Pressure Drop in Packed Shallow Beds of Cylindrical Cork Stoppers

Rangel, N.; Santos, Abel D.; Pinho, Carlos

doi:10.1205/02638760152424316

Cited by 7 publications

(4 citation statements)

References 10 publications

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“…However, various research works have been conducted in which a comparison between modified correlations of Ergun and contemporaneous correlation has been made and as a result a deficiency is obtained in predicting pressure drop by the classical model of Ergun compared to the modified correlations. − It has been established in the literature that deviations from the predicted pressure drop across packed beds that exhibit the classical correlation of Ergun may be due to the high sensitivity of the equation to variations in the bed porosity by which it is necessary to estimate accurately the packed bed porosity especially when dealing with nonspherical geometry . It has been found that several factors influence the bed porosity such as the particle diameter, particle size distribution, surface roughness, Reynolds number, and others. , In summary, the literature reports give both theoretical and experimental evidence that pressure drop depends on flow velocity and physical properties (viscosity and density), the average bed porosity, shape and surface of the particles packaging, bed height, and contribution of the ratio of particle to the container diameters. − …”

Section: Development Of a Generalized Reactor Modelmentioning

confidence: 99%

“…For the proposed model, the pressure drop is calculated by considering the general balance of momentum and an equation of Ergun (Tables and ) recently reported in the literature, where the coefficients that determine the viscous effects and kinetics (inertial) correspond to general constants κ 1 and κ 2 , respectively. The model includes parameters such as β 1 w and β 2 w , which take into account the effects of the reactor wall on pressure drop across the bed …”

Section: Development Of a Generalized Reactor Modelmentioning

confidence: 99%

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Modeling of Catalytic Fixed-Bed Reactors for Fuels Production by Fischer–Tropsch Synthesis

2017

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A comprehensive review of the various studies reported in the literature to date on the mathematical modeling of fixed-bed reactors for the production of fuels by the Fischer–Tropsch synthesis (FTS) was carried out. It is quite clear that most of the proposed models are based on a set of assumptions that allow their wide simplification by reducing the models into forms of low complexity, due to the fact that in most cases the effects of phase equilibrium are neglected, and relatively simple Fischer–Tropsch kinetics of the power law type are used. In addition, most of the proposed modeling schemes neglect the effects of resistances to gas–liquid and liquid–solid mass transfer. On the other hand, few reports consider the energy effects under the consideration of a nonisothermal operation assuming a plug-flow behavior and a gas–liquid system. A generalized model of a fixed-bed FTS reactor is proposed which takes into account all the mass and heat transfer phenomena, as well as hydrodynamics and vapor–liquid equilibrium (VLE), based on the information given in the literature. It is evident that for fixed-bed reactors for fuel production using Fischer–Tropsch technology, there is little experimental information for validation and a need to explore different types of reactor models, such as reactor models under a trickle-flow regime considering the effects of phase distribution and dispersion under transient-state conditions.

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Section: Development Of a Generalized Reactor Modelmentioning

confidence: 99%

Section: Development Of a Generalized Reactor Modelmentioning

confidence: 99%

Modeling of Catalytic Fixed-Bed Reactors for Fuels Production by Fischer–Tropsch Synthesis

2017

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“…Due to entrance pressure drop effects, some of the shorter lengths used in these studies might have led to the determination of a pressure drop that is higher than the bulk pressure drop, so one must be careful when using these results. Another reference to the importance of the length of the porous matrix when compared to the diameter of the particles that constitute this matrix is made by Rangel et al [14]. These authors state that quite often in industrial applications the particles have a size of the order of magnitude of the bed dimension.…”

Section: Introductionmentioning

confidence: 99%

“…The review of the literature presented in the next paragraphs shows that there are not many studies that focus on the entrance and/or exit pressure drop effects in the determination of the pressure drop in porous media. Rangel et al [14] determined experimentally the pressure drop through packed beds of cylindrical cork stoppers. They developed a model for the calculation of the pressure drop in packed beds where the length of the porous medium is of the order of magnitude of the particle size.…”

Section: Introductionmentioning

confidence: 99%

Pressure Drop through Structured Porous Media - Inlet and Outlet Effects

Malico

Sousa

2017

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Inlet and outlet pressure drop effects can contribute significantly to the total pressure drop in porous media if thin solid matrices are used. However, these effects are usually ignored and few are the studies that focus on this topic. This paper uses a numerical simulation approach to determine the importance of the inlet and outlet pressure drop effects on the total pressure drop in a staggered arrangement of square cylinders with equal sizes, dc. The Navier-Stokes equations are solved at the pore level for several matrix lengths (from dc to 34dc) and for several Reynolds numbers based on dc and maximum velocity of the velocity inlet profile (from 36 to 120). Accurate results of the velocity and pressure fields are obtained through the use of the immersed boundary method in combination with the finite differences method, 4th-order compact schemes for spatial discretization and 4th-order Runge-Kutta temporal discretization. The results presented in this paper confirm that the classical models (e.g., Hazen-Dupuit-Darcy model) are only valid when the solid matrix has a length above a certain value, called the critical length. For shorter porous media, the pressure drop does not vary linearly with the matrix length. The deviations to the model that occur at the shortest porous media are explained by the entrance and exit contributions to the total pressure drop that, in these cases, are not negligible when compared to the bulk pressure drop. For the staggered array of square cylinders and range of Reynolds numbers considered, the critical porous medium length is 16dc. A practical outcome of the present study is the quantification of the influence of the pressure tap locations on the measurements of pressure drop in porous media. When the matrix is short when compared to the particle diameter, care must be taken with the pressure taps placement: they should be located outside the porous matrix and not too close to its inlet and outlet sections. If the matrix is thick enough when compared to the particle diameter, the taps can be placed either inside or outside the matrix. Also, if the influence of the side walls on the total pressure drop is not high (i.e., the walls are at a relative large distance when compared to the particle diameter), there is no practical need to correct the measured pressure values to account for the influence of the walls. This correction should be considered for the shortest matrices though.

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Modeling of Fischer–Tropsch Synthesis Reactor

Méndez,

Ancheyta

2024

Mathematical Modeling of Complex Reaction Systems in the Oil and Gas Industry

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Pressure Drop in Packed Shallow Beds of Cylindrical Cork Stoppers

Cited by 7 publications

References 10 publications

Modeling of Catalytic Fixed-Bed Reactors for Fuels Production by Fischer–Tropsch Synthesis

Modeling of Catalytic Fixed-Bed Reactors for Fuels Production by Fischer–Tropsch Synthesis

Pressure Drop through Structured Porous Media - Inlet and Outlet Effects

Modeling of Fischer–Tropsch Synthesis Reactor

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