Article pubs.acs.org/IECR
Determination of Mass-Transfer Coefficient of CO2 in NH3 and CO2 Absorption by Materials Balance in a Rotating Packed Bed Baochang Sun,†,‡ Haikui Zou,*,† Guangwen Chu,*,†,‡ Lei Shao,†,‡ Zequan Zeng,†,‡ and Jianfeng Chen†,‡ †
Research Center of the Ministry of Education for High Gravity Engineering and Technology, Beijing University of Chemical Technology, Beijing 100029, People’s Republic of China ‡ State Key Laboratory of Organic−Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029, People’s Republic of China ABSTRACT: More-accurate overall mass-transfer coefficients in a rotating packed bed (RPB) and local mass-transfer coefficients in different regions of the RPB were deduced by the material balance in order to obtain practical volumetric masstransfer coefficients in the RPB. Experimental studies on the overall volumetric mass-transfer coefficients (KGa) of CO2 in NH3 and CO2 absorption into water in the RPB was carried out under different conditions. The experimental results indicated that there was a great difference between the value of KGa and KGa* attained by different boundary conditions. And it was concluded that an accurate design equation should be adopted to achieve a practical value of KGa in the RPB. It was also found that the KGa of CO2 increased with the increase of rotation speed, liquid volumetric flow rate, gas volumetric flow rate, NH3/CO2 molar ratio, and the decrease of temperature. The KGa of CO2 in the simultaneous absorption process of NH3 and CO2 was 2−6 times higher than that in the single CO2 absorption process.
1. INTRODUCTION A rotating packed bed (RPB) consists mainly of a packed rotor. Because of the high-gravity environment created by the rotation of the packed rotor, mass transfer and micromixing can be significantly intensified in the RPB. Ramshaw and Mallinson1 first reported that RPBs can greatly enhance the efficiency of distillation and absorption. It was also reported that the liquidside mass transfer rate in an RPB was notably higher than that in a conventional packed bed.2,3 Because of the advantages in mass transfer and mixing, the RPB has been employed as a promising reactor for absorption,4 distillation,5 ozonation,6 polymerization,7 devolatilization,8 and production of nanomaterials.9 Fundamental studies on RPBs have been extensively reported. Cheng and Tan10 reported the removal of CO2 from indoor air by alkanolamine in an RPB. An algebraic model was proposed to predicted the overall volumetric mass-transfer coefficient (KGa) in the RPB by assuming stirred tanks connected in series followed by a gas− liquid contactor fit in the outer region of the RPB, and it was found that the mass-transfer rate in the outer region is different from that in the packing itself. Lin and Chen11 studied pressure drop and mass transfer in a cross-flow RPB by CO2 absorption from gas stream. The comparison of KGa between the crossflow RPB and a countercurrent RPB was also conducted, and it was found that the mass-transfer efficiency of the cross-flow RPB was comparable to that of the countercurrent-flow RPB. Sandilya et al.12 presented experimental studies on gas-side mass transfer in an RPB with wire-gauze packing and reported the average gas-side volumetric mass-transfer coefficient of SO2 in the RPB. Lin et al.13 studied the KGa of CO2 in an RPB with different absorbents and operating conditions. It was found that the mass-transfer rate in an RPB was an order of magnitude higher than that in a packed tower. Many studies on the modeling of mass transfer in RPBs have also been carried out in © 2012 American Chemical Society
an attempt to obtain a precise mass-transfer coefficient. The validation data for the mass-transfer coefficient must reflect the practical value of the mass-transfer coefficient. Otherwise, the correlation of the mass-transfer coefficient would lose its significance. Therefore, whether it is for fundamental research or for the design of an RPB, an accurate design equation for the calculation of mass-transfer coefficient is indispensable. The mass-transfer coefficient in an RPB is mainly obtained by material balance in the RPB from experiments. Sandilya et al.14 have performed experiments in a centrifugal contactor to obtain the gas-side mass-transfer coefficient and to examine the effect of rotation and packing on the gas flow and the transfer coefficient. Kelleher and Fair15 calculated volumetric masstransfer coefficients by writing a material balance over a differential volume of the RPB. The similar material balance for mass-transfer coefficient has also been adopted by other researchers.10,11,16,17 In the literature, the same design equation for an RPB was used, and the boundary conditions adopted in the design equation for the RPB were ⎧ x = x i , r = ri ⎨ ⎩ x = xo , r = ro
and
⎧ y = yo , r = ri ⎨ ⎩ y = yi , r = ro
(1)
In the boundary conditions, the volume integral path of the RPB is from ro to ri, but the material concentrations used in the design equation are inlet and outlet concentrations, which do not correspond to the volume integral path. Therefore, the obtained mass-transfer coefficient cannot be regarded as the Received: Revised: Accepted: Published: 10949
December 20, 2011 May 1, 2012 July 6, 2012 July 6, 2012 dx.doi.org/10.1021/ie202983x | Ind. Eng. Chem. Res. 2012, 51, 10949−10954
Industrial & Engineering Chemistry Research
Article
The phase equilibrium equation of the absorption system is
mass transfer in the entire RPB (where the volume integral path of the RPB should be from r = 0 to r = rc). Because the KGa values are attained by the material concentrations at the inlet and outlet of the RPB, the corresponding integral path should be from the inlet to the outlet of the RPB. In addition, to obtain the mass transfer in the entire RPB, the volume integral path of the RPB should be from r = 0 to r = rc. Therefore, as shown in Figure 1, the practical boundary conditions should be ⎧ x = xi , r = 0 ⎨ ⎩ x = xo , r = rc
and
⎧ y = yo , r = 0 ⎨ ⎩ y = yi , r = rc
y* = mx x* =
y m
(4)
As shown in Figure 1, the solute concentration can be obtained from the material balance of the solute at radius r in the RPB: G(y − yr ) = L(x − xr )
⎪
⎪
(3)
(5)
The mole fraction of the solute in liquid stream then can be obtained,
(2)
x = (y − yr )
G + xr L
(6)
and the mole fraction of the solute in the gas stream can be written as y = (x − xr )
L + yr G
(7)
The solution of eq 6 to eq 3 is ⎡ ⎤ G y* = mx = m⎢(y − yr ) + xr ⎥ ⎣ ⎦ L Figure 1. Schematic diagram of the integral path for the material balance in a rotating packed bed (RPB).
(8)
The solution of eq 7 to eq 4 is x* =
With the practical boundary conditions, a precise masstransfer coefficient can be obtained directly from the design equation of the RPB, which is significant for the evaluation of the mass-transfer efficiency of the RPB. However, the design equation adopted to determine the experimental KGa* values in the literature was cited from Kelleher and Fair’s work,15 which was based on the boundary conditions, as expressed in eq 1 and left room for improvement. In this work, the practical mass-transfer coefficients in an RPB and local mass-transfer coefficients in different regions of the RPB were deduced by the material balance. The practical KGa of CO2 during simultaneous absorption of NH3 and CO2 and single absorption of CO2 into water in the RPB were investigated. The difference between KGa and KGa*, as well as KGa and KGaS was analyzed (KGa is the mass-transfer coefficients of CO2 in the simultaneous absorption process obtained by the practical design equation; KGa* is that obtained by the design equation in the literature; KGaS is that obtained in single CO2 absorption process).
⎤ y 1⎡ L = ⎢(x − xr ) + yr ⎥ ⎦ ⎣ m m G
(9)
The following rate equation can be obtained in terms of a material balance calculation over a differential volume of the RPB for both the liquid and gas phases: NAa =
d(Lx) = KLa(x* − x) dV
(10)
NAa =
d(Gy) = K Ga(y − y*) dV
(11) (12)
dV = 2πrh dr
The contact between liquid and gas occurred not only in the packing, but also in the hollow central region of the RPB and the space between the casing and the rotator. Because the KGa values were attained by the inlet and outlet gas/liquid concentrations in the RPB as discussed in section 1, the boundary conditions should correspond to the practical path of integration, which must include the distance from the center of the RPB to the inner wall of the casing. In other words, in addition to the gas−liquid mass transfer in the packing, there is also gas−liquid mass transfer in the hollow central region of the RPB and the space between the casing and the packing in the RPB. Therefore, to obtain the mass-transfer coefficient of the RPB, the practical boundary conditions for eq 10 should be
2. DEDUCING THE MASS-TRANSFER COEFFICIENT IN A ROTATING PACKED BED The mass-transfer coefficient obtained by material balance in an RPB is used to evaluate the precise value of the mass-transfer coefficient. The diagram of the integral path for the material balance in the RPB is shown in Figure 1. It has been proved that:18 (a) liquid residence times are very short in an RPB and the back-mixing of liquid can be ignored; and (b) the maximum pressure drop in a wet bed in the RPB is ∼300 Pa, compared to the experimental pressure (200 kPa), and the maximum radial pressure difference is
