirical correlations. Such correlations are usually developed from "cold flow" measurements which are often not properly designed and evaluated. It is understood that use of empirical correlations is of limited value and their predictions may lead to serious errors. This is particularly valid for those quantities which characterize interfacial properties like mass transfer coefficients, interfacial areas and phase holdups. It is now obvious that properties like density, viscosity, and surface tension are not always sufficient to describe fluid dynamic and interfacial phenomena. 

RTD models for trickle-bed reactors are quite numerous. They are reviewed in part 2 in order to evidence the main fluid flow characteristics that have been considered by the authors developing these models. The fluid mechanics description is based on percolation concepts. The main implications of these concepts are analyzed in part 3 whereas part 4 is devoted to the development of a percolation model describing the liquid flow distribution in a trickle-bed reactor. This model is then applied to derive correlations for the wetting efficiency and the dynamic liquid holdup (part 5) and, finally, for the axial dispersion coefficient (part 6) a classical example... 

The liquid rates throughout the column will not be the same dynamically. They will depend on the fluid mechanics of the tray. Often a simple Francis weir formula relationship is used to relate the liquid holdup on the tray (M,) to the liquid flow rate leaving the tray (L ). 

Basically, two types of correlation for the dynamic or total liquid holdup are reported in the literature. Some investigators have correlated the liquid holdup directly to the liquid velocity nd fluid properties by either dimensional or dimensionless relations. In more recent investigations, the liquid holdup is correlated to the Lockhart-Martinelli parameter APl/APg (or an equivalent of it. as discussed in the earlier section). 

Fransolet, E., Crine, M., Marchot, P, and Toye, D. (2005), Analysis of gas holdup in bubble columns with non-Newtonian fluid using electrical resistance tomography and dynamic gas disengagement technique, Chemical Engineering Science, 60 6118-6123. 

Remarks. Close inspection of the nonequilibrium model outputs reveals that assumption of nonequilibrium capillary pressure in the studied range of experimental conditions was not necessary and static equilibrium described by PcxPg-Pe was sufficient to account for the interfacial forces [54], However, recourse to empirical capillary relationships, such as the Leverett /-function, is unnecessary as the nonequilibrium two-phase flow model enables access to capillary pressure via entropy-consistent constitutive expressions for the macroscopic Helmholtz free energies. Also, the role of mass exchange between bulk fluid phase holdups and gas-liquid interfacial area was shown to play a nonnegligible role in the dynamics of trickle-bed reactor [ 54]. By accounting for the production/destruction of interfacial area, they prompted much briefer response times for the system to attain steady state compared to the case without inclusion of these mass exchange rates. 

While Lapple was laying the groundwork for his book entitled Fluid and Particle Dynamics (published by Delaware Press in 1951), others were busy at work with experiments and dimensional analysis. Piret, Mann and Wall (1940) studied the problem of pressure drop and liquid holdup in a packed tower, and Sarchet and Colburn (1940) completed a study on the economic pipe size for the transportation of fluids. A nomograph was produced for the optimum pipe diameter, and the decade of the nomograph began as literally hundreds were produced during the next ten years. 

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