ERGUN

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... 

The overall pressure drop is expressed as the sum of a laminar term proportional to FT/DT and a turbulent term proportional to FP/DI to yield the Ergun equation (1) ... 

Leva et al (1949) and Ergun (1952) developed similar useful equations. Later, these were refined and modified by Handley and Heggs (1968 ) and by MacDonald et al (1979). All these equations try to handle the transient regime between laminar and turbulent flow somewhat differently but are based on the same principles. 

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 ... 

Pressure drop in the tube can be expressed with the use of the friction factor from the Ergun equation ... 

Axial pressure drop was calculated using the Ergun equation ... 

The convective wave cycle was described in 5.2.4 but its heat transfer properties not quantified. Critoph and Thorpe [22] and Thorpe [23] have measured the convective heat transfer coefficient between flowing gas and the grains within the bed. Preliminary results imply that the pressure drop through the bed can be expressed by a modified Ergun equation ... 

It is important to determine pressure drop of fluid through tubular reaetors, sueh as paeked, fixed, and fluidized bed reaetors where, eatalysts are employed. AP is an important faetor that influenees the design and operation of sueh reaetors. Ergun [3] developed a useful... 

AP equation arising from simultaneous turbulent kinetie and viseous energy losses that is applieable to all flow types. Ergun s equation relates the pressure drop per unit depth of paeked bed to eharaeteristies sueh as veloeity, fluid density, viseosity, size, shape, surfaee of the granular solids, and void fraetion. The original Ergun equation is ... 

For paeked beds in either laminar or turbulent flow the Ergun equation is... 

Ergun, S., Eluid flow through packed columns, Chem. Eng. Prog. 48, No. 2, 89, 1952. 

The next step is to eharaeterize the resistanees offered by the porous eatalyst bed and support sereens. Several eorrelations relating the pressure drop through porous beds and veloeity and bed eharaeteristies are available. We seleet an Ergun equation to represent the resistanee of eatalyst bed ... 

Whilst Ergun (1952) made a linear sum of the laminar and turbulent terms thus... 

Figure 2.12 Packed bed pressure loss Euler number versus particle Reynolds number (Ergun, 1952)...

The pressure drop is given by the Ergun equation (Ergun, 1952), expressed by... 

Ergun, S., 1952. Fluid flow through packed colomns. Chemical Engineering Progress, 48, 89. 

For packed beds in either turbulent or laminar flow, the Ergun equation is often satisfactory ... 

The pressure is also given by an ODE. The Ergun equation. Equation (3.17), applies to a packed bed ... 

Geometrically Similar Scaleups for Packed Beds. As was the case for scaling packed beds in series, the way they scale with geometric similarity depends on the particle Reynolds number. The results are somewhat different than those for empty tubes because the bed radius does not appear in the Ergun equation. The asymptotic behavior for the incompressible case is... 

Note that Sr appears here even though it is missing from the Ergun equation. It arises because throughput is proportional to F u. 

These asymptotic forms may be useful for conceptual studies, but the real design calculations must be based on the full Ergun equation. Turning to the case of compressible fluids, scaleup using geometric similarity with Sr = Sl = S is generally infeasible. Simply stated, the reactors are just too long and have too much inventory. 

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. 

MI199> I. Isikdag, U. Ucucu, K. Benkli, N. Gundogdu, Y. Ozturk, S. Aydin, B. Ergun, Boll. Chim. Farm. 1996,135, 199. 

Ergun, E. et al.. Simultaneous determination of chlorophyll a and chlorophyll b by derivative spectrophotometry. Anal. Bioanal. Ghent., 379, 803, 2004. 

Tun bilek, K., Sari, A., Tarhan, S., Ergunes, G., and Kaygusuz, K., 2005, Laurie and palmitic acids eutectic mixture as latent heat storage material for low temperature heating applications, Energy 30 677—692. 

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)... 

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