Experimental characterization of pressure drop in slender packed bed (1 < D/d < 3)
Introduction
Packed beds have wide applications in the chemical, agricultural and metallurgical industries as reactors, dryers, filters, heat exchangers, and adsorbers. The popularity of packed beds originates largely from the convenience in construction and operation as well as their low cost. It has driven an almost incredible number of studies investigating the mechanisms of heat and mass transfer, and the flow and pressure drop of the fluid through the bed of solid for the high economic value represented by packed beds, and continue to do so (Calis et al., 2001).
Packed bed reactors with large aspect ratios (D/d) suffer from high flow resistance and low heat transport in radial direction. If the process is exothermic, the low heat transport can lead to hot spots in the reactor bed. Therefore, in order to create a highly efficient reactor, slender packed beds are used as reactor tubes, which have advantages on pressure drop reduction and uniformity of temperature (Langsch et al., 2014). It is a promising approach towards the enhancement of packed bed reactors. For industrialization, further investigations and optimizations with regard to an acceptable pressure drop, rapid heat removal and higher reaction rates are necessary.
Understanding the associated pressure drop characterization in porous media is critical as it directly influences convection heat transfer, chemical reaction rates and filtration effectiveness, as well as the required pumping power in applications (Dukhan et al., 2014). Fluid flow in packed beds is complex mainly due to the structure of the media in the path of the fluid. The structure drastically changes the flow field: it destroys boundary layers and compels the fluid travel only through winding and tortuous open flow passages. These effects cause vigorous mixing and occurrence of an added mechanism called dispersion (Bağcı et al., 2014). Therefore, the fluid mechanisms are sensitive to the structure properties in the packed beds.
The superficial axial velocity variations along radial direction are consistent with the radial porosity variations of packed beds, and as expected at places of low porosity, high velocities are observed (Das et al., 2017, Eppinger et al., 2011). Since the geometry of the packing is interrupted by confining wall, the porosity approaches unity in the vicinity of the wall in packed beds. As a result, the velocity profile inside a packed bed can be severely distorted near the wall where the fluid velocity reaches the maximum. This phenomenon is known as flow channeling effect (White and Tien, 1987). Clearly, the annular zone near the wall comprises an increasing fraction of the cross-sectional area in a cylinder column as the aspect ratios decrease. Therefore, the influence of the wall upon the flow distribution becomes more significant with the D/d progressively decreasing and it could lead to non-uniform head loss in packed beds.
The most widely used correlation for pressure drop is the Ergun equation (Eq. (1)) (Ergun, 1952) in packed bed with large aspect ratios. Ergun also defined the modified friction factor fk as Eqs. (2), (3) with the coefficient a = 150 and b = 1.75.
It expresses the pressure drop as the sum of the viscous and inertial energy losses.
When the aspect ratios decease to a certain extent, the Ergun equation is not applicable due to the wall effect. It is thought the wall has twofold influences on pressure drop in packed bed. In the creeping flow regime, the pressure drop may be increased due to the additional wall friction. On the other hand, in turbulent flows, the pressure drop might be reduced by the channeling effect in the near-wall region. Therefore, the flow parameters in Ergun equation become functional dependent upon D/d ratios: the contribution of the confining walls to the hydraulic radius is accounted for analytically by the coefficient a and the channeling effect at high Reynolds numbers is empirically described by the coefficient b (Cheng, 2011, Eisfeld and Schnitzlein, 2001).
The radial porosity distribution for mono-sized spheres in cylindrical containers has been investigated extensively using experimental and numerical methods for decades (Antwerpen et al., 2010, Mueller, 2010). Extensive studies in literature conclude that the radial porosity profile follows an oscillatory fashion with the amplitude decreasing as increase distance from the wall (Klerk, 2004, Mueller, 1992, Suzuki et al., 2008). However, when the aspect ratio decreasing to D/d < 3, radial porosity profiles of slender packed beds are radically different from the profiles in packed beds with relative large aspect ratios. In D/d < 2, the particles in packed bed tend to be arranged in a highly ordered way, being always in contact with the confining wall (Govindarao et al., 1992, Mueller, 1992). As the aspect ratio increases to 2 < D/d < 3, a porosity peak at the center of packed beds is found by experiments and numerical method (Benenati and Brosilow, 1962, Guo et al., 2017, Mueller, 1992, Theuerkauf et al., 2006). This indicates that a free channel can exist along the centerline with quite low porosity in packed bed at 2 < D/d < 3.
Consequently, the fluid mechanism in the packed bed is affected by the structure variations. Ren et al. (2005) studied the visualization of flow in packed beds by Nuclear Magnetic Resonance (NMR) method. For packed bed with large aspect ratios, the velocity maximum was found near the wall. However, a more pronounced velocity peak was observed in the center of the packed bed at D/d = 2.7. Yang et al. (2015) used the electrochemical technique to test flow transitions in random packed beds. For the packed bed at D/d = 2.6, a much higher Reynolds number (Re = 500) was obtained for the end of laminar flow regime than the others at D/d > 5.3 (Re = 110).
With the different packed bed structure and abnormal hydraulic phenomena in packed bed, the pressure drop characteristics of the slender packed beds are expected different from the packed beds with small aspect ratios. Fand et al., 1993, Fand and Thinakaran, 1990 studied the pressure drop in packed beds at 1.08 < D/d < 40. They found that, with the wall effect, the flow parameters became functional dependent upon the aspect ratios at D/d < 40. But the variations of the parameters were different below D/d < 1.40 (where they were monotonically decreasing with aspect ratios) from what was above D/d > 1.40 (where they were monotonically increasing). Bai et al. (2009) studied the pressure drops in packed beds at D/d < 4 by numerical and experimental method. They found that the modified friction factors fk varied dramatically, which confirmed the inconsistency and unreliability of the empirical correlations for the packed beds in this range of aspect ratios. Montillet et al. (2007) studied the pressure drop characteristics of packed beds at 3 < D/d < 14.5. The experimental result of D/d < 3.5 failed to follow the tendency of the others in the analysis. Therefore, they suggested that the pressure drop of packed bed should be investigated separately in this range of aspect ratios.
These studies above demonstrate that not only the local behavior but also the macroscopic characteristics of fluid flow in slender packed bed (D/d < 3) are affected by the geometric features. However, there is scarce experimental work devoted to the pressure drop in slender packed beds in literature. Especially for the pressure drop characteristics in high superficial velocity regime, it is of interest for practical applications of the slender packed bed as reactor tubes for applications such steam reforming or nuclear reactors, which typically operate at high Reynolds numbers (up to 104) (Dixon et al., 2012, Hassan et al., 2012).
Additionally, for validation of Computational Fluid Dynamics (CFD) simulations in packed beds, most studies have computed pressure drop, which was then compared to literature correlations. There is a wide range of pressure drop correlations for fixed beds, especially if wall effects are to be taken into account, different ones have been used in the various studies, with varying agreement (Dixon et al., 2012). Meanwhile, the CFD simulation by Dorai et al., (2015) showed that slender packed bed had a tendency to be subject to high variability on pressure drop. Even pressure drop increase was observed with the increase of mean porosity in packed bed at D/d = 3 (Freund et al., 2003). However, the simulations of packed beds at D/d < 3 can hardly been examined with the scarce experimental data.
To fill this gap, a series of experiments are carried out to investigate the pressure drop characteristics of slender packed beds at high Reynolds numbers. The new set of experimental data is presented. And it is compared with the correlations in literature to discuss and confirm their applicability. Some interesting phenomena are observed in current work. And the data presented might be used for CFD validations and the optimum design in industrial applications.
Section snippets
Test facility
The experimental apparatus used in this investigation is depicted schematically in Fig. 1. It mainly consists of three parts: water flow loop, test section and measurement equipment. Water is supplied by the centrifugal pump from the reservoir tank to the test tube in most cases. For tests at low flow rate, an elevated tank is used to guarantee a steady and constant water head. The flow rate is adjusted by the inflow valve and the bypass valve. After passing through the test tube, water is
Packed beds at D/d < 2
The experimental results of measured pressure drops at D/d < 2 are presented in Fig. 6. The general trend of the pressure gradient is that it increases with the superficial velocity. Remarkable pressure drop increase is obtained of packed bed at D/d = 1.025. Even compared with the packed beds, which have the same mean porosity at large aspect ratios, it is still much higher. For instance, at a velocity of about 0.1 m/s, the pressure gradient in packed bed at D/d = 1.025 is about 100 kPa/m, while at the
Modifications to empirical correlation
Although the in-homogeneities are not well represented by the mean porosity, packed beds at 1 < D/d < 2 have relative ordered structure. The analysis in Section 3.1 provides an indication of the possible functional relationship between the aspect ratios and the flow parameters. Therefore, it seems possible for predicting the pressure drop of packed beds in this range by empirically expressing the coefficient term as functions of aspect ratios.
Fand et al., 1993, Fand and Thinakaran, 1990 expressed
Conclusions
Experiments on single-phase flow through packed beds have been carried out using water at 1.025 < D/d < 2.88. Considering the existence of various stable packing configurations at D/d > 2, the assembly method and its corresponding structure are investigated of the influences on the pressure drop characteristic. Then experimental results are compared with the predictions of empirical correlations in literature. And the major findings are as follows:
- (1)
The mean porosity is hardly to represent the
Acknowledgments
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
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