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Dry pressure drop in rotating packed beds – systematic experimental studies Kolja Neumann, Sira Hunold, Mirko Skiborowski, and Andrzej Górak Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b03203 • Publication Date (Web): 04 Oct 2017 Downloaded from http://pubs.acs.org on October 7, 2017

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Industrial & Engineering Chemistry Research

Dry pressure drop in rotating packed beds – systematic experimental studies Kolja Neumann a*, Sira Hunold a, Mirko Skiborowski a, Andrzej Górak a,b

a

TU Dortmund University, Department of Biochemical and Chemical Engineering, Laboratory of Fluid Separations, Emil-Figge-Straße 70, 44227 Dortmund, Germany

b

Lodz University of Technology, Faculty of Process and Environmental Engineering, Department of Environmental Engineering, Wólczañska 213, 90-924 Lódz, Poland

* Corresponding author. Tel.: +49 231 755 2357; Fax: +49 231 755 3035. E-mail address: [email protected]

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Abstract In rotating packed beds (RPBs) centrifugal forces are exploited in order to intensify the mass transfer between different phases. In order to derive correlations describing the hydrodynamics and the mass transfer in RPBs and to improve the understanding of fundamentals, comprehensive and systematic experimental investigations are required. The present study focuses on the dry pressure drop that was investigated for different packing materials and rotor dimensions. The pressure drop induced by rotation, defined as centrifugal head, mainly depends on the outer diameter of the rotor. The frictional pressure drop in the packed bed depends on the rotor dimensions, the packing properties as well as on the operating conditions. Existing correlations do not predict the pressure drop accurately, thus a modified correlation basing on the extended channel model is proposed, estimating the dry pressure drop in RPBs with deviations below ±15 % for knit meshes and metal foams for rotors with outer packing diameters of 0.36 m and 0.56 m.


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1 Introduction A promising way to intensify separation and reaction processes is the exploitation of centrifugal forces in rotating packed beds (RPBs) to enhance mass transfer processes1. The core element of RPBs is a rotor equipped with an annular packing that is surrounded by a casing (Figure 1). The space between the center of the rotor and the inner radius of the packing is defined as eye of the rotor. The more dense fluid is sprayed by distributors onto the inner cross sectional area of the packing and flows radially outwards, driven by the centrifugal force. In counter-current operation, the less dense fluid is fed into the casing and flows radially inwards. Thin films covering the packing surface and fine droplets that are generated due to the high shear forces acting in the packing, lead to an intensified mass transfer. The benefits are reduced equipment sizes, large throughputs and intense phase contacting at short residence times2.

Figure 1: Schematic of an RPB type. 1) shaft, 2) mechanical seal, 3) labyrinth seal, 4) liquid distributor, 5) rotor plates, 6) annular-shaped packing, 7) casing

In their study, Ramshaw et al.3 discussed results of distillation and absorption experiments that were performed in RPBs. Since then, a multitude of studies has been published and applications of RPBs on an industrial scale are known4,5,6,7. Several publications address the influence of mechanical design parameters (e.g., rotor dimensions and packings) and operating parameters (e.g., gas flow rates and rotational speeds) on mass transfer 8,9,10 and 3 ACS Paragon Plus Environment


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hydrodynamics11,12,13. One important characteristic for RPBs, as well as for conventional columns, is the single phase pressure drop of the gas, named dry pressure drop. Knowledge of the dry pressure drop provides valuable information about the flow pattern in the packed bed and the two-phase counter-current flow14. In a recent published review, Zhao et al.15 summarized most of the available dry pressure drop correlations. In this review, neither the validity of the pressure drop correlations nor selection criteria are discussed in detail. In publications reporting experimental data for pressure drops and providing correlations the data was often derived for one specific rotor with fixed dimensions16,17,18,19,20. The applicability to estimate the pressure drop for different rotor dimensions and packing materials was not verified in the respective publications. In order to initiate a more systematic way to investigate RPBs, comprehensive dry pressure drop data for empty and packed rotors with different dimensions, equipped with varying packing materials are analyzed in this study. The pressure drop in empty and packed rotors was measured in order to gain a better understanding of the gas flow pattern. The experimental data provides the basis to illustrate the mismatch between correlations that are available in the literature and the experimental data. In addition, a modified correlation to calculate the frictional pressure drop in packed rotor, basing on the extended channel model21 is provided. This correlation has the advantage that only one parameter is required, which is characteristic for one specific packing type.


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2 Theory 2.1

Sections influencing the pressure drop

The overall dry pressure drop in RPBs can be subdivided into four sections (see Figure 2)11. These sections are either located in the casing ∆pcasing, in the eye ∆peye, in the gas outlet ∆poutlet or inside the packed bed ∆ppack.

∆pout Gasin

∆pcasing

∆ppack

∆peye

Figure 2: Sections in an RPB contributing to the overall dry pressure drop 11.

In the first section, ∆pcasing, the rotor acts as a compressor, converting the energy induced by rotation into an increase of dynamic pressure in the casing. This dynamic pressure builds up in RPBs even if no external gas flow is applied. It accounts for the resistance that must be negotiated to achieve a gas flow through the packing19. This resistance is defined as the centrifugal head ξCH. The magnitude of the centrifugal head depends on the rotor design which determines whether the energy induced by rotation is converted into dynamic pressure or is dissipated2. In counter-current operation, gas flows from the casing through the packing section ∆ppack towards the center of the rotor. The tangential velocity of the gas at any radial position in the packing is either larger than the tangential velocity of the rotor at this position or the same20. A larger tangential velocity of the gas is existent due to the conservation of angular momentum. In case of large frictional forces between packing and gas, the gas is decelerated to the tangential velocity of the rotor. In RPBs the cross-sectional area changes 5 ACS Paragon Plus Environment


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proportionally to the radius, hence the gas is accelerated towards the eye of the rotor. In addition, besides the pressure drop caused by acceleration, sudden changes of the crosssectional area at the outer and inner radius of the packing contribute to the overall pressure drop. The contribution of these single effects is discussed in the experimental section of our study. After leaving the packing towards the eye of the rotor, section ∆peye, the gas does not experience any frictional forces and maintains its tangential velocity. The flow condition in the eye of the rotor is comparable to that in cyclones used for dust removal22. As a consequence, the formation of a vortex or swirl is expected. From the outer radius to the inner radius of the vortex the tangential velocity of the gas increases. By that, the swirl dynamic pressure increases as well. The energy stored as swirl dynamic pressure in the vortex of a cyclone is often found to be dissipated in the vortex finder22. This energy dissipation results in a measureable pressure drop22. In RPBs the swirl dynamic pressure is dissipated in the gas outlet and by installations, like liquid distributors in the eye of the rotor2. Furthermore, the larger the inner radius of the packing, the larger is the tangential velocity of the gas leaving the packing. As a consequence, the swirl dynamic pressure increases and thereby the pressure drop11. Additionally, the shift in flow direction by 90° in the eye of the rotor and internals influences the fluid dynamics and therefore the pressure drop2. 2.2

Dry pressure drop correlations in the literature

To derive correlations to calculate the overall dry pressure drop in RPBs, the Navier-Stokes Equations (NSE) are mostly applied. The assumptions to simplify the NSE are presented in Appendix S1 and also form the basis of the modified correlation proposed in the present study. The final equation derived from the NSE is given in Eq.(1)11,16,20. The pressure drop is calculated by the sum of the centrifugal head 𝜉𝐶𝐻 and the frictional pressure drop ∆𝑝𝑓 in the packed bed.

∆𝑝𝑡𝑜𝑡𝑎𝑙 = 𝜉𝐶𝐻 + ∆𝑝𝑓

(1) 6 ACS Paragon Plus Environment

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Assuming no slip between the tangential velocities of the gas and the rotor, the centrifugal head can be calculated according to Eq.(2)16.

𝜁𝐶𝐻 =

𝜌𝐺 ∙ 𝜔2 2 (𝑟𝑂 − 𝑟𝑖2 ) 2

(2)

Sandilya et al.20 compared the experimental and calculated centrifugal head and reported an overestimation by 20 %. To correct this mismatch they introduced a parameter ACH (Eq.(3)). The deviation of the calculated from the experimental values can be either negative, ACH < 1, or positive, ACH > 1, depending on the rotor design2. Keyvani and Gardner19 and Zheng et al.11 derived differential equations to calculate the centrifugal head. Due to the number of uncertainties and assumptions and the difficulty to derive the required experimental data, these approaches are not discussed further on. 𝜁𝐶𝐻 = 𝐴𝐶𝐻 ∙

𝜌𝐺 ∙ 𝜔2 2 (𝑟𝑂 − 𝑟𝑖2 ) 2

(3)

The main approach to estimate the frictional pressure drop in RPBs bases on the assumption that the packing is a fixed bed equipped with random fillings and the Ergun equation can be applied (see Table S1 in Appendix S2). The parameters in the Ergun equation are either the original Ergun parameters for a bed packed with mono-sized spheres2,19 or modified Ergun parameters16. A second approach bases on the assumption that the packing can be modeled as a multitude of parallel channels and specific frictional factors depending on the packing characteristics10,20. In order to adjust the coefficients in the correlations for the centrifugal head and the frictional pressure drop, usually the centrifugal head is determined first. Subsequently, the centrifugal head is subtracted from the experimentally determined dry pressure drop, which is measured at different rotational speeds and gas flow rates. The resulting values for the pressure drop without the contribution of the centrifugal head are used in order to regress the parameters of a correlation for the frictional pressure drop. Consequently, the regressed coefficients depend on operating conditions as well as on mechanical design parameters, like the rotor 7 ACS Paragon Plus Environment


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design and packing properties. However, detailed investigations of these relationships have not been conducted yet. Especially the influence of the mechanical design parameters on the pressure drop is poorly understood: The correlations proposed in literature, which report deviations of less than 20 % between experimental and calculated pressure drop data, were specifically determined for the investigated RPB in the respective studies16,19. As will be shown in the current contribution, these available correlations cannot be used to predict the pressure drop for PRBs with different packings and rotors accurately. A similar observation was reported by Trent et al.23, who tried to apply the correlation published by Kelleher and Fair16 in order to determine a scale up from a lab scale RPB to an industrial scale. While the pressure drop model predicted the measured pressure drops in the lab scale RPB with less than 20% deviation, the deviations were significantly larger for the industrialscale RPB, such that the accuracy of the correlation was deemed to be insufficient23. Besides a more dedicated analysis of the deviations resulting from the attempt to transfer these correlations to different RPB setups, the current contribution seeks to identify the causes for these deviations by means of a systematic investigation of the dry pressure drop for different rotor dimensions and packing materials. This includes the investigation of the contribution of the empty rotor to the pressure drop as well as the contribution of the dissipated swirl dynamic pressure. In order to further improve the understanding of the gas flow pattern in RPBs and to gather the experimental data that is required to improve the accuracy of the correlation basing on Eq.(1), a systematic experimental procedure is presented. This procedure follows closely to the experimental procedure for mass transfer measurements proposed by Munjal et al.24, which however did not consider the investigation of the pressure drop, as will be done in the current contribution. Based on the subsequent analysis, a modified correlation to calculate the frictional pressure drop in the packed rotor is proposed. The applicability for different rotor dimensions, packing materials and RPBs is verified.


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2.3

Modified correlation for the frictional pressure drop

A common approach to describe the overall dry pressure ∆ptotal in an RPB is the decomposition into single contributing effects (see Figure 2). Following the approach of Sandilya et al.20 and Zhao et al.11 we recommend to subdivide the single effects into the centrifugal head 𝜉𝐶𝐻 , the frictional pressure drop of the packing without rotation (static) ∆pf,stat, the pressure drop of the rotor without packing ∆pf,rotor and the pressure drop caused by the gas inlets and outlets without an installed rotor ∆pf,empty (Eq.(4)). Furthermore, the pressure drop caused by the rotation ∆prot is considered separately and includes the vortex formation in the eye of the rotor. ∆𝑝𝑡𝑜𝑡𝑎𝑙 = 𝜉𝐶𝐻 + ∆𝑝𝑓,𝑠𝑡𝑎𝑡 + ∆𝑝𝑓,𝑒𝑚𝑝𝑡𝑦 + ∆𝑝𝑓,𝑟𝑜𝑡𝑜𝑟 + ∆𝑝𝑟𝑜𝑡

(4)

Eq.(4) can be further extended by an additional term for the irrigated bed in the presence of a liquid, which is a common approach used for conventional columns14. In order to quantify the contribution to the overall pressure drop, all effects must be investigated individually. In the presence of liquid Eq.(4) can be extended by an additional term. Detailed investigations, as presented for the dry pressure drop in the following, and a precise determination of the liquid holdup in the packing are required in order to derive a generally applicable correlation in the future describing the influence of the liquid on the pressure drop. However, no further investigations on the wet pressure drop are included in the current work. The accuracy of the correlations to predict the overall dry pressure drop is evaluated by calculation of the relative deviation, taking into account the experimentally determined pressure drop ∆𝑝𝑡𝑜𝑡𝑎𝑙,𝑒𝑥𝑝 and the calculated pressure drop ∆𝑝𝑡𝑜𝑡𝑎𝑙,𝑐𝑎𝑙𝑐 according to Eq.(5).

𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 =

∆𝑝𝑡𝑜𝑡𝑎𝑙,𝑒𝑥𝑝 − ∆𝑝𝑡𝑜𝑡𝑎𝑙,𝑐𝑎𝑙𝑐 ∆𝑝𝑡𝑜𝑡𝑎𝑙,𝑒𝑥𝑝

(5)

The current study is intended to initiate the determination of correlations describing the single contributing effects given in Eq.(4). Each effect should be investigated independent from each other for different mechanical design parameters and operating conditions. 9 ACS Paragon Plus Environment


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Experimental data for the overall dry pressure drop should only be used to validate the derived correlation. The centrifugal head ξCH is calculated according to Eq.(3) and ACH is regressed by minimization of the error between experimental and calculated values. Once determined, the parameter can be used for rotors with similar dimensions and design. The Ergun equation to calculate the frictional pressure drop does not include the geometry of the packing, thus it is of limited use to compare different shaped packings with similar specific surface areas and porosities. This topic is also addressed by Maćkowiak21 who stated that for common approaches the resistance coefficients must be experimentally determined and correlations between the shape of the packing and the resistance factor are not identified. In order to include the shape of the packing, the extended channel model21 is used. This model was developed for random and structured packings in conventional columns21 and its applicability to estimate pressure drops in foams and mesh packings is evaluated in scope of this study. According to the extended channel model with partially perforated wall surfaces the frictional pressure drop in the packing is calculated according to Eq.(6)21.

∆𝑝𝑓,𝑠𝑡𝑎𝑡

𝛹0 =

= 𝛹0 ∙ (1 − 𝜑)

2 (𝑟𝑂 − 𝑟𝑖 ) 1 − 𝜀 𝐹̅𝐺,𝑖𝑛𝑡 ∙ ∙ 𝜀3 𝑑𝑃 𝐾

725.6 − 3.203 ̅̅̅̅𝐺,𝑖𝑛𝑡 𝑅𝑒

(6)

(7)

Applying the extended channel model, the packing is assumed to consist of a multitude of identical parallel channels, and the pressure drop is assumed to be solely caused by the flow through channels with non-perforated surfaces21. The pressure drop in the channels is calculated on basis of the equation developed by Darcy and Weißbach for pipe flow25. This assumption is valid for random packings with solid walls, such as Raschig rings or saddles 21. These packings have a common resistance factor Ψ021 depending on the Reynolds number26. This factor Ψ0 remains constant for all types of packings. For packings with perforated walls, the pressure drop decreases, since the length of a channel decreases21. The form factor φ is introduced as a measure for the shortening of the length of a channel 10 ACS Paragon Plus Environment

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(see Eq.(7)) and depends on the packing properties. By providing tables with form factors for a multitude of packings, no further experimental determination of these factors is required21. In addition, a direct comparison of different packings in order to identify dependencies of the form factor on the packing shape is possible. In order to take the changing gas velocity along the radius of the packing into account, the average value of the integrated gas capacity factor 𝐹̅𝐺,𝑖𝑛𝑡 is introduced (see Eq.(8)). Furthermore the applicability of the concept of the hydraulic diameter is assumed to be valid for RPBs (see Appendix S4).

𝐹̅𝐺,𝑖𝑛𝑡 =

𝑟𝑂 𝑉̇𝐺 𝑟𝑂 √𝜌𝐺 ∫ 𝑢𝐺 (𝑟)𝑑𝑟 = 𝑙𝑛 ( ) ∙ √𝜌𝐺 𝑟𝑂 − 𝑟𝑖 𝑟𝑖 2 ∙ 𝜋 ∙ ℎ𝑅 ∙ (𝑟𝑂 − 𝑟𝑖 ) 𝑟𝑖

(8)

The change of the Reynolds number along the packing radius in RPBs is considered by 𝐹̅𝐺,𝑖𝑛𝑡 (see Eq.(9)). The equivalent spherical diameter is calculated according to Eq. (10) and bases on the concept of the hydraulic diameter (see Appendix S4).

̅̅̅̅𝐺,𝑖𝑛𝑡 = 𝑅𝑒

𝑑𝑃 = 6 ∙

𝑑𝑃 𝐹̅𝐺,𝑖𝑛𝑡 ∙ (1 − 𝜀) ∙ 𝜈𝐺 √𝜌𝐺

(9)

(1 − 𝜀) 𝑎𝑝

(10)

Wall effects could not be investigated experimentally. Hence, knit mesh and foam packings in RPBs are assumed to have similar wall effects as structured packings in conventional columns. Accordingly, the factor K in Eq.(6), representing the wall effects, is set to one. The dry pressure drop in RPBs can then be calculated by combination of Eq.(3), Eq.(4) and Eq.(8). Two parameters (ACH and φ) need to be regressed, the pressure drop Δpf,empty and Δpf,rotor are experimentally determined. If their contribution is found to be significant, the pipe analogy can be applied (see Appendix S5).



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∆𝑝𝑡𝑜𝑡𝑎𝑙 = 𝐴𝐶𝐻 ∙

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2 𝜌𝐺 ∙ 𝜔2 2 1 − 𝜀 𝐹̅𝐺,𝑖𝑛𝑡 ∙ ∙ (𝑟𝑂 − 𝑟𝑖 ) (𝑟𝑂 − 𝑟𝑖2 ) + 𝛹0 ∙ (1 − 𝜑) 2 𝜀3 𝑑𝑃

+ ∆𝑝𝑓,𝑒𝑚𝑝𝑡𝑦 + ∆𝑝𝑓,𝑟𝑜𝑡𝑜𝑟 + ∆𝑝𝑟𝑜𝑡

(11)

Besides this approach, Liu et al.17 and Zheng et al.11 developed further approaches, containing a multitude of equations and parameters that need to be regressed for each RPB individually. The correlations of Liu et al.17 were derived for random fillings, not for meshes and foams and the resistance coefficient for each packing material requires seven parameters that must be regressed. Our objective is to provide a simple and quickly applicable correlation to estimate the dry pressure drop in RPBs, therefore these correlations are not considered for a later comparison.


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3 Experiments 3.1

Experimental setup

A single-stage RPB was investigated with a casing volume of 72 litres and an inner casing diameter of 860 mm. A schematic of the RPB used for the investigations is given in Figure 4. Two different rotor diameters, 400 mm and 600 mm, and axial heights, 10 mm and 15 mm, were investigated. Screws at the outer circumference of the rotors (see Figure 3) were used to connect the two parallel rotor plates. Thus, the outer diameter of the packed bed equipped with knit mesh was reduced by 40 mm. The foam packing had an outer diameter of 585 mm. A ring with ten racks (outer diameter 146 mm, inner diameter 136 mm) was used to space the two rotor plates at the inner packing diameter. In addition, this ring served as a packing support, offering a free cross-sectional area of 90 %.

Figure 3: Schematic of the lower rotor plate of the R600 rotor (top view).



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The combination of the chosen outer rotor diameter, axial height and packing defines a rotor configuration. In total five different rotor configurations were investigated (see Table 1). The name of each rotor configuration contains information about the outer rotor diameter (first number), the axial height (second and third number) and the packing. After changing the rotor dimensions, the mesh was installed by coiling it around the packing support. This method leaded to deviations in the amount of mesh installed in the rotor. Still the deviations were found to be small and the influence on the experimental results was negligible. For each rotor configuration equipped with knit mesh, the porosity and the specific surface area were calculated according to Eq.(S4) and Eq.(S5) in Appendix S3. The knit meshes were made of a metal wire with a diameter of 0.23 mm. The specifications for the foam packing were provided by the manufacturer27.

Figure 4: Schematic of the investigated RPB unit, including the position of the sensors to measure the pressure drop across the rotor at the outer (1) and inner (2) circumference of the packing.


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Table 1: List of the investigated rotor configurations Rotor

dO,rotor

di

hR

Packing

ε

aP 2

/m m

-3

configuration

/mm

/mm

/mm

/-

R615 KM I

600

146

15

KM I

2033

0.88

R615 KM II

600

146

15

KM II

2441

0.86

R610 KM II

600

146

10

KM II

2570

0.85

R410 KM II

400

146

10

KM II

2812

0.84

R610 Foam

600

146

10

NCX1116

1000

0.92

Connectors with 51 mm diameter were used to connect the gas inlet and outlet pipes to the RPB. A labyrinth seal was used to minimize the bypassing of the gas. To prevent any leakage to the environment, a mechanical seal with a barrier fluid (propylene glycol) sealed the shaft. Peripheral devices, the location of the sensors and the measurement method used for the experimental investigations, are listed in Table 2 and Table 3, respectively. Table 2: Peripheral devices of the experimental setup Description

Producer, type

Max. capacity

Motor

Nord, M7000

2.2 kW

Frequency inverter

Danfoss, VLT Micro Drive FC 51

Gas flow meter

JUMO 303430

60 m3 h-1

U-Tube, pressure

TU Dortmund

∆p = 6000 Pa



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Table 3: Locations of sensors, applied measuring methods and accuracies Place of sensor installation

Measured value

Method

Accuracy

Gas in

Volume flow

Differential pressure over orifice plate

1%

Temperature

PT 100

0.2 K

Casing

Temperature

PT 100

0.2 K

Casing and eye of rotor

Pressure drop

U-tube manometer

20 Pa

Shaft

Rotational speed

Infrared sensor and frequency inverter

0.2 s-1

3.2

Experimental procedure

In the following, the experimental procedure is presented that was applied for all investigated rotor configurations. The procedure consists of several steps containing different series of experiments (Figure 5). These experiments include the measurements of the centrifugal head, the pressure drop without rotation and the pressure drop in operation with rotation and gas flow rate. In the first step, the pressure drop without installed rotor is investigated, followed by investigations of the rotor without packing. Finally, in the third step, the packing is installed and the pressure drop is measured again. Applying this procedure facilitates the quantification of the single effects contributing to the overall pressure drop (see Eq.(4) or Eq.(11), respectively).


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Figure 5: Procedure to measure the dry pressure drop. UL (upper limit) are restrictions given by the periphery or the RPB. In the present study: UL: 𝑉̇𝐺 = 60 m3 h-1; nrot = 20 s-1

To measure the centrifugal head, all liquid outlets and the gas inlet were closed. To start the measurement, the rotational speed was set to 20 s-1. A rotational speed of 20 s-1 corresponds to 1200 rpm. The pressure drop was recorded at steady state and the rotational speed was decreased. Without rotation, the gas flow rate was adjusted to 15 m3 h-1 and then increased step-wise until the maximal gas flow rate of 60 m3 h-1. The pressure drop was measured at the top of the casing, in the gas inlet and close to the outer diameter of the packing. Preliminary experiments revealed that the location of the pressure sensors in the casing did not influence the measured pressure drop. Hence, the locations were fixed in the casing and in the eye of the rotor. In order to determine the experimental error, the average of at least three measurements was calculated. The maximal absolute error between the experimental values and the average was determined. In case the maximal absolute error was smaller than the measurement error of 20 Pa, the latter error was taken into account. In case of a larger maximal absolute error this error was considered.



4 Results and discussion 4.1

Centrifugal head

Figure 6 illustrates the centrifugal heads measured for rotors without packing and for rotors equipped with packing. An increase of the centrifugal head is observable in the presence of packing material. This increase can be explained by the interaction between packing and gas phase that supports the increase in dynamic pressure in the casing, resulting in a larger centrifugal head. For the investigated packing materials no significant difference in the centrifugal head could be observed. The dashed lines in Figure 6 represent the centrifugal heads that were calculated according to Eq.(2). The experimental centrifugal heads are smaller than the calculated ones. Thus, the conversion of rotational energy into dynamic swirl pressure in the casing is less efficient for the investigated rotor configurations than ideally calculated. Bearing in mind that the centrifugal head is a resistance which has to overcome in counter-current operation, a small centrifugal head is desirable in RPBs. The experimental data indicate the second-order dependency on the rotational speed as reported by Keyvani and Gardner19. 800

800

600

600

pressure drop pdry /Pa


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Page 18 of 39

400

200

0

400

200

0 0

5 10 15 20 rotational speed nrot /s-1 615 emtpy 610 empty CH,calc for do = 600 mm CH,calc for do = 400 mm

25

410 empty

0

5

10 15 20 rotational speed nrot /s-1

615 KM II

615 KM I

410 KM II

610 Foam

CH,calc for do = 600 mm

25 610 KM II

CH,calc for do = 400 mm

Figure 6: Experimentally measured centrifugal head ξCH. Left: empty rotors; Right: packed rotors.


Page 19 of 39

4.2

Frictional pressure drop without rotation

In a first series of experiments, the dry pressure drop without rotor ∆pf,empty was investigated. No pressure drop was detected. Therefore, this contribution is neglected and is not discussed further on. This finding is in accordance with the observations made by Zheng et al.11. The experimental results for the frictional pressure drop in the empty static rotors are shown in Figure 7. Below a gas flow rate of 30 m³ h-1, no pressure drop was measurable. Above 30 m³ h-1, the pressure drop slightly increases, although the absolute values are small compared to the frictional pressure drop of the packing (see Figure 8). The determined pressure drops deviate within the accuracy of the measurement and no dependency on the rotor geometry could be identified. It is strongly recommended to quantify the contribution of the empty rotor to the pressure drop prior to the determination of the form factor, in order to avoid any interference of the rotor geometry on the frictional pressure drop in the bed. 100


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75

50

25

0 0

15 30 45 gas flow rate VG /m3 h-1 610 empty

615 empty

60

410 empty

Figure 7: Frictional pressure drop of the static empty rotors ∆pf,empty as a function of the gas flow rate.

Figure 8 illustrates the dependency of the frictional pressure drop on the gas flow rate for the static packed rotor. The frictional pressure drops measured for rotors with an axial height of 10 mm and outer rotor diameters of 400 mm and 600 mm are in a comparable range. This finding is remarkable, since the packing with larger outer radius has a 80 % larger radial 19 ACS Paragon Plus Environment


packing width compared to the smaller packing. The gas velocity profile changes along the radius, due to the changing cross-sectional area (Figure 8, right). For the packing with 560 mm diameter, the additional radial packing width is linked with small changes in the gas velocity and gas capacity factor, respectively. The pressure drop increases to the square of the gas capacity factor (see Eq. (6)). Thus, the contribution of the outer parts of the packing to the overall pressure drop is small. This effect seems to outweigh the opposing effect of an increasing resistance coefficient for small gas flow velocities (see Eq. (7)). 2000

2.8

gas velocity uG /ms

pressure drop pf,stat /Pa

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Page 20 of 39

1500

1000

500

2.1

1.4 dO = 360 mm

0.7 dO = 560 mm

0 0

15

30

45

60

0.0 0.0

gas flow rate VG /m3 h-1 610 KM II

615 KM II

0.1

0.2

0.3

0.4

radial position /m

410 KM II

Figure 8: Left: Frictional pressure drop of the static packed rotor in dependency of the gas flow rate. Right: Gas velocity as a function of the radius of the packed bed for a gas flow rate of 40 m3∙h-1 and hR = 10 mm.

The same experimental data as plotted in Figure 8 (left) is shown in Figure 9 as a function of the average value of the integrated gas capacity factor 𝐹̅𝐺,𝑖𝑛𝑡 . As expected, rotors with the same outer diameter and radial packing width have the same pressure drop for a fixed 𝐹̅𝐺,𝑖𝑛𝑡 . For packings with a smaller outer diameter and smaller radial packing width, the same 𝐹̅𝐺,𝑖𝑛𝑡 are present at lower gas flow velocities and the pressure drop is lower.


Page 21 of 39

1600

pressure drop pf,stat /Pa

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1200

800

400

0 0

1

2

F-factor FG,int /Pa 615 KM II

610 KM II

3

0.5

410 KM II

Figure 9: Frictional pressure drop of the static packed rotor as a function of the average value of the integrated gas capacity factor 𝐹̅𝐺,𝑖𝑛𝑡 .

4.3

Pressure drop in the RPB during operation

For a first evaluation of the approach to decompose the overall pressure drop into single contributing effects, the sum of the measured centrifugal head 𝜉𝐶𝐻 and the frictional pressure drop of the static packed rotor ∆pf,stat is compared to the experimentally determined total dry pressure drop (Figure 10). As illustrated in the parity plot, the sum of 𝜉𝐶𝐻 and ∆pf,stat provides a good estimate for the total dry pressure drop in RPBs. Additionally, the pressure drop in a rotor without packing is plotted in Figure 10. The measured and calculated values deviate significantly for the empty rotor.



2400

1800 CH + pf,stat /Pa

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Page 22 of 39

+ 20 % - 20 %

1200

600

0 0

500

1000

1500

2000

experimental pressure drop p /Pa 610 empty; FG,int = 0.4 Pa0.5

610 KM II; FG,int = 0.4 Pa0.5

0.5

610 KM II; FG,int = 0.6 Pa0.5

0.5

610 empty; FG,int = 0.8 Pa

610 KM II; FG,int = 0.8 Pa0.5

610 KM II; FG,int = 1.0 Pa0.5

610 KM II; FG,int = 1.0 Pa0.5

610 empty; FG,int = 0.6 Pa

Figure 10: Parity plot to compare the experimental and calculated pressure drop.

A remarkable trend is observable with increased rotational speed (Figure 11). At rotational speeds below 10 s-1 the pressure drop in the packed rotor is larger than in the empty rotor. The larger interaction between packing and gas results in a larger frictional pressure drop. This trend inverses for rotational speeds above 10 s-1 due to the different dynamic pressures of the gas flowing through the empty and the packed rotor. In case of a packed rotor, the friction between gas and packing minimizes the slip between the tangential velocity of the gas and the packing. For the empty rotor this minimization of the slip does not take place to the same extend as in the packed rotor. Consequently, at any radial position in the rotor, the gas circulates faster than the rotor. Additionally, the gas flowing towards the eye of the rotor is deflected because of the Coriolis force and a vortex forms. Towards the center of this vortex, the gas accelerates and the dynamic swirl pressure increases. As known from cyclones the dissipation of the dynamic pressure leads to large pressure drops22. During the experiments with empty rotors larger experimental errors were found compared to the measurements with packed rotors. These deviations grew with increasing rotational speed and gas flow rates and indicate unstable flow conditions.


Page 23 of 39

1600

pressure drop p /Pa

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1200

800

400

0 0

6

12

18

24

rotational speed nrot /s-1 610 empty; FG,int = 0.6 Pa0.5 610 KM II; FG,int = 0.6 Pa0.5

Figure 11: Comparison of the pressure drop dependency on the rotational speed for the empty and packed rotors at a fixed gas velocity of 20 m3·h-1.

4.4

Parameters determination for the correlation

Two parameters, ACH in Eq. (3) and φ in Eq. (6), need to be regressed for the proposed correlation. They were obtained by use of the experimental data obtained without gas flow rate (determination of ACH) and without rotation (determination of φ). The experiments that were conducted with changing rotational speeds and gas flow rates were used to validate the correlation. The values for ACH are listed in Table 4 and were obtained by linear regression. The values for ACH are slightly larger than those published by Sandilya et al.20 but in a similar range as those of Chandra et al.28 reported for a split bed.

Table 4: Investigated rotor configurations to determine the centrifugal head. ACH

KM I, KM II, Foam

ε /0.84-0.92

KM II

0.84

0.89

nrot /s-1 5 – 20

dO /mm 600

hR /mm 10, 15

Packing

5 – 20

400

10

0.85

For each investigated packing the form factor φ in Eq.(6) was fitted by minimisation of the error between calculated and experimental pressure drop measured for the static packed 23 ACS Paragon Plus Environment


rotor. The parity plots for the KM I mesh and the KM II are given in Figure 12. The form factors for the investigated packings are given in Table 5, as well as the form factors that

1600 +20 %

1200 -20 %

800

400

0 0

400

800

1200

calculated pressure drop p /Pa

were fitted to experimental data published by Blass29 for wire meshes.


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Page 24 of 39

1600 +20 %

1200 -20 %

800

400

0 0

1600

400

800

1200

1600

experimental pressure drop p /Pa

experimental pressure drop p /Pa

Figure 12: Parity plots for the calculated and experimentally determined frictional pressure drops of the static rotor the KM II (left) and KM I (right) packing

Table 5: Form factors for the different internals obtained by regression. Packing type

aP /m2·m3

ε /-

φ /-

dwire /mm

KM II

2441 – 2812

0.84 – 0.86

0.46

0.23

KM I

2033

0.88

0.42

0.23

NCX1116

1000

0.92

0.32

-

29

Wire mesh 5

1126

0.73

0.35

1.00

Wire mesh 129

3115

0.86

0.32

0.20

The KM I mesh has a smaller form factor than the KM II mesh. Comparing both knit meshes, several structural differences can be identified. The KM II mesh has a very regular shape and distribution of the mesh cells and has, due to the narrow-knitted structure, a very smooth surface. Packed in the rotor, the single layers of the mesh are orientated in parallel without overlapping. In contrast, the KM I consists of larger mesh cells and the single layers have a 24 ACS Paragon Plus Environment

Page 25 of 39

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waved surface. Installing this mesh in the rotor, leads to an overlapping and interlocking of the mesh layers. In conclusion, the KM I has a less structured shape than the KM II represented by the smaller form factor. As a consequence, the pressure drop is approximately 10 % larger for the KM I mesh than for the KM II mesh. The small form factor of the foam packing can be traced back to the differences in the specific surface area between the knit mesh and the foam. The value given for the foam was provided by the manufacturer and is closer to the real value than the ideally calculated specific surface area for the knit meshes. In reality the specific surface area of the knit mesh is smaller due to overlapping of the single wires. Any decrease in the specific surface area directly results in a decreasing form factor. Therefore, the properties of mesh packings always must be determined by the same equations and assumptions. Regarding the parity plot in Figure 12 (left) a tendency to overestimate the pressure drop for small pressure drops, and to underestimate the pressure drop for large values is present. The coefficient Ψ0 was derived for random fillings with solid walls used in conventional columns21. One assumption made for these random packings is that the pressure drop is only caused by the friction between the fluid and the solid channel wall21. As stated by Blass29, single wires reveal a high form drag and a vortex shedding close behind the wires, which lead to higher pressure drops compared to random packings. A larger database containing experimental data of pressure drops for different knit and wire meshes is required to evaluate the need to readjust Ψ0. 4.5

Comparison of the correlations

To evaluate the accuracy of the modified correlation basing on the extended channel model (defined as new correlation in the following figures) against those published in the literature (see Table S2 in Appendix S2) the parity plots for the KM II mesh are given in Figure 13. Further plots for the rotors with an axial height of 15 mm are given in Appendix S6. The values for ACH are listed in Table 4 and for the form factor φ in Table 5. No further parameters



were adjusted. The modified correlation shows a good agreement between the calculated and experimental values for different rotor geometries. 3200 +30 % +10 %

2400

-10 % -30 %

1600

800


3200


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Page 26 of 39

+30 % +10 %

2400

-10 % -30 %

1600

800

0

0 0

800

1600

2400

3200

experimental pressure drop p /Pa New correlation Rao [2] Kelleher and Fair [24] E F

Singh [11]

0

800

1600

2400

3200

experimental pressure drop p /Pa New correlation Rao [2] Kelleher and Fair [24]

Singh [11]

Figure 13: Parity plots for the calculated and experimental pressure drop for the 610 KM II (left) and 410 KM II rotor (right). As reported by Trent et al.4, the pressure drops are overestimated by the correlation of Kelleher and Fair16. The correlation proposed by Singh et al.10 is in good agreement for the rotor with an outer diameter of 600 mm. The limited applicability of this correlation is illustrated in Figure 13 (right) for the 410 KM II rotor. This observation reveals that the influence of the rotor diameter on the pressure drop is not represented sufficiently by this correlation. To derive the coefficients for their correlation, Singh et al.10 fitted the coefficients to the overall pressure drop. Thus, the influence of the rotor geometry and further design parameters, such as the packing support are included. Although the trends in Figure 13 are reflected by Ergun Equation (correlation Rao2 in Figure 13), the deviations are larger than for the correlation proposed in the present study. This observation supports the need to include the packing shape by a form factor. For the foam packing the proposed correlation is less accurate (Figure 14). The specific surface area of the foam is more than 50 % smaller than the area that was determined for the knit meshes. In addition, the porosity of the foam is larger. Due to the smaller specific surface area and larger porosity, less contact area 26 ACS Paragon Plus Environment

Page 27 of 39

between gas and packing is available. Therefore, the gas flow pattern is less influenced by the packing and a larger slip between the tangential velocity of the gas and packing is expected. This slip leads to a larger contribution of the dynamic pressure dissipation to the pressure drop, which is not considered in the correlation.

2000 calculated pressure drop p /Pa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


+30 % +10 %

1500

-10 % -30 %

1000

500

0 0

500

1000

1500

2000


Singh [11]

Figure 14: Parity plots for the calculated and experimental pressure drop for the 610 Foam rotor.

For both packing types a trend of the proposed correlation is observable to underestimate the values for large pressure drops, corresponding to large rotational speeds and gas capacity factors. This trend can be traced back to the vortex formation in the eye of the rotor. As discussed in the recently published study of Liu et al.30 additional effects might also contribute to the pressure drop in RPBs. Besides the formation of a vortex in the eye of the rotor, the authors discussed the existence of a gas-side end effect. In the casing, close to the rotor, the gas rotates as a solid body with a slightly lower tangential velocity than the packing at the outer radius of the rotor31. As soon as the gas enters the rotor, the sudden change in cross sectional area and the presence of packing lead to changes in the flow direction and



gas velocity in this inlet zone. Large turbulences might be the consequence causing an additional pressure drop in this region30. 4.6

Validation of the correlation

The experimental data published by Sandilya et al.20 is used to demonstrate the transferability of the proposed correlation to predict the pressure drop in RPBs (Figure 15). To estimate the centrifugal head, ACH is determined to 0.8 by use of experimental centrifugal heads reported by Sandilya et al.20. The form factor was chosen according to the form factors that are listed in Table 5. The wire mesh used by Sandilya et al.20 has mesh properties that are in between the wire mesh 1 and 5 listed in Table 5, thus a form factor of 0.33 was selected. No further parameters were adjusted. The influence of the rotor geometry on the pressure drop is neglected. The trend of the relative deviation to become more negative for increasing gas capacity factors and rotational speeds is observable. As previously discussed, an underestimation is expected since effects, such as the vortex formation or the gas-side end effect, are not considered. Table S4 in Appendix S7 contains the data plotted in Figure 15. 1000 calculated pressure drop p /Pa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 39

+20 %

750

-20 %

500

250

0 0

250

500

750

1000


Singh [11]

Figure 15: Parity plots for the calculated and experimental pressure drop for the RPB investigated by Sandilya et al.20.


Page 29 of 39

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5 Conclusion In this study a systematic procedure to investigate the pressure drop in RPBs was proposed as well as a modified and quickly applicable correlation to determine the pressure drop in RPBs. Compared to correlations taken from the literature, this correlation showed the best accuracy for different rotor dimensions and packing. By use of the proposed procedure and systematic investigations the following influences of mechanical design parameters on the pressure drop could be identified. The centrifugal head was found to mainly depend on the outer diameter of the rotor. The frictional pressure drop depends on the rotor geometry, the packing properties and the operating conditions. Remarkably, the pressure drop in an empty rotor was found to exceed that one in a packed rotor for large rotational speeds. This finding underlines the significant contribution of the dissipation of the dynamic pressure to the overall pressure drop. Single effects contributing to the pressure drop were investigated individually in different experimental studies. Future scientific work is required to experimentally determine form factors for different meshes and foams. With help of these data sets the development of equations to determine form factors theoretically is facilitated. In addition, the influence of the rotor geometry on the parameter ACH needs to be further evaluated. Systematic studies following the proposed procedure will facilitate the identification of further effects that influence the dry pressure drop, like vortex formation in the eye of the rotor, the rotor design and gas-side end effects. Furthermore, the dry pressure drop approach can be complemented by a term considering the contribution of liquid to the pressure drop.



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Page 30 of 39

Supporting information The Supporting Information is available free of charge on the ACS Publications website. Navier-Stokes-Equations; pressured drop correlations; packing characteristics; hydraulic diameter; pipe analogy; experimental data for validation

ACKNOWLEDGEMENTS The research leading to these results was done in cooperation with the Institute of Sustainable Process Technology (ISPT) in the framework of the ImPaCCt project. The scientific contributions and advice of Prof. Maćkowiak (ENVIMAC Engineering GmbH, Oberhausen, Germany) is greatly acknowledged. Additionally, we gratefully acknowledge the valuable scientific support of Rüdiger Spitzer from the Laboratory of Fluid Separations.


Page 31 of 39

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NOMENCLATURE Latin letters A

area

m2

ACH

RPB configuration dependent parameter to calculate the

-

centrifugal head aP

specific geometric packing surface area per unit

m2 m-3

d

diameter

m or mm

dP

equivalent spherical diameter, particle diameter

m

FG

gas or vapor load, gas capacity factor

Pa0.5

F̅G,av,int

average value of the integrated gas capacity factor

Pa0.5

Fr

forces in radial direction

N

Fφ

forces in tangential direction

N1

hR

axial height of the rotor

m or mm

K

wall factor

-

m

mass

kg

nrot

rotational speed

s-1

r

radius

m or mm

Rid

gas constant

J mol-1 K-1

Re

Reynolds number

-

̅𝑅𝑒 ̅̅̅𝐺,𝑖𝑛𝑡

average value of the integrated Reynolds number

-

T

temperature

K

uG,0

superficial gas velocity

m s-1

uR

radial velocity

m s-

ux

axial velocity

m s-

uφ

tangential velocity

m s-

V

volume /m³

m³

𝑉̇𝐺

gas flow rate

m³ s-1 or m³ h-1 31 ACS Paragon Plus Environment


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Page 32 of 39

Greek letters ∆p

pressure drop

Pa

ε

porosity

-

κ

isentropic exponent

-

ν

kinematic viscosity

m2 s-1

ζ

resistance coefficient

-

η

dynamic viscosity

kg m-1 s-1

ρ

density

kg m-3

τ

shear stress

kg m-2 s-2

φ

form factor of dry packing

-

Φ

ratio of the cross sectional area at the inner packing radius and the eye of the rotor

Ψ0

resistance coefficient for single-phase flow for classical, non- perforated packing elements such as ceramic Raschig rings

ω

angular velocity

s-1

Subscripts 0

superficial

dry

dry, only gas applied

calc

calculated

casing

casing encasing the rotor

CH

centrifugal head

eye

inner part of the rotor from the middle axis to the beginning of the packing

exp

experimental

empty

no packing installed 32 ACS Paragon Plus Environment

Page 33 of 39

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G

gas

f

friction

H

hydraulic

i

Inner

ICA

cross sectional area of the packing at the inner radius

m

momentum gain

O

outer

P,pack

packing

pore

average diameter of a pore in a foam

rotor

rotor

rot

rotation

stat

static, non-rotating

total

overall, sum of single contributing effects

wire

wire

φ

angular direction

Abbreviations KM

knit mesh

NCX1116

specification of the investigated foam packing

NSE

Navier-Stokes-Equation

RPB

rotating packed bed



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6 LIST OF REFERENCES (1)

Fowler, R. Higee - A status report. Chem. Eng. (London) 1989, 35.

(2)

Rao, D. P.; Bhowal, A.; Goswami, P. S. Process Intensification in Rotating Packed Beds (HIGEE): An Appraisal. Ind. Eng. Chem. Res. 2004, 43, 1150.

(3)

Ramshaw, C.; Arkley, K. Process Intensification by Miniature Mass Transfer. Process Engineering (London) 1983, 64, 29.

(4)

Trent, D. L.; Tirtowidjojo, D. Intensifying the Process. Chem. Eng. (London) 2003, 30.

(5)

Chen, Y. S.; Liu, H. S. Absorption of VOCs in a Rotating Packed Bed. Ind. Eng. Chem. Res. 2002, 41, 1583.

(6)

Qian, Z.; Xu, L. B.; Li, Z. H.; Li, H.; Guo, K. Selective Absorption of H2S from a Gas Mixture with CO2 by Aqueous N-Methyldiethanolamine in a Rotating Packed Bed. Ind. Eng. Chem. Res. 2010, 49, 6196.

(7)

Jassim, M. S.; Rochelle, G.; Eimer, D.; Ramshaw, C. Carbon Dioxide Absorption and Desorption in Aqueous Monoethanolamine Solutions in a Rotating Packed Bed. Ind. Eng. Chem. Res. 2007, 46, 2823.

(8)

Chen, Y. S.; Lin, C. C.; Liu, H. S. Mass Transfer in a Rotating Packed Bed with Various Radii of the Bed. Ind. Eng. Chem. Res. 2005, 44, 7868.

(9)

Chen, Y. S.; Lin, F. Y.; Lin, C. C.; Tai, C. Y. D.; Liu, H. S. Packing Characteristics for Mass Transfer in a Rotating Packed Bed. Ind. Eng. Chem. Res. 2006, 45, 6846.

(10) Singh, S. P.; Wilson, J. H.; Counce, R. M.; Lucero, A. J.; Reed, G. D.; Ashworth, R. A.; Elliott, M. G. Removal of Volatile Organic Compounds from Groundwater using a Rotary Air Stripper. Ind. Eng. Chem. Res. 1992, 31, 574. 34 ACS Paragon Plus Environment

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(11) Zheng, C.; Guo, K.; Feng, Y.; Yang, C.; Gardner, N. C. Pressure Drop of Centripetal Gas Flow through Rotating Beds. Ind. Eng. Chem. Res. 2000, 39, 829. (12) Lockett, M. J. Flooding of Rotating Structured Packing and Its Application to Conventional Packed-Columns. Chem. Eng. Res. Des. 1995, 73, 379. (13) Rajan, S.; Kumar, M.; Ansari, M. J.; Rao, D. P.; Kaistha, N. Limiting Gas Liquid Flows and Mass Transfer in a Novel Rotating Packed Bed (HiGee). Ind. Eng. Chem. Res. 2011, 50, 986. (14) Maćkowiak, J. Fluid dynamics of packed columns; Springer: Berlin, 2010. (15) Zhao, B.; Tao, W.; Zhong, M.; Su, Y.; Cui, G. Process, performance and modeling of CO2 capture by chemical absorption using high gravity: A review. Renewable and Sustainable Energy Reviews 2016, 65, 44. (16) Kelleher, T.; Fair, J. R. Distillation Studies in a High-Gravity Contactor. Ind. Eng. Chem. Res. 1996, 35, 4646. (17) Liu, H. S.; Lin, C. C.; Wu, S. C.; Hsu, H. W. Characteristics of a Rotating Packed Bed. Ind. Eng. Chem. Res. 1996, 35, 3590. (18) Kumar, M. P.; Rao, D. P. Studies on a High-Gravity Gas-Liquid Contactor. Ind. Eng. Chem. Res. 1990, 29, 917. (19) Keyvani, M.; Gardner, N. C. Operating characteristics of Rotating Beds. Technical Progress Report prepared for US Department of Energy Pittsburgh Energy Technology Center, Pittsburgh, PA. DOE # DE-FG22-87PC 79924, 1992. (20) Sandilya, P.; Rao, D. P.; Sharma, A.; Biswas, G. Gas-Phase Mass Transfer in a Centrifugal Contactor. Ind. Eng. Chem. Res. 2001, 40, 384.



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(21) Maćkowiak, J. Extended Channel Model for Prediction of the Pressure Drop in SinglePhase Flow in Packed Columns. Chem. Eng. Res. Des. 2009, 87, 123. (22) Hoffmann, A. C. Cyclone Flow Pattern and Pressure Drop. In Gas cyclones and swirl tubes Cyclone - Principles, Design and Operation; Stein, L. E., Eds.; Springer: Berlin, 2007; pp 49–76. (23) Trent, D.; Tirtowidjojo, D. Commercial operation of a rotating packed bed (RPB) and other applications of RPB technology. In 4th Conference, Process Intensification for the Chemical Industry; Better Processes for better Products; BHR Group, Eds.: Cranfield, 2001; pp 11–19. (24) Munjal, S.; Duduković, M. P.; Ramachandran, P. Mass-Transfer in Rotating Packed Beds—II. Experimental Results and Comparison with Theory and Gravity Flow. Chem. Eng. Sci. 1989, 44, 2257. (25) Barth, W. Der Druckverlust bei der Durchströmung von Füllkörpersäulen und Schüttgut mit und ohne Berieselung. Chem. Ing. Tech. 1951, 23, 289. (26) Kast, W. Gesetzmäßigkeiten des Druckverlustes in Füllkörpersäulen. Chem. Ing. Tech. 1964, 36, 464. (27) Recemat BV. http://www.recemat.nl/eng/datasheets/Datasheet_NCX.pdf (accessed June 2017). (28) Chandra, A.; Goswami, P. S.; Rao, D. P. Characteristics of Flow in a Rotating Packed Bed (HIGEE) with Split Packing. Ind. Eng. Chem. Res. 2005, 44, 4051. (29) Blass, E. Geometrische und strömungstechnische Untersuchungen an Drahtgeweben. Chem. Eng. Tech. 1964, 36, 747.


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(30) Liu, Y.; Luo, Y.; Chu, G. W.; Luo, J. Z.; Arowo, M.; Chen, J. F. 3D Numerical Simulation of a Rotating Packed Bed with Structured Stainless Steel Wire Mesh Packing. Chem. Eng. Sci. 2017, 170, 365. (31) Schultz-Grunow, F. Der Reibungswiderstand rotierender Scheiben in Gehäusen. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 1935, 15, 191.



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7 List of figure captions Figure 1: Schematic of an RPB type. 1) shaft, 2) mechanical seal, 3) labyrinth seal, 4) liquid distributor, 5) rotor plates, 6) annular-shaped packing, 7) casing ........................................... 3 Figure 2: Sections in an RPB contributing to the overall dry pressure drop 12. ....................... 5 Figure 3: Schematic of the lower rotor plate of the R600 rotor (top view) ..............................13 Figure 4: Method to measure the dry pressure drop. UL (upper limit) are restrictions given by the periphery or the RPB. In the present study: UL: 𝑉𝐺= 60 m3 h-1; nrot = 20 s-1 ....................17 Figure 5: Experimentally measured centrifugal head ξCH. Left: empty rotors; Right: packed rotors. ...................................................................................................................................18 Figure 6: Frictional pressure drop of the static empty rotors ∆pf,empty as a function of the gas flow rate. ..............................................................................................................................19 Figure 7: Left: Frictional pressure drop of the static packed rotor in dependency of the gas flow rate. Right: Gas velocity as a function of the radius of the packed bed for a gas flow rate of 40 m3∙h-1 and hR = 10 mm. ................................................................................................20 Figure 8: Frictional pressure drop of the static packed rotor as a function of the average value of the integrated gas capacity factor 𝐹𝐺, 𝑖𝑛𝑡. ...............................................................21 Figure 9: Parity plot to compare the experimental and calculated pressure drop ..................22 Figure 10: Comparison of the pressure drop dependency on the rotational speed for the empty and packed rotors at a fixed gas velocity of 20 m3·h-1 ................................................23 Figure 11: Parity plots for the calculated and experimentally determined pressure drops of the static rotor the KM II (left) and KM I (right) packing .........................................................24 Figure 12: Parity plots for the calculated and experimental pressure drop for the 610 KM II (left) and 410 KM II rotor (right). ..........................................................................................26 Figure 13: Parity plots for the calculated and experimental pressure drop for the 610 Foam rotor......................................................................................................................................27 Figure 14: Parity plots for the calculated and experimental pressure drop for the RPB investigated by Sandilya et al.22. ...........................................................................................28 38 ACS Paragon Plus Environment

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