A New Model for the Calculation of Height Equivalent to Theoretical

ARTICLE pubs.acs.org/IECR

A New Model for the Calculation of Height Equivalent to Theoretical Plate in High Pressure Columns Equipped with Structured Packing for iC4/nC4 Separation Mohmmad Reza Rahimpour,* Hossein Momeni, Khadijeh Paymooni, and Ali Kiani Department of Chemical Engineering, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz 71345, Iran ABSTRACT: A semi-empirical model is proposed to investigate the performance of packed columns equipped with structured packing at high pressures. The mass transfer efficiency is determined in terms of height equivalent to theoretcial plate (HETP) for empirical data of an iC4/nC4 mixture at elevated pressures. Some unexpected phenomena cause predictive models of mass transfer to be inaccurate at high pressures. The effects of the gas phase backmixing and the liquid maldistribution on the gas phase mass transfer coefficient and the effective interfacial area have been investigated in this study. The modified model is developed on the basis of the Delft model to predict the mass transfer behavior of structured packing at high pressures. The proposed model is validated by the empirical data and good agreement is observed between the empirical data and the results of the modified model. The error of HETP calculation by the modified model is less than the other models especially at moderate and high pressures. At low pressures, predicted values of different models are almost the same and they show minor errors. The difference between predicted HETP by various models increases by pressure rising. Moreover, the effect of liquid load on mass transfer in packed columns is investigated. The proposed model can predict the effect of liquid load on mass transfer performance. Proper efficiency has been obtained by the modified model for iC4/nC4 separation process in structured packed column at high pressures.

1. INTRODUCTION For separation operations using packed columns, such as distillation and absorption processes, the best performance is usually obtained with packing techniques that involve low pressure drop, good mass transfer efficiency, and high capacity. The important properties of an efficient packing seem to be a high effective area, good liquid distribution, good gasliquid mixing, low pressure drop, and a structure composed of a material of small thickness.1 Various techniques are known for the separation of normal hydrocarbons from non-normal hydrocarbons. One such separation of practical commercial significance is the separation of iso-butane from normal butane. Isobutane and normal butane are commonly separated by distillation techniques that are effective; however, they are highly energy intensive.2 The general tendency of chemical engineering is to reach high efficiency and capacity of separation units at minimal possible cost. A novel generation of column internals is introduced to improve the mass transfer operation in this regard. Structured packing is made of corrugated sheets and has gained wide acceptance.36 Structured packing has been widely used for mass transfer processes, and its applications in separation process have been developed during past few years. Usually, the column with structured packing has shown better performance than tray column.7 Specific surface area of structured packing is between 100 and 750 m2/m3, and its void fraction is higher than 90%.8 High capacity, high mass transfer surface area, high turn down ratio, low pressure drop, and low liquid hold up are the advantages of the structured packing in comparison with trays or a random packing. One of the constraints in selection of structured packing is the high cost per unit volume, which causes the capital investment of structured packing to be more than that r 2011 American Chemical Society

of random packing.9 The column capacity can increase at least 3050% by revamping the existing tray columns with structured packing columns.10 The performance of packed columns, for distillation or absorption services, is frequently expressed in terms of height equivalent to a theoretical plate (HETP). Mendes et al.11 evaluated the performance of a laboratory scale packing distillation column using a hydrocarbon mixture of known composition (C8C14), which is a blend of linear paraffin from kerosene cut, with the objective of separating 98% weight C10 as top product of the column. Fei et al.12 investigated the effect of a channel opening angle on the hydrodynamic and mass transfer performance of structured packing both numerically and experimentally. Kenig et al.13 developed an analogy between the flow patterns in real separation columns equipped with structured packing and film flow. Sanchez et al.14 presented hydrodynamic and mass transfer performances of a new gasliquid contactor. Kannan et al.15 determined pressure drop and holdup data for KATAPAK-SP 12 packing contained in a 100 mm diameter column. The holdup and pressure drop correlations were extended to the postloading region. Performance of structured packing is very sensitive to liquidand gas-phase maldistribution. Especially, liquid-phase maldistribution causes a high depression in the effective interfacial area. The experiments showed that the performance of structured packing decreased in high pressure columns. Moreover, mass transfer predictive models showed high inaccuracies for structured packing at high pressures.16 Since the 1980s, several models Received: September 4, 2010 Accepted: April 19, 2011 Revised: April 12, 2011 Published: April 19, 2011 6886

dx.doi.org/10.1021/ie101856x | Ind. Eng. Chem. Res. 2011, 50, 6886–6897

Industrial & Engineering Chemistry Research

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Table 1. Delft Model Equations Packing Geometry hpb ¼ npe hpe

(1)

4s ap ¼ bh ffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b2 2 s ¼ 4 þh

(2)

lG, pe ¼ j ¼

(3)

hpe sin R

(4)

2s b þ 2s

(5) Hydrodynamic

uGs ¼

G pFffiffiffiffi FG

uLs ¼ uGs

(6)

FG FL

(7)

uGe ¼

uGs ½εð1 hL Þ sin R

(8)

uLe ¼

uLs ½εhL sin R

(9)

dhG

" # ðbh 2δsÞ2 bh # ¼ "" 2 2 0:5 bh 2δs bh 2δs bh 2δs þ þ 2h b 2h

(10)

ReGe ¼

FG uGe dhG μG

(11)

ReLe ¼

FL uLe dhL μL

(12)

ReGrv ¼

ðFGe ðuGe þ uLe ÞdhG Þ μG

(13)

dhL ¼ 4δ

(14) Liquid Holdup

hl ¼ δap 1=3 L uLe δ ¼ F 3μ gap sin R

(15) (16)

L

Δppreload ¼ ΔpGL þ ΔpGG þ ΔpDC ¼ ðζGL þ ζGG þ ζDC Þ ζGL ¼

h jξGL dhG pbsin R

2

ξGL

FG uGe 2

2

Pressure Drop (17) (18)

2

2

333 2

δ δ 6 6 dhG 6 dhG 777 5:02 14:5 777 6 6 ¼ 6 4 2 log4 3:7 ReGrv log4 3:7 þ ReGrv 555 hpb sin R

hpb sin R

¼ ð1 jÞ0:722ðcos RÞ3:14 dhG

ζGG ¼ ð1 jÞξGG dhG ζDC ¼ ψ ¼

(19)

(20)

hpb hpe ðξbulk

þ ψξwall Þ h 2 0:5 hpe dc 2 tanpe2 R þ π2 arcsin dc tan R

(21)

2hpe πdc 2 tan R

(22)

1:63

ξbulk ¼ 1:76ðcos RÞ ξwall ¼

4092uLs

0:31

(23) 0:445

þ 4715ðcos RÞ ReGe

þ 34:19uLs 0:44 ðcos RÞ0:779

(24) Effective Interfacial Area

ae ¼ ap

1Ω

1þ

A uLs B

A ¼ 0:000002143, B ¼ 1:5

(25) Mass Transfer Coefficient

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi KG ¼ KG, lam 2 þ KG, turb 2

(26)

KG, lam ¼

ShG, lam DG dhG

(27)

KG, turb ¼

ShG, DG dhG

(28)

ShG, lam

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0:664ScG 1=3 ReGrv ldGhG , pe

(29) 6887

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Table 1. Continued

ShG, turb ¼ ScG ¼

ξGL j 2=3 ReGrv ScG 8 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 1 þ ldhG G, pe ξGL j ðScG 2=3 1Þ 1 þ 12:7 8

(30)

μG FG DG

KL ¼ 2

(31)

qffiffiffiffiffiffiffiffiffiffiffi

HETP ¼

DL uLe 0:9πdhG

h

ðln λÞ λ1

(32) Mass Transfer Efficiency

i HTUGo

(33)

HTUGo ¼ HTUG þ λHTUL

(34)

HTUG ¼

uGs KG ae

(35)

HTUL ¼

uLs K L ae

(36)

Figure 1. Velocity profiles of two phases in maximum backmixing condition.

have been proposed to predict mass transfer, pressure drop, liquid hold up, loading, and flooding points. The Separations Research Program (SRP) model was proposed by Bravo et al.1719 In the SRP model, the mass transfer coefficient of gas phase was obtained by analogy of wetted-wall columns.20 The mass transfer coefficient of the liquid phase was calculated by the Higbie penetration theory,21 and finally the effective interfacial area was estimated by the proposed model of Shi and Mersman.22 In the Delft model,8,23,24 the mass transfer coefficient of gas phase was a combination of mass transfer coefficients of laminar and turbulent flows. Mass transfer coefficients of laminar and turbulent flows were estimated from the analogy between mass and heat transfers. The correlations of the mass transfer in a liquid phase in the Delft and the SRP models were similar, while the characteristic length of the Delft model was shorter than the SRP model. The correlations of the Delft model are summarized in Table 1. Gualito et al. modified the SRP model for higher pressures.25 Based on this model, the effective interfacial area for the mass transfer in high pressure columns was smaller than low pressure columns. They believed that the ratio of the superficial velocity of the liquid phase to the gas phase was correlated with the effective interfacial area of mass transfer. Wang et al.26 presented an improved model for calculating the effective interfacial area of

structured packing at elevated pressures. This model was developed on the basis of the SRP and the Gualito et al. models. The advantage of this model to the model of Gualito et al. was an added factor that reflected the pressure effect (in the form of the ratio of liquid to gas density). However, instead of the superficial velocity of liquid phase to gas phase, the effect of superficial velocity of gas on effective interfacial area was considered exclusively. This was the weakness of the Wang model. Billet proposed a model for mass transfer in packed columns. The Billet model derivation starts from the hydraulics of flow in channels and applies the Higbie penetration theory for the mass transfer. Thus, it is not surprising that the equations are structurally similar to the other models. However, holdup and the effective area are treated quite differently.27 In this study, the modified model is developed for packed columns equipped with structured packing for separation of an iC4/nC4 system at high pressures. Unlike the previous models, the effects of the gas phase backmixing and the density ratio are considered to improve the model predictability at high pressures. The capability of the modified model is compared with the previous ones. The empirical data of the iC4/nC4 system is adopted in a wide range of operating pressures at total reflux condition as a criterion to validate the proposed model. Results show a good agreement between this model and the empirical data at high pressures.

2. MODEL DEVELOPMENT As previously mentioned, the performance of structured packing diminishes in high pressure columns, and most of the predictive models show massive errors at elevated pressures. Some phenomena which cause the predicted results of the previous models to be inaccurate in high pressure columns are briefly outlined as follows: Gas Phase Backmixing. The gas phase backmixing occurs when the liquid phase drags a part of the gas phase near the interface downward.16 Figure 1 shows the velocity profiles of two phases in maximum backmixing condition. The gas phase backmixing is very small below the loading point, and its effect on mass transfer is negligible; however, it rises when the pressure or the ratio of gas-to-liquid density increases. Another factor that leads to an increase in the gas phase backmixing is low gas superficial velocity or high liquid superficial velocity. 6888



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Figure 3. A schematic diagram of a high-pressure packed distillation column.

Figure 2. Definition of backmixing parameter.

Liquid Phase Backmixing. The liquid phase backmixing occurs when the gas phase velocity is high enough to push up the liquid phase near the interface. The liquid phase backmixing is not limited by high pressures as it can even occur at low pressures. The liquid mass transfer coefficient decreases owing to liquid phase backmixing. Liquid Maldistribution. Liquid maldistribution has a destroying effect on column efficiency.28 Although, the influence of liquid rate was considered on the previous models, the liquid distribution was neglected. The ratio of the gas-to-liquid density increases by pressure rising, and it has a negative effect on the liquid distribution in columns. Consequently, the increase in the density ratio decreases the effective interfacial area. Droplet Formation. A droplet formation above the loading point causes the effective interfacial area and consequently the mass transfer efficiency to increase. HETP decreases as a result of the droplet formation. None of the predictive mass transfer models for structured packing can predict this phenomenon. 2.1. Proposed Model. By considering above-mentioned phenomena, the modified model is proposed for iC4/nC4 mixture. The operating condition is adjusted to avoid approaching to loading and flooding points while designing a structured packed column. Some problems which can be encountered during the operation of the system near the loading point are (1) pressure drop increases near the loading point and (2) around the loading point, little changes in column parameter lead to the flooding point. The mass transfer rate decreases considerably near the flooding point. Consequently, an operating condition around a loading point is not a stable or reliable condition. Owing to the above-mentioned reasons, most of the predictive models are limited to preloading conditions. In this study, the modified model is limited to a preloading operating condition.

Figure 4. Gas-phase backmixing in test conditions of ref 32 for different pressures.

Among four mentioned phenomena in the previous section, the liquid phase backmixing and the droplet formation take place near the loading point therefore they are not effective for a preloading condition. Thus, the gas phase backmixing and the liquid maldistribution are considered as the effective parameters in the proposed model. This proposed model is based on the Delft model however attempts have been made to add the effects of the above phenomena on the mass transfer in comparison with the previous models. Owing to high accuracy of the Delft model,29 it is chosen as the basis of our modified model. Although some of the correlations in the Delft model are more complicated than those of the SRP model, the trial and error for calculations is not needed in the Delft model. Each of the liquid and gas flow channels in the structured packing is assumed to be circular inclined pipe in which liquid is moving downward near the wall and gas flows upward in the center of the pipe. Upward direction is considered positive. Thus, gas velocity is positive and liquid velocity is negative. Hydraulic diameter of this circular pipe is calculated by the hydraulic 6889



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Table 2. Constant Values of Equations 44 and 45 constant

value

a1

20.22164

a2

0.94554

a3

1.58676

Figure 6. Prediction of HETP by the modified, Delft, and Billet models in comparison with empirical data for the iC4/nC4 system32 at different pressures.

Figure 5. (a) Effect of gas phase backmixing on ratio of gas phase mass transfer coefficient of modified model to Delft model; (b) effect of density ratio on the ratio of effective interfacial area of modified model to Delft model.

diameter equation of the Delft model (Table 1 eq 10) and the liquid film thickness is obtained from eq 16. To calculate the gas phase backmixing, it is necessary to obtain velocity profiles of both phases. 2.1.1. Liquid Phase Velocity Profile. The liquid phase velocity profile of a falling film is extracted from Perry’s Chemical Engineer’s Handbook. 30 " 2 # 2x x UL ¼ 1:5uLe ð37Þ δ δ

Also, it can be used for cylindrical coordinates because the ratio of liquid film thickness to hydraulic pipe diameter is too small. As this model is limited to the preloading condition, gas flow does not have a significant effect on a liquid velocity profile, and therefore eq 37 is applicable for mentioned conditions. 2.1.2. Gas Phase Velocity Profile. Gas flow can have laminar or turbulent regime in structured packing. To compute the gas velocity profile, it is necessary to determine the flow regime according to the Reynold’s number. The Reynold’s number is obtained from Table 1 eq 13. Since gas phase velocity in most cases is in the turbulent zone, it is comprehensively explained as follows: Gas Phase Velocity Profile: A Turbulent Flow Regime. To calculate gas velocity profile at a turbulent flow regime, oneseventh power velocity profile equation has been used.31 This equation has been modified for gas phase velocity in packed column as follows: 0 1ð1=7Þ UG þ ULmax r C B C ¼B @1 d A UGmax hG 2 UGmax ¼ ð1 þ 1:326

pffiffi f Þ ðULmax þ uGe Þ

ULmax ¼ 1:5uLe

ð38Þ

ð39Þ ð40Þ

Maximum velocity of a gas phase can be calculated from eq 39.31 Effective velocities of gas and liquid are computed from the Delft model (Table 1 eqs 8 and 9). Friction factor is obtained from Delft parameters as

Liquid film thickness (δ) is calculated from Table 1 eq 16. This correlation is presented for Cartesian coordinates.

f ¼ φ εGL þ ð1 φÞ εGG 6890

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2.1.3. Definition of a New Parameter. As the velocity profiles of gas and liquid phases are specified, the radius in which the gas velocity gets zero could be calculated. This radius equals (rhyd L1) as shown in Figure 2. The dimensionless parameter of the gas phase backmixing is defined as L1 BM ¼ dhG 2

BM ¼

!7 ðfor turbulent flowÞ

ð43Þ 2.1.4. Effects of Gas Phase Backmixing and Liquid Maldistribution on Mass Transfer. The effects of the gas phase backmixing and the density ratio on the mass transfer coefficient and

Figure 7. Comparison of predicted HETP by five various models (modified, Delft, Billet, SRP, and Gualito) and empirical data for the iC4/nC4 system33 at different pressures.

kG ¼ 1 a1 BMa2 kGDelf t

ð44Þ

F ¼ 1 a3 G FL

ð45Þ

ae

ð42Þ

A correlation is obtained from a gas velocity profile to calculate the gas phase backmixing at turbulent condition. According to this correlation, the gas phase backmixing parameter can be determined straightforwardly from column parameters. 1:5uLe pffiffi ð1:5uLe þ uGe Þ ð1 þ 1:326 f Þ

the effective interfacial area are introduced in the following equations, respectively:

ae Delf t

In the modified model, the mass transfer coefficient in the gas phase and the effective interfacial area are determined with the aid of the Delft equations. It is obvious that the increase in the gas phase backmixing decreases the mass transfer coefficient of the gas phase in the modified model. Therefore, coefficient values of the Delft and the Modified models do not match. Also, the difference between the predicted values of the effective interfacial area by Delft and Modified models increases with an increase in the ratio of gas-to-liquid density. Constant values of eqs 44 and 45 (a1, a2 , a3) are determined by the empirical data. Although a lot of empirical data can be found for the mass transfer of structured packing at low and moderate pressures, limited information is available for structured packing at elevated pressures. The empirical data for calculating the constants of the proposed model are in the following conditions.32 2.2. Experimental Data. A schematic diagram of a high pressure packed distillation column is depicted in Figure 3. The experimental data are obtained with a commercial-scale experimental column of 1.2 m ID with 18 layers of Mellapak250Y structured packing (made in Sulzer Company). A thickness of each layer was 210 mm. Tube drip-pan-liquid distributors were used. The testing system was a mixture of iC4/nC4, and the operating pressures of the tests were 6.9, 11.4, 20.7, and 27.6 bar. Since the diameter of the column was big enough, it could be considered as an industrial scale.32 The modified model was valid for a preloading condition, thus data relevant to an after-loading condition were eliminated. The values of a1, a2, and a3 were determined by the two-dimensional curve fitting of the empirical data. The basis of curve fitting was to minimize the square errors and some tactics were used to prevent the differential in the number of data at different pressures. Since columns containing structured packing were mostly used at moderate pressures rather than elevated pressures, the curve was shifted to fit and obtain the best result at moderate pressures. The fluid properties and parameters at the experiment conditions were calculated to solve the model equations. Figure.4 shows a gas-phase backmixing parameter of the empirical data for different pressures. As seen, pressure has a great influence on the gas-phase backmixing parameter. By increasing the gas velocity, the gas-phase backmixing decreases slightly at different pressures. According to the two-dimensional

Table 3. Mean Absolute Error Percentage of Calculated HETP by Different Models mean absolute error percentage pressures (bar)

new model

Delft model

SRP model

Gualito model

Billet Model

P = 6.89 P = 11.38

15.75792 8.361316

7.088365 20.19175

39.11598 44.17510

16.68353 29.82068

17.98 5.28

P = 20.4

5.301458

48.53995

64.36590

26.36990

14.55

P = 27.58

3.516941

80.64385

86.06565

23.57032

48.57

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Figure 8. Effective interfacial area calculated by various models versus F-factor for iC4/nC4 system.

curve fitting of the empirical data in ref 32, constant values of eqs 44 and 45 are tabulated in Table 2. Figure 5a illustrates the effect of gas-phase backmixing on the mass transfer ratio of the modified model to Delft model. As seen, the predicted mass transfer coefficient by the modified model shifts to the one of the Delft model when the gas phase backmixing approaches zero. Increasing values of gas-phase backmixing causes a decrease in the mass transfer coefficient of the modified model. The effect of the density ratio on the effective interfacial area of the modified model and the Delft model is investigated in Figure 5b. The effective interfacial area of the modified model and the Delft model are equal when the ratio of gas-to-liquid density is approximately zero. By increasing the ratio of gas-to-liquid density, the difference between the effective interfacial area of modified model and Delft model increases. Figure 6 shows the empirical data of iC4/nC4 system32 and predicted HETP by the modified, Delft, and Billet models. The error of HETP calculation increases by pressure augmentation in accordance with the Delft model. The predicted HETP by the modified model has shown more accurate values in comparison with the Delft and Billet models at high pressures. The Billet model overpredicts the HETP at 6.9 and 11.4 bar.

3. MODEL VALIDATION As some of the parameters of the modified model are obtained by the interpolating of empirical data,32 it is obvious that this

model can provide better prediction of these data32 than other models. Thus, new data should be used for model validation. There are other empirical data for iC4/nC4 system at high pressures for Intalox 2T.33 The tests are done for pressures of 6.89, 11.38, 20.68, and 27.58 bar and for a total reflux condition. These data33 are used for model validation. Predicted HETP by five various models (modified, Delft, SRP, Billet, Gualito et al.) and empirical data for iC4/nC4 system33 are shown in Figure 7. The predicted values by the modified model and the empirical data are in good agreements. The error of HETP calculation by the modified model is less than the other models especially at moderate and high pressures. Moreover, HETP decreases with increasing Ffactor at high pressures, where F-factor is the vapor load factor F = ug(Fg)0.5. This is predicted by the modified and Billet models, while the other models predict the HETP rising, which is not in agreement with the empirical data. However, there is not much difference between Delft and modified models at low pressures.

4. MODIFIED MODEL CRITERIA The proposed model is applicable when the ratio of mass transfer coefficient of gas phase by the modified model to mass transfer coefficient of gas phase by the Delft model becomes more than zero, in other words, gas phase backmixing parameter becomes less than 0.041589. Furthermore, the ratio of the 6892



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Figure 9. Predicted gas phase mass transfer coefficient by various models for iC4/nC4 system versus F-factor at different pressures.

new parameter named “deviation coefficient” is proposed. Cdeviation ¼

F 1 a3 G FL

ð1 a1 BM a2 Þ

ð46Þ

Analysis of empirical data shows that the Delft model is more accurate for Cdeviation > 0.9, and the modified model gives more precise results for Cdeviation < 0.9.

5. RESULTS AND DISCUSSION

Figure 10. Effect of liquid load on gas phase backmixing.

effective interfacial area of the modified model to that of the Delft model should be more than zero so that the ratio of gas-to-liquid density should be less than 0.630213. Since the gas phase backmixing parameter and the density ratio are in these ranges, the modified model can be applied. The modified model is more accurate at moderate and high pressures. The model can be used for low pressures; however, the accuracy of HETP calculation decreases. Mean absolute error percentage of calculated HETP by different models is reported in Table 3. As seen, the results of calculated HETP for the modified model are more accurate than the values of other models. At low pressures, the Delft models are slightly more precise than the modified model. To recognize a more accurate model, a

5.1. A Comparison of the Models’ Predictions. As previously mentioned, the modified model is in a good agreement with the empirical data.33 The results of the modified model are compared with the ones of the previous models. The effects of gas phase backmixing and liquid maldistribution on the mass transfer phenomenon are investigated in the proposed model. The calculated values of the effective interfacial area of various models for a wide range of F-factors are illustrated in Figure.8 based on the empirical data of iC4/nC4 system.33 (It should be mentioned that the specific surface of Intalox 2T is 220 m2/m3.) For different pressures, modified and Delft models show a very weak functionality of F-factor, and actually they are independent of it. The difference between predicted values of the effective interfacial area by different models increases with pressure rising. The increases in the ratio of gas-to-liquid density by pressure rising influence the liquid distribution in the packed column. As the gas phase backmixing and liquid maldistribution phenomena are considered in the modified model, the decrease in the effective interfacial area is more considerable at high pressures in comparison with the other models. HETP and consequently 6893



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Figure 11. Effect of liquid load on gas phase mass transfer coefficient for the iC4/nC4 system at different pressures.

the mass transfer operation decreases owing to the decrease in the effective interfacial area. Furthermore, the prediction of gas phase mass transfer coefficient of various models at different pressures for iC4/nC4 system is illustrated in Figure.9. Since SRP and Gualito models have the same mass transfer coefficients, Gualito results are eliminated in this figure. For all models, gas phase mass transfer coefficient increases with increasing the F-factor. For a wide range of pressure and F-factor, the highest and the lowest values of gas phase mass transfer coefficients are predicted by SRP and modified models, respectively. The predicted gas phase mass transfer coefficient by the modified model is less than the one by the other models because the effect of gas phase backmixing phenomenon becomes more considerable on the mass transfer coefficient at high pressures. As known, the mass transfer decreases by increasing the gas phase backmixing. It is worth mentioning that the difference between the predicted values of the modified model and those of the previous models becomes more obvious at higher pressures owing to consideration of the mentioned parameter. As seen in Figure 9, the difference between predicted values of gas phase mass transfer coefficients by Delft and modified models for iC4/nC4 system increases by pressure augmentation however it is minor at low pressures. The low value of the gas phase mass transfer coefficient causes the predicted HETP of the modified model to be more than that of the other models as illustrated in Figure 7. The considerable difference between the predicted values of HETP in all previous models and the empirical data is the neglect of the gas phase backmixing and liquid maldistribution phenomena. The superiority of the modified model to the other models is clearly recognized by the fact that the predicted HETP of the modified model and the empirical data are in good agreement.

5.2. Effect of Liquid Load on Mass Transfer. One of the limitations for choosing a suitable structured packing is the liquid load. Generally, an increase in liquid load leads to reduction of mass transfer performance of packing. Figure 10 illustrates the effect of liquid load on gas phase backmixing. As seen, the gas phase backmixing increases owing to the liquid load. In Delft and SRP models, the effective velocity of liquid phase and also relative velocity Reynolds number (RGrv) increase owing to an increase in liquid load. This leads to an increase in gas phase mass transfer coefficient. The effect of liquid load on the gas phase mass transfer coefficient is depicted in Figure 11. Delft and SRP models predict that the mass transfer coefficient increases owing to liquid load rising. The mass transfer coefficient of the modified model is affected by liquid load in two ways. First, the increase in liquid load increases relative velocity Reynolds number and consequently increases the mass transfer coefficient of gas phase. Second, the increase in liquid load leads to an increase in gas phase backmixing and consequently decreases the mass transfer coefficient of gas phase. The interaction of these factors leads to an augmentation in gas phase mass transfer coefficient at low pressures and a depression of it at high pressures. The SRP and modified models show the highest and the lowest prediction of gas phase mass transfer coefficient for all pressures, respectively. As seen, gas phase backmixing and the difference between predicted mass transfer of gas phase by the Delft and modified models increase owing to an increase in the liquid load. Pressure is another factor which increases gas phase backmixing. The gas phase backmixing increases by pressure rising. Therefore, the differences between predicted values of gas phase mass transfer coefficient by the modified and Delft model increases. 6894



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Figure 12. Effect of liquid load on HETP at various pressures for iC4/nC4 system.

The effect of liquid load on HETP for iC4/nC4 system at various pressures is depicted in Figure 12. The Delft model predicts a minor increase in gas and liquid mass transfer coefficients. The predicted values of HETP decrease slightly by liquid load augmentation. According to the SRP model, the mass transfer coefficients of gas and liquid phases decrease while the effective interfacial area increases considerably by liquid load rising. The interactions of these effects cause a minor decrease in the predicted HETP due to increase in liquid load. Empirical data show that the mass transfer efficiency declines with liquid load rising. Both SRP and Delft models cannot predict the effect of intensification of liquid load on HETP; however, the modified and Gualito models are capable of this prediction. A considerable decrease in effective interfacial area and a remarkable increase in HETP are predicted by Gualito model owing to rising of the liquid load. In the modified model, HETP increases as a result of a slight decrease in the gas phase mass transfer coefficient and the effective interfacial area. The liquid load has a great influence on HETP in accordance with the Gualito model; however, this effect is slighter in the modified model. The effect of liquid load on HETP increases for both models with pressure rising.

6. CONCLUSIONS In this research, performances of different predictive models were studied in structured packed columns for the iC4/nC4 system at high pressures. The predicted HETP showed the performance of a packed column from the mass transfer viewpoint. Two new dimensionless parameters named the gas phase

backmixing and the ratio of gas-to-liquid density were applied. These parameters influenced the mass transfer rate of high pressure columns equipped with structured packing. A new modified model was proposed based on the Delft model for predication of mass transfer in structured packing under high pressures condition. A set of total reflux distillation empirical data for iC4/nC4 mixture was used to validate the modified model. The empirical data demonstrated that the modified model was more accurate than the other models at moderate and high pressures. To recognize which model (modified or Delft) would be more precise at high pressures, a new technique was proposed. Predicted values of effective interfacial area and mass transfer coefficients of gas phase were compared by various models. The modified model could precisely predict reduction of effective interfacial area and the mass transfer coefficient by pressure rising. As another important parameter, the effect of liquid load on performance of a packed column was investigated. Results showed that the efficiency of structured packing reduced by the increase of liquid load. The advantage of this model was that the effect of density ratio was considered. The effect of superficial velocity of liquid phase on mass transfer was neglected in the model of Wang et al. However, this phenomenon was thoroughly studied in the modified model. The Wang and Gualito models were obtained experimentally; however, the modified model was a semi-empirical model and the hydrodynamic of gas phase backmixing was studied completely theoretically in the presented study. The estimated HETP was compared with the empirical data of structured packing for the iC4/nC4 mixture, and the accuracy 6895



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of the proposed model demonstrated acceptable results for separation purposes. Results show the superiority of the modified model to the other models.

V= molar flow rate of vapor, kmol/s WeL= Weber number for the liquid, dimensionless χ= distance from wall, m

’ AUTHOR INFORMATION

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Corresponding Author

*Tel.: þ98 711 2303071. Fax: þ98 711 6287294. E-mail: [email protected].

’ ACKNOWLEDGMENT The authors gratefully acknowledge the National Iranian Central Oil Field Company and South Zagros Oil and Gas Production Company for financial support. ’ NOMENCLATURE a1= constant in eq 44, dimensionless A2= constant in eq 44, dimensionless A3= constant in eq 45, dimensionless ap= specific surface area of packing, m2/m3 ae= effective surface area, m2/m3 B= corrugation base length, m BM= backmixing parameter, dimensionless Cdeviation= deviation coefficient, dimensionless DG= gas-phase diffusion coefficient, m2/s DL= liquid-phase diffusion coefficient, m2/s dc= column diameter, m dhG= hydraulic diameter for the gas phase, m Fload= loading effect factor, dimensionless Ft= partial wetting correction factor, dimensionless Fse= surface enhancement factor, dimensionless FrL= Froude number for liquid, dimensionless G= gravity acceleration, m/s2 HETP= height equivalent to a theoretical plate, m HTUG= height of a gas-phase transfer unit, m HTUL= height of a liquid-phase transfer unit, m HTUGo= height of an overall gas-phase-related transfer unit, m H= corrugation height, m hL= operating liquid holdup, dimensionless hpb= height of the packed bed, m hpe= height of the packing element, m kG= gas-phase mass-transfer coefficient, m/s kL= liquid-phase mass-transfer coefficient, m/s L= molar flow rate of liquid, kmol/s L1= backmixing length in Figure 2 lG,pe= length of gas flow channel in a packing element, m M= slope of the equilibrium line, dimensionless npe= number of packing elements (layers) in a bed, dimensionless R= channel radius, m ReGe= effective gas-phase Reynolds number, dimensionless ReGrv= relative velocity Reynolds number, dimensionless ScG= Schmidt number for gas, dimensionless S= corrugation side length, m UG= gas velocity profile in channel, m uGe= effective gas velocity, m/s uGe,lp= effective loading point gas velocity, m/s uGs= superficial gas velocity, m/s UL= liquid velocity profile in channel, m/s uLe= effective liquid velocity, m/s uLs= superficial liquid velocity, m/s

r= corrugation inclination angle, deg Γ= contact angle between solid and liquid film, deg Δ= liquid film thickness, m ζDC= overall coefficient for direction change losses, dimensionless ζGG= overall coefficient for gas-gas friction losses, dimensionless ζGL= overall coefficient for gasliquid friction losses, dimensionless ε= packing porosity, m3 of voids/m3 of bed Λ= m/(L/V)) stripping factor, dimensionless μ= viscosity, Pa s ξbulk= direction change factor for bulk zone, dimensionless ξGG= gas-gas friction factor, dimensionless ξGL= gasliquid friction factor, dimensionless ξwall= direction change factor for wall zone, dimensionless FG= density of gas, kg/m3 FL= density of liquid, kg/m3 τrz= shear stress, pa Φ= fraction of the triangular flow channel occupied by Liquid, dimensionless Ψ= fraction of gas flow channels ending at column walls, dimensionless Ω= fraction of packing surface area occupied by holes, dimensionless Subscripts

Delft= Delft model E= effective G= gas or vapor Lam= laminar flow L= liquid max= maximum S= superficial turb= turbulent flow

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