Holdup, estimation

Pore diffusion calculation was intended to be included in the reactor model, but the preliminary calculations using the Hoyos method for single spherical particles showed that it does not play any significant role here. Only unrealistically small values of effective diffusivity could make the pore diffusion significant enough. When having low superficial velocities for both gas and liquid, the liquid holdup was known to be very weakly dependent on liquid Reynolds number (Eq. 15.22) and practically independent of superficial velocity of gas. Therefore, it could be treated as constant and is taken as 0.4, which is used in the calculation of reaction rates. The liquid holdup estimate was based on the empty space in the packing... 

The sohd can be contacted with the solvent in a number of different ways but traditionally that part of the solvent retained by the sohd is referred to as the underflow or holdup, whereas the sohd-free solute-laden solvent separated from the sohd after extraction is called the overflow. The holdup of bound hquor plays a vital role in the estimation of separation performance. In practice both static and dynamic holdup are measured in a process study, other parameters of importance being the relationship of holdup to drainage time and percolation rate. The results of such studies permit conclusions to be drawn about the feasibihty of extraction by percolation, the holdup of different bed heights of material prepared for extraction, and the relationship between solute content of the hquor and holdup. If the percolation rate is very low (in the case of oilseeds a minimum percolation rate of 3 x 10 m/s is normally required), extraction by immersion may be more effective. Percolation rate measurements and the methods of utilizing the data have been reported (8,9) these indicate that the effect of solute concentration on holdup plays an important part in determining the solute concentration in the hquor leaving the extractor. 

Gas holdup with Rushton turbine can be estimated from the following correlation ... 

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)]. 

The time of passage in rotarv Idlns (from which holdup can be calculated) can be estimated by the following formula (U.S. Bur. Mines Tech. Pap. 384, 1927) ... 

Static holdup depends upon the balance between surface-tension forces tending to hold hquiciin the bed and gravity or other forces that tend to displace the liquid out of the bed. Estimates of static holdup (for gravity drainage) may be made from the following relationship of Shulman et al. [Am. Jn.st. Chem. Eng. J., 1, 259 (1955)] ... 

Operating holdup may be estimated by the dimensionless equation of Buchanan [Jnd. Eng. Chem. Eundam., 6,400 (1967)] ... 

Gas Holdup (e) in Bubble Columns With coalescing systems, holdup may be estimated from a correlation by Hughmark [Ind. Eng... 

The power for agitation of two-phase mixtures in vessels such as these is given by the cuiwes in Fig. 15-23. At low levels of power input, the dispersed phase holdup in the vessel ((j)/ ) can be less than the value in the feed (( )df) it will approach the value in the feed as the agitation is increased. Treybal Mass Transfer Operations, 3d ed., McGraw-HiU, New York, 1980) gives the following correlations for estimation of the dispersed phase holdup based on power and physical properties for disc flat-blade turbines ... 

Instrument and Plant Air Systems. A typical setup for a large plant could include three to four 50% instrument air compressors and two 100% plant air compressors, with steam drives for normally operated units and electrical drives for spares. Common practice would provide an interconnection to allow makeup from plant air into instrument air, but not vice versa, and two sets (two 100% driers per set—one on-stream and one regenerating) of 1007c instrument air driers. Two main receivers on instrument air near the compressors with several minutes holdup time and satellite receivers at process trains would be likely and proper for feasibility cost estimating. 

This brief discussion of some of the many effects and interrelations involved in changing only one of the operating variables points up quite clearly the reasons why no exact analysis of the dispersion of gases in a liquid phase has been possible. However, some of the interrelationships can be estimated by using mathematical models for example, the effects of bubble-size distribution, gas holdup, and contact times on the instantaneous and average mass-transfer fluxes have recently been reported elsewhere (G5, G9). 

Values of the holdup may be used to estimate the frictional losses in the pipe, since the overall difference in fluid head Ah of the liquid is equal to the friction head less the hold-up of liquid per unit area ... 

The central difficulty in applying Equations (11.42) and (11.43) is the usual one of estimating parameters. Order-of-magnitude values for the liquid holdup and kiA are given for packed beds in Table 11.3. Empirical correlations are unusually difficult for trickle beds. Vaporization of the liquid phase is common. From a formal viewpoint, this effect can be accounted for through the mass transfer term in Equation (11.42) and (11.43). In practice, results are specific to a particular chemical system and operating mode. Most models are proprietary. 

Mathematical methods for determining the gas holdup tine are based on the linearity of the plot of adjusted retention time against carbon number for a homologous series of compounds. Large errors in this case can arise from the anomalous behavior of early members of the homologous series (deviation from linearity in the above relationship). The accuracy with which the gas holdup time is determined by using only well retained members of a homologous series can be compromised by instability in the column temperature and carrier gas flow rate [353,357]. The most accurate estimates... 

The final dimensionless group to be evaluated is the interfacial heat-transfer number, and therefore the interfacial heat-transfer coefficient and the interfacial area must be determined. The interface is easily described for this regime, and, with a knowledge of the holdup and the tube geometry, the interfacial area can be calculated. The interfacial heat trasfer coefficient is not readily evaluated, since experimental values for U are not available. A conservative estimate for U is found by treating the interface as a stationary wall and calculating U from the relationship... 

If the hydrodynamics of the two-phase systems are understood, and the holdups and phase Reynolds numbers known, the rate of heat transfer can be estimated with about the same confidence as that for single-phase systems. 

Macbeth (M5) has recently written a detailed review on the subject of burn-out. The review contains a number of correlations for predicting the maximum heat flux before burn-out occurs. These correlations include a dependence upon the tube geometry, the fluid being heated, the liquid velocity, and numerous other properties, as well as the method of heating. Sil-vestri (S6) has reviewed the fluid mechanics and heat transfer of two-phase annular dispersed flows with particular emphasis on the critical heat flux that leads to burn-out. Silvestri has stated that phenomena responsible for burn-out, due to the formation of a vapor film between the wall and the liquid, are believed to be substantially different from phenomena causing burn-out due to the formation of dry spots that produce the liquid-deficient heat transfer region. It is known that the value of the liquid holdup at which dry spots first appear is dependent on the heat flux qmi. The correlations presented by Silvestri and Macbeth (S6, M5) can be used to estimate the burn-out conditions. 

At present, Eq. (68) only provides a simple estimate of the mass and energy transfer processes in forced-flow nucleation. The methods for evaluating the parameters must be improved by further detailed research on forced-flow nucleation. In particular, the calculation of the rate of nucleation n and of the bubble departure frequency / are the weakest points in the analysis of this heat-transfer region. Obviously, accurate prediction of the pressure drop and holdups are also needed. 

This heat-transfer region has been more widely studied than either Region II or IV. However, the methods for evaluating the parameters have not been tested over a wide range of experimental conditions. Equations (71) and (72) must be coupled with a knowledge of the pressure drop, holdups, and other system parameters if the temperature and mass flow-rate profiles are to be determined. As mentioned earlier in this chapter, the pressure drop and holdups in phase change systems can be estimated by using the Martinelli-Nelson Correlation. 

As shown in Section I, very little is known about predicting liquid-liquid flow patterns and calculating pressure drops, holdups, and interfacial areas however, some estimates can be made by assuming no slip between the phases, using... 

The actual residence time of a reactor is measured by employing residence time distribution (RTD) experiments utilizing tracing techniques. Furthermore, several correlation forms estimating the fluid holdup can be found in the related literature. 

Gas-liquid mass transfer in fermentors is discussed in detail in Section 12.4. In dealing with in gas-sparged stirred tanks, it is more rational to separate and a, because both are affected by different factors. It is possible to measure a by using either a light scattering technique [9] or a chemical method [4]. Ihe average bubble size can be estimated by Equation 7.26 from measured values of a and the gas holdup e. Correlations for have been obtained in this way [10, 11], but in order to use them it is necessary that a and d are known. 

This correlation gives, for perfectly wettable solids, fairly good estimates of the static holdup for different particle-geometries and sizes. Saez and Carbonnel [26] used the hydraulic diameter, instead of the nominal particle diameter, as the characteristic length in the Eotvos number, to include the influence of the particle geometry on the static hold-up. However, no improvement could be obtained in correlating the data with this new representation. 

The preceding estimated values compare well with those experimental values. The percent errors as defined in Example. 1 are -1.4 percent for the power consumption, 15 percent for the gas holdup, and -21.7 percent for the volumetric mass-transfer coefficient. 

Holdup can be estimated by using Buchanan s correlation [lnd. Eng. Chem. Fund. 6, 400 (1967)], as recommended in previous editions of this handbook. More recent correlations by Billet and Schultes [IChemE. Symp. Ser. 104, A159 (1987)], by Mackowiak... 

To estimate the total interfacial area in a given volume, the ad value is multiplied by the fractional holdup of dispersed phase in the total volume. 

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