Ergun correlation

Fig. 10. Normalized drag force at arbitrary Reynolds numbers and gas fractions. The symbols represent the simulation data, the solid line the Ergun correlation Eq. (18), the dashed line the Wen-Yu correlation Eq. (46) for e = 0.8, and the grey line the correlation by Hill et al. (2001a,b) Eq. (47) and the long-dashed line Eq. (19), both for e = 0.5.

There are few reported comparisons to experimental pressure drop data taken by the same workers. An exception is Calis et al. (2001) who compared CFD, the Ergun correlation and experimental data for N — 1-2. They found 10% error between CFD and experimental friction factors, but the Ergun equation... 

Rewriting the definition of the friction factor f from equation 21.3-5, and the Ergun correlation for/given by equation 21.3-7, both at mf, we obtain... 

The Ergun correlation uses a particle diameter defined to be the equivalent diameter of a sphere having the same specific surface (area of particle/volume of particle) as the particle. The Ergun equation for the friction factor is then... 

The dimensionless drag function is composed of a viscous (laminar) and inertial (turbulent) term and can be specified according to bed material properties. The Ergun correlation [127] found wide application for coal bed characterization, which is... 

Since the term Apfr given by Ergun correlation is the contribution of fluid flow resistance in the total static pressure difference Ap, we can write... 

Here, the Reynolds number is based on the particle diameter dp. For a radial aspect ratio K/dp less than 25, Mehta and Hawley (1969) suggest the following modified Ergun correlation, which includes wall elBTects ... 

In the drag force, the influence of the gas on the particle is described with interphase momentum transfer coefficient P p which is calculated depending on the porosity of the soHd phase e. For the dense regimes, when porosity is smaller than 0.8, the coefficient is calculated according to the Ergun correlation (Ergun, 1952) ... 

Pressure Drop. The prediction of pressure drop in fixed beds of adsorbent particles is important. When the pressure loss is too high, cosdy compression may be increased, adsorbent may be fluidized and subject to attrition, or the excessive force may cmsh the particles. As discussed previously, RPSA rehes on pressure drop for separation. Because of the cychc nature of adsorption processes, pressure drop must be calculated for each of the steps of the cycle. The most commonly used pressure drop equations for fixed beds of adsorbent are those of Ergun (143), Leva (144), and Brownell and co-workers (145). Each of these correlations uses a particle Reynolds number (Re = G///) and friction factor (f) to calculate the pressure drop (AP) per... 

For the full range of flow, including the smaller flows and on smaller size catalysts, a more useful correlation for pressure drop is the Ergun... 

Figure 3.4.3 illustrated that the pressure drop is independent of the catalyst quantity charged at any one RPM. This must be so, as will appear later on the modified Ergun equation. Since RPM is constant, so is AP on the RHS of the equation. Therefore, on the LHS, if bed depth (L/dp) is increasing, u must drop to maintain equality. Results over 5, 10, and 15 cm catalyst, and pumping air, all correlate well with the simple equation ... 

The void fraction should be the total void fraction including the pore volume. We now distinguish Stotai from the superficial void fraction used in the Ergun equation and in the packed-bed correlations of Chapter 9. The pore volume is accessible to gas molecules and can constitute a substantial fraction of the gas-phase volume. It is included in reaction rate calculations through the use of the total void fraction. The superficial void fraction ignores the pore volume. It is the appropriate parameter for the hydrodynamic calculations because fluid velocities go to zero at the external surface of the catalyst particles. The pore volume is accessible by diffusion, not bulk flow. 

Several correlating equations for the friction factor have been proposed for both the laminar and turbulent flow regimes, and plots of fM (or functions thereof) versus Reynolds number are frequently presented in standard fluid flow or chemical engineering handbooks (e.g., 96, 97). Perhaps the most useful of the correlations is that represented by the Ergun equation (98)... 

Expression in Eq. (19) is within 8% of all simulation data up to Re — 1000. Since this relation has been derived very recently (Beetstra et al., 2006), it has not been applied yet in the higher scale models discussed in Sections III and IV. However, the expression by Hill et al. in Eq. (47) derived from similar type of LBM simulations is consistent with our data, in particular when compared to the large deviations with the Ergun and Wen and Yu equations. So, we expect that the simulation results presented in Section IV.F using the Hill et al. correlation will not be very different from the results that would be obtained with expression in Eq. (19). A more detailed account of the derivation of expression in Eq. (19) and a comparison with other drag-force relations can be found in Ref. Beetstra et al. (2006). 

Note that the validity of both the Ergun and Wen and Yu equations has recently been questioned on the basis of LB data, and alternative drag-force correlations have been proposed. From LB simulations, Hill et al. (2001a, b) suggest the following relation for Stokes flow (lim Rea->0) ... 

The validation of CFD codes using pressure drop is most reliable when actual experimental data are taken in equipment identical to the situation that is being simulated. Existing literature correlations such as the Ergun equation are known to have shortcomings with respect to wall effects, particle shape effects, application to ordered beds and validity at high Re. The applicability of literature correlations to typical CFD simulation geometries needs to be examined critically before fruitful comparisons can be made. 

The desire to save energy calls for low pressure drop over the catalyst layers because they account for a significant part of the total pressure drop through the sulphuric acid plant. According to simple correlations such as the Ergun equation [12], the pressure drop over a catalyst bed per bed length at a given flow rate and properties of the gas only depends on the bed void fraction e and a characteristic pellet diameter... 

With good dry scrubbing sorbents, the controlling resistance for gas cleaning is external turbulent diffusion, which also depends on energy dissipated by viscous and by inertial mechanisms. It turns out to be possible to correlate mass-transfer rate as a function of the friction factor [Ergun, CEP 48(2) 89 and 48(5) 227(1952)]. 

For flow through ring packings which as described later are often used in industrial packed columns, Ergun(10) obtained a good semi-empirical correlation for pressure drop as follows ... 

This equation is plotted as curve C in Figure 4.1. The form of equation 4.21 is somewhat similar to that of equations 4.16 and 4.17, in that the first term represents viscous losses which are most significant at low velocities and the second term represents kinetic energy losses which become more significant at high velocities. The equation is thus applicable over a wide range of velocities and was found by Ergun to correlate experimental data well for values of Rei/(l — e) from 1 to over 2000. 

Pressure drop Using the Ergun equation, the liquid and die gas pressure drop are 0.726 and 2.12 kPa/m, respectively. Then, by using the correlation of Larkins et al., die two-phase pressure drop is equal to 10.8 kPa/m, ten times lower than in die pulsing-flow regime and low enough to assure diat the gas density is almost constant. Thus, die condition (e) is satisfied. 

Original model (with Ergun constants correlation of [43]). 

The disadvantage is that there is no reliable correlation of the single-phase pressure drop in almost all cases it is possible to use an equation of Ergun s type, but the empirical coefficients of this correlation have to be determined experimentally a priori calculation can be very inaccurate. 

I. Iliuta, F. Larachi and B.P.A. Grandjean, Pressure drop and liquid hold-up in trickle flow reactors improved Ergun constants and slip correlations for the slit model, Ind. Engng. Chem. Res., 37 (1998) 4542-4550. 

A long-established correlation of the friction factor is that of Ergun (Chem. Eng. Prog. 48, 89-94, 1952). The average deviation from his line is said to be 20%. The friction factor is... 

The next step is to characterize the resistances offered by the porous catalyst bed and support screens. Several correlations relating the pressure drop through porous beds and velocity and bed characteristics are available. We select an Ergun equation6 to represent the resistance of catalyst bed ... 

There are a number of pressure drop correlations for two-phase flow in packed beds originating from the Lockhart-Martinelli correlation for two-phase flow in pipes. These correlate the two-phase pressure drop to the single-phase pressure drops of the gas and the liquid obtained from the Ergun equation. See, for instance, the Larkins correlation [Larkins, White, and Jeffrey, AIChE J. 7 231 (1967)]... 

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