Ind. Eng. Chem. Res. 2007, 46, 677-683
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Modeling of Trickle Bed Reactors Involving Beds of Different Configurations under Low and High Interaction Regimes Ajay Bansal,*,† Ravinder K. Wanchoo,‡ and S. K. Sharma‡ Department of Chemical and Bio Engineering, National Institute of Technology, Jalandhar 144011, India, and Department of Chemical Engineering and Technology, Panjab UniVersity, Chandigarh 160014, India
The Lockhart-Martinelli type model originally proposed for two-phase pressure drop estimation in the high interaction regime by Pinna et al. [AIChE J. 2001, 47, 19-30] is modified and extended to high as well as low interaction regimes. The proposed modified model contains an adaptive parameter, Rm. The two-phase pressure drop is related to the Lockhart-Martinelli parameter and liquid saturation. The experimental data corresponding to the two-phase pressure drop and dynamic liquid saturation, for an air-water system on different packings are used to determine the values of Rm for each packing under low and high interaction regimes. It is observed that with decrease in particle sphericity the adaptive parameter, Rm, increases for the same hydrodynamic regime. The variation of adaptive parameter, Rm, for a particular packing with respect to adaptive parameter, Rsph, for spherical packing is found to be a function of particle sphericity. 1. Introduction Multiphase reaction systems are common in chemical engineering practice. They are used in petroleum, petrochemical, chemical, biochemical, and electrochemical processing industries along with other wide applications.1 Among the different threephase reaction systems encountered in industrial practice, trickle bed reactors (TBRs) are the most widely used. With the continuous evolution of the products relying on TBR technology to meet, concomitantly, environmental regulations and economical constraints, any slight modification in the design or performance of these reactors can result in substantial benefits. The annual processing capacity of trickle bed reactors for petroleum sectors alone was estimated to be at 1.6 billion metric tons.2 With increasing market needs for light oil products such as middle distillates and decreasing demands for heavy cuts, the refiners have to keep improving their processing units for upgrading heavy oil and feedstock.3 This stimulates continued research efforts aimed at better understanding of the TBR phenomenon and operation. Any improvement in the understanding of physicochemical phenomena taking place within a TBR may be vital for the accomplishment of better modeling, process design, product quality, cost reduction, and/ or environmentally sustainable technologies. In the present study, a two-phase pressure drop has been measured experimentally for the TBRs of different bed configurations and the model of Pinna et al.4 has been revisited and extended to the low interaction regime in addition to the high interaction regime. Figure 1. Flow through a single channel.
2. Model for the Estimation of Two-Phase Pressure Drop in a Cocurrent Down-Flow Trickle Bed Reactor (Pinna et al.)4 Pinna et al.4 have proposed a theoretical Lockhart-Martinelli5 type model to predict the two-phase pressure drop in the high interaction regime. A procedure similar to the one proposed
earlier by Taitel and Dukler6 for stratified two-phase pipe flow was adopted and was modified to apply to the specific fluid dynamic system (Figure 1). The model equations proposed were as follows:
X2 ) R * To whom correspondence should be addressed. Tel.: +91-812690301 Ext 399. Fax: +91-81-2690932. E-mail:
[email protected]. † National Institute of Technology. ‡ Panjab University.
φ2 )
h 2)1.8 (1 - δ h )0.2(1 - δ δ h 4.8
1 (1 - δ h )0.2(1 - δ h 2)1.8
10.1021/ie060671r CCC: $37.00 © 2007 American Chemical Society Published on Web 12/23/2006
(1) (2)
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Ind. Eng. Chem. Res., Vol. 46, No. 3, 2007
with the liquid saturation given by
β)1-δ h2
(3)
The proposed model contained the only adaptive parameter, R, defined as follows:
R)
fI fG
(4)
which had been regarded as a constant. The information about the geometry of the packing, i.e., tortuosity, equivalent diameter of the channel, etc., was not directly considered in the final form of the model eqs 1 and 2. Such geometrical parameters are assumed to be implicitly taken into account in the evaluation of single-phase pressure drops. For low ratios of L/G (i.e., low values of X), eqs 1 and 2 predict that δ h and φ approach unity and infinity, respectively. Under these conditions, liquid saturation β f 0. For high ratios of L/G (i.e., high values of X), the model estimates a liquid saturation near unity and φ f 1. To estimate the adaptive parameter, R, the authors fitted eq 1 to the liquid saturation measurements by minimizing the function: N
F(R) )
(βi,cal - βi,exp)2 ∑ i)1
(5)
and the best fit was obtained with a value of R ) 3.56 ( 0.302. Once R is known, φ can be estimated using eqs 1 and 2. These model equations do not involve any other parameter. Further, these authors observed that the analysis of the model to variations in the value of R indicated that the predictions of β and φ are not strongly sensitive to an oscillation of R of about 42%, leading to relative variations of less than 30%. Limitations of the Model. Pinna et al.4 have made all the experimentation in the high interaction regime and tested the validity of the model for the same region. Although, a number of TBR processes operate in the low interaction regime or near the transition,7-10 and there is a need to extend the model to the low interaction regime as well. The model explicitly requires the estimation of single-phase pressure drop for further evaluation of the Lockhart-Martinelli parameters. The single-phase pressure drop has been measured by using classical Ergun constants with E1 ) 150 and E2 ) 1.75 for different systems of packings. Further, it had been assumed that the bed geometrical parameters like tortuosity and equivalent channel diameter were implicitly taken into account by Ergun’s constants. However, it is well-established that classical Ergun’s constants are not universal in nature and result in different values for different packings.11-15 Different values for E1 and E2 have been reported by different investigators for different bed geometries. The data of Larkins et al.12 agreed with Ergun’s values for cylindrical packing but recommended E1 and E2 as 118 and 1.0 for 0.95-cm spheres and 266 and 2.33 for 0.95-cm rings. However, this resulted in 20% less pressure
drop for spheres and 75% greater pressure drop for rings as compared to the predictions by Ergun’s classical constants. Quite recently, Lakota et al.16 have observed that the Ergun type inertial constant depends on the particle shape and observed E1 ) 381 and E2 ) 4.7 for 4.1-mm Raschig rings. Macdonald13 has observed that the universal Ergun constants of E1 ) 150 and E2 ) 1.75 can lead to errors of several hundred percent. It is, therefore, not proper to assume that classical Ergun’s constants are able to take care of different bed characteristics (such as tortuosity and equivalent flow channel diameter) as considered by Pinna et al.4 Further, the model (eqs 1 and 2) contains only one adaptive parameter, R, and hence, the model predictions are solely dependent on the evaluation of R. The adaptive parameter has been evaluated from the saturation data by fitting the total liquid saturation data to eq 5 and minimizing the error. The predicted value of R, when used in the model equations, leads to a wide scatter in the prediction of liquid saturation (Figure 8 of Pinna et al.4). These authors further reported that only three out of four packings showed a direct dependence of β on X. Also, the model failed to predict the saturation at the two extremes of the abscissa. However, these authors tried to explain the inaccuracy on the basis of the results of Charpentier.17 If R, which is calculated from the experimental data on liquid saturation, is not able to predict the same data accurately, it cannot be expected to predict the pressure drop reliably for other systems. Hence, there is a need to account for the particle shapes or sphericity in the model equations. 3. Experimental Experiments were carried on a 7.4-cm diameter glass column, packed to a height of 50 cm. Entries for gas and liquid phases were provided at the top of the column. The experiments were performed at the Complex-Fluids Hydrodynamics Research Laboratory, Department of Chemical Engineering and Technology, Panjab University, Chandigarh. The detailed description of the experimental set up and the fluids and packings used is given elsewhere.18 The flow pattern and the transition from one flow regime to another were identified visually for the concurrent down-flow through the packed bed. In the present investigation, only the first transition, i.e., the transition from trickle to pulse flow has been investigated and data corresponding to two-phase pressure drop and dynamic liquid saturation were recorded for the low interaction regime (trickle regime) and high interaction regime (pulse/bubble regime). The transition was recorded by visual observations of the onset of pulses that would start from the bottom of the column with fluctuations in the manometer attached to the top of the packed section. A detailed discussion on the transition is given by Bansal et al.18 4. Results and Discussion The data corresponding to two-phase pressure drop on a trickle bed corresponding to different bed configurations were
Table 1. Observed Values of rm,exp low interaction regime packing glass beads-I catalyst pellets, d×h Raschig rings, d i × do × h
sphericity, ω
R2
Rm, exp, (eq 11)
R2
225/1.58 200/2.29
1.000 0.716
2.7 ( 0.04 3.9 ( 0.08
0.98 0.97
7.2 ( 0.14 8.7 ( 0.11
0.97 0.99
242/3.20
0.423
10.4 ( 0.29
0.94
14.0 ( 0.23
0.98
3.337 4.522 × 7.677 6.336 × 9.130 × 10.274
packing size (mm)
high interaction regime
Rm, exp, (eq 10)
Ergun consts E1/E2
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Figure 2. Plots of φ exp versus X for the low and high interaction regimes.
converted and plotted terms of Lockhart-Martinelli parameters φ and X. However, the evaluation of single-phase air and liquid pressure drops are required for the determination of φ and X. As discussed earlier, many researchers11-15 have pointed out that the classical values of Ergun constants cannot be used as such for different packings. Therefore, the Ergun constants were determined by subjecting the packed column to a single phase. The values thus obtained for different bed configurations are tabulated in Table 1. The data, in terms of Lockhart-Martinelli parameters φ and X, corresponding to different bed configurations is plotted in Figure 2. It was observed that the data followed a particular trend for glass beads-I under the low interaction regime. A similar trend under the high interaction regime was also observed, but the data corresponding to different regimes followed different curves and did not collapse to a single curve. It indicated that φ versus X data do not follow a unique relationship under different regimes. Similar results were found corresponding to different packings with different sphericities (Table 1). Different curves in different regimes are essentially due to different interactions in low and high interaction flow regimes. The pressure drop corresponding to the high interaction regime being higher than that corresponding to the low interaction regime for the same value of X. Further, the data corresponding to the low and high interaction regimes was subjected to the model of Pinna et al.4 It was observed that the model overpredicted the present data (Figure 3) corresponding to the low interaction regime. This was for the obvious reason that the Pinna et al.4 model was developed for the high interaction regime. The predictions by this model for the high interaction regime are given in Figure 4. The model could predict the data better for a value of X greater than 3 for glass beads and catalyst pellets and slightly overpredicted the data corresponding to Raschig rings for the same range of X. However, it underpredicted the pressure drop for low values of X (
