GasâLiquid Mass-Transfer and Hydrodynamic Parameters in a

Ind. Eng. Chem. Res. 2000, 39, 2157-2168

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Gas-Liquid Mass-Transfer and Hydrodynamic Parameters in a Soybean Oil Hydrogenation Process under Industrial Conditions Benoit Fillion and Badie I. Morsi* Chemical and Petroleum Engineering Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15261

This paper presents some experimental data on the volumetric gas-liquid mass-transfer coefficient (kLa), liquid-side mass-transfer coefficient (kL), gas-liquid interfacial area (a), bubble Sauter mean diameter (dS), gas holdup (G), and solubility (C*) for N2 and H2 in soybean oil obtained in a 4 × 10-3 m3 agitated reactor operating under typical industrial conditions as a surface aeration reactor (SAR) and a gas-inducing reactor (GIR). The data were measured in wide ranges of temperature (373-473 K), pressure (0.1-0.5 MPa), mixing speed (10-23.3 Hz), and liquid height (0.171-0.268 m). The central composite statistical design approach was used to distribute the experiments and correlate the kLa and dS results. The solubility values for both gases were found to increase with pressure and temperature and to obey Henry’s law. The effect of temperature on Henry’s law constants was modeled using an Arrhenius-type equation. The mass-transfer and hydrodynamic parameters were significantly affected by the mixing speed and liquid height. At high mixing speeds and low liquid levels, bubbles coalescence was found to control the behavior of the gas-liquid interfacial area for H2 in the GIR, whereas the gas holdup dictated the behavior of aGIR at high mixing speeds and high liquid heights. For both gases, kLa and kL in the SAR increased with temperature. kLa, aGIR, dS, and G in the GIR decreased with temperature because of the decrease of the induced gas bubbles in the liquid. Under the operating conditions investigated, the mass-transfer and hydrodynamic parameters for both gases in soybean oil were independent of pressure. Also, under similar operating conditions, hydrogen mass-transfer and hydrodynamic parameters in the oil were higher than those of nitrogen because of its higher diffusivity and lower momentum. 1. Introduction The hydrogenation of vegetable oils, such as soybean, cottonseed, and rapeseed oils is an important process in the fat industry because of its wide applications to produce margarine, shortenings, and frying oils.1 The purpose of this process is to increase the melting point and to improve the stability of the oil to oxidation and heat.1 The industrial process is typically carried out in a three-phase autoclave reactor operating at 393-473 K and 0.1-0.5 MPa with a nickel-based catalyst loading ranging from 0.01 to 0.2 wt %.2,3 Since the first development of the hydrogenation process in the 1920s, a number of investigators studied the kinetics and mass transfer. A recent extensive review by Veldsink et al.,4 however, showed that no intrinsic, explicit kinetic model is available. Moreover, Albright,5 Bern et al.,6 Marangonzis et al.7 and Chen et al.8 reported that mass transfer is the rate-limiting step in most of the commercial reactors. As can be seen in Table 1, the majority of the authors measured the volumetric mass-transfer coefficient, kLa, by recording of the rate of change of the iodine value,6,8-10 by a chemical method,7,11-14 and by a physical method using a hydrogen probe.15 Bern et al.6 as well as Andersson and Berglin15 proposed correlations for hydrogen in rapeseed oil that relate kLa to the gas velocity, impeller diameter, mixing speed, and liquid volume. Chen et al.8 used a statistical approach to relate kLa for hydrogen * To whom correspondence should be addressed. E-mail: [email protected]. Fax: (412) 624-9639.

in soybean oil to the Reynolds number, power input per unit volume and the ratio of liquid height to reactor diameter. These authors obtained kLa data in different reactor sizes ranging from a bench-scale size to a commercial size. Recently, Trivedi and Vasishtha10 calculated kLa as a function of temperature, rate of change of iodine value, and the ratio of density to pressure for the castor oil-hydrogen system. Unfortunately, no kLa correlations, taking into account the effects of temperature and pressure, are available despite the fact that these operating conditions have a crucial impact on the design, modeling, and scale-up of the industrial hydrogenation process. As shown in Table 2, however, little solubility data for nitrogen and hydrogen in soybean oil are available in the literature. Wisniak and Albright2 and Wisniak and Stein16 calculated the solubility at high pressure (0.8-10 MPa) in cottonseed oil and jojoba oil, respectively. Andersson et al.17 measured the solubility of hydrogen in cottonseed oil at different pressures (0.1-1 MPa) and the solubility values appeared to obey Henry’s law. Bern et al.9 reported that the solubility of hydrogen in rapeseed oil from 0.03 to 1 MPa and 413-473 K obeys Henry’s law and follows an Arrhenius-type equation. Ganguli and van der Berg14 reported some solubility values at 0.1 MPa and at temperatures less than 363 K for the hydrogen-soybean oil system. Though some solubility data for hydrogen solubility in vegetable oil are available, there is no correlation for hydrogen in soybean oil under industrial conditions. Ganguli and van den Berg14

10.1021/ie990882e CCC: $19.00 © 2000 American Chemical Society Published on Web 05/17/2000

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Ind. Eng. Chem. Res., Vol. 39, No. 7, 2000

Table 1. Literature Survey of Mass-Transfer Data for Hydrogen in Vegetable Oils in Stirred Tank Reactors reference

liquid

reactor

Trivedi and Vasishtha10

castor oil

Stenberg and Schoö¨n11

methyl oleate GSR 0.04 dm3 3 baffles

Chen et al.8

soybean oil

0.2 dm3 to 30 m3 no baffles for bench and pilot

Andersson and Berglin15

rapeseed oil

Susu13

Susu and Ogunye12

GSR 5.5 dm3 1-2 impellers 4 baffles

P, MPa

T, K

N, Hz UG, m/s

solid

remarks

0.135-0.5

403-473 0.3-1 wt % Ni (22%)

2.7-5.8 N/A

I.V. value kLa ) 3.2 × 10-4(F/P) × exp(710/T) (dI.V./dt) kLa ) 0.0166-0.209 s-1 kLa increased with N

0.22-0.55

433-453 1 wt % Pt on C

16.7 0.0028

chemical method high catalyst loading gives better accuracy for kLa measurement

0.034-0.135 433-483 0.1 wt % Ni

1.67-10 N/A

I.V. value kLa ) 0.52 + (5.2 × 10-6) × (NRe) +4.1 × 10-5 (P*/VL) - 1.7(H/DT) 1.1 × 10-9(NRe) (P*/VL) - (5.2 × 10-12) × (NRe)2 + 8.1 × 10-11 (P*/VL)2 + 0.5(H/DT)2 kLa decreased w/batch size gas-liquid resistance ∼72% of total

GSR CSTR: 10 m3 4 baffles, 2 turbines pilot: 30 dm3

0.255

333

5 (CSTR) hydrogen probe 0.00049 kLa ) 0.37((N3.15dimp5.35)/ VL1.41)0.32UG0.30 4.3-14.2 (pilot) 0.0078 problems with probe at high T due to corrosion

groundnut oil

0.3 dm3 and 3.8 dm3 4 baffles, turbine

0.38-0.93

373-433 0.7-3 wt % G-111 Ni

soybean oil

0.3 dm3 4 baffles, turbine

0.24-0.42

413-453 0.7-2.2 wt % Ni 28.8 N/A

chemical method method unsuccessful at 373 K kLa ∼ 0.005-0.012 s-1

Ganguli and soybean oil van der Berg14

GSR 13 dm3 6/12 blades impeller

0.114

343

chemical method dS ∼ 1.3 × 10-3 m; kL ∼ 0.00015m.s-1

Marangozis et al.7 cottonseed oil

GSR 5 dm3 fan turbine no baffles

0.5

413-453 0.01-1 wt % Ni 6.7-32.3 0.001

Bern et al.6

rapeseed oil

GSR 30-500 dm3 4 baffles, turbine 24 m3

0.12-0.14

453

Bern et al.9

rapeseed oil

GSR 2 dm3 0.03-0.1 turbine, 2 baffles

wt % N/A Ni Raney

4.9-14.3 N/A

chemical method kLa ) 0.0103(P*/VL)0.34

homogeneous Ni 6.7-11.7 0.01-0.03

0.1 wt % Ni

413-473 0.087 wt % Ni

chemical method mass transfer is the rate-controlling step kLa∼0.016-0.235 s-1

30 dm3: 4-12.5 0.01-0.03 500 dm3: 3-8 0.035-0.055 24 m3: 1.3 N/A

I.V. value kLa ) 0.326(N3.15dimp5.35/ VL1.41)0.37UG0.32 kLa increases with N

4.2 0.0068

I.V. value kLa independent of initial I.V.

Table 2. Literature Survey of Solubility Data for N2 and H2 in Vegetable Oils reference

oil type

P, MPa

C*, kmol‚m-3

T, K

Bailey18

cottonseed

0.1

298-423

H2: -0.00372 + 1.74 × 10-5T N2: -0.00144 + 1.15 × 10-5T

Wisniak and Albright2

cottonseed

0.8-10

325-413

Henry’s law at P < 1 MPa (-3 - 71.2P + 0.48PT - 5.68 × 10-4PT2 - 0.252P2) × 10-3

Wisniak and Stein16

jojoba

0.8-6

323-523

Henry’s law

Andersson et al.17

cottonseed

0.1-1

403-463

(-1.342 + 0.012T) × 10-2P

rapeseed

0.03-1

413-473

0.203e-5900/RTP

Ganguli and van der Berg14

soybean

0.1

313 323 333 343 353 363

0.00195 0.00196 0.00212 0.00231 0.00234 0.00235

Gut et al.19

sunflower

0.3

473

0.0114

Koetsier et al.20

soybean

0.2

453

0.0072

Bern et

al.9

measured the gas holdup for hydrogen in soybean oil from the liquid height expansion and the bubble Sauter mean diameter was calculated from the gas holdup and

the interfacial area. The interfacial area was obtained using a chemical method in temperatures below 363 K.14 This paper is to present a statistical experimental

Ind. Eng. Chem. Res., Vol. 39, No. 7, 2000 2159 Table 3. Chemical Analysis and Fatty Acid Composition of Soybean Oil iodine value peroxide value, mequiv/kgoil moisture, ppm palmitic stearic oleic elaidic linoleic linolenic others

129.0-135.2 0.1-22 330-600

fatty acid composition in mass % C16:0 10.8-10.9% C18:0 3.63-3.83% C18:1 cis 21.38-22.04% C18:1 trans 0-0.05% C18:2 53.0-54.0% C18:3 8.15-8.25% C14:0-C24:0 1.03-2.94%

Table 4. Physical Properties of Soybean Oil properties molecular weight, kg‚kmol-1 viscosity, kg‚m-1‚s-1 density, kg‚m-3 surface tension, N‚m-1 vapor pressure, MPa

values

remarks

Mw ) 875

calculated from the fatty acid composition

log10 µL ) -3.073 + 46.6 × 106/T3 FL ) 1108 0.65 × T σL ) 0.0517 5.71 × 10-5T

Haighton et al.21 Bailey1 Bartsch22

log10 PS ) -1145/T + measured in our laboratory 0.476 at 273-473 K

Figure 1. Diffusivity of N2 and H2 in vegetable oils.

approach to investigate the solubility (C*), the masstransfer parameters (kLa, kL, and a) for N2 and H2 in soybean oil and the hydrodynamic parameters (dS and G) for both gases in soybean oil, in a 4 × 10-3 m3 surface-aerated (SAR) and gas-inducing (GIR) agitated reactor operating under typical industrial conditions. 2. Physico-Chemical Properties of the Systems Used A refined and bleached soybean oil provided by Perdue Farms, Inc. was used in the experiments. The chemical analysis and the physical properties are shown in Tables 3 and 4. The chemical analysis was conducted in accordance with the American Oil Chemists Society Standards. Pure nitrogen and hydrogen (99.999%) were employed in the experiments. Andersson et al.17 measured the diffusivity of hydrogen in cottonseed oil and concluded that the diffusivity does not follow the Stockes-Einstein relation. In this study, the equation proposed by Wilke and Chang23 was modified using literature diffusivity data7,14,17,19 to obtain Φ and n as follows,

DA )

1.858 × 10-15(ΦMw)1/2T µnV0.6 A

(1)

where Φ and n were found to be 3.8 and 0.6, respectively. VA is the molar volume of the diffusing gas at its normal boiling point,24 which is 0.0347 for N2 and 0.0143 for H2. Figure 1 shows a comparison between literature diffusivity values for hydrogen in soybean oil and those predicted using eq 1. As can be seen in this figure, a reasonable agreement can be reported. The diffusivity behavior of N2 in soybean oil presented in Figure 1 was calculated using eq 1 along with the values of Φ and n obtained for H2 and the molar volume of N2. We presume that because hydrogen diffusivities fit well the literature data, nitrogen diffusivity should also be accurately predicted using eq 1.

Figure 2. Schematic of the experimental setup.

3. Experimental Section 3.1. Experimental Setup. The experimental setup used in this study, schematically shown in Figure 2, is similar to that employed by Tekie et al.25 The reactor is a 4 × 10-3 m3 Zipperclave of 0.114-m i.d. and can be operated as a surface aeration reactor (SAR) or as a gasinducing reactor (GIR). The hollow shaft of the agitator contains four holes of 0.0024-m diameter, two in the gas phase and two in the liquid phase at the same level as the impeller. The holes were plugged for SAR experiments and opened in the GIR, enabling the induction of gas bubbles into the liquid phase. The reactor is equipped with four baffles located symmetrically, cooling coil, heating jacket, and two Jerguson sight windows. An agitator, 0.01-m o.d. hollow shaft, provided with a six-flat-blade Rushton turbine (0.05-m diameter) is used for mixing. A gas reservoir of 1 × 10-3 m3 capacity is employed as a gas preheater to heat the gas to a desired temperature. All pressures and temperatures in the reactor and in the preheater were recorded by a computer through an interface system by Keithley Instruments, Inc.

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Table 5. Values and Coded Variables for the Statistical Central Composite Design variable

coded variable

-2

T, K N, Hz H, m P, MPa

x1 x2 x3 x4

373 10 0.171 0.1

values of coded variables -1 0 1 398 13.3 0.195 0.2

423 16.7 0.219 0.3

448 20 0.244 0.4

2 473 23.3 0.268 0.5

3.2. Statistical Experimental Approach. In this study, a 2k central composite statistical design similar to that employed by Kim et al.,26 Li et al.,27 Inga and Morsi,28 and Tekie et al.25 was used to determine the effects of four operating variables on the mass-transfer characteristics. k stands for the number of variables which are temperature (T), pressure (P), liquid height (H), and mixing speed (N). For k ) 4 at five levels, the experimental space is a symmetric and rotatable hypersphere with equidistant design points from the center and a radius of 2. The response surface can be described by the following equation, k

xi2 ) 22 ∑ i)1

(2)

where xi represents the coded value of each variable defined by

[

xi ) 2

]

2Xi - (Xi,L + Xi,H) Xi,H - Xi,L

(3)

Xi is the value of the ith variable and Xi,L and Xi,H are the lowest and highest levels of Xi. It should be noted that the coded values as shown in Table 5 are normalized. The total number of test runs is n ) 2k + 2k + m where m is the number of repeats of the central point which was chosen to be 8.29 4. Calculations of Thermodynamic, Mass-Transfer, and Hydrodynamic Parameters 4.1. Calculations of C* and kLa. The solubility of the gas in soybean oil was calculated using a mole balance in the reactor and in the preheater as presented by Tekie et al.30 In the preheater, the Peng-Robinson EOS was used, and in the reactor, the ideal gas law was employed because the temperature was high and the pressure was low. The kLa values were obtained using the transient physical gas absorption technique (TPGA) similar to that of Tekie et al.30 The pressure decline in the reactor was followed as a function of time, and as the gas is absorbed in the liquid phase, the pressure decreases until it reaches thermodynamic equilibrium. C* was obtained from the equilibrium part of the P-t curve and kLa was calculated from the transient part. 4.2. Calculations of aSAR, kL, aGIR, dS, and EG. In the SAR, no bubbles are induced in the liquid phase and the gas-liquid interfacial area can be estimated as

aSAR )

Ω 1 ) VL H

(4)

The gas-liquid mass-transfer coefficient can then be obtained as

kL )

(kLa)SAR aSAR

(5)

Figure 3. Effect of temperature and pressure on C* for nitrogen in soybean oil.

If the gas holdup is small, kL values in the SAR and the GIR could be assumed the same and subsequently the interfacial area in the GIR (aGIR) can be written as

aGIR )

(kLa)GIR

× aSAR

(kLa)SAR

(6)

The bubble sizes were measured by means of a video camera connected to a video recorder. The images were digitized and analyzed with a particle analysis software OPTIMAS Version 4.1 by Bioscan, Inc. The bubbles appeared to be spherical and over 150 bubbles were measured for each run performed. The bubble Sauter mean diameter was calculated from the measured diameter of each bubble as follows: n

dS )

di3 ∑ i)1 n

(7)

di ∑ i)1

2

The gas holdup was calculated from the following equation,

(aGIR - aSAR)dS G ) 1 - G 6

(8)

where aGIR - aSAR is the interfacial area due to the gas bubbles. 5. Results and Discussion 5.1. Solubility, C*. The solubility values for nitrogen and hydrogen in soybean oil were obtained with an absolute deviation less than 7%. Figures 3 and 4 show that, for the two gases, the solubility increases with pressure and temperature. The effect of pressure on C* can be described by Henry’s law as

Ind. Eng. Chem. Res., Vol. 39, No. 7, 2000 2161

Figure 4. Effect of temperature and pressure on C* for hydrogen in soybean oil.

C* )

P1,F He

(9)

Figure 5. Apparent activation energy of absorption for N2 and H2 in soybean oil. Table 6. Henry’s Law Coefficients for N2 and H2 gas

Figure 5 shows Henry’s law constant for nitrogen and hydrogen presented as a function of the reciprocal of temperature, and as can be seen, the effect of temperature can be well modeled by an Arrhenius-type equation as

He ) H0 exp

(-∆E RT )

(10)

Table 6 lists the calculated apparent activation energy of absorption, ∆E, and the pre-exponential constant, H0, and as can be seen the activation energy value for hydrogen is of the same order of magnitude as the value (-5900 kJ‚kmol-1) reported by Bern et al.9 for hydrogen solubility in rapeseed oil. 5.2. Statistical Correlation of kLa. The experiments were conducted following the statistical central composite design technique and kLa values for nitrogen and hydrogen were obtained with an average absolute deviation less than 12%. The statistical software, Minitab Version 9.1 for Mainframe, was used to correlate the response, kLa, as a function of x1, x2, and x3 because x4 was found to have an insignificant effect on kLa. Generally, quadratic equations are used to model the response obtained with statistical design; however, if the behavior is nonlinear like that of kLa in the GIR, nonlinear terms may be used to correlate kLa. Equations 11-14 were obtained with a confidence level greater than 97.5% and a regression coefficient greater than 99%. In the SAR,

Nitrogen ln(kLa) ) -6.50 + 0.177x1 + 0.474x2 - 0.407x3 + 0.053x32 - 0.0798x2x3 (11)

N2

H2

T, K

He, MPa‚m3‚kmol-1

373 398 423 448 473 373 398 423 448 473

38.97 36.52 34.13 31.68 29.84 44.31 39.65 37.09 34.27 31.10

H0, MPa‚m3‚kmol-1

∆E, kJ‚kmol-1

10.99

-3955

8.84

-5000

Hydrogen ln(kLa) ) -5.99 + 0.229x1 + 0.417x2 - 0.473x3 0.0445x12 + 0.0524x32 - 0.126x2x3 (12) In the GIR,

Nitrogen ln(kLa) ) -4.86 - 0.179x1 + 0.708x2 - 0.596x3 + 0.0759x12 + 0.116x22 - 0.228x1x2 - 0.0763x2x3 0.0754x13 + 0.00269(x2 + 2.5)e2x3 + 1.28 tanh(0.3x2(5.5 - x32) + 0.1(2 - 4x3)) 0.339x1x2x3 (13) Hydrogen ln(kLa) ) -3.868 + 0.516x2 - 0.790x3 + 0.223x12 0.352ex1 + 0.326ex3 - 0.00378(x2 + 3)e2.5x3 + 2.099 tanh(0.3x2(8 - x32) + 0.1(2 - 6x3)) 0.927x1e-|x2| (14) Figure 6 presents a parity plot of predicted and experimental kLa values and very good agreement between both values is obvious. Equations 11-14 were employed

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Figure 6. Comparison between predicted and experimental kLa values for N2 and H2 in soybean oil.

Figure 7. Effect of operating variables on kLa values for N2 and H2 in soybean oil (SAR).

to develop response surfaces for kLa, kL, and aGIR as shown in Figures 7-10. 5.3. Statistical Correlation of dS. Similarly, the bubble Sauter mean diameters obtained in the GIR corresponding to nitrogen and hydrogen in soybean oil were statistically correlated with the following equations:

For nitrogen dS ) 0.375 - 0.117x1 + 0.516x2 - 0.351x3 + 0.0464x12 + 0.0154x32 + 0.0372x1x2 + 0.0437x2x3 (15) For hydrogen ds ) -0.701 - 0.392x1 + 0.639x2 + 0.157x32 + 0.0754x1x2 - 0.0512x23 + 1.44e0.2x1 - 0.194ex3 (16) Those equations were obtained with a confidence level greater than 97.5% and a regression coefficient greater

Figure 8. Effect of operating variables on kLa values for N2 and H2 in soybean oil (GIR).

Figure 9. Effect of operating variables on kL values for N2 and H2 in soybean oil.

than 98%. Figure 11 shows a comparison between experimental and predicted values using eqs 15 and 16. 5.4. Effect of the Operating Variables on kLa. 5.4.1. Effect of Mixing Speed on kLa. The effect of mixing speed on kLa for N2 and H2 in soybean oil in the SAR and GIR are shown in Figures 7 and 8, respectively. As can be seen in these figures, kLa values in the SAR and GIR for both gases appear to increase with mixing speed. Similar results were reported by several investigators for hydrogen in vegetable oil.6,8,10,15 In the SAR, the increase of kLa values with mixing speed is due to the increase of kL because the interfacial area in this reactor type can be considered constant. In the GIR, however, above the critical mixing speed for gas induction, gas bubbles are induced through the hollow shaft into the liquid, leading to an increase of the gas-liquid interfacial area. Therefore, in the GIR, both kL and aGIR increase with mixing speed, resulting in an increase of kLa. The effects of mixing speed on kL, aGIR, dS, and G are discussed in the following.

Ind. Eng. Chem. Res., Vol. 39, No. 7, 2000 2163 Table 7. Comparison between Measured and Literature NCR Values reference Martin32

Figure 10. Effect of operating variables on aGIR values for N2 and H2 in soybean oil.

Figure 11. Comparison between predicted and experimental dS values for N2 and H2 in soybean oil.

As shown in Figure 9, kL values increase with mixing speed, which is contrary to the finding of Ganguli and van der Berg31 who reported that kL was independent of mixing speed. Increasing mixing speed increases the turbulence and surface renewal rate at the gas-liquid surface, and consequently kL. At high liquid level (0.267 m), the relative change of kL values varied from 2 to 3 times when the mixing speed increased from 10 to 23.3 Hz, while kL increased from 12 to 14 times for the same increase of mixing speed at low liquid height (0.171 m). This means that, at high liquid level, kL was slightly dependent on the mixing speed, whereas at low liquid height, kL was strongly affected by the turbulence created by the impeller at the gas-liquid interface. Under these operating conditions, increasing the turbulence decreased the liquid film thickness which resulted in increasing kL. The effect of mixing speed on the gas-liquid interfacial area for nitrogen and hydrogen in the GIR is depicted in Figure 10. For both gases, at a mixing speed below the critical speed for gas induction, NCR, few bubbles were induced into the liquid phase, and accord-

impeller

Fr number

predicted NCR, Hz

flattened 0.097-0.254 cylinder

7.6-12.3

Joshi and Sharma34 pipe 0.156-0.225 flattened 0.107-0.156 cylinder

9.6-12.2 8.0-9.6

Sawant et al.36

disk

0.21(µL/µWater)-0.11 10.4

Rielly39

concave blade

0.305

13.4

Heim et al.38

four-pipe six-pipe disk

0.155 0.162 0.230

9.6 9.8 11.7

this study

rushton

0.323

13.8 (measured for N2 and H2)

ingly the gas-liquid interfacial area in the GIR was independent of mixing speed. Above the critical mixing speed, however, the pumping capacity of the impeller increased,32 leading to an increase of induced gas bubbles and gas holdup as reported by numerous investigators,25,30,32-38 and subsequently aGIR. For both gases, the critical mixing speed was found to be 13.8 Hz at 423 K and 0.219 m. Table 7 reports values of Froude number obtained by different investigators, and the predicted critical mixing speed for gas induction. As can be seen in Table 7, the critical values predicted with available literature correlations are lower than the measured value which can be related to the difference in liquid viscosity and the nature of the impeller used in the present study. For instance, Martin,32 Joshi and Sharma,34 Rielly et al.,39 and Heim38 used the waterair system with lower viscosity than soybean oil. Also, although Sawant et al.36 modified the Froude number with liquid viscosity, the geometry of the Denver-type flotation cell differs from the gas-inducing reactor used in this study. The effect of mixing speed on the gasliquid interfacial area can be explained by the behavior of the bubble Sauter mean diameter and gas holdup as shown in Figures 12-14. The bubble Sauter mean diameters for both gases are found to increase with mixing speed as depicted in Figures 12 and 13. This finding agrees with the available literature that reported an increase of bubble coalescence with gas flow rate in gas-inducing reactors.39,40 Increasing the bubble size should decrease the gas-liquid interfacial area; however, aGIR did not decrease with mixing speed because of the induction of a large number of gas bubbles in the liquid phase, leading to an increase of the gas holdup as shown in Figure 14. For the hydrogen-soybean oil system, the gas-liquid interfacial area values slightly decrease with mixing speed, at high agitation and low liquid height, because of bubbles coalescence. This is because under these conditions the gas flow rate induced into the liquid through the hollow shaft was so high that a secondary circulation loop was formed. Also, because hydrogen bubbles have a small momentum, they most likely recirculate around the impeller and tend to coalesce;41 hence, the bubble Sauter mean diameters increase. Therefore, for H2 it appears that, at high mixing speed and low liquid height, bubble Sauter mean diameters control the behavior of aGIR, whereas at high mixing speed and high liquid levels, the gas holdup dictates the behavior of aGIR. 5.4.2. Effect of Liquid Height on kLa. As can be seen in Figures 7 and 8, kLa values in the SAR and GIR

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Figure 12. dS values for N2 and H2 in soybean oil in the GIR.

Figure 13. Effect of operating variables on dS values for N2 and H2 in soybean oil in the GIR.

Figure 14. Effect of operating variables on G values for N2 and H2 in soybean oil in the GIR.

for both gases decrease with liquid height, which can be related to the behaviors of kL and a. In the SAR, the interfacial area for both gases a priori equals the reciprocal of the liquid height and increasing the liquid height decreases the interfacial area as well as kL, and subsequently kLa. In the GIR, kL and aGIR for nitrogen appear to strongly decrease with increasing liquid height, leading to a decrease of kLa. For hydrogen, on the other hand, aGIR decreases with liquid height at low mixing speed, whereas at high mixing speed, the values increase and then decrease. Although aGIR for hydrogen increases with liquid height at high mixing speed, kLa values in the GIR decrease because of the decrease of kL. The effects of liquid height on kL, aGIR, dS, and G are discussed in the following. Figure 9 shows that kL values for both gases are strongly dependent on the liquid height. For instance, at 10 Hz, kL was almost independent of liquid height, whereas at 23.3 Hz, kL decreased by 10-15 times. This behavior is expected because increasing the liquid height increases the hydrostatic head above the impeller

which decreases the turbulence and the power input per unit liquid volume, and subsequently kL. As shown in Figure 10, the gas-liquid interfacial area for nitrogen, on one hand, in the GIR appears to strongly decrease with increasing liquid level. For hydrogen, on the other hand, at low mixing speed, aGIR decreases with liquid height, whereas at high mixing speed, the values increase and then decrease. Supposedly, the gas-liquid interfacial area should increase because bubble Sauter mean diameters shown in Figures 12 and 13 appear to decrease with liquid height. The gas holdup for both gases, however, is found to decrease with liquid height as shown in Figure 14. Increasing the liquid height decreases the pumping capacity of the impeller and thus increases the critical mixing speed for gas induction,34-36,38 leading to a sharp decrease of the number of induced gas bubbles, that is, the gas holdup as reported by several investigators,25,40,42 and subsequently aGIR. The decrease of the gas bubble population explains the decrease of the bubble Sauter mean diameter because of the decrease of the probability for the

Ind. Eng. Chem. Res., Vol. 39, No. 7, 2000 2165

bubbles to coalesce in the impeller region, as reported by van’t Riet et al.41 Thus, for hydrogen, it seems that, at high mixing speed and low liquid height, the bubble Sauter mean diameter controls the behavior of the gas-liquid interfacial area, whereas at high mixing speed and high liquid height, the gas holdup governs the behavior of aGIR. 5.4.3. Effect of Temperature on kLa. The effect of temperature on kLa for both gases in the SAR and GIR are depicted in Figures 7 and 8. In the SAR, kLa values appeared to increase with temperature whereas the interfacial area appeared to be independent of temperature; thus, kLa increases because of the increase of kL. In the GIR, however, kLa values for N2 and H2 decreased with temperature, which is the resultant of two opposite trends: kL increases with temperature and aGIR decreases with temperature. The effects of temperature on kL, a, dS, and G are discussed in the following. As shown in Figure 9, kL increases with temperature since it is proportional to the gas diffusivity, as depicted in Figure 1, to the power 0.5-1 according to the penetration theory and the two-film model.43 Figure 10 shows that, in the GIR, the gas-liquid interfacial areas for both gases decrease with temperature. This behavior can be related to the decrease of the number of gas bubbles induced. The bubble population was observed to drastically decrease with temperature, leading to a decrease of the bubble Sauter mean diameter and gas holdup as illustrated in Figures 13 and 14. As can be seen in these figures, the bubble Sauter mean diameters appear to decrease with temperature. This is because as the temperature increases, the gas holdup and bubble population decrease, and subsequently the gas bubbles were not likely to coalesce.39,40 As shown in Figure 14 the gas holdups for both gases decrease with temperature, which can be attributed to the decrease of viscosity with temperature; hence, the liquid viscosity was estimated to drop from 6.7 × 10-3 to 2.3 × 10-3 Pa‚s in the temperature range investigated. This behavior was similar to that reported by He et al.42 for water/CMC solution in a gas-inducing reactor. They reported that the induced gas flow rate as well as the gas holdup and bubble population increased with viscosity as long as the viscosity was lower than 5.5 × 10-3 Pa‚s. Also, at viscosities higher than 5.5 × 10-3 Pa‚s, the induced gas flow rate was found to decrease. This finding agrees with that by Aldrich and van Deventer44 who found an optimum viscosity value for the induced aeration rate, which is system-dependent. The change of the trend of induced gas flow rate with viscosity reveals a transition of the flow regime. At low viscosity, that is, high temperature, small cavities, called “clinging cavities” as reported by van’t Riet and Smith45 and Bruijn et al.,46 are attached to the impeller blades. As the viscosity increases, the cavities become bigger and hence the pressure behind the blade decreases, leading to an increase of the impeller suction. Furthermore, at higher viscosity, that is, low temperature, stable cavities are formed46 and the impeller suction efficiency diminishes. 5.4.4. Effect of Pressure on kLa. As can be seen in Figures 7 and 8, in the SAR and GIR, kLa remained independent of pressure for nitrogen and hydrogen in soybean oil. kLa values were reported to increase,25,27,28,47 decrease,27,28,47 or remain constant with pressure.28,48

The pressure could affect both the liquid-side masstransfer coefficient and the gas-liquid interfacial area as discussed below. kL values appear to be independent of pressure in the range investigated as shown in Figure 9. Increasing the pressure increases the solubility of the gas in soybean oil, which in return could alter the density, viscosity, and surface tension of the liquid phase. Because the solubility values of nitrogen and hydrogen in soybean oil were small under the operating conditions investigated, kL was not affected by pressure. The interfacial area appeared to also be independent of pressure as depicted in Figure 10. The increase of pressure could have increased the gas-liquid interfacial area by a decrease in the bubble size as reported by Chang and Morsi,47 Li et al.,27 and Inga and Morsi.28 This behavior, however, was not observed because the pressure range is small, less than 0.5 MPa. Figures 12 and 13 show that the bubble Sauter mean diameters for both gases are not affected by pressure because of the presence of small, rigid spherical gas bubbles which are able to withstand the small pressure. Also, as shown in Figure 14, the gas holdup is unaltered by pressure because the change of the physical properties of the liquid such as density, surface tension, and viscosity was too small to change the induced gas flow rate and subsequently the gas holdup. 5.4.5. Effect of Gas Nature on kLa. As shown in Figures 7 and 8, kLa values of hydrogen are greater than those of nitrogen in the SAR and GIR under the same operating conditions. In the SAR, kL is dependent on the gas nature, and in the GIR both kL and a are dependent on the gas nature. Hydrogen kL values appeared to be higher than those for nitrogen as depicted in Figure 9. This behavior was expected because hydrogen diffusivity is greater than that of nitrogen under the same temperature as described by eq 1, and kL is proportional to the diffusivity to the power 0.5-1. The interfacial area and bubble Sauter mean diameter values of hydrogen are greater than those of nitrogen as shown in Figures 10, 12, and 13. Though hydrogen bubble sizes are greater than those of nitrogen, the hydrogen gas-liquid interfacial area is greater than that of nitrogen. This can be related to the difference between gas holdup values as can be observed in Figure 14 where the hydrogen gas holdup values are much greater than those of nitrogen. Hydrogen bubbles momentum is smaller than that of nitrogen bubbles; therefore, hydrogen bubbles tend to be retained longer in the liquid because of the tangential velocity provided by the impeller. The longer gas bubble retention time contributes to the increase of the gas bubbles population and subsequently the gas holdup. Nitrogen bubbles, however, disengage faster and hence the gas holdup is smaller than that of hydrogen. 5.4.6. Effect of Reactor Type on kLa. Figures15 and 16 show that the behavior of kLa values obtained in the SAR are different from those obtained in the GIR for nitrogen and hydrogen in soybean oil under the operating conditions used. In the SAR, kLa values increased up to 7 times, while in the GIR, kLa values drastically increased up to 500 times because of the increase of the gas holdup. Therefore, in the SAR, kLa values are controlled by kL, whereas in the GIR, kLa values are governed by both kL and a. Under the critical mixing speed for gas induction, no bubbles are induced

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Figure 15. kLa values for nitrogen in soybean oil in the SAR and GIR.

Figure 16. kLa values for hydrogen in soybean oil in the SAR and GIR.

in the GIR and the two reactor types appeared to have the same kLa values. As the gas is induced into the liquid, however, the gas-liquid interfacial area and subsequently kLa are strongly affected by the gas holdup and the bubble size as discussed previously. Figure 17 shows a plot of kLa versus the modified power input per unit liquid volume as defined by Bern et al.6 At high mixing speeds and low liquid heights, kLa values in the GIR reached the region of kLa values for the gas-sparging reactor. Our data can be compared well with available literature values despite the fact that kLa values are expected to be different in the GSR and GIR as discussed by Forrester et al.49 Figure 17 also shows that more energy is needed in the GIR to obtain the same kLa values as those in the GSR. The GIR, however, does not require additional cost when compared with that of the GSR because the gas is selfinduced into the liquid. Therefore, the gas-inducing reactor can be a viable alternative to GSR.

6. Conclusions The mass-transfer and hydrodynamic parameters for nitrogen and hydrogen in soybean oil were obtained in a 4 × 10-3 m3 agitated reactor operating in a surface aeration and in gas-inducing modes under typical industrial conditions. The effect of the operating variables (T, P, N, and H) on the mass-transfer parameters were statistically studied by means of the central composite design and the following conclusions can be drawn: 1. kLa in the SAR and the GIR, kL, aGIR, dS, and G strongly increased with mixing speed and decreased with increasing liquid height. 2. For the hydrogen-soybean oil system, at high mixing speed and low liquid height, the gas-liquid interfacial area was found to decrease with increasing mixing speed and decreasing liquid height because of bubbles coalescence.

Ind. Eng. Chem. Res., Vol. 39, No. 7, 2000 2167 NCR ) critical mixing speed, Hz NRe ) Reynolds number: FNdimp2/µ P ) pressure, MPa P* ) power input, W P1,F ) equilibrium partial pressure of gas, MPa Pm ) mean partial pressure of gas (P1,I + P1,F)/2, MPa PS ) saturation vapor pressure, MPa R ) universal gas constant, kJ‚kmol-1‚K-1 T ) temperature, K t ) time, s UG ) superficial gas velocity, m‚s-1 VA ) gas molar volume, m3‚kmol-1 VL ) liquid volume, m3 Xi ) value of the ith variable in eq 3, unit of the variable x1 ) coded variable for T (T - 423)/25 x2 ) coded variable for N (N - 16.7)/3.3 x3 ) coded variable for H (H - 0.219)/0.024 x4 ) coded variable for P (P - 3)/1 Greek Symbols

Figure 17. kLa values comparison between literature data and this study for H2 in vegetable oil.

3. For both gases, kLa as well as kL in the SAR increased with temperature, whereas kLa in the GIR decreased with temperature because of the decrease of aGIR. The bubble size appeared to decrease with temperature because of the decrease of the gas holdup, leading to a smaller probability for gas bubbles to coalesce. 4. The mass-transfer and hydrodynamic parameters appeared to be independent of pressure from 0.1 to 0.5 MPa under the operating conditions investigated. 5. kLa in the SAR and GIR, kL, aGIR, dS, and G values of hydrogen were higher than those of nitrogen, under similar operating conditions. 6. kLa values in the GIR were found to vary from those in the SAR to those in the GSR. Acknowledgment The authors acknowledge Air Products and Chemicals, Inc., for their financial support and Perdue Farms, Inc., for providing and analyzing the soybean oil. Nomenclature a ) gas-liquid interfacial area per unit liquid volume, m-1 C* ) gas solubility in the liquid at equilibrium, kmol m-3 di ) bubble geometrical diameter, mm dimp ) impeller diameter, m dS ) bubble Sauter mean diameter, mm DA ) diffusivity, m2 s-1 DT ) tank diameter, m Fr ) Froude number: NCR2dimp2/(gHL) H ) liquid height above the bottom of the reactor, m He ) Henry’s constant, MPa‚m3‚kmol-1 HL ) liquid height above the impeller, m H0 ) pre-exponential constant in eq 10, MPa‚m3‚kmol-1 I.V. ) iodine value (100 × number of double bonds × 2 × 127/MwOil) kL ) liquid-side mass-transfer coefficient, m s-1 kLa ) volumetric liquid-side mass-transfer coefficient, s-1 Mw ) molecular weight of oil, kg kmol-1 N ) mixing speed, Hz

∆E ) apparent absorption activation energy, kJ‚kmol-1 G ) gas holdup Φ ) coefficient in eq 1 µ ) viscosity, kg‚m-1‚s-1 or Pa‚s F ) density, kg‚m-3 σ ) surface tension, N‚m-1 Ω ) cross section of the reactor, m2 Acronyms GIR ) gas-inducing reactor GSR ) gas-sparging reactor SAR ) surface aeration reactor

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Received for review December 9, 1999 Revised manuscript received March 14, 2000 Accepted March 20, 2000 IE990882E

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