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A method for calculating effective interfacial area of structured packed distillation columns under elevated pressures
Chemical Engineering and Processing 45 (2006) 691–697
A method for calculating effective interfacial area of structured packed distillation columns under elevated pressures G.Q. Wang a,1 , X.G. Yuan a,b,∗ , K.T. Yu b a
State Key Laboratory of Chemical Engineering, School of Chemical Engineering and Technology, Tianjin University, Tianjin, PR China b Chemical Engineering Research Center, Tianjin University, Tianjin, PR China Received 3 May 2005; received in revised form 14 January 2006; accepted 14 January 2006 Available online 6 March 2006
Abstract Based on comparisons of some published models with experimental data obtained by FRI (Fractionation Research Inc.), an improved model for estimating the effective interfacial area of structured packing applicable to elevated pressure distillation was proposed. This model was developed on the basis of that proposed by Gualito et al., and the improvement was made by adding a factor reflecting pressure effect. The proposed model was validated by comparison with experimental data in the literature. The results showed that the improved model could give a more reliable estimation than the cited ones for structured packed columns under elevated operating pressures. © 2006 Elsevier B.V. All rights reserved. Keywords: Structured packing; Elevated pressure; Effective interfacial area
1. Introduction During the last two decades structured packings have been widely used in mass transfer processes such as distillation and absorption. This is mainly because that with regularly arranged corrugated sheets, structured packed columns can provide larger surface area for gas–liquid contacting, better hydraulic behaviors, i.e. much lower pressure drop and higher load capacity, etc., compared to either random packed and/or trayed columns. Structured packings of 125–350 m2 /m3 apparent (geometrical) specific surface areas are the most commonly used in industries. For some specific purposes, this number could reach to 700 or even more. Then, the mass transfer for a structured packed column could be known as surface dependent. However, in many cases, the size of effective surface for mass transfer differs apparently from the geometrical surface area of the sheets due to the effects of hydraulic conditions and some physical interactions affecting the spreading of liquid on the sheets, for example surface tension of liquid on the solid, capillary forces and condensing effect, etc. The effective interfacial area is an ∗
Corresponding author. Tel.: +86 22 27404732; fax: +86 22 27404496. E-mail addresses: [email protected] (G.Q. Wang), [email protected] (X.G. Yuan). 1 Tel.: +86 22 27401890; fax: 86 22 27404496. 0255-2701/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2006.01.013
important, fundamental parameter in the design of structured packed columns. As far as packed columns are concerned, there exist several definitions of the interfacial area [1], but the wetted surface area is of real importance because it is closely linked to the effective interfacial area under many flowing conditions. In principle, the difference between the wetted surface and the effective interfacial area lies in that the wetted surface area incorporates the surface area of dead zones, whereas the effective interfacial area includes not only the surface area of liquid film on the packing surface but also the surfaces of drops, jets and sprays. In spite of these differences, both are often adopted. So far almost all models we have found in the literature for predicting the effective interfacial area are based on experimental data under atmospheric or vacuum conditions. This is mainly because of experimental difficulties in elevated pressure distillations. However, the works by FRI [2] and some other investigators [3,4] demonstrated that distillation with structured packed columns at elevated pressure exhibits behaviors of separation efficiency differing from those under lower pressures. This opens an issue for mass transfer efficiency prediction for structured packed columns for elevated pressure distillation. It is the aim of the present article to develop a model that can predict the effective interfacial area of structured packings under elevated pressures.
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Table 1 A summary of main effective interfacial area models for structured packing in the literature Model
Application condition and comments
Onda et al. [5] ae ap
= 1 − exp −1.45
σc 0.75 σL
ReL = ρL uL /(ap µL ), FrL = Billet and Schultes [6] ae ap
= 3ε0.5
ρL uL µ L ap
−0.2
−0.05 Re0.1 , where We0.2 L FrL L
u2L ap /g,
ρL u2L ap σL
0.75
WeL = u2L ap g
Random packings, limitations: 0.04 < ReL < 500, 1.2 × 10−8 < WeL < 0.27, 2.5 × 10−9 < FrL < 1.8 × 10−2 , 0.3 < σ c /σ L < 2
ρL u2L /(σL ap )
−0.45 Theoretical model for random or structured packings, surface tension neutral or positive system
Henriques de Brito et al. [7] ae ap
= 0.465
ρL uL µ L ap
0.3
Empirical model obtained from chemical absorption of Mellapak structured packing
Rocha et al. [8] ae ap
= Fse
ν0.2 s0.159 [ρL /(σL g)]0.15 29.12u0.4 L L
Gualito et al.[9] ae ap
ae ap
=
Based on work of Shi and Mersmann [1] for sheet structured packing
(1−0.93 cos θ)(sin α)0.3 ε0.6
Rocha
1.2 1+0.2 exp(15uL /uG )
Correction of Rocha model, applied to high-pressure conditions
Olujic [10] ae ap =
1−Ω 1+2.143×10−6 /u1.5 L
Olujic(modified) [11] ae ap
=
+ ln
ae ap
Pure empirical model from experiments of Montzpak
(1 − Ω)
Onda ae,Onda 250
sin 45 n sin αL
+ 0.49 −
, n= 1−
0.101 p
1.2 −
ap 250 αL 45
1−
αL 45
Modification of Olujic model using Onda model for further improvement. Here αL is effective liquid flow angle calculated according to expression by Spekuljak and Billet [22]
2. Critical summary of previous works A summary of some representative models among those we have found in the literature for predicting effective interfacial areas in packed columns is shown in Table 1. The models proposed by Siminiceanu et al. [12] and Xu et al. [13] have not been included as they are similar to those proposed by Henriques de Brito et al. [7] and Billet and Schultes [6]. The model proposed by Hanley et al. [14] has not been included either as it contains some parameters difficult to evaluate. In order to evaluate the performance of these models for the cases of elevated pressure, experimental results obtained by FRI [2] were employed to make comparisons. The experimental data have been obtained with a commercial-scale experimental column of 1.2 m ID with a bed of 3.78 m high Mellapak250Y structured packing and with an operating pressure range of 0.69–2.76 MPa. Testing system was a mixture of C4 /i-C4 , the physical properties of which are summarized in Table 2. Because physical and transport properties of isomeric mixture almost do not vary with composition, the physical properties in Table 2 are for an average composition.
The effective interfacial area was often back-calculated from the HETP data using proper mass transfer coefficient correlations, because it could hardly be measured. Adopting doublefilm theory for vapor–liquid two-phase mass transfer, for total reflux operation the effective interfacial area ae , can be expressed by the following equation [15]:
ln λ uG 1 ρG 1 (1) ae = +λ λ − 1 HETP kG ρ L kL where λ is the stripping factor, i.e. the ratio of slopes of equilibrium and operating lines, uG is the superficial velocity of gas, kG and kL are mass transfer coefficients of gas and liquid and ρG and ρL are gas and liquid densities, respectively. To calculate ae by Eq. (1), Delft model [16] was used in the present work to estimate gas and liquid phase mass transfer coefficients, kG and kL , in which liquid holdup was estimated by the model given by Shetty and Cerro [17]. It is reasonable to believe that, in viewpoint of thermodynamics, pressure as high as 2.76 MPa within which elevated pressure distillation should fall, would give little difference in behavior of phase equilibrium for most mixtures applicable for distillation, and then has very limited influence
Table 2 Physical properties of the n-butane/isobutane system Pressure (MPa)
ρL
ρG
µL × 10 5
µG × 10 6
DL × 10 8
DG × 10 6
σ L × 10 3
λ
0.69 1.14 2.07 2.76
523 487 426 383
17.0 30.3 58.0 85.0
11.0 8.8 6.2 4.9
8.4 9.0 9.8 10.2
1.05 1.38 2.08 2.68
0.797 0.549 0.356 0.291
7.3 4.8 2.1 1.1
1.30 1.23 1.15 1.10
G.Q. Wang et al. / Chemical Engineering and Processing 45 (2006) 691–697
693
Fig. 1. Comparison of interfacial area predicted by different models with experimental results under different pressure conditions. 1, Onda; 2, Billet/Schultes; 3, Henriques de Brito; 4, Rocha; 5, Gualito; 6, Olujic; 7, Olujic modified; () experiment.
on the film mass transfer coefficients, which are defined based on unit area, if pressure influential factors, such as gas density, could be taken into account, as did in Delft model [16]. Researches [18,19] have indicated that for structured packing the pressure influence on HETP could be attributed to hydraulic effect caused by elevated pressures. This effect could mainly interpreted by the variation of the effective interfacial area. Eq. (1) could then be used to check the suitability of the models for predicting the interfacial area of structured packing under elevated pressures. The comparisons are shown in Fig. 1. The effective surface areas predicted by Onda et al.’s model, which has been developed for random packing at atmospheric conditions, deflects severely from the experimental results and is always smaller than the geometrical surface area and almost keeps constant in a wide range of the gas load and the operating pressures. Very similar predicted results could also be obtained by using Olujic’s models [10,11], which have been developed for structured packing, but for lower operating pressures. Effective interfacial area estimated by the model given by Billet and Schultes usually exceed the geometrical surface area, especially under higher pressures. For pressures above 2 MPa, the predicted interfacial area is often larger than the geometry area in entire load range. The prediction given by the model of Henriques de Brito et
al. is much higher than the geometrical surface area in most part of length of loads axis regardless of pressure variation. The area predicted by Rocha et al.’s model is a little lower than that obtained by Billet and Schultes’ one at lower pressures, but much lower at higher pressures. The prediction by the model of Gualito et al. is a little lower than that given by the model of Rocha et al. at lower pressures, but much lower at higher pressures. It can be seen from Fig. 1 that at lower pressure, 0.69 MPa, the models by Billet and Schultes, Rocha et al. and Gualito et al. can all give predictions following well the tendency of the experiments. With the increase of pressure, 1.14, 2.07 and 2.76 MPa, the curves given by models of Billet and Schultes and of Rocha et al. start to depart from the experiments, whereas that given by Gualito et al. remains closer. It can be seen from Table 1 that the model of Gualito et al. corrected that of Rocha et al., which possesses effective form to predict the trend for the development of interfacial area with the variation of the gas loading factor, by adding a factor incorporating the gas velocity, which can reflect indirectly the pressure effect. In this paper a model is proposed by improving the correcting factor in the model of Gualito et al. to more accurately predict the effective interfacial area of structured packing under elevated pressures.
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Fig. 2. Experimental validation of Eq. (2) for different pressures. Mellapak 250Y, C4 /i-C4 system, total reflux.
Fig. 3. The dependence of coefficient ϕ on the density ratio of liquid to gas and regressive results.
in the following form: β ρL ρL A(p) = ϕ =α ρG ρG
3. Model development
(3)
As can be seen in Table 1 that the correcting factor in the model of Gualito et al. accounted for pressure effect by incorporating the gas phase velocity uG , however the ratio of velocities of liquid and gas (uL /uG ) gives no change for different gas velocity for total reflux operation. An option for effectively reflecting the influences of pressure and the operating load simultaneously is to incorporate the ratio of liquid and gas densities (ρL /ρG ) and, at the same time, the gas velocity into the correcting factor. For this purpose, the FRI experimental data [2] were plotted in a diagram of the ratio of effective interfacial area to that estimated by the model of Rocha (ae /aRocha ) versus gas velocity uG as shown in Fig. 2, and the scatter points under different pressures were fitted by following equation: ae B (2) = A(p) exp ae,Rocha uG
where ϕ is the density ratio dependent function and α and β are parameters to be identified. To check the suitability of the form of function ϕ given by Eq. (3) and identify parameters α and β, the FRI data were plotted again on a diagram of ϕ versus ρL /ρG , as shown in Fig. 3. By regressive analysis, the values of parameters α and β were identified as 0.17 and 0.6, respectively. Combining Eqs. (2) and (3), yields:
0.6 ρL 0.15 (4) ae = ae,Rocha × 0.17 exp − ρG uG
where the coefficient A(p) was assumed to be pressuredependent and its values for different pressures were identified by data regressing and are shown in Table 3, B is another fitting parameter, the value of which was identified as −0.15. As we have discussed, it is convenient to incorporate the ratio ρL /ρG to take the pressure effect into account, then the parameter A(p) could be transformed to a function of the ratio
4. Model validation
Table 3 Regressive results of data in Fig. 2 Pressure (MPa)
A(p)
0.69 1.14 2.07 2.76
1.3623 0.9411 0.5189 0.4590
In the next section the proposed model given by Eq. (4) is validated by comparing its predicted results with those calculated by the model of Gualito et al. via various experimental data.
Data for validating the model was assembled in Table 4. Characteristics of the structured packings involved were given in Table 5. It can be seen from Table 4 that the data we could find in the open literature for elevated pressure distillations were rather limited, and this shows that the work on experimentation of mass transfer tests under elevated pressures was far feebler than that for vacuum or atmospheric conditions. Nevertheless, it still can be seen from Table 5 that the test conditions for the collected data in Table 4 cover a variety of column sizes, test mixtures, packing types and sizes. The experimental values of the effective interfacial areas, the values predicted by Eq. (4) and those calculated by the model of Gualito et al. are plotted in Figs. 4–7. Note that the experimental values were backcalculated by Eq. (1) with the HETP values
G.Q. Wang et al. / Chemical Engineering and Processing 45 (2006) 691–697
695
Table 4 Collection of experimental data for elevated pressure distillation Test system
Column ID (m)
Pressure (MPa)
Packing
Source
Cyclohexane/n-heptane
0.43
0.163; 0.414 0.414
Flexipac2, Gempak 2A; Intalox 2T, Maxpak Montz B1
SRP [8] Deft [20]
i/n-Butane
1.2 1.2
0.69, 1.14, 2.07, 2.76 0.68, 1.12, 2.04
Mellapak250Y Intalox 2T
FRI [2] FRI [21]
Table 5 Characteristics of related structured packings Packing type
Surface area ap (m2 /m3 )
Void fraction ε (m3 /m3 )
Corr. angle/ vert. θ (◦ )
Flexipac2 Gempak 2A Intalox 2T Maxpak Montz B1-250.60 Montz B1-400.60 Mellapak250Y
233 233 213 229 245 390 250
0.95 0.95 0.95 0.95 0.978 0.96 0.97
45 45 45 45 60 60 45
obtained from the experiments reported in the source references summarized in Table 4. It can be seen from the figures that for all the cases we have tested, Eq. (4) gives better predictions than Gualito et al.’s model
that could be known as the best one we could find in the open literature. For the tests, the effective interfacial areas are either under-estimated (Figs. 4 and 7) or over-estimated (Figs. 5 and 6) by Gualito et al.’s model. The figures also demonstrate that the predictions by Eq. (4) follow the tendency of the effective interfacial areas better than the competitor with the variation of the gas load. The comparisons given by Figs. 4–7 and the data in Tables 4 and 5 indicate that Eq. (4) is more robust and reliable than the models we have found in the literature in estimating the effective interfacial areas of structured packings of the types included in Table 4 with specific surfaces from 213 to 390 m2 /m3 , corrugating angle of 45◦ and 60◦ , with column inter diameter of 0.43 and 1.2 m, for operating pressures ranging from 0.16 to 2.76 MPa for the separations of cyclohexane/n-heptane and n/i-butane systems.
Fig. 4. Comparison of experimental and calculated ae , SRP data [8]. Exp, experimental; Gualito, model of Gualito et al.; Eq. (4), our proposed model.
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Fig. 5. Comparison of experimental and calculated ae , FRI data [2]. Exp, experimental; Gualito, model of Gualito et al.; Eq. (4), our proposed model.
5. Conclusion and discussion
Fig. 6. Comparison of experimental and calculated ae , FRI data [21]. Exp, experimental; Gualito, model of Gualito et al.; Eq. (4), our proposed model.
Fig. 7. Comparison of experimental and calculated ae , Delft data [20]. Exp, experimental; Gualito, model of Gualito et al.; Eq. (4), our proposed model.
A comprehensive comparison among the cited models was conducted to investigate their performance for predicting the effective interfacial areas of structured packing under elevated pressures and to provide a guideline for further improvements. For estimating the effective interfacial area of structured packing under elevated pressure, the model developed by Rocha et al. was shown to be a good basis, based on which Gualito et al. have proposed a model giving reasonable prediction by adding a correcting factor that considering the pressure effect. The improvement of the model proposed in the present work was made by incorporating into the correcting factor the ratio of the densities of the liquid to that of the gas and, at the same time, the gas velocity, instead of the ratio of the velocities of the two phases alone incorporated in the Gualito et al.’s correcting factor. The reliability of the proposed model that was demonstrated by comparing with Gualito et al.’s model for a variety of characteristics of packings and operating conditions implies that the ratio of the densities of the two phases and the loading density represented by gas velocity are critical influential parameters for estimating the effective interfacial area of structured packing under elevated operating pressures. It should be noted that the experimental data of the effective interfacial areas based on which all the comparisons were made have been back-calculated from experimental values of HETP, via Eq. (1), which has been developed for an idealized situation, where the equilibrium and operating lines are straight. To use this equation, we assume in the foregoing sections that the pressure effect on the HETP is due uniquely to the effective interfacial area. In fact the influence of pressure on distillation efficiency for structured packed columns under elevated pressures is more complicated. As discussed by Kurtz et al. [3], increase in pressure will lead to increase in axial mixing effect. Zuiderweg and Nutter [4] also showed evidence that under higher pressure conditions packed columns can exhibit significant vapor back-mixing and initial liquid mal-distribution could have heavier effects on the effi-
G.Q. Wang et al. / Chemical Engineering and Processing 45 (2006) 691–697
ciency than under lower pressures. These effects have no doubt influence on both the effective interfacial area and the mass transfer coefficients. Although a model considering pressure effect has been used in estimation of mass transfer coefficients for applying Eq. (1), all the comparisons and data fitting we have made imply that the remaining influence of pressure has been interpreted by the effective interfacial area, ae alone. Nevertheless, with the model proposed in this work for estimating the effective interfacial area of structured packing under elevated pressures, Eq. (4) could be applied to give more reliable HETP in practical design or other applications. Acknowledgement Authors acknowledge the financial support from the National Natural Science Foundation of China under the grant no. 20136010. Appendix A. Nomenclature
ap ae A(p) B D Fse g HDU HETP HTU kG kL p u
packing specific surface area (1/m) effective specific interfacial area (1/m) pressure-dependent parameter in Eq. (2) constant in Eq. (2) diffusion coefficient (m2 /s) packing surface enhancement factor gravitational constant (m/s2 ) height of a dispersion unit (m) height equivalent to a theoretical plate (m) height of mass transfer unit (m) gas-side mass-transfer coefficient (m/s) liquid-side mass-transfer coefficient (m/s) pressure (MPa) velocity (m/s)
Greek letters α corrugation inclination angle, degree constant in Eq. (3) αL effective liquid flow angle (◦ ) β constant in Eq. (3) ε void fraction of packing µ viscosity (kg/m s) θ contact angle (◦ ) λ stripping factor ν kinematic viscosity (m2 /s) ρ density (kg/m3 ) σ surface tension (N/m) σc critical surface tension (N/m) ϕ density ratio dependent function Ω packing surface void fraction Subscripts G gas phase L liquid phase
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References [1] M.G. Shi, A. Mersmann, Effective interfacial area in packed columns, Ger. Chem. Eng. 8 (1985) 87–96. [2] C.W. Fitz, J.G. Kunesh, A. Shariat, Performance of structured packing in a commercial-scale column at pressures of 0.02–27.6 bar, Ind. Eng. Chem. Res. 38 (1999) 512–518. [3] D.P. Kurtz, K.J. McNulty, R.D. Morgan, Stretch the capacity of highpressure distillation columns, Chem. Eng. Prog. 87 (1991) 43–49. [4] F.J. Zuiderweg, D.E. Nutter, Evidence of vapor backmixing in packed columns in the case of high pressure distillation, Inst. Chem. Eng. Symp. Ser. 128 (1992) A481–A488. [5] K. Onda, H. Takeuchi, Y. Okumoto, Mass transfer coefficients between gas and liquid phases in packed columns, J Chem. Eng. Jpn. 1 (1968) 56–62. [6] R. Billet, M. Schultes, Predicting mass transfer in packed columns, Chem. Eng. Technol. 16 (1993) 1–9. [7] M. Henriques de Brito, U. von Stockar, A.M. Bangerer, P. Bomio, M. Laso, Effective mass transfer interfacial area in a pilot column equipped with structured packings and with ceramic rings, Ind. Eng. Chem. Res. 33 (1994) 647–656. [8] J.A. Rocha, J.L. Bravo, J.R. Fair, Distillation columns containing structured packings: a comprehensive model for their performance. 2. Mass transfer model, Ind. Eng. Chem. Res. 35 (1996) 1660–1667. [9] J.J. Gualito, F.J. Cerino, J.C. Cardenas, J.A. Rocha, Design method for distillation columns filled with metallic, ceramic, or plastic structured packings, Ind. Eng. Chem. Res. 36 (1997) 1747–1757. [10] Z. Olujic, Development of a complete simulation model for predicting the hydraulic and separation performance of distillation columns equipped with structured packings, Chem. Biochem. Eng. Q. 11 (1997) 31–47. [11] Z. Olujic, Delft model—a comprehensive design tool for corrugated sheet structured packings, in: Proceedings of the Topical Conference Distillation Tools for the Practicing Engineer, AIChE Spring Meeting, New Orleans, LA, USA, March 10–14, 2002, pp. 142–152. [12] I. Siminiceanu, A. Friedl, M.A. Dragan, Simple equation for the effective mass transfer area of the Mellapak750Y structured packing, in: Scientific Conference Meeting—“35 Years of Petroleum-Gas University Activity”, Ploiesti, November 27–29, 2002. [13] Z.P. Xu, A. Afacan, K.T. Chuang, Predicting mass transfer in packed columns containing structured packings, Chem. Eng. Res. Des. 78 (2000) 91–98. [14] B. Hanley, B. Dunbobbin, D.A. Bennett, Unified model for countercurrent vapor–liquid packed columns. 2. Equations for the mass-transfer coefficients, mass transfer area, the HETP, and the dynamic liquid holdup, Ind. Eng. Chem. Res. 35 (1994) 1222–1230. [15] T.K. Sherwood, R.L. Pigford, C.R. Wilke, Mass Transfer, McGraw-Hill, New York, 1975. [16] Z. Olujic, A.B. Kamerbeek, J.A. de Graauw, A corrugation geometry based model for efficiency of structured distillation packing, Chem. Eng. Process. 38 (1999) 683–695. [17] S. Shetty, R.L. Cerro, Fundamental liquid flow correlations for the computation of design parameters for ordered packings, Ind. Eng. Chem. Res. 36 (1997) 771–783. [18] F.J. Zuiderweg, Z. Olujic, J.G. Kunesh, Liquid backmixing in structured packing in high pressure distillation, Inst. Chem. Eng. Symp. Ser. 142 (1997) 865–872. [19] J.L. Nooijen, K.A. Kusters, J.J.B. Pek, Performance of packing in high pressure distillation applications, Inst. Chem. Eng. Symp. Ser. 142 (1997) 885–897. [20] Z. Olujic, A.F. Seibert, J.R. Fair, Influence of corrugation geometry on the performance of structured packings: an experimental study, Chem. Eng. Process. 39 (2000) 335–342. [21] F. Rukovena, R.F. Strigle, Effect of pressure on structured packing performance, in: Paper Presented at AIChE Spring National Meeting, April, Houston, TX, 1989. [22] Z. Spekuljak, R. Billet, Mass transfer in regular packing, Lat. Am. J. Heat Mass Transfer 11 (1987) 63–72.
A method for calculating effective interfacial area of structured packed distillation columns under elevated pressures G.Q. Wang a,1 , X.G. Yuan a,b,∗ , K.T. Yu b a
State Key Laboratory of Chemical Engineering, School of Chemical Engineering and Technology, Tianjin University, Tianjin, PR China b Chemical Engineering Research Center, Tianjin University, Tianjin, PR China Received 3 May 2005; received in revised form 14 January 2006; accepted 14 January 2006 Available online 6 March 2006
Abstract Based on comparisons of some published models with experimental data obtained by FRI (Fractionation Research Inc.), an improved model for estimating the effective interfacial area of structured packing applicable to elevated pressure distillation was proposed. This model was developed on the basis of that proposed by Gualito et al., and the improvement was made by adding a factor reflecting pressure effect. The proposed model was validated by comparison with experimental data in the literature. The results showed that the improved model could give a more reliable estimation than the cited ones for structured packed columns under elevated operating pressures. © 2006 Elsevier B.V. All rights reserved. Keywords: Structured packing; Elevated pressure; Effective interfacial area
1. Introduction During the last two decades structured packings have been widely used in mass transfer processes such as distillation and absorption. This is mainly because that with regularly arranged corrugated sheets, structured packed columns can provide larger surface area for gas–liquid contacting, better hydraulic behaviors, i.e. much lower pressure drop and higher load capacity, etc., compared to either random packed and/or trayed columns. Structured packings of 125–350 m2 /m3 apparent (geometrical) specific surface areas are the most commonly used in industries. For some specific purposes, this number could reach to 700 or even more. Then, the mass transfer for a structured packed column could be known as surface dependent. However, in many cases, the size of effective surface for mass transfer differs apparently from the geometrical surface area of the sheets due to the effects of hydraulic conditions and some physical interactions affecting the spreading of liquid on the sheets, for example surface tension of liquid on the solid, capillary forces and condensing effect, etc. The effective interfacial area is an ∗
Corresponding author. Tel.: +86 22 27404732; fax: +86 22 27404496. E-mail addresses: [email protected] (G.Q. Wang), [email protected] (X.G. Yuan). 1 Tel.: +86 22 27401890; fax: 86 22 27404496. 0255-2701/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cep.2006.01.013
important, fundamental parameter in the design of structured packed columns. As far as packed columns are concerned, there exist several definitions of the interfacial area [1], but the wetted surface area is of real importance because it is closely linked to the effective interfacial area under many flowing conditions. In principle, the difference between the wetted surface and the effective interfacial area lies in that the wetted surface area incorporates the surface area of dead zones, whereas the effective interfacial area includes not only the surface area of liquid film on the packing surface but also the surfaces of drops, jets and sprays. In spite of these differences, both are often adopted. So far almost all models we have found in the literature for predicting the effective interfacial area are based on experimental data under atmospheric or vacuum conditions. This is mainly because of experimental difficulties in elevated pressure distillations. However, the works by FRI [2] and some other investigators [3,4] demonstrated that distillation with structured packed columns at elevated pressure exhibits behaviors of separation efficiency differing from those under lower pressures. This opens an issue for mass transfer efficiency prediction for structured packed columns for elevated pressure distillation. It is the aim of the present article to develop a model that can predict the effective interfacial area of structured packings under elevated pressures.
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G.Q. Wang et al. / Chemical Engineering and Processing 45 (2006) 691–697
Table 1 A summary of main effective interfacial area models for structured packing in the literature Model
Application condition and comments
Onda et al. [5] ae ap
= 1 − exp −1.45
σc 0.75 σL
ReL = ρL uL /(ap µL ), FrL = Billet and Schultes [6] ae ap
= 3ε0.5
ρL uL µ L ap
−0.2
−0.05 Re0.1 , where We0.2 L FrL L
u2L ap /g,
ρL u2L ap σL
0.75
WeL = u2L ap g
Random packings, limitations: 0.04 < ReL < 500, 1.2 × 10−8 < WeL < 0.27, 2.5 × 10−9 < FrL < 1.8 × 10−2 , 0.3 < σ c /σ L < 2
ρL u2L /(σL ap )
−0.45 Theoretical model for random or structured packings, surface tension neutral or positive system
Henriques de Brito et al. [7] ae ap
= 0.465
ρL uL µ L ap
0.3
Empirical model obtained from chemical absorption of Mellapak structured packing
Rocha et al. [8] ae ap
= Fse
ν0.2 s0.159 [ρL /(σL g)]0.15 29.12u0.4 L L
Gualito et al.[9] ae ap
ae ap
=
Based on work of Shi and Mersmann [1] for sheet structured packing
(1−0.93 cos θ)(sin α)0.3 ε0.6
Rocha
1.2 1+0.2 exp(15uL /uG )
Correction of Rocha model, applied to high-pressure conditions
Olujic [10] ae ap =
1−Ω 1+2.143×10−6 /u1.5 L
Olujic(modified) [11] ae ap
=
+ ln
ae ap
Pure empirical model from experiments of Montzpak
(1 − Ω)
Onda ae,Onda 250
sin 45 n sin αL
+ 0.49 −
, n= 1−
0.101 p
1.2 −
ap 250 αL 45
1−
αL 45
Modification of Olujic model using Onda model for further improvement. Here αL is effective liquid flow angle calculated according to expression by Spekuljak and Billet [22]
2. Critical summary of previous works A summary of some representative models among those we have found in the literature for predicting effective interfacial areas in packed columns is shown in Table 1. The models proposed by Siminiceanu et al. [12] and Xu et al. [13] have not been included as they are similar to those proposed by Henriques de Brito et al. [7] and Billet and Schultes [6]. The model proposed by Hanley et al. [14] has not been included either as it contains some parameters difficult to evaluate. In order to evaluate the performance of these models for the cases of elevated pressure, experimental results obtained by FRI [2] were employed to make comparisons. The experimental data have been obtained with a commercial-scale experimental column of 1.2 m ID with a bed of 3.78 m high Mellapak250Y structured packing and with an operating pressure range of 0.69–2.76 MPa. Testing system was a mixture of C4 /i-C4 , the physical properties of which are summarized in Table 2. Because physical and transport properties of isomeric mixture almost do not vary with composition, the physical properties in Table 2 are for an average composition.
The effective interfacial area was often back-calculated from the HETP data using proper mass transfer coefficient correlations, because it could hardly be measured. Adopting doublefilm theory for vapor–liquid two-phase mass transfer, for total reflux operation the effective interfacial area ae , can be expressed by the following equation [15]:
ln λ uG 1 ρG 1 (1) ae = +λ λ − 1 HETP kG ρ L kL where λ is the stripping factor, i.e. the ratio of slopes of equilibrium and operating lines, uG is the superficial velocity of gas, kG and kL are mass transfer coefficients of gas and liquid and ρG and ρL are gas and liquid densities, respectively. To calculate ae by Eq. (1), Delft model [16] was used in the present work to estimate gas and liquid phase mass transfer coefficients, kG and kL , in which liquid holdup was estimated by the model given by Shetty and Cerro [17]. It is reasonable to believe that, in viewpoint of thermodynamics, pressure as high as 2.76 MPa within which elevated pressure distillation should fall, would give little difference in behavior of phase equilibrium for most mixtures applicable for distillation, and then has very limited influence
Table 2 Physical properties of the n-butane/isobutane system Pressure (MPa)
ρL
ρG
µL × 10 5
µG × 10 6
DL × 10 8
DG × 10 6
σ L × 10 3
λ
0.69 1.14 2.07 2.76
523 487 426 383
17.0 30.3 58.0 85.0
11.0 8.8 6.2 4.9
8.4 9.0 9.8 10.2
1.05 1.38 2.08 2.68
0.797 0.549 0.356 0.291
7.3 4.8 2.1 1.1
1.30 1.23 1.15 1.10
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693
Fig. 1. Comparison of interfacial area predicted by different models with experimental results under different pressure conditions. 1, Onda; 2, Billet/Schultes; 3, Henriques de Brito; 4, Rocha; 5, Gualito; 6, Olujic; 7, Olujic modified; () experiment.
on the film mass transfer coefficients, which are defined based on unit area, if pressure influential factors, such as gas density, could be taken into account, as did in Delft model [16]. Researches [18,19] have indicated that for structured packing the pressure influence on HETP could be attributed to hydraulic effect caused by elevated pressures. This effect could mainly interpreted by the variation of the effective interfacial area. Eq. (1) could then be used to check the suitability of the models for predicting the interfacial area of structured packing under elevated pressures. The comparisons are shown in Fig. 1. The effective surface areas predicted by Onda et al.’s model, which has been developed for random packing at atmospheric conditions, deflects severely from the experimental results and is always smaller than the geometrical surface area and almost keeps constant in a wide range of the gas load and the operating pressures. Very similar predicted results could also be obtained by using Olujic’s models [10,11], which have been developed for structured packing, but for lower operating pressures. Effective interfacial area estimated by the model given by Billet and Schultes usually exceed the geometrical surface area, especially under higher pressures. For pressures above 2 MPa, the predicted interfacial area is often larger than the geometry area in entire load range. The prediction given by the model of Henriques de Brito et
al. is much higher than the geometrical surface area in most part of length of loads axis regardless of pressure variation. The area predicted by Rocha et al.’s model is a little lower than that obtained by Billet and Schultes’ one at lower pressures, but much lower at higher pressures. The prediction by the model of Gualito et al. is a little lower than that given by the model of Rocha et al. at lower pressures, but much lower at higher pressures. It can be seen from Fig. 1 that at lower pressure, 0.69 MPa, the models by Billet and Schultes, Rocha et al. and Gualito et al. can all give predictions following well the tendency of the experiments. With the increase of pressure, 1.14, 2.07 and 2.76 MPa, the curves given by models of Billet and Schultes and of Rocha et al. start to depart from the experiments, whereas that given by Gualito et al. remains closer. It can be seen from Table 1 that the model of Gualito et al. corrected that of Rocha et al., which possesses effective form to predict the trend for the development of interfacial area with the variation of the gas loading factor, by adding a factor incorporating the gas velocity, which can reflect indirectly the pressure effect. In this paper a model is proposed by improving the correcting factor in the model of Gualito et al. to more accurately predict the effective interfacial area of structured packing under elevated pressures.
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Fig. 2. Experimental validation of Eq. (2) for different pressures. Mellapak 250Y, C4 /i-C4 system, total reflux.
Fig. 3. The dependence of coefficient ϕ on the density ratio of liquid to gas and regressive results.
in the following form: β ρL ρL A(p) = ϕ =α ρG ρG
3. Model development
(3)
As can be seen in Table 1 that the correcting factor in the model of Gualito et al. accounted for pressure effect by incorporating the gas phase velocity uG , however the ratio of velocities of liquid and gas (uL /uG ) gives no change for different gas velocity for total reflux operation. An option for effectively reflecting the influences of pressure and the operating load simultaneously is to incorporate the ratio of liquid and gas densities (ρL /ρG ) and, at the same time, the gas velocity into the correcting factor. For this purpose, the FRI experimental data [2] were plotted in a diagram of the ratio of effective interfacial area to that estimated by the model of Rocha (ae /aRocha ) versus gas velocity uG as shown in Fig. 2, and the scatter points under different pressures were fitted by following equation: ae B (2) = A(p) exp ae,Rocha uG
where ϕ is the density ratio dependent function and α and β are parameters to be identified. To check the suitability of the form of function ϕ given by Eq. (3) and identify parameters α and β, the FRI data were plotted again on a diagram of ϕ versus ρL /ρG , as shown in Fig. 3. By regressive analysis, the values of parameters α and β were identified as 0.17 and 0.6, respectively. Combining Eqs. (2) and (3), yields:
0.6 ρL 0.15 (4) ae = ae,Rocha × 0.17 exp − ρG uG
where the coefficient A(p) was assumed to be pressuredependent and its values for different pressures were identified by data regressing and are shown in Table 3, B is another fitting parameter, the value of which was identified as −0.15. As we have discussed, it is convenient to incorporate the ratio ρL /ρG to take the pressure effect into account, then the parameter A(p) could be transformed to a function of the ratio
4. Model validation
Table 3 Regressive results of data in Fig. 2 Pressure (MPa)
A(p)
0.69 1.14 2.07 2.76
1.3623 0.9411 0.5189 0.4590
In the next section the proposed model given by Eq. (4) is validated by comparing its predicted results with those calculated by the model of Gualito et al. via various experimental data.
Data for validating the model was assembled in Table 4. Characteristics of the structured packings involved were given in Table 5. It can be seen from Table 4 that the data we could find in the open literature for elevated pressure distillations were rather limited, and this shows that the work on experimentation of mass transfer tests under elevated pressures was far feebler than that for vacuum or atmospheric conditions. Nevertheless, it still can be seen from Table 5 that the test conditions for the collected data in Table 4 cover a variety of column sizes, test mixtures, packing types and sizes. The experimental values of the effective interfacial areas, the values predicted by Eq. (4) and those calculated by the model of Gualito et al. are plotted in Figs. 4–7. Note that the experimental values were backcalculated by Eq. (1) with the HETP values
G.Q. Wang et al. / Chemical Engineering and Processing 45 (2006) 691–697
695
Table 4 Collection of experimental data for elevated pressure distillation Test system
Column ID (m)
Pressure (MPa)
Packing
Source
Cyclohexane/n-heptane
0.43
0.163; 0.414 0.414
Flexipac2, Gempak 2A; Intalox 2T, Maxpak Montz B1
SRP [8] Deft [20]
i/n-Butane
1.2 1.2
0.69, 1.14, 2.07, 2.76 0.68, 1.12, 2.04
Mellapak250Y Intalox 2T
FRI [2] FRI [21]
Table 5 Characteristics of related structured packings Packing type
Surface area ap (m2 /m3 )
Void fraction ε (m3 /m3 )
Corr. angle/ vert. θ (◦ )
Flexipac2 Gempak 2A Intalox 2T Maxpak Montz B1-250.60 Montz B1-400.60 Mellapak250Y
233 233 213 229 245 390 250
0.95 0.95 0.95 0.95 0.978 0.96 0.97
45 45 45 45 60 60 45
obtained from the experiments reported in the source references summarized in Table 4. It can be seen from the figures that for all the cases we have tested, Eq. (4) gives better predictions than Gualito et al.’s model
that could be known as the best one we could find in the open literature. For the tests, the effective interfacial areas are either under-estimated (Figs. 4 and 7) or over-estimated (Figs. 5 and 6) by Gualito et al.’s model. The figures also demonstrate that the predictions by Eq. (4) follow the tendency of the effective interfacial areas better than the competitor with the variation of the gas load. The comparisons given by Figs. 4–7 and the data in Tables 4 and 5 indicate that Eq. (4) is more robust and reliable than the models we have found in the literature in estimating the effective interfacial areas of structured packings of the types included in Table 4 with specific surfaces from 213 to 390 m2 /m3 , corrugating angle of 45◦ and 60◦ , with column inter diameter of 0.43 and 1.2 m, for operating pressures ranging from 0.16 to 2.76 MPa for the separations of cyclohexane/n-heptane and n/i-butane systems.
Fig. 4. Comparison of experimental and calculated ae , SRP data [8]. Exp, experimental; Gualito, model of Gualito et al.; Eq. (4), our proposed model.
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Fig. 5. Comparison of experimental and calculated ae , FRI data [2]. Exp, experimental; Gualito, model of Gualito et al.; Eq. (4), our proposed model.
5. Conclusion and discussion
Fig. 6. Comparison of experimental and calculated ae , FRI data [21]. Exp, experimental; Gualito, model of Gualito et al.; Eq. (4), our proposed model.
Fig. 7. Comparison of experimental and calculated ae , Delft data [20]. Exp, experimental; Gualito, model of Gualito et al.; Eq. (4), our proposed model.
A comprehensive comparison among the cited models was conducted to investigate their performance for predicting the effective interfacial areas of structured packing under elevated pressures and to provide a guideline for further improvements. For estimating the effective interfacial area of structured packing under elevated pressure, the model developed by Rocha et al. was shown to be a good basis, based on which Gualito et al. have proposed a model giving reasonable prediction by adding a correcting factor that considering the pressure effect. The improvement of the model proposed in the present work was made by incorporating into the correcting factor the ratio of the densities of the liquid to that of the gas and, at the same time, the gas velocity, instead of the ratio of the velocities of the two phases alone incorporated in the Gualito et al.’s correcting factor. The reliability of the proposed model that was demonstrated by comparing with Gualito et al.’s model for a variety of characteristics of packings and operating conditions implies that the ratio of the densities of the two phases and the loading density represented by gas velocity are critical influential parameters for estimating the effective interfacial area of structured packing under elevated operating pressures. It should be noted that the experimental data of the effective interfacial areas based on which all the comparisons were made have been back-calculated from experimental values of HETP, via Eq. (1), which has been developed for an idealized situation, where the equilibrium and operating lines are straight. To use this equation, we assume in the foregoing sections that the pressure effect on the HETP is due uniquely to the effective interfacial area. In fact the influence of pressure on distillation efficiency for structured packed columns under elevated pressures is more complicated. As discussed by Kurtz et al. [3], increase in pressure will lead to increase in axial mixing effect. Zuiderweg and Nutter [4] also showed evidence that under higher pressure conditions packed columns can exhibit significant vapor back-mixing and initial liquid mal-distribution could have heavier effects on the effi-
G.Q. Wang et al. / Chemical Engineering and Processing 45 (2006) 691–697
ciency than under lower pressures. These effects have no doubt influence on both the effective interfacial area and the mass transfer coefficients. Although a model considering pressure effect has been used in estimation of mass transfer coefficients for applying Eq. (1), all the comparisons and data fitting we have made imply that the remaining influence of pressure has been interpreted by the effective interfacial area, ae alone. Nevertheless, with the model proposed in this work for estimating the effective interfacial area of structured packing under elevated pressures, Eq. (4) could be applied to give more reliable HETP in practical design or other applications. Acknowledgement Authors acknowledge the financial support from the National Natural Science Foundation of China under the grant no. 20136010. Appendix A. Nomenclature
ap ae A(p) B D Fse g HDU HETP HTU kG kL p u
packing specific surface area (1/m) effective specific interfacial area (1/m) pressure-dependent parameter in Eq. (2) constant in Eq. (2) diffusion coefficient (m2 /s) packing surface enhancement factor gravitational constant (m/s2 ) height of a dispersion unit (m) height equivalent to a theoretical plate (m) height of mass transfer unit (m) gas-side mass-transfer coefficient (m/s) liquid-side mass-transfer coefficient (m/s) pressure (MPa) velocity (m/s)
Greek letters α corrugation inclination angle, degree constant in Eq. (3) αL effective liquid flow angle (◦ ) β constant in Eq. (3) ε void fraction of packing µ viscosity (kg/m s) θ contact angle (◦ ) λ stripping factor ν kinematic viscosity (m2 /s) ρ density (kg/m3 ) σ surface tension (N/m) σc critical surface tension (N/m) ϕ density ratio dependent function Ω packing surface void fraction Subscripts G gas phase L liquid phase
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References [1] M.G. Shi, A. Mersmann, Effective interfacial area in packed columns, Ger. Chem. Eng. 8 (1985) 87–96. [2] C.W. Fitz, J.G. Kunesh, A. Shariat, Performance of structured packing in a commercial-scale column at pressures of 0.02–27.6 bar, Ind. Eng. Chem. Res. 38 (1999) 512–518. [3] D.P. Kurtz, K.J. McNulty, R.D. Morgan, Stretch the capacity of highpressure distillation columns, Chem. Eng. Prog. 87 (1991) 43–49. [4] F.J. Zuiderweg, D.E. Nutter, Evidence of vapor backmixing in packed columns in the case of high pressure distillation, Inst. Chem. Eng. Symp. Ser. 128 (1992) A481–A488. [5] K. Onda, H. Takeuchi, Y. Okumoto, Mass transfer coefficients between gas and liquid phases in packed columns, J Chem. Eng. Jpn. 1 (1968) 56–62. [6] R. Billet, M. Schultes, Predicting mass transfer in packed columns, Chem. Eng. Technol. 16 (1993) 1–9. [7] M. Henriques de Brito, U. von Stockar, A.M. Bangerer, P. Bomio, M. Laso, Effective mass transfer interfacial area in a pilot column equipped with structured packings and with ceramic rings, Ind. Eng. Chem. Res. 33 (1994) 647–656. [8] J.A. Rocha, J.L. Bravo, J.R. Fair, Distillation columns containing structured packings: a comprehensive model for their performance. 2. Mass transfer model, Ind. Eng. Chem. Res. 35 (1996) 1660–1667. [9] J.J. Gualito, F.J. Cerino, J.C. Cardenas, J.A. Rocha, Design method for distillation columns filled with metallic, ceramic, or plastic structured packings, Ind. Eng. Chem. Res. 36 (1997) 1747–1757. [10] Z. Olujic, Development of a complete simulation model for predicting the hydraulic and separation performance of distillation columns equipped with structured packings, Chem. Biochem. Eng. Q. 11 (1997) 31–47. [11] Z. Olujic, Delft model—a comprehensive design tool for corrugated sheet structured packings, in: Proceedings of the Topical Conference Distillation Tools for the Practicing Engineer, AIChE Spring Meeting, New Orleans, LA, USA, March 10–14, 2002, pp. 142–152. [12] I. Siminiceanu, A. Friedl, M.A. Dragan, Simple equation for the effective mass transfer area of the Mellapak750Y structured packing, in: Scientific Conference Meeting—“35 Years of Petroleum-Gas University Activity”, Ploiesti, November 27–29, 2002. [13] Z.P. Xu, A. Afacan, K.T. Chuang, Predicting mass transfer in packed columns containing structured packings, Chem. Eng. Res. Des. 78 (2000) 91–98. [14] B. Hanley, B. Dunbobbin, D.A. Bennett, Unified model for countercurrent vapor–liquid packed columns. 2. Equations for the mass-transfer coefficients, mass transfer area, the HETP, and the dynamic liquid holdup, Ind. Eng. Chem. Res. 35 (1994) 1222–1230. [15] T.K. Sherwood, R.L. Pigford, C.R. Wilke, Mass Transfer, McGraw-Hill, New York, 1975. [16] Z. Olujic, A.B. Kamerbeek, J.A. de Graauw, A corrugation geometry based model for efficiency of structured distillation packing, Chem. Eng. Process. 38 (1999) 683–695. [17] S. Shetty, R.L. Cerro, Fundamental liquid flow correlations for the computation of design parameters for ordered packings, Ind. Eng. Chem. Res. 36 (1997) 771–783. [18] F.J. Zuiderweg, Z. Olujic, J.G. Kunesh, Liquid backmixing in structured packing in high pressure distillation, Inst. Chem. Eng. Symp. Ser. 142 (1997) 865–872. [19] J.L. Nooijen, K.A. Kusters, J.J.B. Pek, Performance of packing in high pressure distillation applications, Inst. Chem. Eng. Symp. Ser. 142 (1997) 885–897. [20] Z. Olujic, A.F. Seibert, J.R. Fair, Influence of corrugation geometry on the performance of structured packings: an experimental study, Chem. Eng. Process. 39 (2000) 335–342. [21] F. Rukovena, R.F. Strigle, Effect of pressure on structured packing performance, in: Paper Presented at AIChE Spring National Meeting, April, Houston, TX, 1989. [22] Z. Spekuljak, R. Billet, Mass transfer in regular packing, Lat. Am. J. Heat Mass Transfer 11 (1987) 63–72.