Ind. Eng. Chem. Res. 2005, 44, 4051-4060
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Characteristics of Flow in a Rotating Packed Bed (HIGEE) with Split Packing A. Chandra, P. S. Goswami, and D. P. Rao* Department of Chemical Engineering, Indian Institute of TechnologysKanpur, Kanpur 208016, India
The high centrifugal force field in a rotating packed bed (HIGEE) permits the use of packing with a large surface area and enhances the liquid-side mass-transfer coefficient. However, the gas-side mass-transfer coefficient is in the same range as that of the conventional packed columns. Recent studies indicate that the tangential slip velocity between the gas and the packing is negligible. We have split the packing into annular rings to rotate adjacent rings in the counterdirection to promote the tangential slip velocity in the range of 5-30 m/s and to enhance the gas-side mass-transfer coefficient. In this work, we present the frictional and centrifugal pressure drops and the tangential slip velocity of the gas in a HIGEE with split packing. Counter to intuition, the total pressure drop with counterrotation of the rings is found to be less than that with corotation of the rings. 1. Introduction In a conventional distillation column, the liquid flows under the influence of the earth’s gravity. The gravity dictates the allowable liquid and gas throughputs and attainable mass-transfer rates. The high gravity rotating packed bed (HIGEE) provides a means for replacing the gravitational acceleration, g, by a centrifugal acceleration of 100g to 1000g. The high centrifugal force permits the use of packing with a large surface area in the range of 1000-4000 m2/m3, which is 5-10 times higher compared to the packing used in conventional columns, which would lead to a 5-10 times higher masstransfer rate. Since the liquid flows as thin films under the high centrifugal acceleration, there is an enhancement in the liquid-side mass-transfer coefficient. It could be 2-8 times higher than that in a conventional packed column.1,2 However, the gas experiences a large frictional drag in the rotating bed because of the large surface area and acquires the angular velocity of the packing within a short span of time in the packing. Hence, the angular slip velocity between the liquid flowing over the packing and the gas is negligible. Zheng et al.3 and Sandilya et al.4 have shown that the tangential gas velocity in the rotor is nearly the same as that in the packing. Therefore, there would be no enhancement in the gasside mass-transfer coefficient. In fact, the volumetric mass-transfer coefficients, reported by Kelleher and Fair5 and Lin et al.,6 for distillation at total reflux in a HIGEE are in the same range as those for the conventional columns. Rao et al.7 presented an appraisal of the achievable process intensification in the HIGEE. The controlling resistance is on the vapor side for distillation for most of the systems. Hence, the process intensification that is achievable in a HIGEE is only due to the use of packing with a large surface area. This is a severe limitation of the HIGEE. Therefore, there is a need for an alternate design of the rotating packed bed. In this work, we proposed a radically different rotor design to enhance the slip velocity and, hence, the gas* To whom correspondence should be addressed. E-mail:
[email protected].
Figure 1. Rotors and foam-metal packing rings.
side mass-transfer coefficient. This paper presents the studies on the flow characteristics of the proposed rotor. 1.1. Proposed Rotor Design. We propose to split the packing into annular rings with gaps between the rings and to rotate the alternate rings in a counterdirection. Figure 1 presents the proposed rotors (patent pending). The foam-metal and wound wire-mesh packing lend themselves well to the fabrication of the rotor.
10.1021/ie048815u CCC: $30.25 © 2005 American Chemical Society Published on Web 04/20/2005
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Ind. Eng. Chem. Res., Vol. 44, No. 11, 2005
Table 1. Details of the Packing Rings of Rotor 1 height of the rings ) 2.8 cm bed porosity ) 0.8 specific surface area ) 1180 m2/m3 dimensions of packing rings inner diameter, cm
outer diameter, cm
12 19 26
17 24 31
Table 2. Details of the Packing Rings of Rotor 2 axial length of packing ) 3.0 cm bed porosity ) 0.9 specific surface area ) 1700 m2/m3 dimensions of packing rings inner diameter, cm
outer diameter, cm
8.1 10.6 13.1 15.6 18.1 20.6 23.1 25.6 28.1
9.6 12.1 14.6 17.1 19.6 22.1 24.6 27.1 29.6
One set of the alternate rings was fixed to the bottom plate and the other set to the top plate. We have used two rotors in this study. 1.1.1. Rotor 1. In rotor 1, the rings were made using a nylon net. Table 1 presents the details of rotor 1. The top and bottom disks were made of Plexiglas of 1.25 cm thickness and 31 cm diameter. We cut grooves in the disks and fixed stainless steel mesh and wound around them a 2.5-cm-thick layer of cross-threaded nylon net. We used three such rings. To minimize the gas leakage through the gap between the free end of the ring and the end plate, we fixed a piece of woolen felt to the free ends of the rings. 1.1.2. Rotor 2. Rotor 2 had nine nickel-chromium foam rings (supplied by RECEMAT International B.V. Holland) made as per the specifications given in Table 2. A picture of the metal rings and a sketch of rotor 2 are shown in Figure 1. These rings were fixed in the grooves cut in the disks and were screwed to the disks to hold them in place. The radial width of the gaps between the rings was 0.5 cm. A piece of woolen felt was fixed to the free end of each ring to close the clearance between the ring and the disk. 1.1.3. Liquid Distributor. Figure 2 shows a sketch of the liquid distributor. It consisted of six L-shaped copper tubes of 3 mm diameter. These were fixed to a hollow Plexiglas cylindrical header of length 2 cm with a closed end (see Figure 2). The tubes were provided with five equally spaced holes of 0.8 mm diameter facing the inner periphery of the rings. The holes on the tubes were staggered to give a uniform liquid distribution over the inner periphery of the innermost ring. The liquid flowed out from the tubes as jets. To ensure the liquid jets hit the periphery even at the low liquid flow rate, the clearance between the ring and the L-shaped tubes was set at 0.5 cm. 1.1.4. Gas Outlet. In the case of rotor 1, the gas was withdrawn through the eye of the rotor. With rotor 2, the gas was drawn out through one side of the second ring and the ports provided in the side plate as shown in Figure 2. The gas did not flow through the innermost
Figure 2. Liquid distributor and gas-withdrawal port.
Figure 3. Schematic diagram of the experimental setup.
ring. This ring merely served to distribute the liquid uniformly to the next ring as a spray of fine droplets. Since the liquid flowed through the second ring as films gripping the packing, there was no entrainment. This arrangement of the gas withdrawal is expected to permit higher throughputs than the normal arrangement, as in rotor 1. 2. Experimental Setup Figure 3 shows a sketch of the experimental setup. The axis of the rotor was kept horizontal to prevent liquid bypassing the packing as the “separated flow”.7,8 Each shaft was connected to an ac three-phase motor. The two motors were connected to an inverter drive to vary the speed of rotation. The rotational speed was measured using a stroboscope. The casing for the rotor was made of Plexiglas to permit visual observations. The experiments were carried out with the air-water system. The water was circulated from a storage tank with a centrifugal pump. The air was supplied using a
Ind. Eng. Chem. Res., Vol. 44, No. 11, 2005 4053
25-hp blower. The pressure drops were measured across the rotor and across the unit at different gas and liquid flow rates, at different rotational speeds, and with counter- and corotation of the annular rings. 2.1. Pressure Drop Analysis. We measured the pressure drop across the rotor by employing the pressure taps located in the eye of the rotor and close to the outer edge of the rotor. This is referred to as the total pressure drop, ∆PT. Sandilya et al.4 showed that the pressure drop due to the entrance effects at the outer periphery is negligible. Therefore, the total pressure drop is considered as the sum of the pressure drops due to the momentum gain by the gas as it moves radially toward the eye of the rotor, ∆Pm; due to the friction offered by the packing, ∆Pf; and due to the countercentrifugal force, ∆Pc. The total pressure drop can be expressed as
∆PT ) ∆Pm + ∆Pf + ∆Pc
(1)
2.1.1. Pressure Drop Due to Momentum Gain. The ∆Pm is obtained from
∫rr
∆Pm ) Fg
i
2
Vr dr r
o
(2)
where Vr is the gas radial velocity, ri is the inner radius of the packing, ro is the outer radius, and Fg is the gas density. Alternately, it can be written in terms of the volumetric flow rate of the gas, Q, as
( )(
Q 1 ∆Pm ) Fg 2 2πa
2
1 1 - 2 2 ri ro
)
(3)
where a and are the axial width and porosity of the packing, respectively. Generally, the ∆Pm is small compared to the other pressure drops and could be neglected, if the operating pressure is close to 1 bar. In the present study, it was in the range of 0-18 Pa. 2.1.2. Frictional and Centrifugal Pressure Drops. The evaluation of both frictional and centrifugal pressure drops requires the tangential velocity of the gas in the rotor. This, in turn, requires the local friction factor. Sandilya et al.4 gave a method for the evaluation of a single packing element. We extended the method for the split packing. The following assumptions are made: (1) The flow is steady, incompressible, and axisymmetric. (2) The frictional pressure drop in the gaps is negligible. (3) There is no axial flow. (4) The gravitational field is negligible compared to the centrifugal field. The equations of motion in terms of the time-averaged gas velocity are
[
]
dVr Vθ 1 ∂(rτrr) τθθ 1 dp 1 )+ + dr r Fg dr Fg r ∂r r
θ-component: Vr
(6)
2 Vθs 1 ∂(r τrθ) 1 - 2 ) fθFg |Vθs| ∂r 2 dh r
(7)
and
where
dh )
[
]
2 dVθ VrVθ 1 1 ∂(r τrθ) - 2 + ) dr r Fg r ∂r
(4)
4 ap
Vθs ) Vθ - rω
The terms inside the square brackets of eqs 4 and 5 are the contributions due to fluid friction and are represented in terms of the local friction factors as
(9)
where ω is the rotational speed. The equation of continuity yields
Vr dVr )dr r
(10)
Substitution of eqs 6 and 10 into eq 4 gives
-
[
]
Vr2 Vθ2 1 Vr2 dp ) Fg - fr dr r r 2 dh
(11)
The terms within the square brackets of eq 11 correspond to the pressure drops ∆Pm, ∆Pc, and ∆Pf, respectively. On substitution of eq 7 into eq 5, we get
Vθ dVθ 1 Vθs |Vθs| ) fθ dr 2 dhVr r
(12)
We have assumed that fθ ) fr ) f. Further, the frictional pressure drop in the gap was considered to be negligible. With these assumptions, eq 12 can be solved along with the boundary conditions
Vθ ) roω
at r ) ro
(13)
However, the gas would take a curved path if the tangential slip velocity is nonzero. To account for the longer path of the gas, we defined f as
1 fF V 2 dS 2dh g r
(14)
where dS is the differential path length of the gas over a radial span, dr, and could be expressed as
dS ) Vres dt (5)
(8)
and fr and fθ are the friction factors in the radial and tangential directions, respectively, dh is the equivalent hydraulic diameter, and Vr and Vθs are the relative interstitial radial and tangential slip velocities, respectively, relative to an observer stationed on the rotor. The tangential slip velocity is
dPf )
r-component: Vr
2 1 ∂(rτrr) τθθ 1 Vr + ) f r Fg r ∂r r 2 dh
-
(15)
where Vres is the resultant velocity. It could be written as
Vres ) xVr2 + Vθs2
(16)
Replacing dt in eq 15 in terms of Vr and dr, we get
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Ind. Eng. Chem. Res., Vol. 44, No. 11, 2005
x ( )
dS )
Vθs Vr
1+
2
dr
(17)
Further, since the Vr varies in the radial direction, the friction factor is also expected to vary. Therefore, the evaluation of f should be based on the local Vr and Vθs. Adopting the functional form of the Ergun equation, the local friction factor can be expressed as
f)
R +β Re
(18)
where R and β are constants and Re is the Reynolds number and is given by
V h rd h Re ) νg
(19)
where V h r is the superficial gas velocity and νg is the kinematic viscosity of the gas. Substitution of eqs 18 and 19 into eq 14 yields
(
) [ ( )]
V h r2 Vθs 1 R + β Fg 2 1 + dPf ) 2dh Re Vr
2 1/2
dr
(20)
After elimination of Vr in terms of the volumetric gas flow rate and on integration, eq 20 yields
∆Pf )
λFg
( ) [ ( ) ( )] Q
22dh 2πa
2πaυg
2
roj
n
ln ∑ r j)1
R
Qdh
ij
n
1
∑ j)1 r
+β
ij
-
1
roj
(21)
where n is the number of rings in the rotor counted from the innermost ring and the subscripts i and o denote the inner and outer radii. Finally, the centrifugal pressure drop, ∆Pc, can be estimated from
∆Pc )
2
roVθ
∫r
i
r
dr
(22)
2.2. Method of Evaluation of S, Vθs, ∆Pf, and ∆Pc. The ∆Pm was estimated from eq 3. The sum of the frictional and centrifugal pressure drops was obtained by subtracting the ∆Pm from the ∆PT. The evaluation of both the ∆Pf and ∆Pc requires the local tangential velocity of the gas, Vθ, and the local friction factor, f. These were evaluated by an iterative procedure as follows. The iteration was started by setting Vθ ) ωr. The value of the ∆Pc was then calculated from eq 22, and the value of the ∆Pf was obtained from eq 1. For a set of values of ∆Pf for a given rotational speed (RPM, in units of revolutions per minute or rpm) at different gas flow rates, the values of R and β were found by regression from eq 21. The local friction factor was then found from eq 18. The revised values of ∆Pc and Vθs were evaluated from eqs 9, 12, and 22. From these, the ∆Pf and the revised values of R and β were found. The iteration was continued until the R and β converged to a desired tolerance. 3. Results and Discussions From the visual observations, it appeared that the liquid flowed as jets from the liquid distributor onto the inner periphery of the innermost ring. It left the outer periphery of this ring as a spray of fine droplets and
Figure 4. Experimental and estimated total pressure drop versus gas velocity for the stationary case for rotor 1 and rotor 2.
entered the counterrotating next ring. The width of the liquid spray, reaching from the outermost ring onto the casing, was the same as the width of the rotor. The spread of the individual drops hitting the casing could be observed at low liquid flow rates. From these observations, it appeared that the droplet size was
