Distillation in a Counterflow Concentric-Ring Rotating Bed - Industrial

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Distillation in a Counterflow Concentric-Ring Rotating Bed Yumin Li, Xiaohua Li, Ying Wang, YinYin Chen, Jianbing Ji,* Yunliang Yu, and Zhichao Xu Zhejiang Province Key Laboratory of Biofuel, College of Chemical Engineering & Materials Science, Zhejiang University of Technology, Hangzhou, Zhejiang, 310014, China ABSTRACT: Developed from rotating zigzag bed (RZB), the counterflow concentric-ring rotating bed uses a rotor composed of stationary−rotating discs, a set of concentric circular rotating rings with perforations, and a liquid distribution at the eye of the rotor, preserving the outstanding characteristics of RZBs consisting of intermediate feeding and multirotors coaxially installed in series in a casing. A mass-transfer model was proposed from which the local gas- and liquid-side mass-transfer coefficients, gas− liquid effective interfacial area, and height equivalent to theoretical plate (HETP) can be calculated. Total reflux distillation experiments were conducted in a counterflow concentric-ring rotating bed at atmospheric pressure using an ethanol−water system, and the mass-transfer end effects were also investigated. The experimental values of overall volumetric gas-side masstransfer coefficient and HETP agree with the calculated values very well. Obvious end effects exist in the distillation process, and a correlation which takes inner and outer end effects into consideration is given. Compared with RZB, the counterflow concentric-ring rotating bed has lower mass-transfer efficiency, but it has gas−liquid throughput at least 5.576 times greater than that of RZB. Compared with rotating packed bed, the concentric-ring rotating bed has a much higher local gas-side mass-transfer coefficient. the rotor, which divide the rotor space into several flow channels for the contact of gas and liquid. Figure 1b shows blade packing,15−19 made up of 12 rectangular sheets, arranged along the radial direction in the rotor. Figure 1c shows waveform disc packing,20 composed of several concentric annular sheets, arranged along the axial direction in the rotor. The block rotor is incapable of intermediate feeding because of rotation of the entire rotor; therefore, one RPB with a single block rotor is not suitable for continuous distillation. In addition, the gas undergoes solid-body-like rotation in the block rotor, implying little or no increase in the gas-side mass-transfer coefficient.21 Hence, a novel rotor, called a partition rotor, has been developed. The partition rotor is characteristically divided into two separate parts and does not rotate in its entirety, as shown in Figure 2. Partition rotors are of two types: those with one part rotating and the other stationary and those with two separate parts rotating in the counterdirection or codirection. Partition rotors with rotating and stationary parts include rotating zigzag bed (RZB) rotor,22−24 TSCC-RPB rotor,25,26 and rotor of RPB equipped with blade packing and baffles.27 The RZB rotor is composed of two series of concentric circular baffles attached to two separate discs, one baffle and its disc rotate with the rotational shaft whereas the other and its disc remain stationary. Multiple rotors are coaxially installed in series in one casing, as shown in Figure 2a. Two types of intermediate feed can be accommodated by installing inlet tubes that penetrate into the middle of the rotor, which is termed intermediate feed of midrotor, and into the eye of the rotor, which is called intermediate feed of eye-rotor. The TSCC-RPB rotor comprises both a rotating lower disc and a stationary upper disc to which

1. INTRODUCTION In the chemical industries, up to 80% of the investment is used for separation of chemical products. Distillation is undoubtedly one of the most important unit operations.1 Trayed or packed columns are usually used in industrial distillation operations. Because gravity serves as the driving force, distillation columns have the disadvantages of large equipment volume, lower flooding point, and long debugging time. Vivian2 found that centrifugal force can increase the gas−liquid mass-transfer rate in a packed column rotating with the arm of a centrifuge in 1965, and Ramshaw invented the rotating packed bed (RPB) in 19813 and applied the RPB to distillation in 1983.4 Since then, the technology of adopting centrifugal force to intensify the contact and mass-transfer of gas−liquid by rotating a doughnut-shaped rigid bed, named “Higee” (an acronym for high gravity), has been developed. The traditional vertical packed and trayed column became the rotating beds with a reduction in equipment size of up to 100-fold, owing to the fact that the large centrifugal force achieves greatly increased mass-transfer coefficient, effective gas−liquid interfacial area, and gas−liquid throughputs. 2. HIGEE ROTOR The key component of the rotating bed is the rotor. For a gas− liquid countercurrent, the conventional rotor with packing elements that rotates in its entirety is called a block rotor, as shown in Figure 1a. The rotating packed bed (RPB), as the first Higee device, adopts the block rotor. The packing in the block rotor includes random, structured, and sheet packing. The random packing includes wire mesh, reticulated PVC packing,5 wire gauze,6 glass beads,7 rectangular and elliptic cylindrical packing,8 triangular spiral packing,9,10 etc. Wire mesh is the most commonly used packing in most RPBs. Structured packing includes foam metal,6,11,12 sheets of corrugated foil,13 fin baffle packing,14 etc. Sheet packing, as a simple and special rotor packing, is composed of a series of specially designed sheets in © 2014 American Chemical Society

Received: Revised: Accepted: Published: 4821

June 19, 2013 January 3, 2014 February 18, 2014 February 18, 2014 dx.doi.org/10.1021/ie4019337 | Ind. Eng. Chem. Res. 2014, 53, 4821−4837

Industrial & Engineering Chemistry Research

Article

Figure 1. Block-rotor of the rotating bed filled with (a) random or structure packing (b) sheet packing of blades and (c) sheet packing of waveform disk.

Figure 2. Partition-rotor of the rotating bed of (a) RZB rotor, (b) TSCC-RPB rotor, (c) rotor of RPB equipped with blade packing and baffles, and (d) rotor of RPB with split packing.

concentric circular packing rings are attached. The counterdirection rotation promotes a high annular slip velocity between the gas and liquid. Higee devices for continuous distillation include two RPB systems with intermediate feed between the two RPBs14,33,34 and one RPB/RZB with intermediate feed of midrotor or eye-rotor and partition rotors in one casing.22,23,25,26,35 The RZB, because of its first and novel partition rotor, has been successfully commercialized and really achieves noncolumn distillation.35

four concentric circular packed casings and four concentric circular porous sheets are fixed, respectively. Two rotors are coaxially installed in series, and intermediate feed of eye-rotor is used, as shown in Figure 2b. The rotor of a RPB equipped with blade packing and baffles is characterized by rotating blade packings and stationary baffles, alternately aligned in the radial direction, which are fixed to the rotating and stationary discs, respectively, as shown in Figure 2c. The stationary baffles retard gas rotation and provide a high annular slip velocity between the gas and packing. The partition rotor with two rotating parts is the rotor of a RPB with split packing,28−32 as shown in Figure 2d. The rotor consists of two discs rotating in the counterdirection or codirection about a horizontal axis to which two sets of

3. CONSTRUCTION OF THE COUNTERFLOW CONCENTRIC-RING ROTATING BED The rotor of the counterflow concentric-ring rotating bed comprises a rotating disc and a stationary disc, as shown in Figure 4822

dx.doi.org/10.1021/ie4019337 | Ind. Eng. Chem. Res. 2014, 53, 4821−4837


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considerable amount of mass transfer between the outer periphery of the rotor and the casing due to a lot of flying droplets between them, thus leading to obvious mass-transfer end effects.36 The counterflow concentric-ring rotating bed was developed from the RZB. The RZB rotor employs alternating rotating and stationary baffles, with gaps at the top of the rotating baffles and at the bottom of the stationary baffles. Perforations are made on the upper part of the rotating baffles, as shown in Figure 4a.

3a. A set of concentric circular metal rings, fully perforated with small holes as gas and liquid channels, are fixed to the rotating

Figure 3. (a) Schematic structure and (b) partial enlarged structure of counterflow concentric-ring rotating bed with stationary-rotating discs. 1-rotating disc; 2-rotational rings; 3-perforations on rotational rings; 4gas inlet; 5-stationary disc; 6-gas outlet; 7-liquid inlet; 8-intermediate feed; 9-casing; 10-liquid outlet; 11-rotating liquid distributor; 12mechanical seal; 13-gas; 14-concentric circular groove of the stationary disc; 15-flying liquid droplets; 16-liquid film on the inner wall of the rotating rings; 17-vortices at the inner side of the rotating rings; 18liquid film on the wall of the holes on the rotating rings; 19-fine liquid droplets in the hole space.

disc with equal radial spacing, called rotating rings. A set of concentric circular grooves are made on the lower surface of the stationary disc. When the two discs are brought together, the top of the concentric rotating rings extends into the concentric grooves of the stationary disc, forming a tight labyrinth seal to prevent gas from bypassing the rotating rings. A small metal cylinder with minute holes distributed evenly on its wall is installed at the center of the rotating disc and serves as a rotating liquid distributor. The rotating disc with its rings and liquid distributor is driven by a motor through a vertical shaft, and the stationary disc with intermediate feed, liquid inlet, and gas outlet is attached to the casing. Upon entering the rotating liquid distributor through the liquid inlet, the liquid is dispersed into liquid droplets through the perforated cylinder wall, forming a uniform liquid distribution. The liquid, as fine droplets, flows radially outward through the perforations of layers of rotating rings under centrifugal force and is discharged through the liquid outlet of the casing. Tangentially introduced into the casing, the gas continues to flow radially inward through the perforations of layers of rotating rings under pressure drop and is discharged through the gas outlet. Both liquid and gas flow countercurrently through the perforations of the rotating rings, as shown in Figure 3b. Flying in the gaps between the rotating rings, the liquid droplets impact the inner walls of the rotating rings to form a liquid film. The film then flows through the holes on the rings as a thin film on the hole walls for the major liquid component and as fine droplets in the hole spaces for the minor liquid component, which can be ignored. The gas flows through the holes as jets from the outer side to the inner side of the rotating rings, generating a lot of vortices characteristic of boundary layer separation at the inner side of the rings. Contacting with the liquid film on the inner walls of the rotating rings, the gas vortices form a stagnant zone such that mass transfer does not occur. The contact process of mass transfer includes the countercurrent contact of gas with flying liquid droplets in the gaps between two adjacent rotating rings and with the liquid film on the hole walls of the rotating rings, as shown in Figure 3b. In addition, there may be a

Figure 4. Sketch of RZB with (a) schematic structure, (b) partial enlarged structure, and (c) changes made from RZB. 1-rotational baffles; 2-rotating disc; 3-gap between the bottom of stationary baffles and rotating disc; 4-stationary baffles; 5-stationary disc; 6-gap between the top of rotational baffles and stationary disc; 7-perforations on upper part of rotational baffles; 8-intermediate feed; 9-gas; 10-liquid crosscurrently contacting with the gas; 11-liquid entrainment by gas; 12-rotating liquid distributor.

Inside the RZB, the continuous gas flows in a staggered manner accompanied with high pressure drop, and the liquid crosscurrently contacts with the gas resulting in high liquid entrainment and low gas−liquid throughput,22,23,35 as shown in Figure 4b. To eliminate the disadvantages of RZB, some changes in its design can be made. The stationary baffles are eliminated; all parts of the rotating baffles are perforated; and a rotating perforated cylinder serving as the rotating liquid distributor is installed at the eye of the rotor, as shown in Figure 4c. At last, the top of rotating baffles extend up to the stationary disc, such that the RZB becomes the counterflow concentric-ring rotating bed shown in Figure 3a. The gas flows directly through layers of rotating baffles in a nonstaggered manner with lower pressure drop. The liquid also flows through layers of rotating baffles, countercurrently contacting with the gas, with lower liquid entrainment and higher throughput. However, the counterflow concentric-ring rotating bed reserves the structure of the stationary−rotating discs of RZB so that intermediate feeding and a multirotor configuration can be easily achieved. As such, the counterflow concentric-ring rotating bed represents an upgrade of the RZB.

4. MODEL OF MASS TRANSFER 4.1. Model of Interfacial Area and Mass-Transfer Coefficient. Three assumptions are made. (1) Liquid droplets 4823



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impinge the rotating rings one after another, and the surfaces on the droplets are renewed after each impingement.37 (2) Liquid droplets leave the rotating baffles along the direction tangential to the rotating baffles at the velocities of the rotating baffles. (3) The total gas−liquid effective interfacial area is the sum of the surface area of liquid droplets in the gaps between two adjacent rotating rings and the liquid film on the hole walls. The liquid droplets impinging obliquely on the rotating rings have a tangential velocity component, leading to easy dispersion in the tangential direction of the rotating rings and complete wetting of the hole walls in the range of the experimental liquid rate. As a result, the surface area of the liquid film on the hole walls equals that of the hole walls. The space of the rotor is divided into several annular regions, as shown in Figure 5. Region 1 is the annular region between two

The relationship of the effective interfacial area of liquid droplets adi, the liquid holdup of liquid droplets εdi, and the average diameter of the liquid droplets dLi in region i is written as:37 Adi

adi =

2

2

π (ri + 1 − ri )z

6εdi dLi

=

(4)

i.e., Adi =

ri + 12

6Q L 6εdi π (ri + 12 − ri 2)z = dLi ωdLi

−1

ri 2

(5)

where Adi is the surface area of liquid droplets in region i. From assumption (3) above, the surface area Af i of the liquid film on the hole walls of the rotating rings in region i equals that of the hole walls. So Afi is the area of single hole wall times the number of holes. The number of holes equals the hole area 2πri zϕ of the rotating ring in region i divided by the area of a single hole. Thus A fi =

2πrz i ϕ (π /4)d02

8πrz i ϕt d0

πd0t =

(6)

where ϕ is fractional hole area, t the thickness of the rotating ring, and d0 the diameter of the holes passing through the rotating rings. Hence, the gas−liquid effective interfacial area of droplets ad and film af on the rotor are 6Q L

m+1

ad = Figure 5. Annular regions in the space of the concentric rotating ring rotor.

=

ui

ri + 12 − ri 2 ωri

=

1 ω

ri + 12 ri 2

π (ri + 1 − ri )z

−1

m+1

=

6Q LρL 0.5

(1)

a = ad + a f = +

8ϕt ∑i = 1 ri d0(rm + 2 2 − r12)

(7b)

(8)

0.7284σ 0.5

8ϕt d0(rm + 2 2 − r12)

m+1

∑i = 1 ri 0.5

ri + 12 ri 2

−1

π (rm + 2 2 − r12)z m+1

∑ ri = i=1

B1 Q + B2 z L

0.5 2 2 where B1 = (6ρL /0.7284σ ∑i m+1 = 1 ri (ri+1 /ri 2 m+1 2 2 − r1 )) and B2 = (8ϕt∑i = 1 ri/d0(rm+2 − r1 )).

(2)

0.5

(9)

− 1) /π(rm+22 1/2

The surface renewal models of kG = (DGSG)1/2 and kL = (DLSL)1/2 are employed to calculate local gas- and liquid-side mass-transfer coefficients kG and kL, respectively. The rate of gas surface renewal SG relates to the degree of gas turbulence, so SG is proportional to the square of the vapor real radial velocity vG at the inner edge of the rotor.37 Thus

QL πzωri ri + 12 − ri 2

(7a)

Equation 8 is substituted into eq 7a, so the total gas−liquid effective interfacial area a is

where z is axial height of the rotor. Substituting eq 1 into eq 2 gives εdi =

π (rm + 2 2 − r12)z

0.5

2

π (rm + 2 2 − r12)z

⎛ σ ⎞0.5 dLi = 0.7284⎜⎜ 2 ⎟⎟ ⎝ ω riρL ⎠

Q Lτi 2

∑i = 1 A fi

−1

ri 2

Guo has given an equation to determine the average diameter of liquid droplets in the RPB, which can be used to calculate the average diameter of liquid droplets in region i of the counterflow concentric-ring rotating bed:

The liquid holdup of liquid droplets εdi in region i is obtained using the total volume of liquid droplets, which equals the liquid inflow rate QL times the interval time of τi divided by the volume of region i: εdi =

=

ri + 12

37

rings of radii r1 and r2. Region i is the annular region between two adjacent rings of radii ri and ri+1, and so on. Region m + 1 is the annular region between the outer periphery of the rotor and the casing. At region i, liquid droplets leave the rotating ring of radius ri at a velocity ui = ωri along the direction tangential to the rotating ring. Upon reaching the next rotating ring with radius ri+1 during the interval τi, the liquid droplets are captured and then leave at a velocity ui+1 = ωri+1 along the tangential direction. The interval time of τi is written as ri + 12 − ri 2

π (rm + 2 2 − r12)z

m+1 1 dLi

∑i = 1

ω

m+1

af =

τi =

∑i = 1 Adi

(3) 4824


Industrial & Engineering Chemistry Research ⎛ Q G ⎞2 SG = ksvG 2 = ks⎜ ⎟ ⎝ 2πrinzϕ ⎠

Article

The F-factor is calculated on the inner edge of the rotor, where flooding initiates; that is

(10)

F‐factor = Q G ρG /(2πrinz)

where ks is a proportionality coefficient. The local gas-side mass-transfer coefficient kG and the local volumetric gas-side mass-transfer coefficient kGa are written as kG = k Ga =

DGSG = aQ G

QG

DGks

2πrinzϕ

DGks = B3

2πrinzϕ

i.e. QG =

(11a)

aQ G z

where B3 = (DGks)1/2/(2πrinϕ) Under assumption (1) above, the rate of liquid surface renewal SL can be calculated as38 m+2 S L = vL rm + 2 − r1 (12)

QL =

where vL is the liquid average radial velocity in the rotor, expressed as r −r vL = m +m2 + 1 1 ∑i = 1 τi (13)

(15a)

Equation 14 is substituted into eq 15a, so the local volumetric liquid-side mass-transfer coefficient kLa is written as m+2 m+1

∑i = 1

ri + 12 ri

2

= aB4 ω −1

(15b)

where B4 = {DL(m + − 1) ]} The overall mass transfer and overall volumetric mass-transfer coefficients KG and KGa are 2 2 2)/[∑im+1 = 1 (ri+1 /ri

1/2

1/2

m (C / C ) 1 1 = + ̅ G L KG kG kL

(16a)

m (C / C ) 1 1 = + ̅ G L K Ga k Ga kLa

(16b)

where 1/KGa is the overall resistance to mass transfer, 1/kGa the gas film resistance, m̅ (CG/CL)/kLa the liquid film resistance, m̅ the average slope of the vapor−liquid equilibrium curve, CG =P/ RT the total concentration of the gas phase, and CL =ρL/ML the total concentration of the liquid phase. Substituting eqs 9, 11b, and 15b into eq 16b gives K Ga =

B1 QL z z B3Q G

+

+ B2 m̅ (CG / C L) B4 ω

ρL

(20)

B1 (F‐factor)(2πrin) ρL ρG

+

ρG + B2 m̅ (CG / C L) B4 ω

(21)

where (ρG)1/2/[B3(F-factor)(2πrin)] is the gas film resistance and m̅ (CG/CL)/(B4ω1/2) is the liquid film resistance. From eq 21, KGa, independent of z, increases with increasing F-factor and ω. Considering that the gas film is the dominant resistance in distillation, the liquid film resistance given by eq 21 is ignored as the F-factor is smaller. However, with increasing Ffactor, the gas film resistance decreases and is close to the liquid film resistance, so both film resistances are important, thus leading to the fact that the angular velocity ω in the liquid film resistance affects KGa. 4.2. Modified Model for Compound Rings. A single circular metal perforated ring, serving as the main ring, is compounded with two concentric circular metal perforated rings, serving as auxiliary rings, at the inside and outside of the main ring by a small gap between the main and auxiliary rings; this is termed compound ring. The main ring with its auxiliary rings rotates together, and the thickness of the auxiliary ring is very small. A set of concentric compound rings are fixed to the rotating disc. The rotating ring of a single ring without auxiliary rings is termed single ring. It is obvious that the above masstransfer models are suitable for the single-ring rotor, so the model needs to be modified for the compound ring. The circular main ring of radius ri is compounded with two circular auxiliary rings of radii ri,1 and ri,2 at the inside and outside of the main ring, respectively. Thus, region i is taken as the annular region between the two auxiliary rings of radii ri,1 and ri+1,1, as shown in Figure 6. Equation 8 is still available for the compound-ring rotor, and the surface area of the liquid droplets Adi in region i of the compound-ring rotor is

(14)

According to eq 14, the rate of liquid surface renewal SL is the number m + 2 of impingement of droplets divided by the flying time of droplets from region 1 to region m + 1. As already stated, the local liquid-side mass-transfer coefficient kL is written as

kLa = a DL ω

Q GρG

B3(F‐factor)(2πrin)

DL SL

(19)

Substituting eqs 19 and 20 into eq 17 to eliminate QG and QL in eq 17 gives

K Ga =

ri

kL =

F‐factor(2πrinz) ρG

If the total reflux distillation is employed, the vapor from the inner edge of the rotor is completely condensed to the reflux liquid that fully enters the rotor at the inner edge. The mass rate of the vapor is equal to that of the reflux liquid, that is

(11b)

Substituting eqs 13 and 1 into eq 12 gives m+2 m+2 SL = m + 1 = 2 m + 1 ri + 1 1 ∑i = 1 τi ∑ −1 2 i = 1 ω

(18)

(17) 4825



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The rate of liquid surface renewals SL for the compound-ring rotor is SL =

3(m + 1) + 1 ⎛ 1 m+1 ∑i = 1 ⎜ ω ⎝

ri

2

ri ,12

−1 +

ri ,2 2 ri

2

−1 +

ri + 1,12 ri ,2

2

⎞ − 1⎟ ⎠

(for the compound‐ring rotor) (24)

The local liquid-side mass-transfer coefficient kL for the compound-ring rotor is obtained by substituting eq 24 into eq 15a, and kLa for the compound-ring rotor equals kL times a from eq 23. 4.3. Relationship between HETP and KGa. The height equivalent to theoretical plate (HETP) of the rotor is defined as r − rin HETP = out NT (25)

Figure 6. Annular regions in the space of the concentric compound-ring rotor.

Adi =

⎛ 6Q L ⎜ 1 ω ⎜⎝ dLi ,1 +

=

ri 2 ri ,12

1

ri + 1,12

dLi ,2

ri ,2 2

−1 +

1 dLi

ri ,2 2 ri 2

−1

⎞ − 1⎟ ⎟ ⎠

The relationship of the number of transfer units NTUG and the number of theoretical plates NT is written as1

⎛ ri ,2 2 6Q LρL 0.5 ⎜ 0.5 ri 2 0.5 1 r r − + −1 i ,1 i 0.7284σ 0.5 ⎜⎝ ri ,12 ri 2 ⎞ ri + 1,12 ⎟ 1 + ri ,2 0.5 − ⎟ ri ,2 2 ⎠

NTUG = NT

rout − rin ln(1/m̅ ) (27) HETP 1 − m̅ The overall volumetric mass-transfer coefficient KGa is obtained by an equation provided by Mondal:28 NTUG =

(22)

Because the thickness of the auxiliary ring is very small and ignored, af for the compound rings equals that of the single rings. Therefore, the total mass-transfer effective interfacial area a for the compound-ring rotor is

π (rout 2 − rin 2) = (ATUG)(NTUG)

=

ri ,12

− 1 + ri 0.5 2

+ =

ri 2

8ϕt d0(rm + 2 2 − r12)

m+1

π(rm + 2 −

ri ,2 2 ri 2

− 1 + ri ,2 0.5

ri + 1,12 ri ,2 2

⎞ − 1⎟ ⎠

ATUG =

r12)z

NTUG =

∑ ri

where 6ρL 0.5

=

⎛ m+1 ∑i = 1 ⎜ri ,10.5 ⎝

ri 2 ri ,12

− 1 + ri 0.5

ri ,2 2 ri 2

− 1 + ri ,2 0.5

ri + 1,12 ri ,2 2

⎞ − 1⎟ ⎠

π(rm + 2 2 − r12)

and

B2 =

zK Ga

∫y

y2

(29a)

dy y* − y

(29b)

where the limit y1 in eq 29b is the vapor composition in equilibrium with the experimentally measured liquid composition x1 in the reboiler, and the limit y2 is the vapor composition in the gas outlet of the rotating bed that is equal to the liquid composition x2 of the reflux liquid if the vapor is totally condensed; y and y* are the vapor composition in the bulk vapor and that in equilibrium with the composition x of the bulk liquid, respectively. Substituting eq 29a into eq 28 gives

(23)

0.7284σ 0.5

QG

1

i=1

B1 Q + B2 (for the compound‐ring rotor) z L

B1

(28)

where ATUG (the area of transfer unit) and NTUG are defined as

a = ad + af ⎛ m+1 ∑i = 1 ⎜ri ,10.5 0.7284σ 0.5 ⎝

(26)

The total reflux of distillation gives L/G = 1. Substituting L/G = 1 and eq 25 into eq 26 gives

(for the compound‐ring rotor)

6Q LρL 0.5

ln[L /(Gm̅ )] 1 − (Gm̅ )/L

K Ga = m+1 8ϕt ∑i = 1 ri d0(rm + 2 2 − r12)

Q G(NTUG) zπ (rout 2 − rin 2)

(30)

Substituting eq 30 into eq 27 gives HETP =

By comparison of eq 9 and eq 23, it is evident that B1 for the compound-ring rotor is greater than that of the single-ring rotor. The local gas-side mass-transfer coefficient kG for the compound-ring rotor is still calculated by eq 11a, and kGa for the compound-ring rotor equals kG times a from eq 23.

QG

ln(1/m̅ ) zπ (rout + rin)K Ga 1 − m̅

(31)

Equation 31 indicates the relationship between HETP and KGa, which is available for the distillation of other RPBs. Substituting eqs 19 and 21 into eq 31 gives 4826



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Figure 7. Experimental setup of distillation.

Figure 8. Rotating ring of concentric-ring rotor and RZB rotor: (a) rotating single ring of rotor A1 and A2, (b) rotating compound-ring of rotor B1 and B2, (c) photograph of metal hole sheet with circular holes, (d) photograph of metal net sheet with regular diamond holes, and (e) RZB rotor.

1+ HETP = B3π (rout + rin) ln(1/m̅ ) 1 − m̅

rotor tangentially through the gas inlet and flowed over the rotor radially inward, intimately contacting the liquid flowing countercurrently. Leaving the rotor and the casing through the vapor outlet located at the top of the casing, the vapor was introduced to the overhead condenser and was fully condensed to a liquid as reflux by cooling water. The reflux liquid ran downward through a rotameter and then entered the rotating liquid distributor through the liquid inlet at the eye of the rotor by gravity. By centrifugal force, the liquid was sprayed onto the inner periphery of the rotor and then flowed radially outward through the rotor. The liquid that collected by the casing wall exited through the liquid outlet at the bottom of the casing into the reboiler by gravity. The rotor was driven by a motor with a pulley. A frequency modulator was used to change the rotational speed of the motor. Four counterflow concentric-ring rotors A1, A2, B1, and B2, and a RZB rotor were employed, as shown in Figure 8. Rotors A1, A2, B1, and B2, with an inner diameter of 0.140 m and outer diameter of 0.272 m, were all composed of seven rotating rings with diameters of 0.140, 0.160, 0.184, 0.208, 0.228, 0.250, and 0.272 m. The axial heights of rotors A1, A2, B1, and B2 were 0.015, 0.045, 0.015, and 0.045 m, respectively. Rotors A1 and A2 employed the rotating single rings of circular metal hole-sheets

B3m̅ (CG / C L)(2πrin) F‐factor B4 ρG ω

(

B1 ρG ρL

(2πrin)(F‐factor) + B2

) (32)

From eq 32, HETP is a function of F-factor and rotational speed.

5. EXPERIMENTAL SECTION AND DATA ANALYSIS 5.1. Experimental Apparatus and Procedure. A schematic diagram of the experimental setup for the distillation operation at total reflux with an ethanol−water system at atmospheric pressure is shown in Figure 7. The experimental system consisted of a rotating bed with a 0.3 m casing diameter, a reboiler, a condenser, and a motor. A rotating liquid distributor of 0.08 m diameter, consisting of 45 holes of 0.0005 m diameter distributed evenly on its wall, was located at the eye of the rotor. The amount and composition of the ethanol−water solution as feed was charged initially to the reboiler. The liquid was vaporized in the reboiler. The vapor from the reboiler entered the 4827



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Figure 9. Effect of (a) F-factor and (b) rotational speed on KGa.

methods. The gas−liquid phase equilibrium curve of the ethanol−water system is written as αx y* = 1 + (α − 1)x (33a)

with thickness of 0.0008 m fully perforated with holes of 0.0018 m diameter and with 0.0026 m distance between the holes. Rotors B1 and B2 employed the rotating compound rings of a single circular metal hole sheet compounded with two circular metal net sheets with thickness of 0.0002 m at the inside and outside of the hole sheet by a gap of 0.002 m between the net sheet and hole sheet. The net sheets were perforated with regular diamond holes with side lengths of 0.001 m and with a fractional hole area of 44.4%. The diamond holes have very sharp edges, as shown in Figure 8b, such that the thickness of the diamond holes is approximately zero. Some soft packing was placed in the concentric circular grooves of the stationary disc, contacting with the top of the rotating single rings and compound rings for a tighter seal to prevent gas from flowing through the circular grooves of the stationary disc, as shown in Figure 8a,b. The RZB rotor, with an inner diameter of 0.117 m and outer diameter of 0.284 m and height of 0.053 m, was composed of nine coupled rotating−stationary baffles, as shown in Figure 8e. The rotating baffles had diameters of 0.117, 0.145, 0.168, 0.189, 0.217, 0.239, 0.242, 0.260, and 0.276 m. The stationary baffles had diameters of 0.130, 0.157, 0.178, 0.197, 0.216, 0.235, 0.250, 0.265, and 0.284 m. The rotating and stationary baffles had heights of 0.044 m and 0.038 m, respectively. Small holes with diameters of 0.0015 m and with 0.0029 m distance between holes were made on the upper parts of the rotating baffles. The reflux liquid rate was measured by a rotameter, and the rotational speed of the rotor was measured using a laser tachometer. The reflux liquid rate QL ranged from 2.78 × 10−6 to 3.61 × 10−5 m3/s, and the rotational speed n ranged from 800 to 1400 rpm. After the temperature reached a steady state, samples of the reflux liquid and liquid in the reboiler were collected. The liquid compositions of the reflux liquid x2 and of the liquid x1 in the reboiler were obtained from analysis of the liquid sample by gas chromatography. At the same time, the pressure drop ΔP between the gas inlet and outlet was measured by a pressure difference sensor. In addition, the mass-transfer end effects were investigated with the successive removal of one, two, and three rotating rings at the outermost and innermost portions of rotor B1. 5.2. Data Analysis. The number of transfer units NTUG and number of theoretical plates NT are obtained from the following

where x is the liquid composition in the bulk liquid phase and α is the relative volatility of the ethanol−water system. Correlating α with x gives −1.5235 ⎧ x ≤ 0.292 ⎪1.1213(x + 0.2) α=⎨ ⎪ −1.062 ⎩ 0.8938x x > 0.292

(33b)

The total reflux was employed, so the liquid composition x in the bulk liquid phase was equal to the vapor composition y in the bulk vapor phase in the rotor: x=y (34) In accordance with the measured liquid composition x1 in the reboiler and x2 of the reflux liquid, the vapor composition y1 in equilibrium with x1 and y2 that equals x2 were obtained. Substituting eqs 33a, 33b, and 34 into eq 29b and integrating with y1 and y2 gives NTUG, and then KGa was obtained from eq 30. The number of theoretical plates NT plus one theoretical plate given by the reboiler between the liquid inlet and the reboiler were determined from x1 and x2, so HETP was obtained from eq 25. Substituting KGa and HETP into eq 31 gives m̅ . The kGa could be obtained by eq 16b using the measured KGa, calculated a and kL from the mass-transfer model, and m̅ from eq 31. Substituting the thus obtained kGa and calculated a values into eq 11b gave the proportional coefficient ks. As a result, the average m̅ and ks were obtained because m̅ and kG were slightly altered by F-factor and n. Consequently, the calculated kG, kL, kGa, kLa, KG, and KGa for single-ring and compound-ring rotors were obtained from the mass-trasfer model.

6. RESULTS 6.1. Mass-Transfer Coefficient, HETP, and Pressure Drop of Rotors A1 and B1. Rotors A1 and B1 had the same average value of ks = 9425 for all F-factor values, based on the experimental data. The average values of m̅ were obtained such that m̅ = 0.191 and 0.212 at an F-factor of 0.32 m/s (kg/m3)0.5, m̅ = 0.307 and 0.417 at a F-factor of 0.64 m/s (kg/m3)0.5, and m̅ = 4828



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0.546 and 0.646 at F-factor ≥ 0.96 m/s (kg/m3)0.5 for rotor A1 and rotor B1, respectively. The calculated KGa for single-ring and compound-ring rotors was obtained from eq 16b, using kL and a from the mass-transfer model and the average values of ks and m̅ . The effect of F-factor and rotational speed n on the calculated and experimental KGa is shown in Figure 9, where the calculated KGa agrees with the experimental KGa very well. Figure 9a shows a remarkable increase in KGa with increasing F-factor. The fact that the slope of the curve of KGa ∼ F-factor for rotor B1 is greater than that of rotor A1 is predicted by B1 in eq 21 because B1 for rotor B1 given by eq 23 is greater than that of rotor A1 given by eq 9. Figure 9b shows that KGa increases slightly with increasing n. The liquid film resistance containing ω is smaller than the gas film resistance containing none of ω, leading to the slight effects of rotational speed n on KGa, which is also predicted by eq 21. Figure 10 shows the diagonal plot of the calculated and experimental values, showing a good agreement.

K Gad0 2 = 0.005818ReG 0.9867GrG 0.09167ScG−1/3 DG

The average error is 0.03829, and the greatest error is 0.1536. KGad0 2 = 0.005757ReG1.0989GrG 0.05156ScG−1/3 DG

A distillation correlation of KGa for rotors A1 and B1 is given by the modification of the correlation provided by Kelleher:38 (35)

where ReG = {[QG/(2πravez)]d0ρG}/μG, GrG = (d0 ρG ac/μG2), and ScG = (μG/ρGDG). According to the dimensions of rotors A1 and B1, we obtain that rave = (rin + rout)/2 = 0.103 m, z = 0.015 m, and d0 = 0.0008 m. Using the experimental results and regression analysis, the coefficient of A1, A2, and A3 in eq 35 can be obtained for rotor A1 (eq 36a) and rotor B1 (eq 36b): 3

(36b)

The average error is 0.02537, and the greatest error is 0.1358. The effect of F-factor on calculated HETP from eq 32 and experimental HETP from eq 25 is shown in Figure 11, with good agreement of the calculated and experimental HETP. With increasing F-factor, the experimental HETP of rotors A1 and B1 decrease rapidly and then slightly increases for rotor A1 and decreases for rotor B1. The reason is that the liquid entrainment by vapor with high vapor velocity gives worse mass-transfer and higher HETP in rotor A1. In addition, the net sheets of compound rings of rotor B1 can intercept most of the liquid entrainment, thus leading to lower HETP. The HETP for rotor B1 is lower than that of rotor A1 because of the greater KGa for rotor B1, and the HETP at 1200 rpm is slightly lower than that at 1000 rpm because the KGa at 1200 rpm is slightly greater than that at 1000 rpm in Figure 9. The pressure drop ΔP of rotors A1 and B1 increases with increasing F-factor and n, as shown in Figure 12. Not surprisingly, the pressure drop of rotor B1 is greater than that of rotor A1 because the compounded net sheets of rotor B1 increase the gas flow resistance. To further illustrate the composite characteristic of pressure drop and mass transfer, the pressure drop per theoretical plate ΔP/NT is employed, and we find that ΔP/NT of rotor B1 is greater than that of rotor A1. 6.2. Mass-Transfer Characteristic for Distillation of Counterflow Concentric-Ring Rotating Bed. From eq 9 for the single-ring rotor and eq 23 for the compound-ring rotor, the total effective interfacial area a, the interfacial area of the liquid film af, and the interfacial area of liquid droplets ad are calculated. The total effective interfacial area a equals ad plus af, and ad increases while af remains constant with increasing F-factor, as shown in Figure 13. At an F-factor of 3.69 m/s (kg/m3)0.5, ad is 48.4% and 58.4% of a for the single-ring rotor and compoundring rotor, respectively. The ad of rotor B1 is 1.5−1.6 times as much as that of rotor A1 because the compounded net sheets of rotor B1 are equivalent to the increase in the number of rotating rings. The overall resistance to mass transfer 1/KGa is obtained from the measured KGa, and the liquid film resistance m̅ (CG/CL)/kLa is obtained from the kLa calculated by the mass-transfer model; so the gas film resistance 1/kGa is 1/KGa minus m̅ (CG/CL)/kLa,

Figure 10. Comparison of experimental and calculated values of KGa.

K Gad02 = A1ReG A 2GrG A3ScG−1/3 DG

(36a)

2

Figure 11. Effect of F-factor on HETP for (a) rotor A1 and (b) rotor B1. 4829



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Figure 12. Effect of F-factor on (a) pressure drop and (b) pressure drop per theoretical stage.

because SL for rotor B1, given by eq 24, is greater than that of rotor A1, given by eq 14. The fact that the two curves of kG ∼ Ffactor for rotors A1 and B1 almost entirely overlap indicates that rotors A1 and B1 have the same values of ks in eq 11a. This implies that the compounded net sheets of rotor B1 do not increase the gas turbulence and ks because the gas flowing through the hole sheets is highly turbulent. Equation 11a with ks = 9425 gives the model curve of kG ∼ F-factor, as shown by the dashed line in Figure 14a. The good agreement of the predicted and experimental kG verifies the accuracy of the mass-transfer model. The local liquid-side coefficient kL slightly increases with increasing n according to eq 15a in conjunction with eqs 14 and 24. The local gas-side coefficient kG also slightly increases with increasing n, as shown in Figure 14b. The reason may be that the gas circumferential velocity increases with increasing rotational speed n, leading to the increase in the gas turbulence and kG. The effect of F-factor and n on KGa, kGa, and kLa is shown in Figure 15. The KGa, kGa, and kLa exhibit the same trend with increasing F-factor and n as KG, kG, and kL because KGa, kGa, and kLa equal KG, kG, and kL times a. The values of KGa, kGa, and kLa for rotor B1 are all greater than those of rotor A1 because a of rotor B1 is greater than that of rotor A1. With increasing F-factor, the overall resistance 1/KGa and the gas film resistance 1/kGa exhibit similar trends, that is, they decrease sharply first and then decrease slowly, while the liquid film resistance m̅ (CG/CL)/kLa is approximately invariable. The

Figure 13. Mass-transfer effective interfacial area of liquid droplets and liquid film.

from which kGa is obtained. The three mass-transfer coefficients KG, kL, and kG are obtained from KGa, kLa, and kGa divided by a as calculated by eqs 9 and 23. Therefore, the effect of F-factor and rotational speed n on the three mass-transfer coefficients, three volumetric mass-transfer coefficients, and three resistances to mass transfer are shown in Figures 14, 15, and 16, respectively. With increasing F-factor, the local liquid-side mass-transfer coefficient kL maintains constant because of eq 15a in conjunction with eqs 14 and 24, and the local gas-side masstransfer coefficient kG increases because of eq 11a, as shown in Figure 14a. The kL for rotor B1 is greater than that of rotor A1

Figure 14. Comparison of three mass-transfer coefficients of KG, kG, and kL with (a) F-factor and (b) rotational speed. 4830



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Figure 15. Comparison of three volumetric mass-transfer coefficient of KGa, kGa, and kLa with (a) F-factor and (b) rotational speed.

Figure 16. Three resistances to mass-transfer with (a) F-factor and (b) rotational speed.

6.3. Comparison of Rotors A2 and B2 with RZB Rotor. On the basis of the mass-transfer model, the rotor axial height z is independent of KGa in eq 21. However, the experimental KGa for rotors A2 and B2 with axial heights of 0.045 m are 11.25−13.80% and 3.50−3.86% lower than that of rotors A1 and B1 with axial heights of 0.015 m, respectively, as shown in Figure 18. This may be attributed to better contact of gas−liquid for the rotors with less axial height. This phenomenon has also been reported by Lin.39 As shown in Figure 19a, KGa for rotors A2 and B2 and RZB rotor all increase with increasing F-factor, and KGa for RZB rotor is approximately equal to that of rotor B2 at the lower F-factor.

three resistances of rotors A1 and B1 decrease slightly with increasing n, as shown in Figure 16. The ratio of liquid film resistance to overall resistance increases with increasing F-factor, as shown in Figure 17, where the ratio is less than 10% as F-factor ≤ 0.64 m/s (kg/m3)0.5. Therefore, the distillation process is gasfilm controlled with liquid film resistance ignored when F-factor ≤ 0.64 m/s (kg/m3)0.5, and both gas and liquid film resistances are important when F-factor ≥ 0.64 m/s (kg/m3)0.5.

Figure 17. Ratio of liquid film resistance to overall resistance with Ffactor.

Figure 18. Effect of axial height of the rotor on KGa. 4831



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Figure 19. Comparison of rotor A2, B2, and RZB rotor on (a) KGa, (b)NTR, (c)ΔPR, and (d) ΔP/NT at n = 1000 rpm.

Figure 20. Mass-transfer end-effects of rotor B1 where KGa varies with F-factor at different (a) inner and (b) outer radii of the rotor and with rotational speed at different (c) inner and (d) outer radii of the rotor.

However, KGa for RZB rotor suddenly decreases at a F-factor of 0.66 m/s (kg/m3)0.5 because of the occurrence of flooding resulting from the liquid entrainment by vapor at a high vapor velocity,23 whereas KGa for rotors A2 and B2 continues to increase as F-factor ≥ 0.66 m/s (kg/m3)0.5, indicating that rotor B1 has a turndown ratio higher than that of RZB rotor.

The rotors A2 and B2 and the RZB rotor are all composed of metal concentric sheets. Just asthe RZB rotor contains couples of rotating−stationary baffles acting as discrete steps to provide gas−liquid contact, rotors A2 and B2 contain rotating rings acting as discrete steps. Therefore, it is necessary to compare the number of theoretical plates per discrete step NTR and the 4832



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⎛V ⎞ ⎛ V ⎞⎞ K Gad0 2 ⎛ ⎜⎜1 − A4′ ⎜ o ⎟ − A5′⎜ i ⎟⎟⎟ = A1′ReG A 2′GrG A3′ScG−1/3 DG ⎝ ⎝ Vt ⎠ ⎝ Vt ⎠⎠

pressure drop per discrete step ΔPR of rotors A2 and B2 and RZB rotor. The NTR and ΔPR of rotors A2 and B2 are NT and ΔP divided by 7 because of the use of 7 rotating rings (i.e., 7 discrete steps), and NTR and ΔPR of RZB rotor are NT and ΔP divided by 9 because of the use of 9 couples of baffles (i.e., 9 discrete steps). The NTR of RZB rotor is greater than that of rotors A2 and B2, and ΔPR and ΔP/NT of RZB rotor are close to those of rotors A2 and B2 when F-factor < 0.66 m/s (kg/m3)0.5. When F-factor > 0.66 m/s (kg/m3)0.5, flooding takes place in the RZB rotor, leading to the sudden reduction in NTR and the rapid increase in ΔPR and ΔP/NT of RZB rotor, but flooding does not occur in rotors A2 and B2, leading to smooth change of NTR, ΔPR, and ΔP/NT of rotors A2 and B2, as shown in Figures 19b−d. This indicates that the turndown ratio and gas−liquid throughput of rotors A2 and B2 is much greater than those of RZB rotor. Additionally, flooding does not occur in rotors A1 and B1 even though F-factor reaches 3.68 m/s (kg/m3)0.5, as shown in Figure 18. Therefore, the gas−liquid throughput of rotors A1 and B1 of the counterflow concentric-ring rotating bed is at least 5.576 times greater than that of the RZB rotor. 6.4. Mass-Transfer End Effects of Rotor B1. With the successive removal of one, two, and three rotating rings in the outermost and innermost portions of the rotor B1, it is found that KGa varies with the radius of the rotor, as shown in Figure 20. When the rotational speed n remains invariable, KGa increases with increasing rin at a fixed rout, and KGa also increases with decreasing rout at a fixed rin. When the reflux liquid rate QL remains invariable, similar experimental results are obtained. The greater the space between the liquid distributor and the inner edge of the rotor and between the outer edge of the rotor and the casing, the greater KGa is, which indicates that obvious end effects existed. Chen40,41 investigated the mass-transfer end effect in RPBs, including inner end effects (mass transfer between the liquid distributor and the inner edge of the rotor) and outer end effects (mass transfer between the outer edge of the rotor and the casing). Two correlations, which take inner and outer end effects into consideration, were proposed to predict the local volumetric liquid- and gas-side mass-transfer coefficients.

(38)

π(rs2

where Vo = − rout )z, Vi = and Vt = Using experimental data, we obtain

= 0.003407ReG1.0629GrG 0.07682ScG−1/3

where WeL = [QL2/(2πravez)2ρLdp]/σ, ReL = [QL/(2πravez)ρLdp]/ μL, FrL = [QL2/(2πravez)2]/(acdp) From eq 40, a is proportional to QL and ω to powers of 0.77 and 0.24, respectively, i.e., a ∝ QL0.77 and a ∝ ω0.24. With combination of eqs 37a, 37b, and 40, kG and kL can be obtained as kG = kGa/a and kL = kLa/a, from which kG ∝ QG1.13, kG ∝ ω0.38, kG ∝ QL−0.49, kL ∝ QL0, and kL ∝ ω0.36 are obtained. Because F-factor is proportional to QG and QL for total reflux distillation, the powers of a, kG, and kL with F-factor and ω for RPB with stainless steel wire mesh packing are obtained: a ∝ (F‐factor)0.77

and

k G ∝ (F‐factor)0.64 kL ∝ (F‐factor)0

and and

a ∝ ω0.24

k G ∝ ω0.38 kL ∝ ω0.36

(41a) (41b) (41c)

The powers of a, kG, and kL with F-factor and ω for rotor B1 are obtained from the mass-transfer model of eqs 23, 11a, and 15a in conjunction with eq 24. a ∝ F‐factor

a ∝ ω0

and

kL ∝ (F‐factor)0

⎛ ⎞−0.5⎛ σc ⎞0.14 0.5 0.17 0.3 0.3 a t = 0.65Sc L ReLa GrLd WeLa ⎜ ⎟ ⎜ ⎟ ⎝ aP′ ⎠ ⎝ σw ⎠

and and

k G ∝ ω0 kL ∝ ω0.5

(42a) (42b) (42c)

By comparison of eqs 41a−c and 42a−c, the powers in eq 41 approach those in eq 42, and especially eq 41c, which has the same equation of kL ∝ (F-factor)0 as eq 42c, indicating that the mass-transfer model is reasonable. To compare all mass-transfer coefficients kGa, kLa, KGa, kG, kL, KG, and a in distillation of rotor B1 and the RPB rotor with stainless steel wire mesh packing at the same reflux liquid rate, rotational speed, and rotor dimensions, eqs 37a, 37b, and 40 were used together for the calculation of all mass-transfer coefficients for the RPB rotor. The packing used in the RPB rotor was 0.00022 m diameter stainless steel wire mesh with ε of 0.954, at of 829 m2/m3, and dp of 0.000333 m from Chen.36 The RPB rotor had inner radius, outer radius, and axial height that were the same as those of rotor B1, and the vapor and liquid properties ρL, ρG, σ, μL, μG, DG, and DL in eqs 37a, 37b, and 40 were taken from the distillation experiments of rotor B1. The values of σc, σw, and a′p in eqs 37a and 37b were 0.075 kg/s2, 0.072 kg/s2, and 3000 m2/m3, respectively, from Chen.41 The value of φ in eq 40 was set to 1 for

(37a)

⎛ Vo ⎞⎞ k Ga ⎛ ⎜ 1 0.9 − ⎜ ⎟⎟⎟ ⎜ DGa t 2 ⎝ ⎝ Vt ⎠⎠ =

(39)

The average error is 3.453%, and the greatest error is 11.35%. 6.5. Comparison with Other RPBs. An empirical correlation for total gas−liquid effective interfacial area a of RPB with stainless steel wire mesh packing was proposed by Luo:42 a = 66510ReL−1.41FrL−0.12WeL1.21ϕ−0.74 at (40)

k G ∝ F‐factor

⎛ a t ⎞1.4 ⎟ ⎝ aP′ ⎠

πrs2z.

⎛V ⎞ ⎛ V ⎞⎞ K Gad0 2 ⎛ ⎜⎜1 − 0.6981⎜ o ⎟ − 1.0818⎜ i ⎟⎟⎟ DG ⎝ ⎝ Vt ⎠ ⎝ Vt ⎠⎠

⎛V ⎞ ⎛ V ⎞⎞ kLad p ⎛ ⎜⎜1 − 0.93⎜ o ⎟ − 1.13⎜ i ⎟⎟⎟ DL a t ⎝ ⎝ Vt ⎠ ⎝ Vt ⎠⎠

0.023ReGa1.13ReLa 0.14GrGd 0.31WeLa 0.07⎜

πrin2z,

2

(37b)

where ReGa = [QG/(2πravez)ρG]/atμG, ReLa = [QL/(2πravez)ρL]/ atμL, GrGd = dp3ρG2ac/μG2, GrLd = dp3ρL2ac/μL2, ScL = μL/(ρLDL), and WeLa = [QL2/(2πravez)2ρL]/(atσ) A correlation for distillation, which takes inner and outer end effects into consideration, is given by modification of eqs 37a and 37b: 4833



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Figure 21. Comparison of (a) KG, kG, and kL; (b) a; and (c) KGa, kGa, and kLa of rotor B1 and the RPB rotor at n = 1000 rpm.

the sake of simplicity. The comparison of all mass-transfer coefficients for rotor B1 and the RPB rotor is shown in Figure 21. The kL for rotor B1 is close to that of the RPB rotor, independent of F-factor because of eqs 41c and 42c. The kG value for rotor B1 is much greater than that of the RPB rotor; it is about 3.37 times greater than that of the RPB rotor at a F-factor of 3.53 m/s (kg/m3)0.5, as shown in Figure 21a. However, the effective interfacial area a for rotor B1 is smaller than that of the RPB rotor, thus leading to kLa and kGa for rotor B1 smaller than those of the RPB rotor, as shown in Figure 21b,c. As a partition rotor, the KGa for rotor B1 is compared with that of RPB with split packing. An empirical correlation of KGa for RPB with split packing, where the total reflux distillation experiments were conducted with F-factor ranging from 0.36 to 0.60 m/s (kg/m3)0.5 using methanol/ethanol system, was proposed by Mondal:28 K Ga = 1.06(F‐factor)2.14 ac 0.51

Figure 22. Comparison of the overall volumetric mass-transfer coefficient of rotor B1 and rotor of RPB with split packing.

(43) 2

KGa for rotor B1. The counterdirection rotation of rotor of RPB with split packing leads to a remarkable increase in kG and KGa.

3

Using stainless steel wire mesh packing with at of 280 m /m , the rotor of RPB with split packing had inner diameter of 0.06 m, outer diameter of 0.310 m, i.e., rave= 0.0925 m, and axial height of 0.027 m, with the two discs rotated in the counter-direction. Rotor B1 has rave= 0.103 m, giving ac of 1128.38 m/s2 and 1624.86 m/s2 at n of 1000 rpm and 1200 rpm, respectively. Substituting ac of 1128.38 m/s2 and 1624.86 m/s2 into eq 43 gives the curves of KGa ∼ F-factor for RPB with split packing, which is compared to the experimental curves for rotor B1, as shown in Figure 22. The KGa for rotor B1 is close to that of RPB at lower F-factor, but the KGa for RPB rapidly increases with increasing F-factor and rotational speed n in comparison with

7. CONCLUSION Developed from the RZB, the counterflow concentric-ring rotating bed employs the partition rotor of rotating−stationary discs with intermediate feed and multirotors coaxially installed in series in a casing. The mass-transfer efficiency and pressure drop per discrete step for the concentric-ring rotating bed are lower than those of RZB, and the gas−liquid throughput for the concentric-ring rotating bed is at least 5.576 times greater than that of the RZB. The overall volumetric gas-side mass-transfer coefficient for the concentric-ring rotating bed, which is correlated with dimensionless numbers, ranges from 3.18 s−1 4834



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to 92.30 s−1 at F-factor of 0.21−3.53 m/s (kg/m3)0.5 in total reflux distillation using ethanol−water system. A mass-transfer model for the concentric-ring rotating bed is proposed. Using the surface renewal model, the local gas and liquid-side mass-transfer coefficients are calculated with gas turbulence and the impingement of liquid droplets on the rotating rings one after another. The gas−liquid effective interfacial area is obtained by calculation of the surface areas of liquid droplets and liquid film. Compared with RPB, the local liquid-side mass-transfer coefficient for the concentric-ring rotating bed is close to that of RPB, the local gas-side masstransfer coefficient is much higher, and the gas−liquid effective interfacial area is much lower. The overall volumetric gas-side mass-transfer coefficient is obtained using two-film theory; it shows good agreement with experimental values. According to the mass-transfer model, the distillation process is gas-film controlled at a F-factor lower than 0.64 m/s (kg/m3)0.5, and both gas- and liquid-film resistances are important at a high F-factor. Furthermore, an equation that indicates the relationship between HETP and KGa is proposed. The equation is available for the distillation of other RPBs. According to the equation, HETP decreases rapidly at first and then slowly with increasing F-factor. Obvious mass-transfer end effects exist in the distillation process of the concentric-ring rotating bed, and a correlation that takes the inner and outer end effects into consideration is given.

■

DG = vapor diffusivity, m2/s DL = liquid diffusivity, m2/s HETP = height equivalent to theoretical plate, m kGa = local volumetric gas-side mass-transfer coefficient, 1/s kLa = local volumetric liquid-side mass-transfer coefficient, 1/s KGa = overall volumetric gas-side mass transfer coefficient, 1/s kG = local gas-side mass-transfer coefficient, m/s kL = local liquid-side mass-transfer coefficient, m/s KG = overall gas-side mass transfer coefficient, m/s ks = proportional coefficient in eq 10 L/G = ratio of liquid to vapor m = number of annular region in the space of the rotor m̅ = average slope of vapor−liquid equilibrium curve ML = average molar mass of liquid phase, kg/kmol n = rotational speed, rpm NT = number of theoretical plates NTR = number of theoretical plates per discrete step NTUG = number of transfer units P = average pressure in the distillation process in the rotor, Pa ΔP = pressure drop between the gas inlet and outlet, Pa ΔPR = pressure drop per discrete step, Pa ΔP/NT = pressure drop per number of theoretical plates, Pa QG = vapor rate, m3/s QL = liquid rate, m3/s ri = radius of the rotating ith ring, m ri,1 = radius of the circular auxiliary ring compounded at the inside of the circular main ring with radius of ri, m ri,2 = radius of the circular auxiliary ring compounded at the outside of the circular main ring with radius of ri, m rin, rout = inner and outer radius of the rotor, m rave = average radius of the rotor, m R = gas constant in the ideal gas state equation, J/(kmol K) SG = rate of gas surface renewal, 1/s SL = rate of liquid surface renewal, 1/s t = thickness of the rotating ring, m T = average temperature in the distillation process in the rotor, K ui = velocity of the liquid droplets leaving along the tangent of the rotating ring with radius of ri, m/s vG = vapor real radial velocity at the inner edge of the rotor, m/ s vL = liquid average radial velocity in the rotor, m/s Vi = volume inside the inner radius, m3 Vo = volume between the outer radius of the rotor and the casing, m3 Vt = total volume of the casing, m3 x = liquid composition in the bulk liquid phase x1 = liquid composition in the reboiler x2 = liquid composition of reflux liquid y = vapor composition in the bulk vapor phase y1 = vapor composition in equilibrium with liquid composition x1 in the reboiler y2 = vapor composition in the gas outlet of rotating bed that equals the liquid composition x2 of reflux liquid if the vapor are totally condensed y* = vapor composition in the bulk vapor phase in equilibrium with liquid composition x of the bulk liquid phase z = height of the rotor, m

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86 571 88320053. Fax: +86 571 88320053. E-mail: jjb@ zjut.edu.cn. Notes

The authors declare no competing financial interest.

■

NOMENCLATURE

Variables

a = gas−liquid effective interfacial area, m2/m3 ac = centrifugal acceleration, m/s2 ad = gas−liquid effective interfacial area of liquid droplets in the rotor, m2/m3 adi = gas−liquid effective interfacial area of liquid droplets in region i of the rotor, m2/m3 af = gas−liquid effective interfacial area of liquid film in the rotor, m2/m3 ap′ = surface area of the 0.002 m diameter bead per unit volume of the bead, m2/m3 at = surface area of the packing per unit volume of the rotor, m2/m3 A1, A2, A3 = coefficients of eq 35 A1′ , A2′ , A3′ , A4′ , A5′ = coefficients of eq 38 Adi = surface area of liquid droplets in region i of the rotor, m2 Afi = surface area of liquid film on the hole wall at the rotating rings in region i of the rotor, m2 ATUG = area of transfer unit, m2 B1, B2, B3, B4 = coefficients of eqs 9, 11b, and 15b CG = total concentration of gas phase, kmol/m3 CL = total concentration of liquid phase, kmol/m3 d0 = diameter of the holes on the rotating rings, m dLi = average diameter of the liquid droplets in region i of the rotor, m dp = spherical equivalent diameter of the packing [6(1 − ε)/ at], m

Greek Letters

α = relative volatility ε = porosity of the packing εdi = liquid holdup of liquid droplets in region i of the rotor ρG = vapor density, kg/m3

4835



Article

ρL = liquid density, kg/m3 μG = viscosity of vapor, Pa s μL = viscosity of liquid, Pa s σ = surface tension, kg/s2 σc = critical surface tension of packing, kg/s2 σw = surface tension of water, kg/s2 τi = interval time for liquid droplets to fly in the gap between two adjacent rotating rings, s ω = angular speed, rad/s ϕ = fractional hole area of the rotating ring φ = ratio of the square opening area of one cell to the whole area of one cell of the wire mesh

(4) Ramshaw, C. Higee distillationAn example of process intensification. Chem. Eng. 1983, 90, 13. (5) Burns, J. R.; Ramshaw, C. Process intensification: Visual study of liquid maldistribution in rotating packed beds. Chem. Eng. Sci. 1996, 51, 1347. (6) Singh, S. P.; Wilson, J. H.; Counce, R. M.; Villiers-Fisher, J. F.; Jennings, H. L.; 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. (7) Basic, A.; Dudukovic, M. P. Liquid holdup in rotating packed beds: Examination of the film flow assumption. AICHE 1995, 41. (8) 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. (9) Yan, Z. Y.; Lin, C.; Ruan, Q. Hydrodynamics in a rotating packed bed. I. A novel experimental method. Ind. Eng. Chem. Res. 2012, 51, 10472. (10) Yan, Z. Y.; Lin, C.; Ruan, Q. Hydrodynamics in a rotating packed bed. II. A mathematical model. Ind. Eng. Chem. Res. 2012, 51, 10482. (11) Zheng, C.; Guo, K.; Feng, Y. D.; Yang, C.; Gardner, N. C. Pressure drop of centripetal gas flow through rotating beds. Ind. Eng. Chem. Res. 2000, 39, 829. (12) Keyvani, M.; Gardner, N. C. Operating characteristics of rotating beds. Chem. Eng. Prog. 1989, 85, 48. (13) Lockett, M. J. Flooding of rotating structured packing and its application to conventional packed columns. Chem. Eng. Res. Des. 1995, 73, 379. (14) Li, X. P.; Liu, Y. Z. Characteristics of Fin Baffle Packing Used in Rotating Packed Bed. Chin. J. Chem. Eng. 2010, 18, 55. (15) Sung, W. D.; Chen, Y. S. Characteristics of a rotating packed bed equipped with blade packings and baffles. Sep. Purif. Technol. 2012, 93, 52. (16) Lin, C. C.; Lin, Y. C. Mass transfer performance of a rotating packed bed equipped with blade packings in removing methanol and 1butanol from gaseous streams. Chem. Eng. Process. 2012, 53, 76. (17) Lin, C. C.; Lin, Y. C.; Chen, S. C.; Hsu, L. J. Evaluation of a rotating packed bed equipped with blade packings for methanol and 1butanol removal. J. Ind. Eng. Chem. 2010, 16, 1033. (18) Lin, C. C.; Jian, G. S. Characteristics of a rotating packed bed equipped with blade packings. Sep. Purif. Technol. 2007, 54, 51. (19) Lin, C. C.; Chien, K. S. Mass-transfer performance of rotating packed beds equipped with blade packings in VOCs absorption into water. Sep. Purif. Technol. 2008, 63, 138. (20) Jian, Q. F.; Deng, X. H.; Deng, S. J. Experimental investigation of gas flow resistance and gas-liquid mass-transfer performance in supergravity force rotating packed bed with wave form disk packing. Chemical Reaction Engineering and Technology (China) 1998, 14, 42. (21) Sandilya, P.; Rao, D. P.; Sharma, A.; Biswas, G.. Gas-phase masstransfer in a centrifugal contactor. Ind. Eng. Chem. Res. 2001, 40, 384. (22) Wang, G. Q.; Xu, Z. C.; Yu, Y. L.; Ji, J. B. Performance of a rotating zigzag bed-A new HIGEE. Chem. Eng. Process. 2008, 47, 2131. (23) Wang, G. Q.; Xu, O. G.; Xu, Z. C.; Ji, J. B. New HIGEE-rotating zigzag bed and its mass transfer performance. Ind. Eng. Chem. Res. 2008, 47, 8840. (24) Li, Y. M.; Ji, J. B.; Yu, Y. L.; Xu, Z. C.; Li, X. H. Hydrodynamic Behavior in a Rotating Zigzag Bed. Chin. J. Chem. Eng. 2010, 18, 34. (25) Chu, G. W.; Gao, X.; Luo, Y.; Zou, H. K.; Shao, L.; Chen, J. F. Distillation studies in a two-stage counter-current rotating packed bed. Sep. Purif. Technol. 2013, 102, 62. (26) Luo, Y.; Chu, G. W.; Zou, H. K.; Xiang, Y.; Shao, L.; Chen, J. F. Characteristics of a two-stage counter-current rotating packed bed for continuous distillation. Chemical Engineering and Processing: Process Intensification 2012, 52, 55. (27) Sung, W. D.; Chen, Y. S. Characteristics of a rotating packed bed equipped with blade packings and baffles. Sep. Purif. Technol. 2012, 93, 52. (28) Mondal, A.; Pramanik, A.; Bhowal, A.; Datta, S. Distillation studies in rotating packed bed with split packing. Chem. Eng. Res. Des. 2012, 90, 453.

Dimensionless Groups

FrL =

Q L 2/(2πravez)2 acd p d0 3ρG 2 ac

GrG =

μG 2

d p3ρG 2 ac

GrGd =

μG 2 d p3ρL 2 ac

GrLd =

μL 2

Q G/(2πravez)d0ρG

ReG =

μG Q G/(2πravez)ρG

ReGa =

ReL =

a tμG Q L /(2πravez)ρL d p μL

Q L /(2πravez)ρL

ReLa =

ScG =

Sc L =

a tμL

μG ρG DG

μL ρL DL Q L 2/(2πravez)2 ρL

WeLa =

WeL =

a tσ

Q L 2/(2πravez)2 ρL d p

■

σ

REFERENCES

(1) McCabe, W. L.; Smith, J. S. Harriott, P. Unit Operations of Chemical Engineering; McGraw-Hill Companies: New York, 2005. (2) Vivian, J. E.; Brian, P. L. T.; Krukonis, V. J. Influence of Gravitational Force on Gas Absorption in Packed Columns. AICHE 1965, 111, 1088. (3) Ramshaw, C.; Mallinson, R. H. Mass Transfer Process. U.S. Patent 4,283,255. 1981 4836



Article

(29) 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. (30) Bhattacharya, S.; Mondal, A.; Bhowal, A.; Datta, S. Evaporative Cooling of Water in a Rotating Packed Bed (Split Packing). Ind. Eng. Chem. Res. 2010, 49, 847. (31) Reddy, K. J.; Gupta, A.; Rao, D. P.; Rama, O. P. Process intensification in a HIGEE with split packing. Ind. Eng. Chem. Res. 2006, 45, 4270. (32) 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. (33) Short, H. New mass transfer find is a matter of gravity. Chem. Eng. 1983, 90, 23. (34) Li, X. P.; Liu, Y. Z.; Li, Z. Q.; Wang, X. L. Continuous Distillation Experiment with Rotating Packed Bed. Chin. J. Chem. Eng. 2008, 16, 656. (35) Wang, G. Q.; Xu, Z. C.; Ji, J. B. Progress on Higee distillationIntroduction to a new device and its industrial applications. Chem. Eng. Res. Des. 2011, 89, 1434. (36) 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. (37) Guo, F.; Zheng, C.; Guo, K.; Feng, Y. D.; Gardner, N. C. Hydrodynamics and mass transfer in cross-flow rotating packed bed. Chem. Eng. Sci. 1997, 52, 3853. (38) Kelleher, T.; Fair, J. R. Distillation studies in a high-gravity contactor. Ind. Eng. Chem. Res. 1996, 35, 4646. (39) Lin, C. C.; Ho, T. J.; Liu, W. T. Distillation in Rotating Packed Bed. J. Chem. Eng. Jpn. 2002, 35, 1298. (40) Chen, Y. S.; Lin, F. Y. Packing characteristics for mass transfer in a rotating packed bed. Ind. Eng. Chem. Res. 2006, 45 (20), 6846−6853. (41) Chen, Y. S. Correlations of mass transfer coefficients in a rotating packed bed. Ind. Eng. Chem. Res. 2011, 50 (3), 1778−1785. (42) Luo, Y.; Chu, G. W.; Zou, H. K.; Zhao, Z. Q.; Dudukovic, M. P.; Chen, J. F. Gas−liquid effective interfacial area in a rotating packed bed. Ind. Eng. Chem. Res. 2012, 51, 16320.

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Distillation in a Counterflow Concentric-Ring Rotating Bed - Industrial

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