Liquid holdup calculations

Figure 4-8b shows a comparison between the experimental data hp exp for type X structured packings and for stacked 25—50 mm metal Bialecki rings and the liquid holdup calculated using method (4-32), with a packing constant of Cp = 0.465, acc. to Eq. (4-33b). The experimental data is spread around the graph in the flow range of Rep = 2 to Rep 100 with a relative deviation of 8(hp) < 15%. 

It may be noted that the liquid holdup was adjusted between 0.4-0.5 to have a good agreement with experimental data. The liquid holdup calculated from literature correlation (Sato et. al., (1973)) was in the range of 0.6-0.8. The disagreement may be due to the fact that the correlation was not proposed for ion exchange resin catalysts. 

One disadvantage of Beggs and Brill correlations is that it calculates rather high liquid holdup for downhill piping. Liquid holdup calculated by the Mukherjee and Brill method is reasonable when compared with the OLGA method. From this point of view, the Mukherjee and Brill method gives a more conservative pressure drop. 

Baker, A., Nielsen, K., and Gabb, A., Pressure loss, liquid-holdup calculations developed. Oil and Gas Journal, March 14, 55-59,1988. 

Pressure drop due to hydrostatic head can be calculated from hquid holdup B.]. For nonfoaming dilute aqueous solutions, R] can be estimated from f i = 1/[1 + 2.5(V/E)(pi/pJ ]. Liquid holdup, which represents the ratio of liqmd-only velocity to actual hquid velocity, also appears to be the principal determinant of the convective coefficient in the boiling zone (Dengler, Sc.D. thesis, MIT, 1952). In other words, the convective coefficient is that calciilated from Eq. (5-50) by using the liquid-only velocity divided by in the Reynolds number. Nucleate boiling augments conveclive heat transfer, primarily when AT s are high and the convective coefficient is low [Chen, Ind Eng. Chem. Process Des. Dev., 5, 322 (1966)]. 

FIG. 14-60 Comp arison of measured and calculated values of liquid holdup for Gempak 2A structured packing, air-water system. [Rocha et al., Ind. Eng. Chem., 32, 641 (1.9.93).] Reproduced with permission. Copyright 199.3 American Chemical Society. 

Except for special sihiations, pressure relief devices are not provided for fire exposure of heat exchangers, air fins, or piping, nor are the exposed surfaces of such items included for calculating the fire exposure heat input. Special situations may be congestion and substandard spacing, or unusually large equipment with normal liquid holdup over about 4 m and/or which represents over 15% of the total wetted surface of the system to which it is directly connected for pressure relief. 

Fractionators and Other Towers - An equivalent "tower dumped" level is calculated by adding the liquid holdup on the trays to the liquid at normal tower bottom (high liquid level). The surface that is wetted by this equivalent level and which is within 7.5 m of grade is used. 

Hoogendoorn and Lips (H10) carried out residence-time distribution experiments for countercurrent trickle flow in a column of 1.33-ft diameter and 5- and 10-ft height packed with -in. porcelain Raschig rings. The fluid media were air and water, and ammonium chloride was used as tracer. The total liquid holdup was calculated from the mean residence time as found... 

The program is rather slow in execution and therefore the model is limited to an eight-plate column, which is rather unrealistic for this multicomponent separation. The program is therefore given only for example purposes and a real simulation should involve rather more plates. As in BSTILL, the speed of calculation is also very sensitive to the magnitude of the liquid holdup on the plates, which again are large compared to normal practice. 

A separated flow model for stratified flow was presented by Taitel and Dukler (1976a). They indicated analytically that the liquid holdup, R, and the dimensionless pressure drop, 4>G, can be calculated as unique f unctions of the Lockhart-Martinelli parameter, X (Lockhart and Martinelli, 1949). Considering equilibrium stratified flow (Fig. 3.37), the momentum balance equations for each phase are... 

Calculate new total liquid holdups from the sum of the component holdups. Then calculate the new liquid mole fractions from the component holdups and the total holdups. 

From the above equation, the variation of equilibrium disjoining pressure and the radius of curvature of plateau border with position for a concentrated emulsion can be obtained. If the polarizabilities of the oil, water and the adsorbed protein layer (the effective Hamaker constants), the net charge of protein molecule, ionic strength, protein-solvent interaction and the thickness of the adsorbed protein layer are known, the disjoining pressure II(x/7) can be related to the film thickness using equations 9 -20. The variation of equilitnium film thickness with position in the emulsion can then be calculated. From the knowledge of r and Xp, the variation of cross sectional area of plateau border Qp and the continuous phase liquid holdup e with position can then be calculated using equations 7 and 21 respectively. The results of such calculations for different parameters are presented in the next session. 

Alternatively, experimental measurement of the variation of equilibrium continuous liquid holdup with position for a concentrated oil-in-water emulsion can be employed to infer the variation of disjoining pressure with film thickness. Since the continuous phase liquid holdup e is known as a function of position, xp, Op and r can be calculated using equations 7,21 and 24. Equation 24 will then yield the disjoining pressure II at the film thickness xp. ... 

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 ... 

The measured cross-sectionally averaged liquid holdup (i.e. measured liquid saturation times the bed voidage) are consistent with previously reported results [4], For a similar packing structure, Illiuta and Larachi [4] found liquid holdups, as calculated by their mechanistic model and compared with the reported experimental results, slightly lower than the values obtained in this study. However, there are some differences between the two studies this work was performed in a smaller diameter column ( 30 cm versus... 

Since liquid does not completely wet the packing and since film thickness varies with radial position, classical film-flow theory does not explain liquid flow behavior, nor does it predict liquid holdup (30). Electrical resistance measurements have been used for liquid holdup, assuming liquid flows as rivulets in the radial direction with little or no axial and transverse movement. These data can then be empirically fit to film-flow, pore-flow, or droplet-flow models (14,19). The real flow behavior is likely a complex combination of these different flow models, that is, a function of the packing used, the operating parameters, and fluid properties. Incorporating calculations for wetted surface area with the film-flow model allows prediction of liquid holdup within 20% of experimental values (18). 

The volumetric liquid holdup, 4>L, depends on the gas/vapor and liquid flows and is calculated via empirical correlations (e.g., Ref. 65). For the determination of axial temperature profiles, differential energy balances are formulated, including the product of the liquid molar holdup and the specific enthalpy as energy capacity. The energy balances written for continuous systems are as follows ... 

Step 3. Determine the number of liquid phase transfer units NL in this step. As you did for vapor, first calculate the liquid holdup time on the tray, and then calculate NL from a proven empirical equation. 

Step 3. The Reynolds number Re is calculated in this step. Dukler developed experimental data determining liquid holdup in two-phase flow systems. Re values above 200,000 are free of liquid slugs and holdup. If Re is greater than 200,000, then the flow is in the froth zone, or it is simply homogeneous flow as a mixture. For homogeneous flow, the average density of the two-phase flow fluid mixture is ... 

For single separation duty, Farhat et al. (1990) considered the operation of an existing column for a fixed batch time and aimed at maximising (or minimising) the amount of main-cuts (or off-cuts) while using predefined reflux policies such as constant, linear (with positive slope) and exponential reflux ratio profile. They also considered a simple model with negligible liquid holdup, constant molar overflow and simple thermodynamics, but included detailed plate to plate calculations (similar to Type III model). 

The term Uj is the material holdup on the tray. The vapor holdup is very small and the liquid holdup here is assumed not to change with time. The composition for the next trial, k + 1, is calculated using Enler s equation ... 

A model is presented to predict flow transition between trickling and pulsing flow in cocurrent downflow trickle-bed reactors. Effects of gas and liquid flow rates, particle size, and pressure on the transition are studied. Comparison of theory with published transition data from pilot-scale reactors shows good agreement. Since the analysis is independent of reactor size, calculations are extended to include large-scale columns some interesting observations concerning flow transition and liquid holdup are obtained. 

The liquid holdup for different regions of the bed are shown for different inlet pressures in Figure 5. The values for liquid holdup were calculated using Sato s correlation. 

The average gas holdup calculated from the difference between the heights of the gas-liquid dispersion and the clear liquid has been compared to the average holdup obtained from Equation (10). The average absolute relative error is less than 10 percent for all measurements. 

Then the inventory loops are revisited. The liquid holdups in surge volumes are calculated so that the time constants of the liquid level loops (using proportional-only controllers) are a factor of 10 larger than the product-quality time constants. This separation in time constants permits independent tuning of the material-balance loops and the prod-... 

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