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Influence of dissolved hydrocarbons on volumetric oxygen mass transfer coefficient in a novel airlift contactor
Chemical Engineering Science 61 (2006) 4111 – 4119 www.elsevier.com/locate/ces
Influence of dissolved hydrocarbons on volumetric oxygen mass transfer coefficient in a novel airlift contactor Babak Jajuee, Argyrios Margaritis ∗ , Dimitre Karamanev, Maurice A. Bergougnou Department of Chemical and Biochemical Engineering, Faculty of Engineering, University of Western Ontario, London, Ont., Canada N6A 5B8 Received 5 September 2005; received in revised form 25 January 2006; accepted 30 January 2006 Available online 22 March 2006
Abstract Hydrocarbon compounds are sparsely soluble in aqueous systems but, nonetheless, their presence can influence significantly mass transfer behavior in gas–liquid systems. water–p-xylene and water–p-xylene–naphthalene mixtures were employed in order to determine the influence of dissolved hydrocarbons on mass transfer of oxygen from air bubbles to water. The surface renewal-stretch model has been modified for predicting the volumetric mass transfer coefficient, (KL a)h , in the presence of surface contaminant molecules, including hydrocarbon compounds and surfactants. Theory and experimental oxygen transfer results were found to be in satisfactory agreement with average absolute deviation of 15%. Pendant drop and contact angle measurements by axisymmetric drop shape analysis were carried out to determine the reduction in surface tension of water due to the addition of p-xylene and naphthalene. Molecular orientation caused by instantaneous attraction of the polar moieties of the organic compounds toward the water interface has been found to be the main cause of reduction in surface tension. It was predicated that changes in gas–liquid mass transfer behavior resulted from surface contamination and that the significant parameter was the reduction in surface tension. 䉷 2006 Elsevier Ltd. All rights reserved. Keywords: Volumetric mass transfer coefficient; Airlift contactor; Hydrocarbon contaminants; Surface tension; Surface renewal-stretch mass transfer model; Membrane airlift contactor
1. Introduction It is of fundamental importance to understand the influence of dissolution of water-soluble hydrocarbon pollutants on interfacial mass transfer between gas bubbles and contaminated bulk of liquid. Petroleum-based products are widely used in many industrial processes and accidental discharge of these chemicals from storage facilities, pipeline leaks, tanker disasters, or from contamination of soil around factories may cause water and groundwater contamination. When these chemicals enter the surface or subsurface environment, some components dissolve and leach out of the slick, some evaporate, and the majority may eventually be biodegraded. The ecotoxicity of oil fractions including soluble aromatic compounds (PAHs) and BTEX is higher to aquatic organism and plants. Knowledge of effects of dissolution of potentially water-soluble hydrocarbon ∗ Corresponding author. Tel.: +1 519 661 2146; fax: +1 519 661 4275.
E-mail address: [email protected] (A. Margaritis) URL: http://www.eng.uwo.ca/people/amargaritis/ (A. Margaritis). 0009-2509/$ - see front matter 䉷 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2006.01.044
pollutants on oxygen mass transfer behavior is important for evaluating their impact on water quality and assessing the potential of water-based technologies in biotreatment of crude and fuel oil contaminated waters. Improving oxygen supply in cell culture systems has always been a central topic for many biochemical processes (Petersen and Margaritis, 2001). In general, slightly soluble substances spread out to a thick duplex film or in some cases monomolecular film when placed at a liquid–air interface. Spills of hydrocarbon compounds spread out almost immediately in water to form a semi-rigid film (slick) on the surface (Ghoshal et al., 2004). When studying the thermodynamic behavior of surface films on liquid substrates, the solution properties are not usually of much interest. Instead, the emphasis shifts to more direct measurements of the interfacial properties so, little effort is made even of the ability to compute changes in solution concentration through the Gibbs equation (Adamson and Gast, 1997). On the environmental side, a belief that a slight change in solution concentration can affect the transport of mass of various species, such as nutrients, oxygen, and chemicals shifts emphasis to the latter. Girifalco and
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Good (1957) remarked that spreading coefficient of a mass of some substance with lower surface tension placed on a liquid surface with higher surface tension changes since they will become mutually saturated, so that the surface tension of each liquid will change. In the case of benzene on water, the change of individual surface tensions of benzene and water are merely 0.1 and 10.9 mN/m, respectively. However, spreading coefficient changes appreciably from 8.9 to −1.6 mN/m (Harkins, 1952). Likewise, the change in surface tension, though imperceptible, is believed to be the measure of impact on mass transport. The influence of dissolved hydrocarbons on oxygen mass transfer in aqueous systems has not been fully assessed to date. Certain observations reported in the literature support the hypothesis that dissolution of contaminants in general may significantly affect oxygen mass transfer rates in water (Clift et al., 1978; Eckenfelder and Barnhart, 1961; Yoshida et al., 1970). The objective of this study is to evaluate the effect of two chemical-constituents, namely p-xylene and naphthalene on oxygen mass transfer characteristics in a novel airlift contactor. The results are of importance in extending the influence of any surface contaminant including surfactants on oxygen mass transfer characteristics in gas–liquid contactors. 2. Theoretical model development To capture the essence of deviations from fluid mass transfer behavior resulting from surface contamination, one should be aware of the mechanism of mass transfer from gas bubbles to non-contaminated bulk phase. The surface renewal-stretch model which has been proposed elsewhere to predict KL a from many bubbles (Jajuee et al., 2006) is now used as the basis of our analysis. Based on this model, the z-directed flux of A in the absence of chemical reaction becomes ∞ dA(T ) DA A(T ) NA,z = cA dT , (1) A2∞ 0 0 dT T 2 A () d 0 whereby the following correlation has been developed for volumetric mass transfer coefficient in Newtonian liquids 1.022 Sh = √ Sc0.5 Re0.72 Bo0.6 F r 0.1 .
(2)
dimensionless parameters: Re(inertia forces/viscous forces), Eo(buoyancy forces/capillary forces), W e(inertia forces/ca− pillary forces), and/or combinational parameters like M(Eo W e2 /Re4 ) (Grace et al., 1976; Grace, 1973). Instead, interfacial flows are characterized by Group (II) of dimensionless parameters: Re, Ca(viscous forces/capillary forces), and De(bubble residence time/equilibrium time) (Vogtländer and Meijboom, 1974a,b). In surface renewal-stretch model, the extent to which the overall exposed surface area of mass transfer might be stretched is determined by Group (I) forces. On the other hand, the influence of contamination on mass transfer behavior is in effect due to alternation of interfacial flows (or velocities) determined by Group (II) forces. It may be of value, therefore, to show that how interfacial flows affect the overall exposed surface area for mass transfer and change mass transfer behavior. As will be seen later on, it is preferable to use the differential form of the exposed surface area in order to study the effect of contamination on mass transfer behavior. According to surface renewal-stretch model (see the Appendix): zh 2 √ DA dA dz (NA,z )h = 2 2cA dz, (3) 2 A∞ 0 dz dT 0 where subscript h designates the presence of contamination in general, and zh is the depth in which the concentration of contaminants is equal to that of bulk concentration. Fig. 1 is a schematic representation of fluid flow and mass transfer phenomena at the gas–liquid interface of a rising bubble. Contaminants with the greatest effect on the interface mobility, thus on mass transfer, are hardly soluble (Clift et al., 1978). When dealing with bubble swarms released from a
v
The change of mass transfer has been ascribed to interfacial motion, which in turn is attributed to hydrodynamic and molecular effects (Vasconcelos et al., 2002, 2003; Clift et al., 1978; Davies and Rideal, 1963). These effects are explicable in terms of forces acting on bubble series, namely: inertia forces = c dB2 Ur2 , viscous forces = c dB Ur , capillary forces = dB , drag forces = (gravity force − buoyancy) = dB3 (c − B )g. 6 Acting forces that are responsible for shapes and velocities of bubbles are usually determined by Group (I) of
Fig. 1. Coordinates on a rising gas bubble for stagnant cap model in the presence of hydrocarbon contaminants.
B. Jajuee et al. / Chemical Engineering Science 61 (2006) 4111 – 4119
submerged sparger, therefore, it is plausible to assume that a thin film of contaminants is formed at the gas–liquid interface as though contaminant molecules are exchanged between interface and bulk of liquid in equilibrium. Griffith (1962) introduced the stagnant cap model that pictures surface contamination as an unimpeded mobile area on the forward surface of bubbles where the most significant reduction in KL a occurs and an immobile cap over the rear of bubbles with a less sever depression of KL a. The model describes how interfacial tension gradients act on surface flow with a force balance at any point in which equilibrium exists on the interface. Behavior of contaminants in vicinity of gas bubbles is in such a way that adsorbed concentration is lower at the top than at the bottom of rising bubbles, because their molecules are dragged by adjacent liquid (Griffith, 1962; Davies and Rideal, 1963; Vasconcelos et al., 2002). We assume the same model for hydrocarbon components being the source of contamination in aqueous systems, in the sense that these contaminants are incessantly transferred from the bulk to the top of bubbles and leave from the bottom of bubbles to the bulk of the liquid (see Fig. 1). When the concentration of contaminant hydrocarbons in the bulk of the liquid is different from that at the gas–liquid interface, the net mass flux of the contaminant for the top of bubbles becomes T √ DH cH (dA/d)2 NH,z = 2 d t A2∞ 0 0 (dA/d)2 d √ = 2 2cH
DH A2∞ 0
T 0
dA d
z DH dcH −2 2 2 A∞ 0 0 dz ⎛ ⎞ T 2 dA ×⎝ d⎠ dz, d 0 √
2
A = 2nRz,
d
(4)
(5)
or
dz dA = −z , d A d
(6)
where dA=2nR dz, and the negative sign denotes the direction of z in Fig. 1. Further, dz dA = 2nRv i , d d where vi = d/d.
On the other hand, the drag force on bubbles can be defined by the surface tension gradient, as follows: =
dW (H ) d
(7)
=
dW (H ) dcH i dz . , . dz d dcH i
(10)
where W (H ) is the surface tension of water changing with concentration of contaminants. Combining Eqs. (8) and (10) gives
−1/2 T dA 2 d C1 v 2nRv i 0 d 0 =
0
where n is the number of bubbles. This definition is compatible with the basic assumption of the surface renewal-stretch model (Jajuee et al., 2006) that requires: d ln A d
where v = v − vi .v and vi are velocities along the interface in the absence and presence of contaminants, respectively. These may be approximated as follows (Beek and Kramers, 1962), √ v = 2gz and vi = C2 z. (9)
dW (H ) dcH i , dcH i dz
where T
where cH = cbulk − cH i , in which cH i is the interfacial concentration of contaminants and cbulk is the concentration far enough from the surface region so the bulk phase properties prevail. Since A represents the total area exposed to interface mass transfer, it is plausible to assume that
vz = −z
Thus, the stress in the liquid phase becomes (see the Appendix)
−1/2 T dz dA 2 d , (8) 2nR i = C1 v 0 d 0 d
0
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dA d
2
d =
(11)
T
2
d d
(2nR) 0 Z dz = C3 vi dz. d 0
2
dz d dz d d (12)
Since dW (H ) /dcH i is assumed to be constant, according to Eqs. (9) and (11), dcH i = C4 · z dz
Z 0
√ dz dz z d
−1/2 ,
(13)
where (see Fig. 1) dz z 1/2 . = 1− 1− d R Since R z, it is likely to assume that 1 − (1 − z/R)1/2 (z2 /4R 2 ≈ 0, see Fig. 1). Therefore, dz z ≈ . d 2R
(14) √
z/2R ≈
(15)
It follows from Eq. (13) that dcH i −dcH ≈ = constant. dz dz
(16)
Integrating this from zh in which the concentration of the contaminant is equal to that of bulk concentration (cH = 0) to an
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arbitrary z, one gets cbulk zh −dcH dcH i = dz dz cBi z
(17a)
or, cH = cbulk − cH i = −
dcH (zh − z). dz
(17b)
T Substituting 0 (dA/d)2 d from Eq. (11) and cH from Eq. (17b) in Eq. (4) yields √ DH dcH i NH,z = 4 2nRC 1 2 2 d 2 A ∞ 0 W (H ) z × (zh − z)vv i + vv i dz , (18) 0
where by definition, v = v√ − vi , and = /. √ When one recalls v = 2gz and vi = C2 z, Eq. (18) reduces to DH NH,z = 8nRC 1 C2 ( 2g − C2 ) A2∞ 20 2 dcH i z2 zzh − × . (19) dW (H ) 2 If concentration of the contamination is known at the interface, the flux of hydrocarbon contaminant can be obtained by writing the following material balance NH,z = ∗ vi 2nr,
(20)
where ∗ denotes the surface excess per unit area and represents the concentration of the contaminant at the interface; r is the curvature of the sphere in Fig. 1 and is defined as √ r = z 2R − zh . (21) Assuming ∗ is in equilibrium with cH i , one can estimate the concentration of the surface contaminant through Gibb’s equation ∗ =
−cH i dW (H ) . RT dcH i
(22)
The surface excess is an algebraic quantity. If positive, as in the case of surface contaminants, dW (H ) /dcH i is negative and an actual excess of the components is present and, if negative, as in the case of sugars, dW (H ) /dcH i is positive and there is a surface deficiency of solute. Combination of Eqs. (20)–(22) provides another expression for NH,z , which can be eliminated afterwards by equating to Eq. (19) √ √ ∗ C2 z2n z 2R − zh DH = 8nRC 1 C2 ( 2g − C2 ) A2∞ 20 2 dcH i z2 . (23) zzh − × dW (H ) 2
Taking the approximation of z2 ≈ zzh (Vogtländer and Meijboom, 1974a) leads to the following expression for C2 : √ ∗ (dW (H ) /dcH i ) 2R − zh C2 = 2g − 2C2 Rzh 8DH /A2∞ 20 2 ∗ dW (H ) = 2g 1 − C5 , (24) dcH i whence,
vi = v 1 − C 5
∗ dW (H )
dcH i
.
(25)
√ Eq. (24) states that when dW (H ) /dcH i is so small, C2 = 2g. Worded differently, the behavior of gas bubbles in the bulk of liquid becomes similar to pure systems with no contamination. With the preceding introduction of surface excess quantities, one can proceed to the derivation of the net flux of mass transfer of oxygen in the presence of contaminants by substituting Eq. (7) in Eq. (3) (see also Eq. (E) from the Appendix) zh √ DA dz (NA,z )h = 2 2cA 2nR vi dz. (26) 2 A∞ 0 d 0 It should be bore in mind that if there were no contamination in the bulk phase, vi would be replaced by v . When using the assumption of Eq. (15), the integrand is determined analytically, and therefore the derivatives do not suffer a loss of accuracy √ DA nR (NA,z )h = 2 2cA C2 √ (27) zh . 4 A2∞ 0 2R Combination of Eqs. (24)–(27) gives the net flux of species A in presence of contamination dW (H ) ∗ 1 − C5 , (28) (NA,z )h = NA,z dcH where dW (H ) /dcH i = dW (H ) /dcH = constant in equilibrium. It is noteworthy that no matter if surface excess takes positive or negative quantities the second part of the square term of Eq. (28) will be always negative. By recalling ∗ = (−cH /RT ) dW (H ) /dcH Eq. (28) takes the form dW (H ) 2 (NA,z )h = NA,z 1 − C6 cH NA,z (29) dcH and thus, the overall flux of species A remains less than that of pure water. The only requirement that should be met is −√
dW (H ) 1 1 √ . dcH C 6 cH C6 cH
(30)
Unlike surface contaminants, hydrophilic solutes (like NaCl) are repelled by the water–air interface, thereby pervading the whole bulk of the aqueous solvent. The water–air interface depleted of these molecules gives rise to surface tension which is only a few mN/m higher than that of pure water, (dW /dc 0)
B. Jajuee et al. / Chemical Engineering Science 61 (2006) 4111 – 4119 0.35
W(h)
0.0026
60
0.0024
ch(dW(h) /dch )
40
2
0.0022
20 0.0020
(KLa)h 0 0
50
100
150
200
0.30 0.25 0.20 0.15 0.10 0.05
ch(dW(h) / dch ) 2 (kgm3/s4)
KLa in pure water
Volumetric mass transfer coeff., KLa (s-1)
0.0028
80
Surface tension, W(h) (mN/m)
4115
0.00
0.0018 250
Concentration of p-Xylene, ch (mg/L)
Fig. 2. The effect of p-xylene concentration on W (h) (——), ch (dW (h) /dch )2 (-·-·-·-·-), and (KL a)h in p-xylene contaminated water (——) compared to KL a in pure water (- - - - - - -).
(Docoslis et al., 2000). Accordingly, their effect on mass transfer is negligible since such chemicals do not induce surface contamination. The question as to whether Eq. (29) can be extended to mass transfer into non-aqueous contaminated solutions has not been, to our knowledge, definitely resolved. The effect of contaminant p-xylene concentration in water on W (h) , ch (dW (h) /dch )2 , and (KL a)h are shown in Fig. 2 at Usg = 2.10 × 10−3 m/s. The obvious shortcoming of some models reported in the literature is that they cannot predict the reduction in KL a as a function of contaminant concentration followed by KL a increase (Vasconcelos et al., 2003). Nor do they treat mass transfer characteristics in the presence of more than one contaminant. On the contrary, Eq. (29) predicts that the group ch (dW (h) /dch )2 might bring about a drastic depression ensued by a less sever upturn of (KL a)h . Such an influence of surface contaminants on mass transfer behavior in gas–liquid systems has been observed by other authors (Jajuee et al., 2006; Vogtländer and Meijboom, 1974a,b; Yoshida et al., 1970). 3. Experimental Mass transfer data were obtained from a novel airlift contactor with a semipermeable membrane (Jajuee et al., 2006). Surface tension measurements were carried out using pendant and sessile drop shape analysis method (Hoorfar et al., 2005; Adamson and Gast, 1997). Drops were photographed with a horizontally mounted Hitachi Model HV-20 3-CCD color camera equipped with a AF Micro Nikkor 60 mm lens. The images were captured and analyzed using Northern Eclipse software. Pendant drops were formed on squared tips of stainless steel hypodermic needles of various diameters from 18 to 25 gauges. The needles were mounted onto a Gilmont ultraprecision micrometer syringe attached to a micromanipulator which permitted easy adjustment of the drop for photography.
The solid support used for the sessile drops was silicon wafer [1 1 1]. Naphthalene 99% and p-xylene 99% were supplied by Sigma Aldrich. Water used as solvent was doubly distilled and deionized. All solutions were prepared by weighing the solutes and solvent on a Mettler AT 261 balance. The concentration of p-xylene and naphthalene were exhaustively measured in the aqueous solutions by gas chromatography instrument (Jajuee et al., 2005). 4. Results and discussion In marked contrast to conventional airlift contactors whose gas–liquid oxygen mass transfer rate is fairly lower than that of bubble columns, the new modified airlift contactor with textile membrane showed significant improvement in the rate of mass transfer to the same extent of bubble columns (Jajuee et al., 2005). The literature data obtained from different configurations of bubble columns have been correlated by Eq. (2) for Newtonian fluids with the average absolute deviation of ±25% (Jajuee et al., 2006). Fig. 3 illustrates that KL a for pure water in the new airlift contactor has the absolute deviation of +19% from Eq. (2). Some of the properties of substances used are tabulated in Table 1. The differences in W (H ) between pendant drop and sessile drop (contact angle) techniques have been justified below. Hydrocarbon compounds endowed with a significant hydrophobic moiety are strongly attracted to the air–water interface when dissolved in water and deplete the surface tension of the solution. On that account, the hydrophobic moiety protrudes into the air due to inevitable hysteresis caused by the orientation of the polar moieties of the organic compound toward water, similar to what happens to aqueous solutions of surfactants (Van Oss et al., 2002; Vasconcelos et al., 2002; Jeng et al., 1986). The main difference is that compared to surfactants, hydrocarbon compounds have much less solubility in water, thereby reducing the surface tension of water to
B. Jajuee et al. / Chemical Engineering Science 61 (2006) 4111 – 4119 76
Average absolute deviation of 19%.
9%
+1
Surface tension, W(H) (mN/m)
100x103
10x103
p-Xylene Naphthalene
Naphthalene solubility limit
74
Top clearance & Bottom clearance = 12 cm
72 70 68 66
p-Xylene solubility limit
64 62 60 0
10x103 100x103 Sherwood number, calculated, Shcal (dimensionless)
Fig. 3. Experimental Sherwood number for Newtonian fluids vs predicted Sherwood number based on surface renewal-stretch model. Experimental results from Jajuee et al., (2006).
a lesser extent. Instantaneous orientation of hydrocarbon compounds is changed by unknown repulsion or attraction energy vis-à-vis solid surfaces in contact with drops, and hence makes it difficult to ascertain how much the periphery of surface attached was repelled or attracted. Therefore, the results from pendant drop shape analysis were preferable to those of sessile drops (Docoslis et al., 2000). Oss and co-workers (Docoslis et al., 2000) pointed out that contact angle measurements are not generally advisable in measuring the surface tension of solutions because of the foregoing solid–drop interactions. In order to verify Eq. (29), solutions of p-xylene and naphthalene were studied in different concentrations. The results of pendant drop measurements are shown in Figs. 4 and 5. It can be seen from Fig. 4 that since dissolution of naphthalene was so low, the depression of surface tension was hardly measurable. No change of mass transfer was detected for such a low solubility. However, in the presence of p-xylene (76 mg/L), naphthalene could get dissolved in water more easily and affected surface tension of water and oxygen mass transfer, as shown in Figs. 5 and 7. Mass transfer data for p-xylene solutions are listed in Table 2. The mean value of 1.6 s4 /kg/m3 was taken for C6 . In Fig. 6 the measured values have been compared with the calculated values of NA,z (1 − 1.6cH (dW (H ) /dcH )2 )0.5 (in which cH (dW (H ) /dcH )2 has been determined from Fig. 4) and plotted as a function of the concentration of p-xylene. Similarly,
25
50
75
100
125
150
175
200
Concentration of hydrocarbon compounds, cH (mg/L)
Fig. 4. Surface tension of water vs concentration of dissolved p-xylene and naphthalene in pure water. Maximum solubility of p-xylene and naphthalene were 198 and 18 mg/L, respectively.
68 p-Xylene = 76 mg/L
Surface tension, W(H) (mN/m)
Sherwood number, experimental, Shexp (dimensionless)
4116
66
64
62
60
58 0
5
10
15
20
25
30
Concentration of Naphthalene, CH (mg/L)
Fig. 5. Surface tension of water vs concentration of dissolved naphthalene in water at constant concentration of p-xylene =76 mg/L.
the effect of dissolution of naphthalene on mass transfer coefficient has been plotted vs the concentration of naphthalene when the concentration of p-xylene remained constant at 76 mg/L, as shown in Fig. 7. The mean value of C6 was 5 s4 /kg/m3 for these measurements and NA,z was the flux of mass transfer
Table 1 Properties of substances used at 20 ◦ C, density (), solubility (S), surface tension of hydrocarbon compounds (H ), interfacial surface tension (W H ), and surface tension of water saturated with hydrocarbon compounds (W (H ) )
Water p-Xylene Naphthalene
(g/cm3 )
S (mg/L)
H
W H
W (H ) pendant drop
W (H ) sessile drop
0.9982 0.8811 1.145
— 200 28
— 28.3 —
73.6 37.77 —
73.6 61.88 72.83
73.6 58.7 69.53
Volumetric mass transfer coeff., KLa (s-1)
1.70 1.49 1.60 1.45 1.47 1.44 1.72 1.5 1.54 1.47 1.4 0.00 0.28 0.30 0.31 0.31 0.31 0.30 0.28 0.28 0.23 0.21 0.15
d cH dcH
2 (kg/m3 /s4 )
C6 (s4 /kg/m3 )
B. Jajuee et al. / Chemical Engineering Science 61 (2006) 4111 – 4119
4117
0.0050 0.0045 0.0040 0.0035 0.0030 0.0025 0.0020 0.0015 0.0010
Volumetric mass transfer coeff., KLa (s-1)
2.71 1.71 1.61 2.03 1.82 2.14 1.93 2.25 2.14 2.03 2.25 2.35 0.00 41.72 53.17 63.84 67.31 84.30 94.10 111.09 112.80 146.62 156.85 197.53 1.69 1.49 1.61 1.45 1.48 1.42 1.75 1.49 1.53 1.47
103 KL aU =2.1×10−3 (s−1 ) sg p-Xylene (mg/L) C6 (s4 /kg/m3 )
50
75
100
125
150
175
200
Fig. 6. Volumetric mass transfer coefficient, KL a, in a membrane airlift contactor as a function of p-xylene concentration in water at zero naphthalene concentration and superficial gas velocities Usg = 4.24 × 10−3 m/s and Usg = 2.10 × 10−3 m/s.
0.0020 Usg=2.1x10-3 m/s p-Xylene Conc. = 76 mg/L
0.0018
0.0016
0.0014
0.0012
0.0010 0
5
10
15
20
25
30
2 (kg/m3 /s4 )
Concentration of Naphthalene (mg/L)
4.77 3.24 3.49 3.50 3.37 3.37 3.62 3.37 3.37 3.50 3.81 0.00 36.99 54.02 55.33 65.88 85.04 92.97 93.75 96.30 118.39 146.39
0.00 0.26 0.30 0.30 0.31 0.31 0.30 0.30 0.30 0.27 0.23
Fig. 7. Volumetric mass transfer coefficient, KL a, in a membrane airlift contactor as a function of naphthalene concentration in water at 76 mg/L p-xylene concentration and superficial gas velocity Usg = 2.10 × 10−3 m/s.
103 KL aU =4.2×10−3 (s−1 ) sg
d cH dcH
25
Concentration of p-Xylene (mg/L)
p-Xylene (mg/L)
Table 2 Mass transfer data at different superficial gas velocities, Usg = 4.2 × 10−3 m/s and Usg = 2.1 × 10−3 m/s, in three-phase membrane airlift contactor
0
contaminated formerly with 76 mg/L of p-xylene. The experimental data are in good agreement with Eq. (29), showing the average absolute deviation of merely 15%. Surfactants with similar but more pronounced effect on mass transfer can be also correlated by Eq. (29). Vogtländer and Meijboon (1974b) used a special form of Eq. (29) developed for single bubbles to investigate the effect of 1-butanol on oxygen mass transfer in aqueous systems. In the presence of several surface contaminants, however, deviation of mass transfer might go either way. Yoshida et al. (1970) notified that increasing fractions of kerosene in water could decrease KL a while addition of surfactants (Tween 85) increased KL a. Systems with more than one contaminant are so complex that one should first specify the change of surface tension of water as a function of concentration of surface contaminants to determine the influence of overall contamination on KL a.
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5. Conclusion Several models are available in the literature regarding the influence of surface contaminants on mass transfer characteristics at gas–liquid interfaces. Satisfactory agreement between theory and experiment remains elusive for models that cannot predict a reduction in KL a followed by a softer trend of KL a increase. No adequate theory has been developed as yet to study the effect of hydrocarbon contaminants on mass transfer. Contributions made by experimental studies suggest that dissolved hydrocarbon components cause changes in mass transfer behavior from pure water. In brief, the extent to which the overall exposed interfacial surface area of mass transfer might be stretched is contingent upon the shape of gas bubbles, which in turn depends on gravity and surface tension effects (Adamson and Gast, 1997). Therefore, changes in gas–liquid interface mass transfer resulting from surface contaminants are due to the reduction in surface tension. The model developed in this study predicts the effects of surface contaminants on gas–liquid oxygen mass transfer coefficient and satisfactorily fits experimental mass transfer data obtained from hydrocarbon contaminated aqueous systems.
Notation a A A∞ Bo cA cA,i Ci Ca D Dc De Eo F Fr g JA KL a M n NA r Re s Sc Sh T
specific interfacial surface, m2 /m3 exposed area of time-dependent surface, m2 total area of the surface exposed to gas, m2 Bond number, gD 2c / time-dependent molar concentration of species A, mol/m3 molar concentration of species A at the interface, mol/m3 constant capillary number, c Ur / molecular diffusivity, m2 /s column diameter, m Deborah number, −KL RT /(dc/d)c=0 Eötvos number, gd 2B (c − d )/ defined by Eq. (B) 2 /D g Froude number, Usg c gravitational acceleration, m s−2 molar flux of diffusion of species A relative to the molar average velocity, mol/m2 s overall volumetric mass transfer coefficient, s−1 Morton number, g4c /c 3 number of bubbles overall flux of species A relative to a phase boundary, mol/m2 s the curvature of sphere in Fig. 1, m Reynolds number, Dc Usg / fractional rate of surface renewal, s−1 Schmidt number, D/ Sherwood number, KL aD 2c /D dimensionless time variable
Ur Usg v We x y z zh
terminal velocity of fluid particle, m/s superficial gas velocity, m/s velocity, m/s Weber number, c dB Ur2 / rectangular coordinate, m rectangular coordinate, m rectangular coordinate, m distance from the interface in which cH =0, m
Greek letters 0 ∗
surface tension, mN/m time, s characteristic constant defined for each system; e.g., for gas-fluid contactors 0 might be bubble formation time, s kinematic viscosity, m2 sn−2 viscosity, kg/m s surface concentration, mol/m2 density, kg/m3 shear stress, mN/m2 coordinate, see Fig. 1, m
Subscripts B c d h H i W
bubble continuous phase dispersed phase contamination hydrocarbon material interface water
Acknowledgments The authors are grateful to Surface Science Western at the University of Western Ontario for providing surface analytical instrumentation used for pendant drop and contact angle measurements. They also wish to thank Imperial Oil Ltd. and Natural Sciences and Engineering Research Council (NSERC) of Canada for financial support. B. Jajuee acknowledges support by the Western Engineering Scholarship. Appendix The surface renewal-stretch model introduced by Jajuee et al. (2006) predicts mass transfer rate and the molar flux of diffusion of species A, as follows:
∞ dA(T ) DA A(T ) dT 2 A∞ 0 0 dT T 2 A () d 0 DA s ≈ 2cA , DA A(T ) , jA,z = cA 0 T 2 A () d 0
NA,z = cA
(A)
(B)
B. Jajuee et al. / Chemical Engineering Science 61 (2006) 4111 – 4119
where dA/dT = sA∞ 0 e−s 0 T . If one substitutes A(T ) in Eq. (A) with dA/dT , the rate of mass transfer changes to function F : ∞ DA cA (dA/dT )2 dT . (Ca ) F= A2∞ 0 0 T 2 (dA/d) d 0 Eq. (B) can be rewritten for constant driving force (constant cA ) as ∞ 2 DA dA F = 2cA dT , (Cb ) 2 A∞ 0 dT 0 whence,
F = 2cA
D A s 2 0
∞
(exp(−2s0 T )) dT 0
√ DA s = 2cA . The clear inference from comparing Eqs. (A) and (D) is √ NA,z = 2F .
(D)
(E)
The reason for the close affinity between A(T ) and dA/dT is that A(T ) is an exponential function. The molar flux of diffusion of species A is also achieved by substituting A(T ) with dA/dT and considering a constant like C1 : jA,z = − DA
dcA dz
= C1 cA
DA dA/dT . 0 T 2 (dA/d) d 0
By analogy, the drag force on bubbles can be written as dv dA/dT = − . = C1 v d 0 T 2 (dA/d) d 0
(F)
(G)
References Adamson, W.A., Gast, A.P., 1997. Physical Chemistry of Surfaces. Wiley, New York. pp. 26–30, 65–113. Beek, W.J., Kramers, H., 1962. Mass transfer with a change in interfacial area. Chemical Engineering Science 16, 909–921. Clift, R., Grace, J.R., Webter, M.E., 1978. Bubbles, Drops, and Particles. Academic Press, London. pp. 35–41, 125–137, 169–199.
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Davies, J.T., Rideal, E.K., 1963. Interfacial Phenomena. second ed. Academic Press, NY, London. pp. 318–319. Docoslis, A., Giese, R.R., Van Oss, C.J., 2000. Influence of the water–air interface on the apparent surface tension of aqueous solutions of hydrophilic solutes. Colloids and Surfaces B 19, 147–162. Eckenfelder, W.W., Barnhart, E.L., 1961. The effect of organic substances on the transfer of oxygen from air bubbles in water. A.I.Ch.E. Journal 7 (4), 631–634. Ghoshal, S., Pasion, C., Alshafie, M., 2004. Reduction of benzene and naphthalene mass transfer from crude oils by aging-induced interfacial films. 38, 2102–2110. Girifalco, L.A., Good, R.J., 1957. A theory for the estimation of surface and interfacial energies. I. Derivation and application to interfacial tension. Journal of Physical Chemistry 61 (7), 904–909. Grace, J.R., 1973. Shapes and velocities of bubbles rising in infinite liquids. Transactions of the Institution of Chemical Engineers 51, 116–120. Grace, J.R., Wairegi, T., Nguyen, T.H., 1976. Shapes and velocities of bubbles moving freely through immiscible liquids. Transactions of the Institution of Chemical Engineers 54, 167–173. Griffith, R.M., 1962. The effect of surfactant on the terminal velocity of drops and bubbles. Chemical Engineering Science 17 (12), 1057–1070. Harkins, W.D., 1952. The Physical Chemistry of Surface Films. Reinhold, New York. pp. 102–106. Hoorfar, M., Kurz, M.A., Neumann, A.W., 2005. Evaluation of the surface tension measurement of axisymmetric drop shape analysis (ADSA) using a shape parameter. Colloids and Surfaces A 260, 277–285. Jajuee, B., Margaritis, A., Karamanev, D., Bergougnou, M.A., 2005. Hydrodynamic and mass transfer characteristics of an airlift contactor with a semipermeable membrane. Chemical Engineering Journal, submitted. Jajuee, B., Margaritis, A., Karamanev, D., Bergougnou, M.A., 2006. Application of surface renewal-stretch model for interface mass transfer. Chemical Engineering Science, in press, doi:10.1016/j.ces.2006.01.026. Jeng, J.J., Maa, J.R., Yang, M.Y., 1986. Surface effects and mass transfer in bubble column. Industrial and Engineering Chemistry Process Design and Development 25, 974–978. Petersen, E.E., Margaritis, A., 2001. Hydrodynamic and mass transfer characteristics of three-phase gaslift bioreactor systems. Critical Reviews in Biotechnology 21 (4), 233–294. Van Oss, C.J., Giese, R.F., Good, R.J., 2002. The zero time dynamic interfacial tension. Journal of Dispersion Science and Technology 23 (4), 455–464. Vasconcelos, J.M.T., Orvalho, S.P., Alves, S.S., 2002. Gas–liquid mass transfer to single bubbles: effect of surface contamination. A.I.Ch.E. Journal 48 (6), 1145–1154. Vasconcelos, J.M.T., Rodrigues, J.M.L., Orvalho, S.C.P., Alves, S.S., Mendes, R.L., Reis, A., 2003. Effect of contaminants on mass transfer coefficients in bubble column and airlift contactors. Chemical Engineering Science 58, 1431–1440. Vogtländer, J.G., Meijboom, F.W., 1974a. Influence of surface-active agents on the mass transfer from gas bubbles in a liquid-II. Chemical Engineering Science 29, 949–955. Vogtländer, J.G., Meijboon, F.W., 1974b. A new method for measuring the transfer of oxygen in liquids. Measurements of oxygen transfer from bubbles in water and in water +1-Butanol. Chemical Engineering Science 29, 799–803. Yoshida, F., Yamane, T., Miyamoto, Y., 1970. Oxygen absorption into oilin-water emulsions a study on hydrocarbon fermentors. Industrial and Engineering Chemistry Process Design and Development 9 (4), 570–577.
Influence of dissolved hydrocarbons on volumetric oxygen mass transfer coefficient in a novel airlift contactor Babak Jajuee, Argyrios Margaritis ∗ , Dimitre Karamanev, Maurice A. Bergougnou Department of Chemical and Biochemical Engineering, Faculty of Engineering, University of Western Ontario, London, Ont., Canada N6A 5B8 Received 5 September 2005; received in revised form 25 January 2006; accepted 30 January 2006 Available online 22 March 2006
Abstract Hydrocarbon compounds are sparsely soluble in aqueous systems but, nonetheless, their presence can influence significantly mass transfer behavior in gas–liquid systems. water–p-xylene and water–p-xylene–naphthalene mixtures were employed in order to determine the influence of dissolved hydrocarbons on mass transfer of oxygen from air bubbles to water. The surface renewal-stretch model has been modified for predicting the volumetric mass transfer coefficient, (KL a)h , in the presence of surface contaminant molecules, including hydrocarbon compounds and surfactants. Theory and experimental oxygen transfer results were found to be in satisfactory agreement with average absolute deviation of 15%. Pendant drop and contact angle measurements by axisymmetric drop shape analysis were carried out to determine the reduction in surface tension of water due to the addition of p-xylene and naphthalene. Molecular orientation caused by instantaneous attraction of the polar moieties of the organic compounds toward the water interface has been found to be the main cause of reduction in surface tension. It was predicated that changes in gas–liquid mass transfer behavior resulted from surface contamination and that the significant parameter was the reduction in surface tension. 䉷 2006 Elsevier Ltd. All rights reserved. Keywords: Volumetric mass transfer coefficient; Airlift contactor; Hydrocarbon contaminants; Surface tension; Surface renewal-stretch mass transfer model; Membrane airlift contactor
1. Introduction It is of fundamental importance to understand the influence of dissolution of water-soluble hydrocarbon pollutants on interfacial mass transfer between gas bubbles and contaminated bulk of liquid. Petroleum-based products are widely used in many industrial processes and accidental discharge of these chemicals from storage facilities, pipeline leaks, tanker disasters, or from contamination of soil around factories may cause water and groundwater contamination. When these chemicals enter the surface or subsurface environment, some components dissolve and leach out of the slick, some evaporate, and the majority may eventually be biodegraded. The ecotoxicity of oil fractions including soluble aromatic compounds (PAHs) and BTEX is higher to aquatic organism and plants. Knowledge of effects of dissolution of potentially water-soluble hydrocarbon ∗ Corresponding author. Tel.: +1 519 661 2146; fax: +1 519 661 4275.
E-mail address: [email protected] (A. Margaritis) URL: http://www.eng.uwo.ca/people/amargaritis/ (A. Margaritis). 0009-2509/$ - see front matter 䉷 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2006.01.044
pollutants on oxygen mass transfer behavior is important for evaluating their impact on water quality and assessing the potential of water-based technologies in biotreatment of crude and fuel oil contaminated waters. Improving oxygen supply in cell culture systems has always been a central topic for many biochemical processes (Petersen and Margaritis, 2001). In general, slightly soluble substances spread out to a thick duplex film or in some cases monomolecular film when placed at a liquid–air interface. Spills of hydrocarbon compounds spread out almost immediately in water to form a semi-rigid film (slick) on the surface (Ghoshal et al., 2004). When studying the thermodynamic behavior of surface films on liquid substrates, the solution properties are not usually of much interest. Instead, the emphasis shifts to more direct measurements of the interfacial properties so, little effort is made even of the ability to compute changes in solution concentration through the Gibbs equation (Adamson and Gast, 1997). On the environmental side, a belief that a slight change in solution concentration can affect the transport of mass of various species, such as nutrients, oxygen, and chemicals shifts emphasis to the latter. Girifalco and
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B. Jajuee et al. / Chemical Engineering Science 61 (2006) 4111 – 4119
Good (1957) remarked that spreading coefficient of a mass of some substance with lower surface tension placed on a liquid surface with higher surface tension changes since they will become mutually saturated, so that the surface tension of each liquid will change. In the case of benzene on water, the change of individual surface tensions of benzene and water are merely 0.1 and 10.9 mN/m, respectively. However, spreading coefficient changes appreciably from 8.9 to −1.6 mN/m (Harkins, 1952). Likewise, the change in surface tension, though imperceptible, is believed to be the measure of impact on mass transport. The influence of dissolved hydrocarbons on oxygen mass transfer in aqueous systems has not been fully assessed to date. Certain observations reported in the literature support the hypothesis that dissolution of contaminants in general may significantly affect oxygen mass transfer rates in water (Clift et al., 1978; Eckenfelder and Barnhart, 1961; Yoshida et al., 1970). The objective of this study is to evaluate the effect of two chemical-constituents, namely p-xylene and naphthalene on oxygen mass transfer characteristics in a novel airlift contactor. The results are of importance in extending the influence of any surface contaminant including surfactants on oxygen mass transfer characteristics in gas–liquid contactors. 2. Theoretical model development To capture the essence of deviations from fluid mass transfer behavior resulting from surface contamination, one should be aware of the mechanism of mass transfer from gas bubbles to non-contaminated bulk phase. The surface renewal-stretch model which has been proposed elsewhere to predict KL a from many bubbles (Jajuee et al., 2006) is now used as the basis of our analysis. Based on this model, the z-directed flux of A in the absence of chemical reaction becomes ∞ dA(T ) DA A(T ) NA,z = cA dT , (1) A2∞ 0 0 dT T 2 A () d 0 whereby the following correlation has been developed for volumetric mass transfer coefficient in Newtonian liquids 1.022 Sh = √ Sc0.5 Re0.72 Bo0.6 F r 0.1 .
(2)
dimensionless parameters: Re(inertia forces/viscous forces), Eo(buoyancy forces/capillary forces), W e(inertia forces/ca− pillary forces), and/or combinational parameters like M(Eo W e2 /Re4 ) (Grace et al., 1976; Grace, 1973). Instead, interfacial flows are characterized by Group (II) of dimensionless parameters: Re, Ca(viscous forces/capillary forces), and De(bubble residence time/equilibrium time) (Vogtländer and Meijboom, 1974a,b). In surface renewal-stretch model, the extent to which the overall exposed surface area of mass transfer might be stretched is determined by Group (I) forces. On the other hand, the influence of contamination on mass transfer behavior is in effect due to alternation of interfacial flows (or velocities) determined by Group (II) forces. It may be of value, therefore, to show that how interfacial flows affect the overall exposed surface area for mass transfer and change mass transfer behavior. As will be seen later on, it is preferable to use the differential form of the exposed surface area in order to study the effect of contamination on mass transfer behavior. According to surface renewal-stretch model (see the Appendix): zh 2 √ DA dA dz (NA,z )h = 2 2cA dz, (3) 2 A∞ 0 dz dT 0 where subscript h designates the presence of contamination in general, and zh is the depth in which the concentration of contaminants is equal to that of bulk concentration. Fig. 1 is a schematic representation of fluid flow and mass transfer phenomena at the gas–liquid interface of a rising bubble. Contaminants with the greatest effect on the interface mobility, thus on mass transfer, are hardly soluble (Clift et al., 1978). When dealing with bubble swarms released from a
v
The change of mass transfer has been ascribed to interfacial motion, which in turn is attributed to hydrodynamic and molecular effects (Vasconcelos et al., 2002, 2003; Clift et al., 1978; Davies and Rideal, 1963). These effects are explicable in terms of forces acting on bubble series, namely: inertia forces = c dB2 Ur2 , viscous forces = c dB Ur , capillary forces = dB , drag forces = (gravity force − buoyancy) = dB3 (c − B )g. 6 Acting forces that are responsible for shapes and velocities of bubbles are usually determined by Group (I) of
Fig. 1. Coordinates on a rising gas bubble for stagnant cap model in the presence of hydrocarbon contaminants.
B. Jajuee et al. / Chemical Engineering Science 61 (2006) 4111 – 4119
submerged sparger, therefore, it is plausible to assume that a thin film of contaminants is formed at the gas–liquid interface as though contaminant molecules are exchanged between interface and bulk of liquid in equilibrium. Griffith (1962) introduced the stagnant cap model that pictures surface contamination as an unimpeded mobile area on the forward surface of bubbles where the most significant reduction in KL a occurs and an immobile cap over the rear of bubbles with a less sever depression of KL a. The model describes how interfacial tension gradients act on surface flow with a force balance at any point in which equilibrium exists on the interface. Behavior of contaminants in vicinity of gas bubbles is in such a way that adsorbed concentration is lower at the top than at the bottom of rising bubbles, because their molecules are dragged by adjacent liquid (Griffith, 1962; Davies and Rideal, 1963; Vasconcelos et al., 2002). We assume the same model for hydrocarbon components being the source of contamination in aqueous systems, in the sense that these contaminants are incessantly transferred from the bulk to the top of bubbles and leave from the bottom of bubbles to the bulk of the liquid (see Fig. 1). When the concentration of contaminant hydrocarbons in the bulk of the liquid is different from that at the gas–liquid interface, the net mass flux of the contaminant for the top of bubbles becomes T √ DH cH (dA/d)2 NH,z = 2 d t A2∞ 0 0 (dA/d)2 d √ = 2 2cH
DH A2∞ 0
T 0
dA d
z DH dcH −2 2 2 A∞ 0 0 dz ⎛ ⎞ T 2 dA ×⎝ d⎠ dz, d 0 √
2
A = 2nRz,
d
(4)
(5)
or
dz dA = −z , d A d
(6)
where dA=2nR dz, and the negative sign denotes the direction of z in Fig. 1. Further, dz dA = 2nRv i , d d where vi = d/d.
On the other hand, the drag force on bubbles can be defined by the surface tension gradient, as follows: =
dW (H ) d
(7)
=
dW (H ) dcH i dz . , . dz d dcH i
(10)
where W (H ) is the surface tension of water changing with concentration of contaminants. Combining Eqs. (8) and (10) gives
−1/2 T dA 2 d C1 v 2nRv i 0 d 0 =
0
where n is the number of bubbles. This definition is compatible with the basic assumption of the surface renewal-stretch model (Jajuee et al., 2006) that requires: d ln A d
where v = v − vi .v and vi are velocities along the interface in the absence and presence of contaminants, respectively. These may be approximated as follows (Beek and Kramers, 1962), √ v = 2gz and vi = C2 z. (9)
dW (H ) dcH i , dcH i dz
where T
where cH = cbulk − cH i , in which cH i is the interfacial concentration of contaminants and cbulk is the concentration far enough from the surface region so the bulk phase properties prevail. Since A represents the total area exposed to interface mass transfer, it is plausible to assume that
vz = −z
Thus, the stress in the liquid phase becomes (see the Appendix)
−1/2 T dz dA 2 d , (8) 2nR i = C1 v 0 d 0 d
0
4113
dA d
2
d =
(11)
T
2
d d
(2nR) 0 Z dz = C3 vi dz. d 0
2
dz d dz d d (12)
Since dW (H ) /dcH i is assumed to be constant, according to Eqs. (9) and (11), dcH i = C4 · z dz
Z 0
√ dz dz z d
−1/2 ,
(13)
where (see Fig. 1) dz z 1/2 . = 1− 1− d R Since R z, it is likely to assume that 1 − (1 − z/R)1/2 (z2 /4R 2 ≈ 0, see Fig. 1). Therefore, dz z ≈ . d 2R
(14) √
z/2R ≈
(15)
It follows from Eq. (13) that dcH i −dcH ≈ = constant. dz dz
(16)
Integrating this from zh in which the concentration of the contaminant is equal to that of bulk concentration (cH = 0) to an
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B. Jajuee et al. / Chemical Engineering Science 61 (2006) 4111 – 4119
arbitrary z, one gets cbulk zh −dcH dcH i = dz dz cBi z
(17a)
or, cH = cbulk − cH i = −
dcH (zh − z). dz
(17b)
T Substituting 0 (dA/d)2 d from Eq. (11) and cH from Eq. (17b) in Eq. (4) yields √ DH dcH i NH,z = 4 2nRC 1 2 2 d 2 A ∞ 0 W (H ) z × (zh − z)vv i + vv i dz , (18) 0
where by definition, v = v√ − vi , and = /. √ When one recalls v = 2gz and vi = C2 z, Eq. (18) reduces to DH NH,z = 8nRC 1 C2 ( 2g − C2 ) A2∞ 20 2 dcH i z2 zzh − × . (19) dW (H ) 2 If concentration of the contamination is known at the interface, the flux of hydrocarbon contaminant can be obtained by writing the following material balance NH,z = ∗ vi 2nr,
(20)
where ∗ denotes the surface excess per unit area and represents the concentration of the contaminant at the interface; r is the curvature of the sphere in Fig. 1 and is defined as √ r = z 2R − zh . (21) Assuming ∗ is in equilibrium with cH i , one can estimate the concentration of the surface contaminant through Gibb’s equation ∗ =
−cH i dW (H ) . RT dcH i
(22)
The surface excess is an algebraic quantity. If positive, as in the case of surface contaminants, dW (H ) /dcH i is negative and an actual excess of the components is present and, if negative, as in the case of sugars, dW (H ) /dcH i is positive and there is a surface deficiency of solute. Combination of Eqs. (20)–(22) provides another expression for NH,z , which can be eliminated afterwards by equating to Eq. (19) √ √ ∗ C2 z2n z 2R − zh DH = 8nRC 1 C2 ( 2g − C2 ) A2∞ 20 2 dcH i z2 . (23) zzh − × dW (H ) 2
Taking the approximation of z2 ≈ zzh (Vogtländer and Meijboom, 1974a) leads to the following expression for C2 : √ ∗ (dW (H ) /dcH i ) 2R − zh C2 = 2g − 2C2 Rzh 8DH /A2∞ 20 2 ∗ dW (H ) = 2g 1 − C5 , (24) dcH i whence,
vi = v 1 − C 5
∗ dW (H )
dcH i
.
(25)
√ Eq. (24) states that when dW (H ) /dcH i is so small, C2 = 2g. Worded differently, the behavior of gas bubbles in the bulk of liquid becomes similar to pure systems with no contamination. With the preceding introduction of surface excess quantities, one can proceed to the derivation of the net flux of mass transfer of oxygen in the presence of contaminants by substituting Eq. (7) in Eq. (3) (see also Eq. (E) from the Appendix) zh √ DA dz (NA,z )h = 2 2cA 2nR vi dz. (26) 2 A∞ 0 d 0 It should be bore in mind that if there were no contamination in the bulk phase, vi would be replaced by v . When using the assumption of Eq. (15), the integrand is determined analytically, and therefore the derivatives do not suffer a loss of accuracy √ DA nR (NA,z )h = 2 2cA C2 √ (27) zh . 4 A2∞ 0 2R Combination of Eqs. (24)–(27) gives the net flux of species A in presence of contamination dW (H ) ∗ 1 − C5 , (28) (NA,z )h = NA,z dcH where dW (H ) /dcH i = dW (H ) /dcH = constant in equilibrium. It is noteworthy that no matter if surface excess takes positive or negative quantities the second part of the square term of Eq. (28) will be always negative. By recalling ∗ = (−cH /RT ) dW (H ) /dcH Eq. (28) takes the form dW (H ) 2 (NA,z )h = NA,z 1 − C6 cH NA,z (29) dcH and thus, the overall flux of species A remains less than that of pure water. The only requirement that should be met is −√
dW (H ) 1 1 √ . dcH C 6 cH C6 cH
(30)
Unlike surface contaminants, hydrophilic solutes (like NaCl) are repelled by the water–air interface, thereby pervading the whole bulk of the aqueous solvent. The water–air interface depleted of these molecules gives rise to surface tension which is only a few mN/m higher than that of pure water, (dW /dc 0)
B. Jajuee et al. / Chemical Engineering Science 61 (2006) 4111 – 4119 0.35
W(h)
0.0026
60
0.0024
ch(dW(h) /dch )
40
2
0.0022
20 0.0020
(KLa)h 0 0
50
100
150
200
0.30 0.25 0.20 0.15 0.10 0.05
ch(dW(h) / dch ) 2 (kgm3/s4)
KLa in pure water
Volumetric mass transfer coeff., KLa (s-1)
0.0028
80
Surface tension, W(h) (mN/m)
4115
0.00
0.0018 250
Concentration of p-Xylene, ch (mg/L)
Fig. 2. The effect of p-xylene concentration on W (h) (——), ch (dW (h) /dch )2 (-·-·-·-·-), and (KL a)h in p-xylene contaminated water (——) compared to KL a in pure water (- - - - - - -).
(Docoslis et al., 2000). Accordingly, their effect on mass transfer is negligible since such chemicals do not induce surface contamination. The question as to whether Eq. (29) can be extended to mass transfer into non-aqueous contaminated solutions has not been, to our knowledge, definitely resolved. The effect of contaminant p-xylene concentration in water on W (h) , ch (dW (h) /dch )2 , and (KL a)h are shown in Fig. 2 at Usg = 2.10 × 10−3 m/s. The obvious shortcoming of some models reported in the literature is that they cannot predict the reduction in KL a as a function of contaminant concentration followed by KL a increase (Vasconcelos et al., 2003). Nor do they treat mass transfer characteristics in the presence of more than one contaminant. On the contrary, Eq. (29) predicts that the group ch (dW (h) /dch )2 might bring about a drastic depression ensued by a less sever upturn of (KL a)h . Such an influence of surface contaminants on mass transfer behavior in gas–liquid systems has been observed by other authors (Jajuee et al., 2006; Vogtländer and Meijboom, 1974a,b; Yoshida et al., 1970). 3. Experimental Mass transfer data were obtained from a novel airlift contactor with a semipermeable membrane (Jajuee et al., 2006). Surface tension measurements were carried out using pendant and sessile drop shape analysis method (Hoorfar et al., 2005; Adamson and Gast, 1997). Drops were photographed with a horizontally mounted Hitachi Model HV-20 3-CCD color camera equipped with a AF Micro Nikkor 60 mm lens. The images were captured and analyzed using Northern Eclipse software. Pendant drops were formed on squared tips of stainless steel hypodermic needles of various diameters from 18 to 25 gauges. The needles were mounted onto a Gilmont ultraprecision micrometer syringe attached to a micromanipulator which permitted easy adjustment of the drop for photography.
The solid support used for the sessile drops was silicon wafer [1 1 1]. Naphthalene 99% and p-xylene 99% were supplied by Sigma Aldrich. Water used as solvent was doubly distilled and deionized. All solutions were prepared by weighing the solutes and solvent on a Mettler AT 261 balance. The concentration of p-xylene and naphthalene were exhaustively measured in the aqueous solutions by gas chromatography instrument (Jajuee et al., 2005). 4. Results and discussion In marked contrast to conventional airlift contactors whose gas–liquid oxygen mass transfer rate is fairly lower than that of bubble columns, the new modified airlift contactor with textile membrane showed significant improvement in the rate of mass transfer to the same extent of bubble columns (Jajuee et al., 2005). The literature data obtained from different configurations of bubble columns have been correlated by Eq. (2) for Newtonian fluids with the average absolute deviation of ±25% (Jajuee et al., 2006). Fig. 3 illustrates that KL a for pure water in the new airlift contactor has the absolute deviation of +19% from Eq. (2). Some of the properties of substances used are tabulated in Table 1. The differences in W (H ) between pendant drop and sessile drop (contact angle) techniques have been justified below. Hydrocarbon compounds endowed with a significant hydrophobic moiety are strongly attracted to the air–water interface when dissolved in water and deplete the surface tension of the solution. On that account, the hydrophobic moiety protrudes into the air due to inevitable hysteresis caused by the orientation of the polar moieties of the organic compound toward water, similar to what happens to aqueous solutions of surfactants (Van Oss et al., 2002; Vasconcelos et al., 2002; Jeng et al., 1986). The main difference is that compared to surfactants, hydrocarbon compounds have much less solubility in water, thereby reducing the surface tension of water to
B. Jajuee et al. / Chemical Engineering Science 61 (2006) 4111 – 4119 76
Average absolute deviation of 19%.
9%
+1
Surface tension, W(H) (mN/m)
100x103
10x103
p-Xylene Naphthalene
Naphthalene solubility limit
74
Top clearance & Bottom clearance = 12 cm
72 70 68 66
p-Xylene solubility limit
64 62 60 0
10x103 100x103 Sherwood number, calculated, Shcal (dimensionless)
Fig. 3. Experimental Sherwood number for Newtonian fluids vs predicted Sherwood number based on surface renewal-stretch model. Experimental results from Jajuee et al., (2006).
a lesser extent. Instantaneous orientation of hydrocarbon compounds is changed by unknown repulsion or attraction energy vis-à-vis solid surfaces in contact with drops, and hence makes it difficult to ascertain how much the periphery of surface attached was repelled or attracted. Therefore, the results from pendant drop shape analysis were preferable to those of sessile drops (Docoslis et al., 2000). Oss and co-workers (Docoslis et al., 2000) pointed out that contact angle measurements are not generally advisable in measuring the surface tension of solutions because of the foregoing solid–drop interactions. In order to verify Eq. (29), solutions of p-xylene and naphthalene were studied in different concentrations. The results of pendant drop measurements are shown in Figs. 4 and 5. It can be seen from Fig. 4 that since dissolution of naphthalene was so low, the depression of surface tension was hardly measurable. No change of mass transfer was detected for such a low solubility. However, in the presence of p-xylene (76 mg/L), naphthalene could get dissolved in water more easily and affected surface tension of water and oxygen mass transfer, as shown in Figs. 5 and 7. Mass transfer data for p-xylene solutions are listed in Table 2. The mean value of 1.6 s4 /kg/m3 was taken for C6 . In Fig. 6 the measured values have been compared with the calculated values of NA,z (1 − 1.6cH (dW (H ) /dcH )2 )0.5 (in which cH (dW (H ) /dcH )2 has been determined from Fig. 4) and plotted as a function of the concentration of p-xylene. Similarly,
25
50
75
100
125
150
175
200
Concentration of hydrocarbon compounds, cH (mg/L)
Fig. 4. Surface tension of water vs concentration of dissolved p-xylene and naphthalene in pure water. Maximum solubility of p-xylene and naphthalene were 198 and 18 mg/L, respectively.
68 p-Xylene = 76 mg/L
Surface tension, W(H) (mN/m)
Sherwood number, experimental, Shexp (dimensionless)
4116
66
64
62
60
58 0
5
10
15
20
25
30
Concentration of Naphthalene, CH (mg/L)
Fig. 5. Surface tension of water vs concentration of dissolved naphthalene in water at constant concentration of p-xylene =76 mg/L.
the effect of dissolution of naphthalene on mass transfer coefficient has been plotted vs the concentration of naphthalene when the concentration of p-xylene remained constant at 76 mg/L, as shown in Fig. 7. The mean value of C6 was 5 s4 /kg/m3 for these measurements and NA,z was the flux of mass transfer
Table 1 Properties of substances used at 20 ◦ C, density (), solubility (S), surface tension of hydrocarbon compounds (H ), interfacial surface tension (W H ), and surface tension of water saturated with hydrocarbon compounds (W (H ) )
Water p-Xylene Naphthalene
(g/cm3 )
S (mg/L)
H
W H
W (H ) pendant drop
W (H ) sessile drop
0.9982 0.8811 1.145
— 200 28
— 28.3 —
73.6 37.77 —
73.6 61.88 72.83
73.6 58.7 69.53
Volumetric mass transfer coeff., KLa (s-1)
1.70 1.49 1.60 1.45 1.47 1.44 1.72 1.5 1.54 1.47 1.4 0.00 0.28 0.30 0.31 0.31 0.31 0.30 0.28 0.28 0.23 0.21 0.15
d cH dcH
2 (kg/m3 /s4 )
C6 (s4 /kg/m3 )
B. Jajuee et al. / Chemical Engineering Science 61 (2006) 4111 – 4119
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0.0050 0.0045 0.0040 0.0035 0.0030 0.0025 0.0020 0.0015 0.0010
Volumetric mass transfer coeff., KLa (s-1)
2.71 1.71 1.61 2.03 1.82 2.14 1.93 2.25 2.14 2.03 2.25 2.35 0.00 41.72 53.17 63.84 67.31 84.30 94.10 111.09 112.80 146.62 156.85 197.53 1.69 1.49 1.61 1.45 1.48 1.42 1.75 1.49 1.53 1.47
103 KL aU =2.1×10−3 (s−1 ) sg p-Xylene (mg/L) C6 (s4 /kg/m3 )
50
75
100
125
150
175
200
Fig. 6. Volumetric mass transfer coefficient, KL a, in a membrane airlift contactor as a function of p-xylene concentration in water at zero naphthalene concentration and superficial gas velocities Usg = 4.24 × 10−3 m/s and Usg = 2.10 × 10−3 m/s.
0.0020 Usg=2.1x10-3 m/s p-Xylene Conc. = 76 mg/L
0.0018
0.0016
0.0014
0.0012
0.0010 0
5
10
15
20
25
30
2 (kg/m3 /s4 )
Concentration of Naphthalene (mg/L)
4.77 3.24 3.49 3.50 3.37 3.37 3.62 3.37 3.37 3.50 3.81 0.00 36.99 54.02 55.33 65.88 85.04 92.97 93.75 96.30 118.39 146.39
0.00 0.26 0.30 0.30 0.31 0.31 0.30 0.30 0.30 0.27 0.23
Fig. 7. Volumetric mass transfer coefficient, KL a, in a membrane airlift contactor as a function of naphthalene concentration in water at 76 mg/L p-xylene concentration and superficial gas velocity Usg = 2.10 × 10−3 m/s.
103 KL aU =4.2×10−3 (s−1 ) sg
d cH dcH
25
Concentration of p-Xylene (mg/L)
p-Xylene (mg/L)
Table 2 Mass transfer data at different superficial gas velocities, Usg = 4.2 × 10−3 m/s and Usg = 2.1 × 10−3 m/s, in three-phase membrane airlift contactor
0
contaminated formerly with 76 mg/L of p-xylene. The experimental data are in good agreement with Eq. (29), showing the average absolute deviation of merely 15%. Surfactants with similar but more pronounced effect on mass transfer can be also correlated by Eq. (29). Vogtländer and Meijboon (1974b) used a special form of Eq. (29) developed for single bubbles to investigate the effect of 1-butanol on oxygen mass transfer in aqueous systems. In the presence of several surface contaminants, however, deviation of mass transfer might go either way. Yoshida et al. (1970) notified that increasing fractions of kerosene in water could decrease KL a while addition of surfactants (Tween 85) increased KL a. Systems with more than one contaminant are so complex that one should first specify the change of surface tension of water as a function of concentration of surface contaminants to determine the influence of overall contamination on KL a.
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5. Conclusion Several models are available in the literature regarding the influence of surface contaminants on mass transfer characteristics at gas–liquid interfaces. Satisfactory agreement between theory and experiment remains elusive for models that cannot predict a reduction in KL a followed by a softer trend of KL a increase. No adequate theory has been developed as yet to study the effect of hydrocarbon contaminants on mass transfer. Contributions made by experimental studies suggest that dissolved hydrocarbon components cause changes in mass transfer behavior from pure water. In brief, the extent to which the overall exposed interfacial surface area of mass transfer might be stretched is contingent upon the shape of gas bubbles, which in turn depends on gravity and surface tension effects (Adamson and Gast, 1997). Therefore, changes in gas–liquid interface mass transfer resulting from surface contaminants are due to the reduction in surface tension. The model developed in this study predicts the effects of surface contaminants on gas–liquid oxygen mass transfer coefficient and satisfactorily fits experimental mass transfer data obtained from hydrocarbon contaminated aqueous systems.
Notation a A A∞ Bo cA cA,i Ci Ca D Dc De Eo F Fr g JA KL a M n NA r Re s Sc Sh T
specific interfacial surface, m2 /m3 exposed area of time-dependent surface, m2 total area of the surface exposed to gas, m2 Bond number, gD 2c / time-dependent molar concentration of species A, mol/m3 molar concentration of species A at the interface, mol/m3 constant capillary number, c Ur / molecular diffusivity, m2 /s column diameter, m Deborah number, −KL RT /(dc/d)c=0 Eötvos number, gd 2B (c − d )/ defined by Eq. (B) 2 /D g Froude number, Usg c gravitational acceleration, m s−2 molar flux of diffusion of species A relative to the molar average velocity, mol/m2 s overall volumetric mass transfer coefficient, s−1 Morton number, g4c /c 3 number of bubbles overall flux of species A relative to a phase boundary, mol/m2 s the curvature of sphere in Fig. 1, m Reynolds number, Dc Usg / fractional rate of surface renewal, s−1 Schmidt number, D/ Sherwood number, KL aD 2c /D dimensionless time variable
Ur Usg v We x y z zh
terminal velocity of fluid particle, m/s superficial gas velocity, m/s velocity, m/s Weber number, c dB Ur2 / rectangular coordinate, m rectangular coordinate, m rectangular coordinate, m distance from the interface in which cH =0, m
Greek letters 0 ∗
surface tension, mN/m time, s characteristic constant defined for each system; e.g., for gas-fluid contactors 0 might be bubble formation time, s kinematic viscosity, m2 sn−2 viscosity, kg/m s surface concentration, mol/m2 density, kg/m3 shear stress, mN/m2 coordinate, see Fig. 1, m
Subscripts B c d h H i W
bubble continuous phase dispersed phase contamination hydrocarbon material interface water
Acknowledgments The authors are grateful to Surface Science Western at the University of Western Ontario for providing surface analytical instrumentation used for pendant drop and contact angle measurements. They also wish to thank Imperial Oil Ltd. and Natural Sciences and Engineering Research Council (NSERC) of Canada for financial support. B. Jajuee acknowledges support by the Western Engineering Scholarship. Appendix The surface renewal-stretch model introduced by Jajuee et al. (2006) predicts mass transfer rate and the molar flux of diffusion of species A, as follows:
∞ dA(T ) DA A(T ) dT 2 A∞ 0 0 dT T 2 A () d 0 DA s ≈ 2cA , DA A(T ) , jA,z = cA 0 T 2 A () d 0
NA,z = cA
(A)
(B)
B. Jajuee et al. / Chemical Engineering Science 61 (2006) 4111 – 4119
where dA/dT = sA∞ 0 e−s 0 T . If one substitutes A(T ) in Eq. (A) with dA/dT , the rate of mass transfer changes to function F : ∞ DA cA (dA/dT )2 dT . (Ca ) F= A2∞ 0 0 T 2 (dA/d) d 0 Eq. (B) can be rewritten for constant driving force (constant cA ) as ∞ 2 DA dA F = 2cA dT , (Cb ) 2 A∞ 0 dT 0 whence,
F = 2cA
D A s 2 0
∞
(exp(−2s0 T )) dT 0
√ DA s = 2cA . The clear inference from comparing Eqs. (A) and (D) is √ NA,z = 2F .
(D)
(E)
The reason for the close affinity between A(T ) and dA/dT is that A(T ) is an exponential function. The molar flux of diffusion of species A is also achieved by substituting A(T ) with dA/dT and considering a constant like C1 : jA,z = − DA
dcA dz
= C1 cA
DA dA/dT . 0 T 2 (dA/d) d 0
By analogy, the drag force on bubbles can be written as dv dA/dT = − . = C1 v d 0 T 2 (dA/d) d 0
(F)
(G)
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