Dynamic liquid hold

Fig. 31. (a) Dynamic liquid hold-up, and (b) wetting efficiency as a function of liquid superficial velocity for 1.5- and 3-mm cylinders. Gas fiow rate was constant at 31.3mms . The line shows the best fit of the data to the percolation model of Crine et al. (104). Reprinted from reference (103) with permission from Elsevier, Copyright (2003). 

For the TBR design the dynamic liquid hold-up is a basic parameter because it is related to other important hydrodynamic parameters (including the pressure drop, wetting, and mean-residence-time of liquid). 

The first method for determining the dynamic liquid hold-up uses weighing experiments. After the TBR has reached its desired operating point, the gas-aid liquid inlets are closed simultaneously. The amount of liquid trickling out of the column is called the dynamic holdup. 

Figure 5.2-26. Dynamic liquid hold-up versus liquid Reynolds number at different gas velocities and total pressures for the N2-H2O system (after Wammes [17]).

Figures 5.2-26 and 5.2-27 show, respectively, the influence of the total reactor pressure and of the superficial gas velocity on the dynamic liquid hold-up with water-nitrogen and aqueous 40 % ethyleneglycol-nitrogen. Similar trends are observed for the two systems. In the trickle-flow regime, the total operating pressure has no influence on the dynamic liquid hold-up at low liquid flow-rates and at low gas velocity (lower than few mm/s). Note that the influence is however, more noticeable for the viscous system.

Then, in contrast to the operation at atmospheric pressure a small increase in the superficial gas velocity reduces considerably the dynamic liquid hold-up. This effect is more pronounced at higher liquid flow-rate values and total reactor pressures. Because of this high influence of the gas flow on the hydrodynamics, Wammes et al. [34] recommend avoidance of the use of the term, "low interaction regime", for the trickle-flow regime at high pressure. 

In processing the quantitative effect of the liquid flow-rate, the superficial gas velocity, and the total reactor pressure on the dynamic liquid hold-up, good results have been obtained by using ... 

Figure 5.2-28. Comparison between the experimental dynamic liquid hold-up and the predicted values given by Equation (5.2-27) (after Wammes et al. [34]).

When deriving the methods for calculating the dynamic liquid hold-up, it is assumed that the liquid hold-up is only associated with the trickle film in the random or structured packing. It is also assumed that there are no droplets in the packing and the liquid sprays are also associated with the trickle film. 

The total external liquid hold-up is equal to the sum of the static-and dynamic-hold-ups. 

The dynamic formulation of the model equations requires a careful analysis of the whole system in order to prevent high index problems during the numerical solution [96]. As a consequence, a consistent set of initial conditions for the dynamic simulations and a suitable description of the hydrodynamics must be introduced. For example, pressure drop and liquid hold-up must be correlated with the gas and liquid flows. 

The dynamic behavior of the coke gas purification process has been investigated systematically [92, 93, 97]. For example, local perturbations of the gas load and its composition have been analyzed. A significant dynamic parameter is represented by the liquid hold-up. Figure 9.14 illustrates the changes in solvent composition after a decrease of the gas flow rate from 67 m3 h-1 to 36.4 m3 h-1 and a simultaneous small increase of the liquid flow rate. 

The degrees of freedom of a process at dynamic state are equal in number or more than those at steady state. This is due to the fact that the dynamic balance equations contain the accumulation terms, whereas for steady-state balances the accumulation is zero. An incorrect estimate of the number of degrees of freedom can have a profound effect on the design of the appropriate controller. Consider the simple liquid holding tank of Example 10.1. The dynamic mass balance yields... 

The balance contains just two adjustable hydrodynamic parameters, tl l and PeL. The Peclet number is estimated from the separate impulse experiments carried out with the inert tracer (NaCl), while the quantity Tl l is estimated from the kinetic experiments in order to ensure a correct description of the reactor dynamics. The flow pattern of the reactor is characterised by separate impulse experiments with an inert tracer component injecting the tracer at the reactor inlet and measuring in this case the conductivity response at the outlet of the reactor with a conductivity cell operated at atmospheric pressure. In order to get a proper conductivity response, water was employed as the liquid phase. The liquid and hydrogen flow rates should be the same as in the hydrogenation experiments and the liquid hold up was evaluated by weighing the reactor. Some results from the tracer experiments are given in Figure 8.12. 

The aim of this research is to show the influence of cross-flow model and ADPF model on the estimation of mass transfer coefficient, liquid hold up and adsorption factor by dynamic analysis of a TBR. 

This means that the total liquid hold-up hL can be equated with the dynamic liquid holdup hj). According to Mersmann and Deixler [44], the static hquid hold-up hL,st prevails in the case of very low, dimensionless liquid load Bl, acc. to Eq. (4-16) ... 

Worse was to come. Boltzmann in 1872 made the same weird statistical equality hold for every mode in a dynamical system. It must, for example, apply to any internal motions that molecules might have. Assuming, as most physicists did by then, that the sharp lines seen in the spectra of chemical elements originate in just such internal motions, any calculation now of Cp/C would yield a figure even lower than 1.333. Worse yet, as Maxwell shatteringly remarked to one student, equipartition must apply to solids and liquids as well as gases Boltzmann has proved too much. ... 

The more incisive calculation of Springett, et al., (1968) allows the trapped electron wave function to penetrate into the liquid a little, which results in a somewhat modified criterion often quoted as 47r/)y/V02< 0.047 for the stability of the trapped electron. It should be noted that this criterion is also approximate. It predicts correctly the stability of quasi-free electrons in LRGs and the stability of trapped electrons in liquid 3He, 4He, H2, and D2, but not so correctly the stability of delocalized electrons in liquid hydrocarbons (Jortner, 1970). The computed cavity radii are 1.7 nm in 4He at 3 K, 1.1 nm in H2 at 19 K, and 0.75 nm in Ne at 25 K (Davis and Brown, 1975). The calculated cavity radius in liquid He agrees well with the experimental value obtained from mobility measurements using the Stokes equation p = eMriRr], with perfect slip condition, where TJ is liquid viscosity (see Jortner, 1970). Stokes equation is based on fluid dynamics. It predicts the constancy of the product Jit rj, which apparently holds for liquid He but is not expected to be true in general. 

Van der Waals, whose theory has been further developed by Hulshoff and by Bakker, went one step further than Gibbs by assuming that there exists a perfectly continuous transition from one medium to the other at the boundary. This assumption limits him to the consideration of one particular case that of a liquid in contact with its own saturated vapour, and mathematical treatment becomes possible by the further assumption that the Van der Waals equation (see Chapter II.) holds good throughout the system. The conditions of equilibrium thus become dynamical, as opposed to the statical equilibrium of Laplace s theory. Van der Waals arrives at the following principal results (i) that a surface tension exists at the boundary liquid-saturated vapour and that it is of the same order of magnitude as that found by Laplace s theory (2) that the surface tension... 

Finally, we note that a different type of exponential scaling that links single-particle dynamics to entropy has now been found to hold for atomistic super-cooled liquids.122 In particular, the relationship,... 

The interfacial area in the contactor, which is directly related to the solids hold-up, strongly influences the mass transfer rate. To maximise the overall mass-transfer rate per unit volume of equipment, a high solids hold-up is necessary. On the other hand, the solids hold-up also influences the pressure drop over the contactor. The pressure drop has a hydrostatic and a dynamic component, both of which rise with increased solids hold-up. Since the adsorbent consists of extremely small particles, fluid friction between liquid and solids may lead to a relatively high dynamic pressure drop. The hydrostatic pressure drop is attributable to the density difference between the suspension in the contact zone and in the liquid. 

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