Dynamic liquid holdup

For different particle sizes, the dynamic holdup can be calculated as follows. According to the related holdup equations, the dynamic liquid holdup based on the void (available) bed volume is proportional to dp 0Mi 0/ 6, dp particle sizes, which is true for low df/D values (see the following subsection). Thus, the following analogy can be used ... 

Here, the dynamic liquid holdup (in m3/m3) refers to the portion of the void (available) bed volume that has been occupied by the liquid. There are also correlations for the static holdup, that is, when the flow rate is zero after wetting. Dynamic liquid holdup is normally between 0.03 and 0.25, whereas the static liquid holdup is between 0.01 and 0.05, and for nonporous catalysts, usually he s < 0.05 (see Section 3.6.3 Perry and Green, 1999). 

A proper sizing criteria Is to determine the liquid volume that could be dumped before the ESD system shuts in the relief valve source of overpressure. Thus, a dynamic liquid holdup determines the size of the relief drum. It will generally be smaller with the liquid holdup sizing criteria than a comparable horizontal API sized vessel. 

Figure 5.2-25. Influence of the total reactor pressure and of the liquid flow-rate on the dynamic liquid holdup for the single water operation (after Wammes et al. [34]).

A variety of correlations have been developed for the total and the dynamic liquid holdup. For instance, the total liquid holdup has been correlated with the Lockhardt-Martinelli parameter X for spherical and cylindrical particles [Midou, Favier, and Charpentier, J. Chem. Eng. Japan, 9 350 (1976)]... 

Correlations for the dynamic liquid holdup have also been developed as function of various dimensionless numbers including the liquid and gas Reynolds number, and the two-phase pressure drop [see, e.g., Ramachandran and Chaudhari, Three-Phase Catalytic Reactors, Gordon and Rreach, 1983 and Hofmann, Hydrodynamics and Hydrodynamic Models of Fixed Bed Pieactors, in Gianetto and Silveston (eds.), Multiphase Chemical Pieactors, Hemisphere 1986],... 

In practice, the thickness of liquid films in trickle beds has been estimated to vary between 0.01 and 0.2 mm (0.004 and 0.008 in). The dynamic liquid holdup fraction is 0.03 to 0.25, and the static fraction is 0.01 to 0.05. The high end of the static fraction includes the liquid that partially fills the pores of the catalyst. The effective gas-liquid interface is 20 to 50 percent of the geometric surface of the particles, but it can approach 100 percent at high liquid loading. This results in an increase of reaction rate as the amount of wetted surface increases (i.e., when the gas-solid reaction rate is negligible). 

The following developments will be restricted to laminar liquid flow with weak gas-liquid interactions. However, this is not a limitation of the proposed methodology which could be easily applied to any other flow regime. Applications will be presented for the modelling of the irrigation rate, the dynamic liquid holdup and the apparent reaction rate in the absence of external mass transfer limitations and in the case of non volatile liquid reactants (i.e. approximatively the operating conditions of petroleum hydrotreatment). 

The dynamic liquid holdup h[Pg.412]

The averaging of the dynamic liquid holdup is achieved in a similar way by introducing Eq.2 and 9 into Eq.7. 

Figure 5. Dynamic liquid holdup against the liquid superficial velocity. Key --------------------------, Equation 16 and---------> Equation 17.

Ga modified Galileo number (dp- p (p g+6 g)) hj dynamic liquid holdup,... 

Various methods for estimating KLs are described by Satterfield.150 The most conservative estimate of KLS is obtained as KI S = D/<5,, where D is the molecular diffusivity of the reactant in the liquid phase and <5L the average thickness of liquid film surrounding the particles. This estimation assumes no turbulence in the liquid film. The average thickness of the liquid film can be obtained from a knowledge of the dynamic liquid holdup and the outside area of catalyst particles per unit volume of the reactor, os. For example, if the dynamic liquid holdup is 50 percent of the void volume e, then <5L = e/2as. Various methods for estimating fcL and Ks under trickle-flow conditions are described in Chap. 6. 

Here, K = k /hiL, where hiL is the dynamic liquid holdup in the reactor. hdL is assumed to be constant along the length of the reactor. The reactor efficiency can be defined as... 

The dynamic liquid holdup haL can be obtained from the mean residence time, liquid flow QL, and the reactor volume V as haL = tmQ JV. This approach for correlating the performances of pilot-scale hydrodesulfurization reactors was evaluated by Murphree et al.,31 Cecil et al.,s and Ross.40 It should be noted that the efficiency 0 is very sensitive to the percentage conversion at high conversion levels, where a small change in 0 can significantly change the level of conversion. 

When the reaction occurs only in the liquid phase, only dynamic or operating holdup is important for kinetic data evaluation. However, when the reaction occurs both in the liquid and gas phases, both static and dynamic liquid holdups affect the reaction rates. 

Satterfield et al.80 studied the liquid holdup characteristics of flow over a string of spheres. Based on their data with 0.825-cm-diameter spherical porous catalyst pellets of palladium-on-alumina they proposed the following dimensionless relation for the dynamic liquid holdup ... 

Specchia and Baldi90 presented separate correlations for the dynamic liquid holdup in the poor interaction regime (i.e., gas-coirtinuous-flow regime) and the high-in teraction regime (i.e., pulsed and spray flow).In the poor-interaction regime, they presented a relation... 

Figure 6-7 Dynamic liquid holdup as a function of liquid Reynolds number." ...

An empirical correlation for the liquid holdup has been given by Otake and Okada.38 They correlated the dynamic liquid holdup to the liquid-phase Reynolds number and the Galileo number by a relation... 

Sater and Levenspiel43 studied an air-water system in a 10.16-cm-i.d. glass column packed with either 1.27-cm ceramic Berl saddles or 1.27-cm Raschig rings to a height of 3.66 m. Iodine-131 was used as liquid-phase tracer. The dynamic liquid holdup data obtained under trickle-flow conditions correlated well with the above Eq. (8-3) of Otake and Okada.38... 

The liquid holdup characteristics of a countercurrent, three-phase spouted-bed column are studied by Vukovic et al.141 They found that the total liquid holdup increased with the gas flow rate. Both the total and dynamic liquid holdups were comparable to those obtained in cocurrent-upflow three-phase fluidized-bed columns operating with similar gas and liquid flow conditions. 

In the drainage method, the dynamic liquid holdup is measured in which the inlet and outlet streams are... 

Xiao, Q. Anter, A.M. Cheng, Z.M. Yuan, W.K. Correlations for dynamic liquid holdup under pulsing flow in a trickle-bed reactor. Chem. Eng. J. 2000, 78, 125. 

A further advantage of absorption plus reaction is the increase in the mass-transfer coefficient. Some of this increase comes from a greater effective interfacial area, since absorption can now take place in the nearly stagnant regions (static holdup) as well as in the dynamic liquid holdup. For NHj absorption in H2SO4 solutions, K a was 1.5 to 2 times the value for absorption in water.Since the gas-film resistance is controlling, this effect must be due mainly to an increase in effective area. The values of K a for NH3 absorption in acid solutions were about the same as those for vaporization of water, where all the interfacial area is also expected to be effective. The factors and... 

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