Coalescers sizing equations

Coalescer sizing. The general sizing equation for plate coalescers with flow parallel to or perpendicular to the direction of bulk water flow is ... 

Cross-flow device sizing. Cross-flow devices obey the same genera) sizing equations as plate coalescers. Although some manufacturers claim these units arc more efficient than CPIs, the reason for this is neither apparent from theory nor from lab or field tests. 

Based on the critical droplet sizes for breakup and coalescence in Equations 19.12 and 19.20, the droplet size in polymer blends as a function of flow intensity (shear rate) can be mapped out [28], as shown in Figure 19.4. The critical droplet sizes for droplet breakup and coalescence become equal at a certain critical shear rate. For shear rates larger than this critical value, the critical droplet size for breakup is smaller than the critical droplet size for coalescence and the final droplet size is determined by a dynamic equilibrium between breakup and coalescence. However, below the critical shear rate, the critical droplet size for breakup is larger than the critical droplet size for coalescence, which results in a range of droplet sizes for which neither breakup nor coalescence will occur. This phenomenon is called morphological hysteresis and changing the flow conditions within this region... 

Cross-flow devices obey the same general sizing equations as plate coalescers. Although some manufacturers claim greater efficiency than CPIs, the reason for this is not apparent from theory, laboratory, or field tests as a result, verification is unavailable. If the height and width of these cross-flow packs are known. Equations (3.18a) and (3.18b) can be used directly. It may be necessary to include an efficiency term, normally 0.75, in the denominator on the right side of Equations (3.18a) and (3.18b) if the dimensions of H or W are large and a spreader is needed. 

For a general dimension d, the cluster size distribution fiinction n(R, x) is defined such that n(R, x)dR equals the number of clusters per unit volume with a radius between andi + dR. Assuming no nucleation of new clusters and no coalescence, n(R, x) satisfies a continuity equation... 

The prediction of drop sizes in liquid-liquid systems is difficult. Most of the studies have used very pure fluids as two of the immiscible liquids, and in industrial practice there almost always are other chemicals that are surface-active to some degree and make the pre-dic tion of absolute drop sizes veiy difficult. In addition, techniques to measure drop sizes in experimental studies have all types of experimental and interpretation variations and difficulties so that many of the equations and correlations in the literature give contradictoiy results under similar conditions. Experimental difficulties include dispersion and coalescence effects, difficulty of measuring ac tual drop size, the effect of visual or photographic studies on where in the tank you can make these obseiwations, and the difficulty of using probes that measure bubble size or bubble area by hght or other sample transmission techniques which are veiy sensitive to the concentration of the dispersed phase and often are used in veiy dilute solutions. 

This equation has been experimentally verified in liquids, and Figure 2 shows that it applies equally well for fluidized solids, provided that G is taken as the flow rate in excess of minimum fluidization requirements. In most practical fluidized beds, bubbles coalesce or break up after formation, but this equation nevertheless gives a useful starting point estimate of bubble size. 

The terminal settling velocity is given by Equation 8.6 or 8.8. Decanters are normally designed for a droplet size of 150 p,m3,9, but can be designed for droplets down to 100 p,m. Dispersions of droplets smaller than 20 p,m tend to be very stable. The band of droplets that collect at the interface before coalescing should not extend to the bottom of the vessel. A minimum of 10% of the decanter height is normally taken for this3. 

Analytical solutions of the self-preserving distribution do exist for some coalescence kernels, and such behavior is sometimes seen in practice (see Fig. 40). For most practical applications, numerical solutions to the population balance are necessary. Several numerical solution techniques have been proposed. It is usual to break the size range into discrete intervals and then solve the series of ordinary differential equations that result. A geometric discretization reduces the number of size intervals (and equations) that are required. Litster, Smit and Hounslow (1995) give a general discretized population balance for nucleation, growth and coalescence. Figure 41 illustrates the evolution of the size distribution for coalescence alone, based on the kernel of Ennis Adetayo (1994). 

The formation of bubbles at orifices in a fluidised bed, including measurement of their size, the conditions under which they will coalesce with one another, and their rate of rise in the bed has been investigated. Davidson el alP4) injected air from an orifice into a fluidised bed composed of particles of sand (0.3-0.5 mm) and glass ballotini (0.15 mm) fluidised by air at a velocity just above the minimum required for fluidisation. By varying the depth of the injection point from the free surface, it was shown that the injected bubble rises through the bed with a constant velocity, which is dependent only on the volume of the bubble. In addition, this velocity of rise corresponds with that of a spherical cap bubble in an inviscid liquid of zero surface tension, as determined from the equation of Davies and Taylor ... 

The derivation of equations 13.34 and 13.35 has been carried out assuming that u0 is constant and independent of the flowrates, up to and including the flooding-point. This in turn assumes that the droplet size is constant and that no coalescence occurs as the hold-up increases. Whilst this assumption is essentially valid in properly designed spray towers, this is certainly not the case with packed towers. Equations 13.34 and 13.35 cannot therefore be used to predict the flooding-point in packed towers and a more empirical procedure must be adopted. 

From experiments, equations have been derived that enable calculation of the minimum velocity in the nozzle, the nozzle velocity, and the Sauter diameter at the drop size minimum. They provide the basis for the correct design of a sieve tray [3,4]. Figure 9.4a shows the geometric design of sieve trays and their arrangement in an extraction column. Let us again consider toluene-phenol-water as the liquid system. The water continuous phase flows across the tray and down to the lower tray through a downcomer. The toluene must coalesce into a continuous layer below each tray and reaches... 

This equation reflects the possibility to measure [3,0] and Dg, both diameters being directly deduced from the experimental droplet size distributions. Of course, this procedure is to be applied at long times, that is, in the regime governed by coalescence ( >j > D ). In Fig. 5.7, it appears that CO exhibits a regular decrease with time. 

If the bubbles supply reactant into the liquid phase, then the bubbles are decreasing in size because of reaction so we need to find R it) or / b(z) of the bubbles as they rise in the reactor. Thus we have the problem of a sphere that varies in diameter as the reaction proceeds. We considered this in Chapter 9 where we were concerned primarily with reaction of solid spheres instead of liquid spheres. The bubbles usually have a distribution of sizes because larger bubbles usually rise faster than small ones, and they can coalesce and be redispersed by mixers. However, to keep the problem simple, we will assume that all particles have the same size. For the reactant A supplied from the bubble, we have to solve the equation... 

Forced coalescence. Referring again to Stoke s equation. notice that the panicle radius occurs taken to (lie second power. II the particle can Ik- increased, the settling velocity increases by the square ol this change. Particle size then becomes the overriding parametei in the separation process. 

After an initial period, increasing retention time has a small impact on the rate of particle growth.J Thus, for practically sized treaters with retention times of 10 to 60 minutes, retention time is not a determinant variable. Intuitively, one expects viscosity to have much greater effect upon coalescence than would temperature. With this in mind, the following equation appears to give reasonable results ... 

It is possible to theoretically trace particle size distribution up the tubing, through the choke, flowlines, manifolds and production equipment into the free water knockout using equations presented in previous installments However, many parameters needed to solve these equations, especially those involving coalescence, are unknown... 

Equation (A12) is widely used in RE, but it does not account for the specific interactions of the dispersed phase. In this respect current research is focused on drop population balance models, which account for the different rising velocities of the different-size droplets and their interactions, such as droplet breakup and coalescence (173-180). 

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