Ind. Eng. Chem. Res. 1997, 36, 3879-3888
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Mass Transfer Parameters of O2 and N2 in Cyclohexane under Elevated Pressures and Temperatures: A Statistical Approach Zeru Tekie, Jianjun Li, and Badie I. Morsi* Chemical and Petroleum Engineering Department, University of Pittsburgh, Pittsburgh, Pennsylvania 15261
The solubility, volumetric mass transfer coefficient, gas-liquid interfacial area, mass transfer coefficient, gas holdup, and bubble Sauter mean diameter for O2 and N2 in liquid cyclohexane were obtained in 4-L gas-inducing and surface-aerated agitated reactors. The modified PengRobinson equation of state and the transient gas absorption and photographic techniques were employed. The experiments were statistically designed and the results were statistically correlated with a 95% confidence level. The solubilities for O2 and N2 showed an increase with pressure and temperature, and Henry’s law adequately modeled the values. All mass transfer parameters obtained were found to be higher in the gas-inducing than those in the surfaceaerated reactor. Mixing speed and liquid height significantly affected the volumetric mass transfer coefficients and gas holdup in both reactors. The pressure and temperature slightly affected the volumetric mass transfer coefficients whereas the bubbles Sauter mean diameter for both gases remained constant at about 0.76 mm. 1.0. Introduction The liquid-phase cyclohexane oxidation process is primarily used to produce cyclohexanol and cyclohexanone, which are widely consumed in the production of caprolactam and adipic acid. Caprolactam and adipic acid are mainly utilized as monomers in nylon-6 and nylon-6,6 polymerization processes. Cyclohexane, adipic acid, and caprolactam were among the top 60 produced chemicals in the U.S. in 1995 with annual productions of 2.13, 1.80, and 1.58 billion pounds, respectively (ACS, 1996). Conventionally, cyclohexane oxidation is carried out in a liquid phase using air as a feed gas and liquid cyclohexane with or without catalyst. Literature data on the kinetics of cyclohexane oxidation are numerous (Spielman, 1964; Berezin et al., 1966; Alagay et al., 1974; Emanuel et al., 1984; Suresh et al., 1988a; Rao, 1990; Wu and Shi, 1992), and several investigators (Alagay et al., 1974; Suresh et al., 1988b; Khar’kova et al., 1989; Pohorecki et al., 1992; Wu and Shi, 1992) proposed mathematical models for catalytic and noncatalytic liquid phase cyclohexane oxidation processes. Unfortunately, despite the fact that these investigators recognized the importance of the kinetics and gasliquid mass transfer, most of them, except Suresh et al. (1988b), either neglected the effect of mass transfer or used predictions from literature correlations developed for an air-water system under ambient conditions. This is not surprising, since available literature data on mass transfer in liquid-phase cyclohexane oxidation process are actually scarce (Tekie et al., 1997). In this study, a statistical approach was used to obtain the solubility (C*), volumetric mass transfer coefficient (kLa), interfacial area (a), mass transfer coefficient (kL), gas holdup (G) and Sauter mean diameter (dS) of O2 and N2 in liquid cyclohexane. These mass transfer parameters were obtained in wide ranges of pressures (7-35 bar), temperatures (330-430 K), mixing speeds (400-1200 rpm), and liquid heights (0.170.27 m) in a gas-inducing reactor (GIR) and a surface * To whom correspondence should be addressed: telephone, (412) 624-9650; fax, (412) 624-9639; e-mail, morsi@ engrg.pitt.edu. S0888-5885(96)00761-0 CCC: $14.00
Figure 1. Schematic of the experimental setup.
aeration reactor (SAR). The justification of using pure oxygen in the experiments stems from the fact that with the advent of a specialized liquid phase oxidation reactor (LOR), using pure oxygen instead of air in hydrocarbon oxidation processes is more advantageous, since the process can be carried out under lower pressures and temperatures (Roby and Kingsley, 1996). 2.0. Experimental Section The experimental setup used is schematically depicted in Figure 1 and it consists mainly of the following units: reactor, preheater, computer/data acquisition/ control unit, and high shutter speed video and image processing system. The reactor is a 4-L Zipperclave of 0.114 m inside diameter. It is equipped with four symmetrically located baffles, a 0.01 m outside diameter hollow shaft provided with two holes (0.0015 m) located in the gas and another two in the liquid phase, and a six flat-blade turbine impeller (0.05 m diameter). The reactor is glass lined and can be operated in surfaceaeration or gas-inducing mode, depending upon whether the holes in the hollow shaft are sealed or not. The reactor is modified by welding two Jerguson sight windows to allow the measurement of bubble sizes under high temperature and pressure and is provided with a heating jacket fitted with four heating elements. A shutter speed video camera (Panasonic Model PVIQ604D) was used to record live images of gas bubbles © 1997 American Chemical Society
3880 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997
and the recorded image was processed and analyzed using Photoshop and Global Image software, respectively. Automatic data acquisition and control of the entire experimental setup were carried out using a Model 575 measurement and control system from Keithley corporation. For an oxygen-cyclohexane system, reaction free mass transfer parameters were measured within the induction period (Suresh et al., 1988c; Tekie et al., 1997) which lasted about 20-30 min depending on the rate of mass transfer and temperature used. The original liquid volume in the reactor was varied to ensure the desired liquid level as set by the experimental design. The properties of gaseous O2 and N2 and liquid cyclohexane used can be found elsewhere (Tekie et al., 1997). The safety issue associated with using an oxygen/ cyclohexane system has been rigorously followed as discussed by Tekie et al. (1997) and Suresh et al. (1988c).
Table 1. Distribution of the Experiments According to the Central Composite Design
3.0. Statistical Approach The statistical design and analysis method is an effective tool which allows studying a multivariable system through a statistically designed specific number of experiments. Some of the advantages of statistical design are adequate observation of variables, optimum number of experiments, and highly accurate statistical correlations (Montgomery, 1991). A central composite experimental design and analysis technique, similar to that employed by Li et al. (1996a) and Kim et al. (1994), was used in this study. In this technique, for k independent variables at five levels the total number of experiments is 2k factorial points augmented by 2k axial points and a number of replicates of the central point. The factorial and axial points are equidistant from the central point. In this study, four variables, temperature, pressure, mixing speed, and liquid height, were studied, and hence k ) 4. The coded variables Xi (i )1, 2, 3, 4) as defined by eq 1 were used in the distribution and analysis of the experiments
Xi )
Ei - Ei,c ∆i
(1)
where Ei and Ei,c are the values of the ith variable at any point and the central point, respectively, and ∆i is the step size of the ith variable. The distribution of experiments for k ) 4 can be mathematically represented by eq 2 4
Xi2 ) 22 ∑ i)1
(2)
The coordinates of the experiments with the coded variables are (0, 0, 0, 0) for the central point, ((1, (1, (1, (1) for the factorial points, and ((2, 0, 0, 0), (0, (2, 0, 0,), (0, 0, (2, 0), and (0, 0, 0, (2) for the axial points. Table 1 shows the spatial settings of all the experiments and Table 2 shows the range of each operating variable and its coded value.
Table 2. Operating Variables and Their Coded Values variable N (Hz) P (bar) T (K) H (m)
coded variable
-2
X1 X2 X3 X4
6.67 7 330 0.171
10.00 14 355 0.195
13.33 21 380 0.220
16.67 28 405 0.244
2 20.00 35 430 0.268
4.2. Bubble Size, dS. Several direct techniques, such as high-speed flash photography (Burgess and Calderbank, 1975; Veljkovic and Skala, 1988; Kasireddy and Taweel, 1990; Takahashi and Nienow, 1993) and light scattering (Calderbank, 1959; Calderbank and Moo-Young, 1961) were used to measure gas bubble size. These techniques, however, are limited to nonopaque, low-pressure, and low-temperature systems. Indirect techniques, including ultrasound (Chang and Harvel, 1992), electrical resistivity probe (Burgess and Calderbank, 1975; Sun and Furusaki, 1988), photoelectric capillary (Lu et al., 1993), acoustic (Pandit et al., 1992), capillary probe (Barigou and Creaves, 1992), and gas disengagement (Sriram and Mann, 1977; Daly et al., 1992), have also been employed. It is imperative to mention that most of these indirect techniques cannot be applied at high pressures and temperatures. In this study, a high shutter speed video camera was used to record live images of gas bubbles through the sight window of the reactor. The images were taken above, below, and around the impeller. The recorded images were digitized, processed, and analyzed using Adobe Premier, Photoshop, and Global image softwares, respectively, as shown in Figure 2. For each run, between 400 and 500 gas bubbles were counted and the Sauter mean diameter was calculated using eq 3
4.0. Measurement and Calculation Methods 4.1. C* and kLa. The C* and kLa values for O2 and N2 in cyclohexane in both GIR and SAR were obtained using the Peng-Robinson equation of state (Peng and Robinson, 1976) as modified by Panagiotopolous and Reid (Panagiotopolous and Reid, 1985) and the transient physical absorption technique (Chang and Morsi, 1991), respectively.
values of coded variables -1 0 1
M
dS )
nidB,i3 ∑ i)1 M
∑ i)1
nidB,i2
where M is the total number of gas bubbles.
(3)
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 3881
The mass transfer coefficient, kL can be estimated from
kL ) (kLa)SAR/aSAR
(5)
Assuming kL values in both SAR and GIR at the same operating conditions are the same, the total gas-liquid interfacial area in the GIR can be calculated from
aGIR ) (kLa)GIR/kL
(6)
Since the total gas-liquid interfacial area in the GIR is actually the sum of the area of the gas-liquid interface and the interfacial area due to induced gas bubbles, then
aGIR ) aSAR + aBUB
(7)
where aBUB is the gas-liquid interfacial area due to induced gas bubbles. Using the above equations, aBUB can be calculated as
[
aBUB ) aSAR
Figure 2. Digitized gas bubbles under high pressure and temperature.
4.3. Interfacial Area (a) and Mass Transfer Coefficient (kL). The gas-liquid interfacial areas have been measured for different systems using physical as well as chemical methods. Several physical optical methods such as photography, light reflection, and light scattering are among the commonly used physical techniques. All these techniques, however, are restricted to transparent reactors and low gas holdup fractions (Chang and Harvel, 1992). Other less frequently used physical techniques include real-time neutron radiography (Chang and Harvel, 1992) and γ-ray radiography (Bukur et al., 1996). In this study, the interfacial area was calculated indirectly from kLa values measured in the GIR and SAR as discussed below. In the SAR, visual observations showed that even at high mixing speeds few gas bubbles are entrained through the flat gas-liquid interface. Also, when a high-resolution differential pressure (DP) cell was used to measure gas holdup, very small values (
