modeling of mass transfer in nonideal multicomponent mixture with maxwell-stefan

SEPARATION SCIENCE AND ENGINEERING Chinese Journal of Chemical Engineering, 18(3) 362371 (2010)

Modeling of Mass Transfer in Nonideal Multicomponent Mixture with Maxwell-Stefan Approach*

SONG Yiming ()1,2, SONG Jinrong ()1,2, GONG Ming ()1,2, CAO Bin ()1,2, YANG Yanhong ()1,2 and MA Xiaoxun ()1,2,** 1 School of Chemical Engineering, Northwest University, Xian 710069, China 2 Chemical Engineering Research Center of the Ministry of Education for Advanced Use Technology of Shanbei

Energy, Xian 710069, China

Abstract The Intalox metal tower packing was used to simulate an industrial relevant extractive distillation col-umn for purifying azeotropic multicomponent mixture. In order to explain the inconsistencies in the modeling of transfer process in nonideal multicomponent distillation column, a method was developed with equilibrium stage models (EQ) and non-equilibrium model (NEQ) incorporated with Maxwell-Stefan diffusion equations in the framework of AspenONE simulator. Dortmund Modified UNIFAC (UNIFAC-DMD) thermodynamic model was employed to estimate activity coefficients. In addition, to understand the reason for the diffusion against driving force and the different results by EQ and NEQ models, explicit investigations were made on diffusion coefficients, component Murphree efficiency and mass transfer coefficients. The results provide valuable information for basic design and applications associated with extractive distillation. Keywords rate based model, equilibrium model, mass transfer coefficient, Murphree efficiency, extractive distil-lation, simulation

1 INTRODUCTION

There is considerable industrial interest in design and optimization of extractive distillation due to the large number of industrial columns in operation and the potential of developing improved separation schemes so as to minimize energy consumption [1-3]. As a result, various extractive distillation systems have been investigated, such as solvent selection methods [4], development of new extractive distilla-tion systems [5-7], and introduction of a salt to the solvent to improve the separation [8]. However, there are few publications [9-12] on modeling and simula-tion of azeotropic multicomponent extractive distilla-tion using non-equilibrium (NEQ) approach. In indus-trial design, chemical engineers usually develop their design procedures for separation equipment using Ficks law of diffusion [13, 14], in which the flux Ji is linearly dependent on molar average mixture velocity and composition gradient ix

( )i i i i i iJ c v v c D x = (1) This constitutive relation is strictly valid only under the following conditions: (i) binary mixtures, (ii) dif-fusion of dilute species in a multicomponent mixture, and (iii) in the absence of electrostatic or centrifugal force field. For practical purpose, we usually use Murphree vapor efficiency (EiMV) for a plate and the height equivalent to a theoretical plate (HETP) for packings. The concept works quite well for binary sepa-ration [14, 15], based on the assumption that the effi-ciencies of two components are equal and the physical

properties are constant along the column. However, it is difficult to relate the concept to the construction and performance of equipment, and to apply it to nonideal multicomponent mixtures [16, 17]. In addition, some bizarre behavior may appear, such as unbounded component Murphree efficiencies [17], and the diffu-sion in ternary mixture is much more complex than that in binary mixture [18] because of coupling between species concentration gradients. To avoid the am-biguous component efficiencies and the limitation of Ficks law for describing diffusion in multicomponent mixture, a realistic model is needed. It is now gener-ally accepted that the Maxwell-Stefan formulation provides the most general and convenient approach for describing transport process in multicomponent mixture [11, 15, 19]. Lao and Taylor [20] first developed a model based on the Maxwell-Stefan formulation for multicomponent distillation for a single tray. In this study, the NEQ approach incorporated with Maxwell- Stefan diffusion theory is applied to simulate an in-dustrial relevant extractive distillation column, and the mass transfer process and associated influence factors, such as mass transfer coefficients, Murphree effi-ciency and diffusion coefficients, are investigated.

2 SIMULATION PROCESURE AND MODELING

2.1 Numerical set up and conditions

Figure 1 illustrates the schematic presentation of an extractive distillation column. The column consists of 27 stages, including the total condenser (stage 1)

Received 2009-12-24, accepted 2010-03-29.

* Supported by the National Natural Science Foundation of China (20776118), Science & Technology Bureau of Xian [CXY09019 (1)], Innovation Foundation for Graduated Student of Northwest University (08YJC21), Shaanxi Research Center of Engineering Technology for Clean Coal Conversion (2008ZDGC-13).

** To whom correspondence should be addressed. E-mail: [email protected]

Chin. J. Chem. Eng., Vol. 18, No. 3, June 2010 363

and partial reboiler (stage 27). Table 1 lists the principal configuration data. In both EQ and NEQ approaches

the vapor phase is assumed to be thermodynamically ideal. In addition, the test for the presence of the sec-ond liquid phase is considered in EQ approach. To determine the bulk properties in NEQ approach, which is relative to the inlet and outlet properties for each phase on each stage, mixed and countercurrent flow are considered as flow patterns for bubble cap tray and random packing respectively. The 25 mm Intalox metal tower packing (IMTP) applied has a HETP value of 0.42 m in the EQ simulation.

2.2 Mathematic modeling incorporated with Maxwell-Stefan theory

2.2.1 Film model and Maxwell-Stefan theory Simulation of distillation process is often carried

out with the equilibrium stage model [21]. However, the equipment and flow pattern, which present the hydrodynamic characteristics and influence the ther-modynamic property, are beyond the scope of EQ ap-proach. In most equipment, the flow of both phases is highly turbulent [22-24], so on not-too large scales the concentrations and temperatures in the bulk fluids can be considered as uniform. Near the phase interface turbulence dies out and eddies do not pass across it. Fig. 2 presents the simplest model, the film model, for mass and heat transfer [17, 22, 24].

Figure 2 The simplest non-equilibrium model

In the film model, it is assumed that all the resis-tance to mass transfer is concentrated in a thin film adjacent to the interface [24-26], in which the transfer occurs by steady state molecular diffusion. Outside this film, in the bulk fluid, all composition gradients are wiped out by turbulent eddy. A fully turbulent flow of bulk phase is adjacent to the thin film in laminar flow parallel to the interface. Mass transfer through this film is in the direction normal to the interface, and any constituent molecular diffusion or convection parallel to the surface resulted from composition gradients along the interface is negligible. To calculate the interphase mass transfer fluxes in multicomponent mixtures, it is now generally accepted that the Maxwell-Stefan diffu-sion formulation is adopted for the fluid phases [27-32], in which chemical potential gradients are used as the driving forces for diffusion. A linear relation is postulated

Figure 1 Schematic presentation of extractive distillation column

Table 1 Principal configuration data

Input data and specified parameters

Operating specifications

feed stage of entrainer above stage 6

feed stage of C4 above stage 19

temperature of entrainer 50 C pressure of entrainer 1 MPa

pressure of C4 stream 0.51 MPa

reflux ratio 2

C4 condition vapor

flow rate of C4 10000 kgh1

mass fraction of C4

n-butane 50%

1-butene 3%

cis-2-butene 16%

trans-2-butene 31%

flow rate of entrainer 80000 kgh1

entrainer condition liquid

mass fraction of water in entrainer 8.30%

Column parameters

number of stage 27

diameter of packing in the column 1.25 m

number of wash tray 5

diameter of wash tray 1.2 m

random packing IMTP, 25mm-metal

wash tray bubble cap tray


between the driving forces and the fluxes:

1 1 1

n n Nj i i j j i i j

ij ij j ji ij i ij

j i j i

x j x j x N x Nc c

= = =

= = (2) where xi represents the mole fraction in the fluid phase, Ni is the molar flux, ij is the Maxwell-Stefan diffu-sivity, and i is the chemical potential gradient, which is from the frictional drag of one group of mole-cules moving through the others. It does not matter whether the frictional drag arises purely from inter-molecular collisions as in the simple kinetic theory of gases or additionally from intermolecular forces be-tween two groups of molecules. The Maxwell-Stefan diffusivity is given by

( )2 1 2dd iRT x v v

z = (3)

With this definition, the Maxwell-Stefan diffusivity (m2s1) is related to the drag coefficient, and is easier to interpret and predict than Ficks diffusivity. For an ideal binary gas mixture it is equal to Ficks diffusivity. Following the approach of Krishna and Taylor [24] Eq. (2) can be recast in terms of the mass transfer coefficients kij

1 11,2, , 1

n nj i i j

ij jj j i ij

j i

x N x Nx i n

c k

= =

= = (4) where xj represents the difference in composition between the bulk fluid and interface, and ij represents thermodynamic correction factor related to the non-ideal behavior. For a highly nonideal mixture, the ther-modynamic factor is usually a strong function of the mixture composition and vanishes in the region of the critical point [17, 21]. The driving force contains con-tributions due to mole fraction and activity coefficient of species i, and the contribution of mole fraction gra-dient is similar to that of concentration in Ficks equa-tion. However, Ficks equation does not consider the effect of nonideality via the activity coefficient [33, 34]. Thus the formulation is useful in relating the practical coefficients to the molecular collision processes and the intermolecular interactions in the mixture [24]. It takes proper account of diffusional coupling between the species transfer, i.e. the flux of any species de-pends on the driving forces of all the species present in the mixture.

2.2.2 Model formulation For the system considered in the simulation as

shown in Fig. 2, our immediate task is to develop the balances for describing the transport processes.

Material and energy balances for the bulk liquid and vapor:

L F L L1 , 1 0j ij j i j ij ij j ijF x L x N r L x + + + = (5)

V FV V V V V1 1 0j j j j j j j jF H V H Q q V H+ + + + + = (6)

V F V V1 , 1 0j ij j i j ij ij j ijF y V y N r V y+ + + + + = (7)

L FL L L L L1 1 0j j j j j j j jF H L H Q q L H + + + = (8)

Material and energy balances for liquid and vapor film: I fL L 0ij ij ijN r N+ = (9)

V fV I 0ij ij ijN r N+ = (10) I L 0j jq q = (11) V I 0j jq q = (12)

Phase equilibrium: I I 0ij ij ijy K x = (13)

Mole fraction summation for bulk liquid and vapor:

11 0

n

iji

x=

= (14)

11 0

n

iji

y=

= (15) Mole fraction summation for interface:

I

11 0

n

iji

x=

= (16) I

11 0

n

iji

y=

= (17) Mass flux for bulk liquid and vapor:

( ) ( )( )

EL I

L L L 0

j jjj j j

j j t j

x zx x

R N N x

+ = (18)

( ) ( )I I V V V 0j j j j j t jy y R N N y + = (19) where is the matrix of thermodynamical factors:

L

LL, , ,

, ,

ln

j j

iji k j i k ij

kj T P

xx

= + (20)

V

VV, , ,

, ,

ln

j j

iji k j i k ij

kj T P

yy

= + (21)

The symbol means fixing the mole fractions of all other components except for the n-th component while evaluating the differentiation. The inverse matrixes of mass transfer coefficients R are

L, , L I L L I L

1, , , ,

1, , 1

nij mj

i i jmj j i n j j j i m jm i

x xR

a k a k

i n

== +

=

(22)

LL L L L L L, ,

, , , ,

1 1

1, , 1,

i k j ijj j i k j j j i n j

R xa k a k

i n i k

= = (23)


V, , V I L V I V

1, , , ,

1, , 1

nij mj

i i jmj j i n j j j i m jm i

y yR

a k a k

i n

== +

=

(24)

VV I V V I V, ,

, , , ,

1 1

1, , 1,

i k j ijj j i k j j j i n j

R ya k a k

i n i k

= = (25)

The heat stream for the bulk liquid and vapor phase is given by

( )I L L L LI L1

0n

j j j ij ijj ji

a h q N HT T=

+ = (26) ( )I V V V VV I

10

n

j j j ij ijj ji

a h q N HT T=

+ = (27) To reduce the size of Jacobian elements, the mass transfer coefficients are written as

o, , , ,

ji k j j i k jk k D

= (28) where ojk is a function of flow, temperature, composi-tion and other properties but independent of compo-nents i and k.

2.3 Correlation methods

Accurate transfer efficiency and knowledge of the maximum hydraulic capacity [35] and pressure drop [36] of a packing are essential for design and operation of packed columns. The transfer process in packed col-umns is dependent on many factors, such as flow rates of vapor and liquid, physical properties, and vapor-liquid equilibrium [37-42], which change from location to location along the column. Most of the existing mod-els for prediction of height of a transfer unit (HTU) are inappropriate if the factors stated above change along the column significantly, especially for nonideal and chemical reaction systems.

2.3.1 Correlations for interfacial area and mass trans-fer coefficients

For bubble cap tray, the correlation of Gerster et al. [43] is used to estimate the interfacial area and mass transfer coefficients, which is as follows.

Binary mass transfer coefficient for the liquid and vapor:

( ) ( )0.58 L s L,L, L I

0.21313 0.154.127 10 i ki k

F LtDk

a+= (29)

V Lw s,

w

0.5 VV, , b

I

104.850.776 4.567 0.2377i k

i k s

Qh Fkl

Sc A va

+ += (30)

Interfacial area:

I 0.375 0.247 0.515b V L w0.27a A Re Re h= (31)

Superficial F-factor:

( )0.5V Vs s tF u = (32) Average residence time for liquid:

L L w L0.9998 /t h Zl Q= (33) Liquid height:

L w L w s0.04191 0.19 2.4545 / 0.0135h h Q l F = + + (34) Average volumetric flow rate per pass for liquid:

L L p/Q Q N= (35) For IMTP packing, the correlation of Onda et al.

[44] is used to predict the interfacial area and mass transfer coefficients.

Binary mass transfer coefficient for the liquid and vapor:

( ) ( )0.333L0.40.667L 0.5

p p, L, ,L L0.0051i k i kga dk ScRe

=

(36)

( ) 2V 0.7 0.333 V p p, V V, , p ,5.23i k i k i k a dk Re Sc a D = (37) Effective interfacial area for mass transfer:

I w t pa a A h= (38) Wetted surface area per unit volume:

0.750.1 0.05 0.2c

w p L L L1 exp 1.45a a Re Fr We

=

(39)

2.3.2 Correlations for heat transfer coefficients The Chilton and Colburn method is based on the

relationship of Chilton-Colburn analogy and calcu-lates heat transfer coefficients from the binary mass transfer coefficients. It is probably the most successful and widely used analogy and proved to be the most accurate [45-50].

Heat transfer coefficients for vapor and liquid: 2/ 3L

L L L LL L LP

Pk C

C D

= (40)

2/3VV V V V

V V VPP

k CC D

= (41)

Average diffusivity and mass transfer coefficient:

( )( )( )( )

c c

c c

1

1 11

1 1

n n

ij kj ikji k i

j n n

ij kji k i

x x DD

x x

= = +

= = +

+ +=

+ +

(42)


( )( )( )( )

c c

c c

1

1 11

1 1

n n

ij kj ikji k i

j n n

ij kji k i

x x DK

x x

= = +

= = +

+ +=

+ +

(43)

where nc is the number of components. The Chilton- Colburn averaging parameter has the default value of 104. Eqs. (5)-(43) describe the transport process for the investigated system and the numerical solution represents the behavior in the column. The set of equa-tions is solved using Newtons method. Property moni-tors are configured to verify the convergence. How-ever, for some properties, such as diffusivities, partial molar enthalpies and activity coefficients, the deriva-tives are not available for the property monitors as they involve derivatives of matrices or derivatives of deriva-tives. The next section gives the results of the simulation.

2.4 Thermodynamic property

In the nonequilibrium model, we assume that equilibrium exists at the interface. Thermodynamic model is needed to describe the equilibrium for the mixture. Due to the highly nonideal behavior in extrac-tive distillation, it is necessary to apply relative com-plex thermodynamic method for accurate prediction of the corresponding phase equilibria. The choice of spe-cific thermodynamic model has a great effect on the results of simulation [8, 27, 46]. Two models are usually used in multicomponent distillation: multicomponent equations of state and Gibbs excess energy models. The latter are useful for strongly nonideal mixtures at not-too-high pressures [27, 33]. In this study it is found that the predictions, especially the temperature profiles, by NRTL, UNIQUAC and ASOG are quite different. The estimated profiles by UNIFAC and UNIFAC-DMD with parameters regressed from VLE data are similar. To regress the UNIFAC-DMD parameters, the values provided by Detherm V2.0 are used in this work. Ta-bles 2 and 3 show the definition of UNIFAC group parameter and UNIFAC group vector, respectively. Fig. 3 shows that the prediction results are in good agreement with experimental data selected from Detherm V2.0.

Table 2 Definition of UNIFAC groups

Group ID Group number Molecular structure

G1005 1005 G1010 1010 G1015 1015 G1060 1060 G1065 1065 G1070 1070 G1300 1300 H2O

G3450 3450 C5H9NO

Table 3 UNIFAC-DMD group vector containing the UNIFAC group number and the number of

occurrence of each group

No. a b c d e f

1 1010 1010 1015 1015 1300 3450

2 2 1 2 2 1 1

3 1015 1015 1065 1060

4 2 1 1 1

5 1070

6 1

Components: a, n-butane; b, 1-butene; c, cis-2-butene; d, trans-2-butene; e, water; f, N-methylpyrrolidone.

Figure 3 Temperature predicted by UNIFAC-DMD with parameters regressed by vapor liquid equilibrium data cis-2-butene & n-butane; cis-2-butene & NMP; cis-2-butene & I-butene

3 SIMULATION RESULTS

We have developed equations to describe the thermo- and hydrodynamic behavior in the region ad-jacent to the interface with the appropriate boundary conditions at the interface, and considered the trans-port process across the interface. Both EQ and NEQ simulations are carried out in the framework of As-penONE. Fig. 4 shows column composition profiles predicted by EQ and NEQ models and experimental values, in which only the profiles of n-butane and trans-2-butene in vapor phase are plotted for a better

Figure 4 Composition profiles predicted by EQ and NEQ models n-butane (NEQ); n-butane (EQ); experiment (n-butane); trans-2-butene (NEQ); trans-2-butane (EQ)


view of the profiles without the loss of generality. The composition profiles predicted by EQ and NEQ mod-els differ significantly. The composition profile of n-butane predicted by NEQ model shows an excellent agreement with experimental data, while that by EQ model differs significantly from the experimental val-ues. In order to understand the reason, Murphree effi-ciency, diffusion coefficients and mass transfer coeffi-cients are investigated.

3.1 Murphree vapor efficiency and diffusion co-efficients

In this section, we present information on com-ponent Murphree vapor efficiencies and binary diffu-sion coefficients. The NEQ approach does not use the efficiency, but the efficiencies of each component on each tray can be calculated from its results. Fig. 5 pre-sents component Murphree vapor efficiencies calcu-lated from the results of NEQ simulation. The differ-ences in EiMV are from the differences in the diffusivities of binary pair vapor in the mixture, and Maxwell-Stefan diffusion takes proper account of diffusional coupling between the species. Moreover, the efficiencies vary greatly from stage to stage and some are abnormal. Some of the components have extreme values of 2400% and +800%. In particular, the efficiencies of n-butane are negative on some stages. Such odd behavior as negative efficiency was observed experimentally for acetone, methanol and water mixture in a sieve tray column [51]. The main reasons are as follows. On the one hand, the entrainer acts as a selective semiperme-able filter, which lets those more soluble components, 1-butene, cis-2-butene and trans-2-butene, pass pref-erentially. These components in the vapor phase enter the liquid region through the interface and release its latent heat. n-butane in the liquid absorbs the energy released at the interface and moves from its low con-centration region into n-butane rich vapor phase, leading reverse diffusion of n-butane. On the other hand, because of the poor solubility the equilibrium of n-butane does not exist at the interface, so that the driving force yi of n-butane in vapor boundary layer vanishes, i.e. yi0. Its flux is resulted from the

movement of other components in the mixture, mainly by 1-butene, cis-2-butene and trans-2-butene, so the component efficiencies are greater than 100% and may be positive or negative. At the same time, com-ponent efficiency changes along the column signifi-cantly. As a result, the mole fraction of component (Fig. 4) on any stage with the NEQ approach is dif-ferent from that by the EQ approach. In Fig. 5 with increasing vapor loading from top to bottom, the effi-ciencies for trans-2-butene, 1-butene and cis-2-butene increase slightly. The situation is changed dramatically when vaporous C4 mixture is introduced. The sudden jump discontinuity in the efficiencies appears from stage 19 (feed stage of vaporous C4 mixture) to stages 18 and 17, with the largest positive values (220% for 1-butene and 150% for cis-2-butene). The negative efficiencies of n-butane appear from stage 11 to stage 23, which drive n-butane from the low concentration liquid region into the rich vapor region. Tables 4 and 5 show the binary diffusion coefficients in vapor phase on stages 8 and 22 respectively. The binary diffusion coefficients of NMP have the smallest values and those of n-butane are the next, which indicates that the flux of n-butane is resulted from the movement of other components. Table 6 shows the corresponding mole fraction on stages 8 and 22, on which the driving force of n-butane is much greater than that of others and the mole fractions of n-butane in vapor phase are much greater than that in liquid phase. n-butane moves into vapor phase from liquid phase against the driving

Figure 5 Component Murphree vapor efficiencies along column n-butane; trans-2-butene; cis-2-butene; 1-butene; NMP; water

Table 4 Binary diffusion coefficients in vapor phase on stage 8 (106 m2s1)

a b c d e f

a 0 1.0284 1.0216 1.0226 2.3961 0.7522

b 1.0284 0 1.0640 1.0651 2.5320 0.7880

c 1.0216 1.0640 0 1.0570 2.4994 0.7841

d 1.0226 1.0651 1.0570 0 2.4846 0.7831

e 2.3961 2.5320 2.4994 2.4846 0 1.7884

f 0.7522 0.7880 0.7841 0.7831 1.7884 0



force. The component Murphree efficiency in Fig. 5 indicates that the values of HETP or HTU are different from stage to stage, so the application of classical HTU- NTU approach and constant EiMV for packed-column design will lead to poor results compared with the more rigorous approach with the Maxwell-Stefan model. Olano et al. [52] also obtained similar conclusion for other process. In addition, EQ model offers no explicit

information about diffusion and transfer across the interface, so that the variation of Murphree vapor effi-ciency along column is not considered. As a result, process design based on EQ concept involves uncer-tainties of Murphree efficiency and limitation of Ficks diffusion theory. On the contrary, NEQ ap-proach gives us quite a detailed understanding of what is going on in the equipment.

3.2 Mass transfer rate and mass transfer coeffi-cients of component

Since NEQ approach presents quite detailed be-havior in the column, it is possible to investigate the mass transfer rate of component across the interface, diffusion coefficients and mass transfer coefficients on each stage. Fig. 6 illustrates the transfer rate of com-ponent across the interface along the column. The flux of n-butane across the interface is from liquid phase to vapor phase, and the fluxes of other components such as 1-butene, cis-2-butene, trans-2-butene, water and NMP are from vapor phase to liquid region. On the

Table 5 Binary diffusion coefficients in vapor phase on stage 22 (106 m2s1)

a b c d e f

a 0 1.0842 1.0773 1.0793 2.5292 0.7930

b 1.0842 0 1.1199 1.1215 2.6564 0.8312

c 1.0773 1.1199 0 1.1131 2.6230 0.8270

d 1.0793 1.1215 1.1131 0 2.6142 0.8255

e 2.5292 2.6564 2.6230 2.6142 0 1.8792

f 0.7930 0.8312 0.8270 0.8255 1.8792 0


Table 6 Mole fraction in vapor and liquid phase on stage 8 and 22

Mole fraction/molmol1 Stage Phase

a b c d e f

8 vapor 0.800337 0.017297 0.047475 0.126164 0.008403 0.000324

liquid 0.142389 0.004061 0.012969 0.032672 0.269374 0.538535

22 vapor 0.396424 0.040453 0.175672 0.374683 0.012286 0.000482

liquid 0.062889 0.009248 0.047499 0.095076 0.261728 0.523560


Figure 6 Mass transfer rates of component across the interface predicted by NEQ models (Positive values refer to transfer from vapor to liquid)


feed stages (6 and 19), the fluxes for C4 components change dramatically, mainly because the introduction of fresh feed stream increases the driving force for transfer and intensity of turbulence. The mass transfer rate reduces from stage 6 to stage 19 but increases from stage 20 to the bottom with the increase of vapor loading. To investigate the mass transfer, it is custom-ary to determine mass transfer coefficients [38, 45, 53, 54]. Eqs. (42) and (43) are used to calculate the average diffusion and mass transfer coefficients of stage from binary pair diffusion and mass transfer coefficients, which are estimated with Eqs. (29), (30), (36) and (37). Figs. 7-9 illustrate the average diffusion and mass

transfer coefficients in liquid and vapor phases along the column. Both diffusion coefficients and mass transfer coefficients in vapor phase are much greater than those in liquid phase, mainly due to the differ-ences in viscosity and density of the phases. In NEQ approach, the movement of molecule or a group of molecules depends on the driving forces of all the species present in the mixture, while in EQ approach the driving forces are merely the forces between the key component and other species. Moreover, the in-terfacial area is reduced as the deformation of fluid surface is hindered due to the increase of inner friction in the fluid, leading a decrease in mass transfer rate.

Figure 7 Average diffusion and mass transfer coefficients in liquid phase along column DL; kL

Figure 8 Average mass transfer coefficients in vapor phase and vapor Reynolds number along column ReV; kV

Figure 9 Kinematic viscosity and average diffusion coefficients of vapor V; DV


In addition, the mass transfer coefficient in vapor phase is sensitive to the vapor loading, so it changes dramatically on the feed stage. The diffusion coeffi-cients for both phases and mass transfer coefficients in liquid phase increase from the top to the bottom of the column. This can be explained as follows. On the one hand, the selective semipermeable filter lets the more soluble components cross the interface preferentially and release their condensation heat freely, leading an enrichment of n-butane in the vapor film adjacent to the interface. On the other hand, liquid n-butane ab-sorbs the energy released and vaporizes, which also enriches n-butane in the vapor film adjacent to the interface. Consequently, n-butane diffuses from the interface to the bulk vapor phase and carries away those components diffusing towards the interface. The resistance for diffusion and mass transfer is hence re-duced, increasing the mass transfer and diffusion co-efficients and leading the movement of n-butane from its low concentration liquid region to n-butane rich vapor phase. For other components, the mechanism is the same in the liquid phase. On stage 6, where fresh entrainer is introduced into the column, the diffusion and mass transfer coefficients in liquid phase take the smallest values (Fig. 7), but the flux of n-butane from liquid phase to vapor region has the highest value (Fig. 6) due to the largest driving forces for extraction. On the contrary, the mass transfer coefficient in vapor phase takes relative large value, though the diffusion coefficient on this stage has the smallest value. This is mainly due to the relative large kinematic viscosity, which can be traced back to vapor density.

4 CONCLUSIONS

The limitations of Ficks law for describing dif-fusion in nonideal multicomponent mixture are dis-cussed. The Maxwell-Stefan diffusion theory is used to describe transfer processes and associated influence factors are investigated on the basis of EQ and NEQ simulations. The major conclusions are as follows.

(1) The flux of n-butane, which has the smallest solubility, is resulted from the movement of all the species present in the C4 mixture. Diffusion against driving force is explained by NEQ approach.

(2) The Murphree efficiencies of components in C4 mixture differ from each other and vary greatly from stage to stage. The unbounded and negative effi-ciencies are the results of diffusional coupling.

(3) The differences in the results with NEQ and EQ are from the difference in the Murphree efficiencies of components, which can be traced back to the differ-ence in diffusivities Dy,ij of the binary pair vapor phase.

(4) The NEQ approach takes proper account of diffusional coupling between the species transfer, which helps understanding of what is going on in the extrac-tive distillation column, and avoids the uncertainties of tray efficiency or HETP concept. The effects of design parameter and equipment geometry are in-cluded. This is an important extension of the classical

analysis using equilibrium stages. Thus for the simulation of extractive distillation

column to separate n-butane from 1-butene, cis-2-butene and trans-2-butene mixture, the rigorous NEQ ap-proach is more appropriate.

NOMENCLATURE

Ab active bubbling area on the tray, m2 At cross-sectional area of the column, m2 ap specific surface of packing, m2m3 aw wetted area, m2 c molar concentration, molm3 D diffusions coefficient, m2s1 Maxwell-Stefan diffusions coefficient, m2s1 d diameter, m dh hydraulic diameter, m dp nominal packing size, m F feed stream, kgh1 g gravitational acceleration, ms2 H enthalpy, kJ h specific enthalpy, kJkmol1 hL liquid height, m hp height of the packed section, m hw average weir length per liquid pass, m K equilibrium coefficient k mass transfer coefficients, ms1 L mass stream of liquid, kgh1 M mole mass, kgkmol1 Np number of liquid flow passes nc number of component Q heat input to stage, Js1 QL, QV volumetric flow rate for liquid and vapor, m3s1 q heat transfer rate, Js1 R gas constant, JK1mol1 r reaction rate, kmols1 T absolute temperature, K tL average residence time for liquid, s u inner energy, kJkmol1 V vapor stream, kgh1 v velocity, ms1 x mole fraction in liquid , molmol1 y mole fraction in vapor , molmol1 z height of package, m heat transfer coefficient, Wm2K1 thermodynamic correction factor film thickness, m heat conductivity, Wm1K1 dynamic viscosity, Pas kinematic viscosity, m2s1 density, kgm3 surface tension, Nm1 to surface tension of liquid to the stage fugacity, Pa fugacity coefficient E driving force caused by electric potential

Superscripts F feed f film I interface L liquid phase V vapor phase

Subscripts i index of component j index of stage


k bulk of phase L liquid m component n last component p packing s surface t total V vapor w wetted area

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modeling of mass transfer in nonideal multicomponent mixture with maxwell-stefan

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