Packed Ergun equation

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... 

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. 

The pressure drop through the packed bed reactor is governed by the Ergun equation discussed earlier as equation 12.7.4. 

Contributions to pressure drop have also been studied by lattice Boltzmann simulations. Zeiser et al. (2002) postulated that dissipation of energy was due to shear forces and deformational strain. The latter mechanism is usually missed by capillary-based models of pressure drop, such as the Ergun equation, but may be significant in packed beds at low Re. For a bed of spheres with N — 3, they found that the dissipation caused by deformation was about 50% of that... 

To calculate the pressure drop in a packed bed, the semi-empirical Ergun equation [54] may be used... 

The Eulerian continuum approach, based on a continuum assumption of phases, provides a field description of the dynamics of each phase. The Lagrangian trajectory approach, from the study of motions of individual particles, is able to yield historical trajectories of the particles. The kinetic theory modeling for interparticle collisions, extended from the kinetic theory of gases, can be applied to dense suspension systems where the transport in the particle phase is dominated by interparticle collisions. The Ergun equation provides important flow relationships, which are useful not only for packed bed systems, but also for some situations in fluidized bed systems. 

The Ergun equation relates the pressure drop in a packed bed to the flow rate and the properties of particle and gas. However, the application of this equation has been extended beyond the limits of fixed bed systems since it was first formulated in 1951. Thus, a detailed account of the origin of this equation is necessary. 

For packed-bed and turbulent flows, Darcy s law can be rewritten as the Ergun equation (9) ... 

AP equation arising from simultaneous turbulent kinetic and viscous energy losses that is applicable to all flow types. Ergun s equation relates the pressure drop per unit depth of packed bed to characteristics such as velocity, fluid density, viscosity, size, shape, surface of the granular solids, and void fraction. The original Ergun equation is ... 

Flow Through a Packed Bed of Spheres. The Ergun Equation (46), gives the pressure drop through a packed bed of spheres 2... 

In general, the Ergun equation for flow through a packed bed of non-spherical and polydisperse-sized particles becomes ... 

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)]... 

A somewhat different expression for d can be derived by solving Eq. (45) with the Ergun (E3) packed-bed equation, but since the spout is a high-voidage system, the use of Eq. (49) is more appropriate. 

These workers, who originally suggested the above approach, made use of the Ergun (E3) packed-bed equation for relating Umt to gas and solids properties by putting APfH in Ergun s equation equal to (ps — Pi) (1 —... 

For packed columns with single-phase flow, the Ergun equation can be used for the momentum balance and is ... 

Des. Dev., 8 (1969) 280] provided a correction factor to the Ergun equation to consider both the frictional losses from the wall and the packing, and their friction factor expression is ... 

Equation (4-28) will be the one we use when multiple reactions are occurring or when there is pressure drop in a membrane reactor. However, for single reactions in packed-bed reactors it is more convenient to express the Ergun equation in terms of the conversion X. RecaUing Equation (3-42) for Fj-,... 

Differential form of Ergun equation for the pressure drop in packed beds... 

We now proceed (Example 4-6) to combine pressure drop with reaction in a packed for the case where we will assume that eX 1 in the Ergun equation bat not in the rate law in order to obtain an anal3rtical solution. Example 4-7 removes this assumption and solves Equations (4-21) and (4-31) numerically. 

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