Pressure drop Ergun correlation

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 ... 

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... 

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... 

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 ... 

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. 

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. 

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)]... 

The particle model This model attributes pressure drop to friction losses due to drag of a particle. The preeence of liquid reduces the void fraction of the bed and also increases the particle dimensions. Ergun (94) applied this model for single-phase flow (e.g., fixed and fluidized beds). Stichlmair et al. (95) successfully extended this model to correlate pressure drop and flood for both random and structured packings. Their correlation is complex and requires some additional validation, but is the most fundamental correlation available. 

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... 

The most commonly used pressure drop equations for fixed beds of solid ndsoibem are those of Brownell et a].,66 of Ergun. and of Leva.47 Each of these correlations requires the use of the puiticle Reynolds number,... 

Fluid. In the fluid phase, we track the molar flows of all species, the temperature and the pressure. We can no longer neglect the pressure drop in the tube because of the catalyst bed. We use an empirical correlation to describe the pressure drop in a packed tube, the well-known Ergun equation [1 Of Therefore, we have the following differential equations for the fluid phase... 

Figure 7.36 Correlation of pressure drop in fixed beds according to the Ergun equation Re dpup/fi). [From S. Ergun, Chem. Eng. Prog., 48, 89, with permission of the American Institute of Chemical Engineers, (1952).]...

Determination of the minimum fluidization velocity is a little more complicated, but still straightforward. The well-accepted correlation for pressure drop of a fluid flowing through a packed bed, from Ergun, we repeat here, but written in terms of the minimum fluidization velocity. 

The pressure drop for concurrent downflow of gas and liquid in a packed bed can be predicted using correlations of the Lockhart-Martinelli type [22]. The pressure drop for each phase flowing separately through the bed is calculated using the Ergun equation [Eq. (3.64)], and these values define a parameter x ... 

The pressure drop in ceramic and metallic foams can thus be estimated based on a modified Ergun equation [39]. Recently, Dietrich [40] evaluated the pressure drop measurements of nearly 100 different foams reported by about 25 authors. He could describe the experiments with an error of 40% in a broad range of Re numbers (10 < Re < 10 ) with the following correlation ... 

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