Ergun expression

At low particle Reynolds numbers for a bubbling bed, the Ergun expression can be simplified using only the first term in Eq. (31). 

The Reynolds number used in these correlations is based on particle diameter (or equivalent diameter) and superficial gas velocity. Although the numerical forms these expressions are different, they show reasonably close numerical agreement when the bed voidage is about 0.35, as may be seen from Figure 7.1. The Ergun expression shows clearly the dependence on bed voidage and may therefore be considered preferable. 

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) ... 

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

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

If the definitions of /PM and ARcRM are inserted into the Ergun equation, the resulting expression for the frictional energy loss (dissipation) per unit mass of fluid in the medium is... 

The dimensionless drag coefficient fiL/ ps u0) in Eq. (30) can be expressed in terms of other fluid parameters by the use of Eqs. (31-33). For low voidages where the Ergun-like expression holds,... 

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). 

The minimum fluidising velocity, umf, may be expressed in terms of the free-falling velocity o of the particles in the fluid. The Ergun equation (equation 6.11) relates the Galileo number Ga to the Reynolds number Re mj in terms of the voidage < , / at the incipient fluidisation point. 

The Richardson-Zaki equation has been found to agree with experimental data over a wide range of condifions. Equally, if is possible fo use a pressure drop-velocity relationship such as Ergun to determine minimum fluidization velocity, just as for gas-solid fluidizafion. An alternative expression, which has the merit of simplicify, is fhaf of Riba ef al. (1978)... 

The second term in the right-hand side of Eq. (5.392) represents the fluid inertia, whereas the first term represents the viscous contribution to the pressure drop. At low Reynolds numbers, the Ergun equation can be simplified by neglecting the inertial term. Under this condition, Eq. (5.392) can be expressed as... 

The review published by Ergun (E2) provides a definitive description of pressure drop in packed tubes when the ratio of particle diameter to tube diameter is sufficiently low. In addition, although the complicated relationship between the diameter ratio, the fraction void and the friction factor can not be accurately represented without some explicit dependence of the friction factor on the diameter ratio, Ergun showed that his correlation does work for a wide variety of experimental conditions. The friction factor is calculated from the expression... 

In the preceding analysis, the velocity-hold-up relationship was expressed in terms of the Richardson-Zaki equation. Alternatively, the relationship can be derived from the Ergun (1952) equation. This latter approach was used by Molerus (1993). 

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. 

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-,... 

Using the relationship between z and W [Equation (4-26)] we can change our variables to express the Ergun equation in terms of catalyst weight ... 

Ergun reduces however the reaction rate to a different expression in order to show the importance of the ratio CO/CO2 ... 

For a quick first approximation in the case of trickle flow, pressure loss may be expressed by an Ergun-type relationship in which the porosity c is replaced by c(l - /3), the total liquid extraparticle holdup /3 being calculated either by the correlation proposed by Sato et al. for spheres (S7) of diameter 2 mm or larger ... 

The state of fluidization begins at the point of minimum or incipient fluidization. At the minimum fluidization point, the pressure drop for a fixed bed and that for a fluidized bed are equivalent. This relationship is used as the basis for the formation of the predictive equation for the minimum fluidization velocity. The pressure drop in the fixed bed can be described by the Ergun equation. Under the minimum fluidization condition, the Ergun equation can be expressed as... 

The Ergun equation (described subsequently) assumes this fimctionality and incorporates explicit expressions for the two coefficients. For Re 1, turbulent flow is observed. However, due to the distribution of length scales and velocities, and the large surface area for viscous dissipation, the onset of turbulence is gradual as Re is increased, rather than sudden. 

For flow through a packed-bed reactor, the pressure drop is expressed in terms of the Ergun equation ... 

In this expression dp is the effective packing sine [= 6(1 — t)/ap) and K is the Ergun-Brauer wall factor... 

Kostakoglu L, Kiratli P, Ruacan S, Hayran M, Emri S, Ergun EL et al. Association of tumor washout rates and accumulation of technetium-99m-MIBI with expression og P-glycoprotein in lung cancer. J Nucl Med 1998 39 228 234. 

Many empirical and semi-empirical two-term expressions have been suggested to represent the hydrodynamic drag force experienced by a spherical particle in a concentrated suspension. It seems that the first expression of this kind was presented in the now classical work by Ergun [36]. Since then, many authors repeatedly returned to the problem and proposed other versions of the two-term hydraulic resistance law. One of the latest versions can be found in reference [37]. In the present paper, we will use the two-term law that has been advocated and discussed in reference [25]. According to this law. 

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