**3. Rate-based mass transfer efficiency analysis**

To evaluate the effect of viscosity on mass transfer in the extractive distillation process with ionic liquids, it is necessary to use the concept of mass transfer efficiency. The most used mass transfer efficiency model is the Murphree Tray Efficiency [39]. However, this calculation requires the vapor composition per tray and this would not reflect the decrease in mass transfer due to viscosity in the liquid phase. The concept of efficiency that represents the changes in liquid phase viscosity is the tray efficiency defined from the point efficiency assuming that there is no concentration gradient in the axial direction [34, 40], this is:

$$E\_{\rm OV} = 1 - \exp\{-N\_{\rm OV}\} \tag{2}$$

where Λ is the stripping factor calculated from an activity coefficient model [23]. When using packing as internal in an ED column the mass transfer efficiency can be determined using the

where *HOV* is overall height of transfer units calculated from transfer height id the vapor phase

*HOV* = *HV* + Λ *HL* (5)

Equations (2)–(5) describe the changes in efficiency with physical properties, vapor-liquid equilibrium and the column internals. These equations are used to compare the mass transfer efficiency performance of the different solvents studied in this work. The number of transfer units and the height of transfer units are calculated using the mass transfer correlations depending on the column internal. This work is focused on two internals to evaluate the changes in mass transfer efficiency with viscosity: sieve trays and structured packing. For the case of sieve trays, AIChE mass transfer correlation calculates the number of transfer units in

coefficient. This last transport property accounts for the decrease in mass transfer efficiency due to the high liquid phase viscosity and it is calculated using the Wilke-Chang correlation [42]:

the solvent. To use this diffusion coefficient in the above correlation, a mixing rule has to be previously applied for concentrated solutions [34]. For the case of structured packings, Rocha mass transfer correlation describes well the height of transfer units in the liquid phase [43]:

> 2*a* [ *DL u* \_\_\_\_\_*Le <sup>π</sup>SCE*]

is the superficial liquid phase velocity, *a* is the interfacial area per volume, *uLe* is the

is the molar volume of the solute at its normal boiling point and *η*<sup>2</sup>

effective liquid phase velocity, *S* is the side dimension of corrugation and *CE*

) as follows:

*NL* = 19700 (*DL*)0.5(0.4 *FS* + 0.17) *t*

is the liquid phase residence time, *FS*

*<sup>D</sup>*<sup>12</sup> <sup>=</sup> 7.4*<sup>x</sup>* 10−12 (<sup>Φ</sup> *MW*,2)

*HL* <sup>=</sup> *<sup>u</sup>* \_\_\_\_\_\_\_\_\_ *<sup>L</sup>*

ln(Λ) \_\_\_\_\_

<sup>Λ</sup> <sup>−</sup> <sup>1</sup> (4)

http://dx.doi.org/10.5772/intechopen.76544

111

Mass Transfer in Extractive Distillation when Using Ionic Liquids as Solvents

*<sup>L</sup>* (6)

0.6 (7)

0.5 (8)

the Fick diffusion

is the viscosity of

is a constant for

the superficial factor, and *DL*

0.5 *<sup>T</sup>* \_\_\_\_\_\_\_\_\_ *η*<sup>2</sup> *V*<sup>1</sup>

is the molecular weight if the solvent, Φ is the association factor, *T* is the tempera-

concept of height equivalent to a theoretical plate:

*HETP* = *HOV*

) and in the liquid phase (*HL*

the liquid phase [41]:

where *t L*

where *MW*,2

ture, *V*<sup>1</sup>

where *uL*

surface renewal.

(*HV*

where *EOV* is the tray efficiency and *NOV* is the overall number of transfer units which is calculated from the number of transfer units in the vapor phase (*NV* ) and in the liquid phase (*NL* ) as follows:

$$\frac{1}{N\_{\rm OV}} = \frac{1}{N\_{\rm V}} + \frac{\Lambda}{N\_{\rm L}} \tag{3}$$

where Λ is the stripping factor calculated from an activity coefficient model [23]. When using packing as internal in an ED column the mass transfer efficiency can be determined using the concept of height equivalent to a theoretical plate:

$$HETP = H\_{\text{ov}} \frac{\ln(\Lambda)}{\Lambda - 1} \tag{4}$$

where *HOV* is overall height of transfer units calculated from transfer height id the vapor phase (*HV* ) and in the liquid phase (*HL* ) as follows:

$$H\_{\rm OV} = H\_{\rm V} \star \Lambda H\_{\rm L} \tag{5}$$

Equations (2)–(5) describe the changes in efficiency with physical properties, vapor-liquid equilibrium and the column internals. These equations are used to compare the mass transfer efficiency performance of the different solvents studied in this work. The number of transfer units and the height of transfer units are calculated using the mass transfer correlations depending on the column internal. This work is focused on two internals to evaluate the changes in mass transfer efficiency with viscosity: sieve trays and structured packing. For the case of sieve trays, AIChE mass transfer correlation calculates the number of transfer units in the liquid phase [41]:

1-hexyl-3-methylimidazolium tetracyanoborate ([hmim][TCB]) produced much higher relative volatilities than organic solvent. This is an indication that, a column with less separation stages or a less usage of solvent is expected to achieve a good separation. However, ionic liquids also show higher viscosity values than traditional solvents. Therefore, the mass transfer

**Table 1.** Relative volatilities at a solvent-to-feed (S/F) ratio (mass basis) for different solvents and pure solvent viscosities

Solvent S/F = 1 Ref. *T* = 298.15 K Ref.

110 Heat and Mass Transfer - Advances in Modelling and Experimental Study for Industrial Applications

[emim][Cl] 2.62 [23] 2597.69<sup>a</sup> [36] [emim][OAc] 2.24 [23] 132.9 [27] [emim][DCA] 1.89 [23] 14.9 [27] EG 1.83 Aspen® 16.6 [37]

[hmim][TCB] 9.4 [25] 47.8 [38] NMP 2.8 Aspen® 1.9 Aspen®

**α** *η***/mPa s**

*α η***/ mPa s**

S/F = 5 Ref *T* = 298.15 K Ref.

To evaluate the effect of viscosity on mass transfer in the extractive distillation process with ionic liquids, it is necessary to use the concept of mass transfer efficiency. The most used mass transfer efficiency model is the Murphree Tray Efficiency [39]. However, this calculation requires the vapor composition per tray and this would not reflect the decrease in mass transfer due to viscosity in the liquid phase. The concept of efficiency that represents the changes in liquid phase viscosity is the tray efficiency defined from the point efficiency assuming that

*EOV* = 1 − exp(−*NOV*) (2)

where *EOV* is the tray efficiency and *NOV* is the overall number of transfer units which is calcu-

= \_\_\_<sup>1</sup> *NV* + \_\_\_ <sup>Λ</sup> *NL* '

*NOV*

) and in the liquid phase (*NL*

(3)

) as

efficiency is expected to decrease.

Water-ethanol separation [35]

a

Methylcyclohexane-toluene separation [38]

extrapolated value from experimental data.

(*η*) at *T* = 298.15 for both case studies.

follows:

**3. Rate-based mass transfer efficiency analysis**

there is no concentration gradient in the axial direction [34, 40], this is:

lated from the number of transfer units in the vapor phase (*NV*

\_\_\_\_ <sup>1</sup>

$$N\_{\rm L} = 19700 \left( D\_{\rm L} \right)^{\alpha 5} \left( 0.4 \, F\_{\rm s} + 0.17 \right) t\_{\rm L} \tag{6}$$

where *t L* is the liquid phase residence time, *FS* the superficial factor, and *DL* the Fick diffusion coefficient. This last transport property accounts for the decrease in mass transfer efficiency due to the high liquid phase viscosity and it is calculated using the Wilke-Chang correlation [42]:

$$D\_{12} = 7.4 \times 10^{-12} \frac{(\Phi M\_{\text{\textquotedblleft}2})^{\text{as}} T}{\eta\_{\text{\textquotedblleft}1} V\_{\text{\textquotedblright}}^{\text{ns}}} \tag{7}$$

where *MW*,2 is the molecular weight if the solvent, Φ is the association factor, *T* is the temperature, *V*<sup>1</sup> is the molar volume of the solute at its normal boiling point and *η*<sup>2</sup> is the viscosity of the solvent. To use this diffusion coefficient in the above correlation, a mixing rule has to be previously applied for concentrated solutions [34]. For the case of structured packings, Rocha mass transfer correlation describes well the height of transfer units in the liquid phase [43]:

$$H\_L = \frac{u\_l}{2a\left[\frac{D\_l u\_u}{\pi \mathcal{S} C\_v}\right]^{0.5}}\tag{8}$$

where *uL* is the superficial liquid phase velocity, *a* is the interfacial area per volume, *uLe* is the effective liquid phase velocity, *S* is the side dimension of corrugation and *CE* is a constant for surface renewal.
