Holdup model

Sepn. Purif., 3, 19 (1989)] takes holdup into account and applies to random as well as structured packings. It is somewhat cumbersome to use and requires three constants for each packing type and size. Such constants have been evaluated, however, For a number of commonly used packings. A more recent pressure drop and holdup model, suitable for extension to the flood point, has been pubhshed by Rocha et al. [Jnd. Eng. Chem. Research, 35, 1660 (1996)]. This model takes into account variations in surface texturing of the different brands of packing. 

A subset of the type IV model equations can be obtained using the assumption of constant molar holdup in the condenser and in intermediate plates and fast energy dynamics. These assumptions will make the resulting set of DAEs an index 1 rather than index 2 system. In the literature this type of model is referred to as the rigorous constant molar holdup model. Galindez and Fredenslund (1988), Mujtaba and Macchietto (1988, 1992, 1993, 1996, 1998) used this type of model in their studies. Refer to Mujtaba and Macchietto (1998) for the model equations. 

Referring to the simple zero holdup model (described in 5.5.1.1), the maximum profit problem can now be written as ... 

Note using a holdup model, Logsdon and Biegler also reported an optimal reflux ratio profile for the same example but it was significantly different than that obtained by using no holdup model. Refer to the original reference for further details. 

This relation, although conceptually different, is mathematically similar in predicting the dependence of In (Cj/C0) on L and LHSV. However, it differs from the holdup model in predicting the effects of dp, vL, and er, on In (C /C0). 

Figure 4-2 First-order kinetic plots based on the holdup model fot removal reactions (after Paraskox et al. 1). (a) the vanadium removal reaction, (ft) the sulfur removal reaction, (c) the nitrogen removal reaction, (d) the nickel removal reaction.

Figure 4-3 Effects of analyst bed length on the desulfurization (u) and denitrogenation (h of gas oils first-order kinetic plots based on the holdup model (after Paraskas et til.1 ).

Figure 4-4 Correlations of the experimental data for 36 percent KATB by the effective catalyst-wetting and holdup models (after Montagna anti Shah2 1).

The following parameters are specific to the broth used in fitting the above gas holdup model. In this example these parameters have values of ... 

Physically, the effective wetting model seems to be the most appropriate one. This is supported by the fact that also hydrodesulphurization of vacuum and atmospheric residuals are better correlated by an effective catalyst wetting model than by the holdup model [60]. 

Holdup models are extensively reported in the open literature and validated for specific types of packing and under specific operating conditions. Generally, a holdup expression is a function of the internals geometry, flow regime and physical properties of the involved phases. 

On the basis of measurements for hydrocracking and hydro-den itrogenat ion, the authors concluded that contacting in normally used pilot plants run at liquid velocities between 5 x 10 to 0.3 cm/s are sensitive to liquid flow rate and contacting increases with increasing velocity. On the basis of the holdup model, they also suggested that the contacting efficiency should be a function of the diameter of the catalyst and the liquid viscosity as shown by the equation above. 

The models can be classified according to the basic hydro-dynamic premise underlying the model. The "holdup model" assumes that liquid-catalyst contacting is proportional to the amount of liquid that is held up in the bed. The "wetting model" presupposes that the key factor controlling catalyst utilization is the extent of wetting of the particles by liquid. The "partial... 

The "holdup" model assumes that contacting is- proportional to the liquid holdup in the catalyst bed. This model, proposed by Henry and Gilbert [23], uses total holdup measurement as a basis and presupposes that each element of liquid hold-up is associated with an equivalent catalyst element and that all of these equivalences are of equal efficiency without respect to the nature of the reaction. Liquid velocity, particle size and fluid physical property affect contacting only as those parameters affect holdup. 

Other workers have interpreted ric ss a function of other parameters. Henry and Gilbert [26] considered pc to depend on liquid holdup and proposed an external holdup model ... 

The Simplified Holdup Model Used for Analysis and Simulation... 

Note that the holdup model, while complicated slightly by the quotient terms, has an advantage in that Eq. 1-53 is symmetric with 1-52 and thus is easier to manipulate symbolically than with Eqs. 1-37 and, particularly, 1-38. The model also has one less parameter. 

A number of reaction engineering models in literature have already utdized the concepts of TBC or single-bubble-class (SBC) together with the axial dispersion models to couple the hydrodynamics, mass transfer, and reaction in bubble column reactors. While some researchers claim that there is less difference in the SBC and TBC model predictions, others believe that the TBC model prediction is in better agreement with experiments. We find that the difference is actually relevant to the submodels for hydrodynamics, mass transfer, and reaction kinetic as well as gas contraction, and in particular the gas holdup model and whether the system is limited by reaction or mass transfer. Then a new reactor model is developed to replace the empirical... 

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