static mixers as heat exchangers in supercritical fluid extraction processes.pdf

7/30/2019 Static mixers as heat exchangers in supercritical fluid extraction processes.pdf

1/29

Accepted Manuscript

Title: Static mixers as heat exchangers in supercritical fluidextraction processes

Authors: Pedro C. Simoes, Beatriz Afonso, Joao Fernandes,

Jose P.B. Mota

PII: S0896-8446(07)00287-2

DOI: doi:10.1016/j.supflu.2007.07.015

Reference: SUPFLU 1421

To appear in: J. of Supercritical Fluids

Received date: 4-5-2007

Revised date: 4-7-2007

Accepted date: 27-7-2007

Please cite this article as: P.C. Simoes, B. Afonso, J. Fernandes, J.P.B. Mota, Static

mixers as heat exchangers in supercritical fluid extraction processes, The Journal of

Supercritical Fluids (2007), doi:10.1016/j.supflu.2007.07.015

This is a PDF file of an unedited manuscript that has been accepted for publication.

As a service to our customers we are providing this early version of the manuscript.

The manuscript will undergo copyediting, typesetting, and review of the resulting proofbefore it is published in its final form. Please note that during the production process

errors may be discovered which could affect the content, and all legal disclaimers that

apply to the journal pertain.
http://localhost/var/www/apps/conversion/tmp/scratch_4/dx.doi.org/doi:10.1016/j.supflu.2007.07.015http://localhost/var/www/apps/conversion/tmp/scratch_4/dx.doi.org/10.1016/j.supflu.2007.07.015http://localhost/var/www/apps/conversion/tmp/scratch_4/dx.doi.org/10.1016/j.supflu.2007.07.015http://localhost/var/www/apps/conversion/tmp/scratch_4/dx.doi.org/doi:10.1016/j.supflu.2007.07.015


2/29

Ac

cepted

Manu

script

1

STATIC MIXERS AS HEAT EXCHANGERS IN SUPERCRITICAL FLUID

EXTRACTION PROCESSES

Pedro C. Simes*, Beatriz Afonso, Joo Fernandes, Jos P. B. Mota

REQUIMTE/CQFB, Departamento de Qumica, Faculdade de Cincias e Tecnologia,

Universidade Nova de Lisboa, 2829-516 Caparica, Portugal

E-mail: [email protected]; Phone: + 351 212 948 300; Fax: + 351 212 948 385

Abstract

The performance of a Kenics static mixer as a heat transfer device for supercritical

carbon dioxide (CO2) flow is studied and compared with conventional tube-in-tube heat

exchangers. Measurements were carried out at pressures ranging from 8 to 21 MPa,

temperatures from 283 to 323K, and mass flow rates from 2 to 15 kg/h. The

corresponding Reynolds and Prandtl numbers, at bulk conditions, ranged between 103

and 2 104

and between 2 and 7, respectively. The temperature increase experienced by

the supercritical CO2 stream varied between 10 and 35 K. The heat fluxes obtained with

the static mixer are one order of magnitude higher than the ones observed with a tube-

in-tube heat exchanger for the same set of operating conditions. The heat-transfer

enhancement is caused by the cross-sectional mixing of the fluid and to a lesser extent

by conduction across the metallic mixing elements. Heat transfer is also affected by

temperature-induced variation of physical properties, especially in the pseudocritical

region of the fluid. From the experimental data, a correlation was developed for

convective heat transfer to supercritical CO2 in terms of the Nusselt number.

nuscript revised

Pag


3/29

Ac

cepted

Manu

script

2

Keywords: static mixer, heat exchanger, supercritical carbon dioxide, modelling

Introduction

Supercritical Fluid Extraction (SFE) is a process that uses fluids at supercritical

conditions to selectively extract substances from solid or liquid mixtures. By changing

pressure and temperature, the solvating power of the fluid (usually carbon dioxide) can

be adjusted to obtain good solubilities, selectivities and transport properties. SFE

technology has the potential to enhance product quality, while at the same time being an

environmentally clean extraction technology. Heat transfer to supercritical fluids (SCF)

is important when dealing with technological applications of these fluids, especially for

extraction, reaction or particle formation processes. Every SFE unit has several heat

exchangers (HXs) in its flowsheet; their purpose can be, among others, to preheat the

supercritical fluid before being fed to the high pressure vessel, to cool down the SCF

before compression, or to change temperature conditions of the high pressure flow

before separation of the solubilized solutes from the SCF solvent takes place.

Conventional heat exchangers, such as double-pipe or shell-and-tube, have been used in

SFE. They present important advantages (established design and manufacturing), but

also show some undesirable features, such as relatively high surface areas to attain

desired thermal exchange and heat-transfer inefficiencies due to non-negligible laminar

film build-up on the tube walls.

Static mixers have been considered credible alternatives to conventional HXs,

because they provide very high and uniform heat-transfer rates. They are currently

being used in a wide range of applications, such as blending of gases or miscible liquids

Pag


4/29

Ac

cepted

Manu

script

3

in laminar or turbulent flow, continuous co-current liquid/liquid or gas/liquid

dispersions, heat exchangers, and interphase mass transfer between immiscible phases

[1-3].

A static mixer consists of a contacting device with a series of internal stationary

mixing elements of specific geometry, inserted into a pipe. The added effects of

momentum reversal and flow division due to the internal elements of the mixer

contribute to a maximization of mixing efficiency. The benefits of dispersion efficiency,

short residence times, and low flow resistance, are advantages for the use of static

mixers in mass and heat-transfer applications [4]. Recently, the use of static mixers in

SFE processes has been proposed as, e.g., alternative contacting devices [5-6],

equilibrium cells for high-pressure thermodynamic studies [7-8] and mixers of powder

coatings and additives with SC CO2 to make fine, coated particles from gas-saturated

solutions [9]. Static mixers have advantages over conventional equipment for use at SC

conditions. These include lower capital costs at a large scale of operation, no possibility

of flooding even if there is a low density difference between the phases, short residence

times, and minimal space requirements for location in a SFE plant.

In this work, the performance of a Kenics static mixer to heat a SC-CO2 stream is

studied and compared with conventional tube-in-tube HXs. The Kenics mixer is

comprised of a series of mixing elements aligned at 90 degrees, each element consisting

of a short helix of one and a half pipe diameters in length. Each helix has a twist of 180

degrees with right-hand and left-hand elements being arranged alternatively in the pipe

(Fig. 1a). The internal mixing elements direct the flow of material radially toward the

pipe walls and back to the center. Additional velocity reversal and flow division results

from combining alternating right- and left-hand elements, thus increasing mixing

Pag


5/29

Ac

cepted

Manu

script

4

efficiency. All material is continuously and completely mixed, eliminating radial

gradients in temperature in the bulk fluid. This in turn increases the thermal gradient

near the hot wall and, consequently, the heat-transfer rate into the fluid.

Measurements are carried out at pressures ranging from 8 to 21 MPa, temperatures

ranging from 288 to 323K, and mass flow rates ranging from 2 to 15 kg/h. The effect of

the density of the supercritical fluid, the heat flux, and the fluid flow rate, on the heat-

transfer performance of the static mixer at high-pressure conditions is examined. Based

on the experimental data, a correlation is developed for convective heat transfer to SC-

CO2 on the basis of a Nusselt number.

The design and optimization of HXs for supercritical fluids have an additional

difficulty when compared with normal liquids or gases. Near its critical point, a fluid

exhibits strong variations of the physical properties with temperature, especially near

the pseudocritical point, Tpc (that is, the temperature at which the specific heat reaches a

maximum for a given pressure), that strongly influences the heat transfer. Therefore, the

effect of these strong variations on the thermal efficiency of the static mixer is also

investigated.

Experimental apparatus and procedure

The experimental apparatus used in the experiments is shown schematically in Fig.

1b; it is essentially the same as that used for vapor-liquid equilibrium measurements at

high-pressure conditions [8]. A Kenics static mixer (model 37-04-065 from Chemineer,

Inc.) was used in these experiments. The main characteristics of this mixer are an

internal diameter of 4.623 mm, an overall length of 178 mm, and 21 helical mixing

elements with a length-to-diameter ratio of 1.7.

Pag


6/29

Ac

cepted

Manu

script

5

Carbon dioxide, which was previously liquefied, is compressed to the desired

pressure with the help of a metering pump, P01 (Model M51OS, Lewa) and fed to the

static mixer which is in a horizontal position. The solvent flow rate is measured using a

mass-flow meter, MFM (Model RHM 01 GNT, Rheonik), with an accuracy of0.2% of

rate. A pressure gage transducer (Model S-10, WIKA) is used to measure the carbon

dioxide pressure at the inlet section of the heat exchanger, while a differential pressure

transducer (model SMART 1151HP, Fisher-Rosemount) is installed at both ends of the

static mixer to measure the pressure drop. The accuracy of both transducers is 0.25%

of span. The CO2 flow after exiting the static mixer is depressurized through the air-

driven valve EV, and the low-pressure CO2 is then recirculated back to the metering

pump.

An electrical resistance wire wrapped around the outer wall of the static mixer is

used as the heat supplier of the test section and is thermally insulated from the ambient

atmosphere with flexible elastomeric rubber material. The outer wall temperature of the

static mixer is monitored by a platinum resistance sensor and controlled by means of an

automatic PID regulator (ERO Electronics), which drives the power dissipated by the

heating tape. An additional platinum resistance sensor is attached to the outer wall of

the static mixer to provide an independent temperature monitoring. Special care has

been taken to minimize the space between the thermo resistance and the metallic wall of

the mixer. The CO2 temperatures at the inlet and outlet of the static mixer are measured

with the help of platinum resistance sensors. All the resistance sensors have been

previously calibrated to an accuracy of 0.1K. The main operating variables are

monitored and recorded over the course of each experiment by means of an automated

data acquisition system.

Pag


7/29

Ac

cepted

Manu

script

6

Under steady-state conditions, the experimental heat-transfer rate, Q, from the inner

tube wall of the static mixer to the CO2 stream can be obtained from a steady-state

energy balance to the flowing gas:

,G,out

G,in

T

p G GTQ G C dT (1)

where the scripts in and out denote the conditions at the inlet and outlet of the heat

exchanger, respectively. Symbols G, Cp,G and TG are, respectively, the mass flow rate,

heat capacity, and temperature of the carbon dioxide. It is worth noting that for the

lowest pressure conditions of the experiments, 8 and 9 MPa, the heat capacity of carbon

dioxide attains a maximum between the inlet and the outlet temperatures. Fig. 2 shows

the how the main thermophysical properties of SC-CO2 change with temperature near

the pseudocritical point at 9 MPa [10].

Because the outer wall temperature of the static mixer, Tw, is kept constant by the

PID controller, the wall boundary condition for the mixer is one of constant temperature

rather than one of constant heat flux. The average heat-transfer coefficient in the gas

phase, hG, over the entire heated length, can be determined from the following equation:

(2 )i i lmQ U R Z T (2)

where

1 1ln

i i w

i G w i

R R x

U h k R(3)

and Tlm is the logarithmic mean temperature difference between the gas and outer wall

temperatures:

( ) ( )

( )ln

( )

w in w out lm

w in

w out

T T T T T

T T

T T

(4)

The physical properties of CO2, required to analyze the experimental data, were

Pag


8/29

Ac

cepted

Manu

script

7

taken from the NIST Refrigerants Database [10]. Taking into consideration the

uncertainties in the experimental data, it is estimated that the relative standard

uncertainty for the fluid-phase heat-transfer coefficient is within 7%.

Results and discussion

In the series of heat-transfer experiments reported here, CO2 is circulated through

the static mixer at different conditions of mass flow, pressure and temperature. The

experiments were carried out at four pressures (8, 9, 15 and 21 MPa) and three heating

tape temperatures (313, 333 and 353K). The CO2 mass flowrate varied between 2 and

15 kg/h. For each run, the outlet wall temperature, the inlet and outlet temperatures, the

gas flowrate, as well as the inlet pressure and pressure drop across the static mixer, were

continuously measured and recorded.

The measured temperature differences between the flowing gas and the inner wall of

the static mixer ranged from 15 to 55 K, and the heat fluxes ranged from 1104

to 5105

W/m2. The corresponding Reynolds and Prandtl numbers, at bulk conditions, varied

between 103

and 2104

and between 2 and 7, respectively. The fluid-side temperature

increase, (Tout Tin), varied between 10 K and 35 K.

The influence of the inlet pressure and mass flowrate on the heat-transfer

coefficient, hG, is shown in Fig. 3, where hG is plotted as a function of the gas-phase

Reynolds number at bulk conditions for three different pressure conditions. The

experimental data shown in the figure were obtained for a constant wall temperature of

313 K. As expected, the heat-transfer coefficient increases with fluid velocity [11]. At

the highest Reynolds numbers, a heat-transfer enhancement is observed for the data

Pag


9/29

Ac

cepted

Manu

script

8

obtained at 8 MPa, when compared with the data obtained for the other two pressures.

There is no significant difference between the values obtained at 15 and 21 MPa.

The heat-transfer enhancement observed at 8 MPa can be explained by the

temperature induced variation of the physical properties of the fluid nearby the

pseudocritical region. This effect is better seen in Fig. 4, where hG is plotted as a

function of the CO2 outlet temperature, for a constant inlet pressure of 8 MPa and a wall

temperature of 353 K. This figure shows that hG attains a maximum value at a bulk

temperature ofca. 312K, nearby the corresponding pseudocritical temperature, which

according to Liao and Zhao [12] is 307.8 K at 8 MPa. This enhancement effect of the

heat transfer coefficient in the vicinity of the pseudocritical temperature is mainly due to

the fact that the specific heat follows the same trend near the pseudocritical region [11-

12]. This effect was not observed at 15MPa and 21MPa. This is because not only the

pseudocritical temperature is shifted to higher temperatures when the pressure increases

(Tpc = 338 K at 15 MPa and Tpc = 350 K at 21 MPa) but also the maximum peak is

decreased in height with increasing pressure (Cp(Tpc) 35, 3.5 and 2.5 kJ kg-1

K-1

at 8,

15 and 21 MPa, respectively [10]). Since the bulk temperatures of SC-CO2 in the

experiments at 15 and 21 MPa are distant from the corresponding pseudocritical

regions, no significant effect on hG was observed for those cases. Table 1 lists the range

of values for each physical property spanned by the series of heat transfer experiments

reported in this work. As can be seen, the specific heat and the viscosity are the

properties whose values have the widest variations at 8 MPa and 9 MPa.

The performance of the static mixer as a heating device for supercritical carbon

dioxide was compared with conventional tube-and-tube heat exchangers. Fig. 5 shows

the heat flux, Q/Ai, as a function of the gas-phase Reynolds number at bulk conditions

Pag


10/29

Ac

cepted

Manu

script

9

for two types of heat exchangers: (i) the Kenics mixer used in our experiments; and (ii)

a double-pipe tube-in-tube HX, where CO2 flows downward through the inner tube and

hot water flows countercurrently in the annulus [13]. The inner pipe is made of stainless

steel AISI 316, with an OD of 6.35 mm and a wall thickness of 1.8 mm. The inlet

pressure of CO2 is fixed at 21 MPa in this set of experiments. It is clearly seen that the

Kenics mixer performs much better than the tube-in-tube HX for the same range of

operating conditions. The higher performance of the static mixer is of relevance if one

considers that the heat-transfer area available by the static mixer is only ca. 15% of the

area available by the double-pipe heat exchanger. Moreover, the residence time of CO2

in the static mixer is also lower than in the conventional HX. Fig. 6 presents the same

data as Fig. 5 but corrected for the residence time,GZ u . Note that Q/Ai gives the

average amount of heat released to the fluid over a residence time . Although the tube-

in-tube heat exchanger has a smaller internal diameter than the static mixer (therefore

resulting in higher superficial velocities for the same flowrate), its total length is more

than 4 times longer than the static mixer. In the above calculations of Reynolds number

and residence time for the static mixer, we have employed the internal diameter for the

open tube rather than the hydraulic diameter. The results, however, are globally the

same regardless of the diameter definition used.

Other authors [12] have reported heat fluxes in the range of 5104

to 1105

W/m2

for convective heat transfer to SC-CO2 flowing in small, horizontal heated tubes of 1.40

mm of inner diameter and 110 mm of length, at 8 MPa and 6 kg/h. At these operating

conditions, the heat fluxes measured with the Kenics static mixer range from 6104

to

4105

W/m2. The higher performance of the static mixer is due to its high mixing

efficiency. The mixer elements direct the flow of material radially toward the pipe and

Pag


11/29

Ac

cepted

Manu

script

10

back to the center. Additional velocity reversal and flow division results from

combining alternating right- and left-hand elements, thus increasing mixing efficiency.

Since all fluid is continuously and completely mixed, thermal gradients are eliminated

in the bulk of the fluid and steepened near the hot wall. This increases significantly the

wall-to-fluid heat flux.

The pressure drop across the Kenics static mixer was also measured over the

operating conditions studied in this work. The influence of the carbon dioxide mass

flowrate on the pressure drop is shown in Fig. 7. As expected, the pressure drop

increases with fluid velocity. At the highest flowrate tested, 17.0 kg/h (equivalent to a

Reynolds number of 1.7104) the pressure drop is 4.3 kPa. A straight tube with a similar

internal diameter but without internal fittings has a lower pressure drop, in the range of

50100 Pa. However, despite of the higher pressure drops exhibited by the static mixer,

their values are comparatively small and did not exceed 5.0 kPa in this study. A

pressure drop of this magnitude does not influence the design of a SCF process.

Free convective flow or buoyancy, originated by temperature-induced density

gradients, can be important in SCF processes, especially when operating near the

pseudocritical region. Therefore, the effect of buoyancy on the flow and heat transfer in

the static mixer was also assessed in the present study. The strongest buoyancy effects

should be observed for low flowrates and high heating fluxes [14]. The effect of

buoyancy flow in heat transfer for horizontal tubes is negligible when the following

condition is fulfilled [12]:

2 3bGr Re 10

b (5)

where Grb is the Grashof number evaluated at bulk conditions,

Page


12/29

Ac

cepted

Manu

script

11

3

b 2

2Gr

b w b i

b

R

(6)

b and w denote the density of CO2 evaluated at the bulk mean temperature Tb and the

wall temperature Tw, respectively.

The importance of free convective flow in the Kenics static mixer is shown in Fig.

8, where the ratio Grb/Reb2

is plotted against the bulk Reynolds number. According to

the criterion advocated by Liao and Zhao [12], one would expect buoyancy effects to be

significant over the whole range ofReb studied in this work. However, it is shown

below that this criterion is not applicable for SCF heat-transfer in the Kenics mixer.

Heat transfer correlations

For heat transfer involving supercritical fluids in horizontal or vertical heated tubes,

a Dittus-Boelter type correlation has been proposed by many authors [11-12]:

0.8 0.4

b b bNu 0.023Re Pr (7)

where the Nusselt, Reynolds and Prandtl numbers are all evaluated at bulk conditions.

As suggested by van der Kraan et al. [15], eq. (7) can be used to estimate SCF heat-

transfer coefficients when the temperature difference between tube wall and bulk

conditions is small. In that case, physical properties can be regarded as constant along

the radial direction. For higher wall-to-bulk temperature differences, temperature-

induced variations of physical properties, and possibly buoyancy effects, have to be

taken into account. Free convection effects on heat transfer in horizontal tube flow can

be accounted for by the parameterGrb/Reb2, as discussed above, while the influence of

the temperature difference between wall and bulk mean conditions on the heat transfer

Page


13/29

Ac

cepted

Manu

script

12

coefficient can be taken into account by introducing appropriate property parameter

groups raised to an empirical power,

b dc

bvp p w b2

cp p,b b b

aNu c GrNu c Re

. (8)

Here, Nubvp andNucp are, respectively, the Nusselt numbers for buoyancy and variable-

property, and constant-property conditions. pc is the mean specific heat and defined as,

w bp

w b

H Hc

T T

(9)

Hw and Hb denote the specific enthalpy of carbon dioxide evaluated at the bulk and

average wall temperatures, respectively.

Equation (8) was applied to our experimental hG values; a least square fit gave the

following correlation for convective heat-transfer to SC-CO2 in the Kenics mixer:

0.362 0.070.224

p0.8 0.4 w bbvp b b 2

p, b b b

c GrNu 0.558Re Pr

c Re

(10)

The mean relative error between eq. (10) and the experimental data was found to be

11.6% and more than 80% of the experimental data fall within 20%. A comparison

between the experimentally measured values of Nub and the predicted by eq. (10) is

shown in Fig. 9 in the form of a parity plot. The fitting of Eq. (10) is reasonably good if

one considers that the relative uncertainty in the experimental Nusselt numbers is within

10%. The proposed correlation should work well for convective heat transfer to

supercritical fluids with static mixers of the Kenics type within the studied range of

Reynolds and Prandtl numbers. It may also be equally applicable to Kenics mixers with

other dimensions, as long as a specific length-to-diameter aspect ratio is included in the

original correlation (8), Nu = Nubvp (di/Z)e

[16].

Page


14/29

Ac

cepted

Manu

script

13

In the proposed correlation, the buoyancy parameterGrb/Reb2, is raised to the power

of 0.07. Since the value ofGrb/Reb2

ranges from 0.06 to 37 (see Fig. 8), when this term

is raised to the power of 0.07 its valued varies between 0.82 and 1.3. It can thus be

concluded that buoyancy effects have only a negligible influence on the heat transfer

process, although the criterion put forward by Liao and Zhao [12] is largely violated. It

is very probable that buoyancy be suppressed by the high degree of cross-sectional

mixing.

Conclusions

The efficiency of a Kenics static mixer for heating SC-CO2 was studied and

compared with data for conventional tube-and-tube HXs. For the range of operating

conditions studied, the static mixer provides heat fluxes one order of magnitude higher

than the ones obtained in conventional tube-tube heat exchangers. The influence of the

variation of physical properties, in particular, the specific heat, with the temperature

nearby the pseudocritical region of carbon dioxide was found to be significant. A

correlation was developed for the Nusselt number of convection heat transfer to

supercritical carbon dioxide.

Acknowledgments

Financial support by Fundao para a Cincia e Tecnologia, under project grant

number POCTI/EME/61713/2004 is gratefully acknowledged.

Nomenclature

Page


15/29

Ac

cepted

Manu

script

14

Cp isobaric specific heat (J/K.kg)

hG heat transfer coefficient in the gas phase (W/m2.K)

G gas phase mass flowrate (kg/s)

Gr Grashof number

H Specific enthalpy of carbon dioxide (J/kg)

k thermal conductivity (W/m.K)

Nu Nusselt number

Pr Prandtl number

Q heat transfer rate (W)

Re Reynolds number

Ri internal radius of the static mixer (m)

xw static mixer wall thickness (m)

T temperature (C or K)

U overall heat transfer coefficient (W/m2.K)

Z heated length of the static mixer (m)

Greek symbols

density (kg/m3)

dynamic viscosity (Pa s)

residence time, s

Subscripts

b property evaluated at the bulk temperature

in carbon dioxide conditions at inlet of static mixer

Page


16/29

Ac

cepted

Manu

script

15

out carbon dioxide conditions at outlet of static mixer

G gas phase

pc pseudo critical condition

w property evaluated at the wall temperature

References

[1] F. Grosz-Rll, J. Bttig, F. Moser, Gas/Liquid Mass Transfer with Static Mixing

Units, in: Proceedings of the Fourth European Conference on Mixing, BHRA Fluid

Eng. Eds., Bedford, England, 1982, pp.225-236.

[2] F. Grosz-Rll, J. Bttig, F. Moser, Gas/Liquid Mass Transfer with Static Mixers,

Verfahrenstechnik 17 (12) (1983) 698-707.

[3] J.R. Baker, Motionless Mixers Stir up New Uses, Chem. Eng. Prog. 87 (6) (1991)

32-38.

[4] A. Heyouni, M. Roustan, Z. Do-Quang, Hydrodynamics and mass transfer in gas-

liquid flow through static mixers, Chem. Eng. Sci. 57 (2002) 3325-3333.

[5] A. Pietsch, R. Eggers, The mixer-settler principle as a separation unit in supercritical

fluid processes, J. Supercritical Fluids 14 (1999) 163-171.

[6] O.J. Catchpole, P. Simes, J.B. Grey, E.M.M. Nogueiro, P.J. Carmelo, M. Nunes da

Ponte, Fractionation Of Lipids In A Static Mixer And Packed Column using

Supercritical CO2, Ind. Eng. Chem. Res. 39 (2000) 4820-4827.

[7] J. Fonseca, P.C. Simes, M. Nunes da Ponte, An Apparatus for high-pressure VLE

measurements using a static mixer. Results for (CO2+limonene+Citral) and

(CO2+limonene+linalool), J. Supercritical Fluids 25 (2003) 7-17.

[8] R. Ruivo, A. Paiva, P. Simes, Phase Equilibria of the Ternary System Methyl

Page


17/29

Ac

cepted

Manu

script

16

Oleate / Squalene / CO2 at High Pressure Conditions, J. Supercrit. Fluids 29 (2004) 77-

85.

[9] E. Weidner, Powder Generation by High-Pressure Spray Process, in: N. Dahmen, E.

Dinjus (Eds.), Proceedings of the High Pressure Chemical Engineering Meeting,

Wissenschaftliche Berichte, Karlsruhe, Germany, 1999, pp. 217-222.

[10] E.W. Lemmon, M.O. McLinden, D.G. Friend, Thermophysical Properties of Fluid

Systems, in: P.J. Linstrom and W.G. Mallard (Eds.), NIST Chemistry WebBook, NIST

Standard Reference Database Number 69, June 2005, National Institute of Standards

and Technology, Gaithersburg MD, 20899 (http://webbook.nist.gov).

[11] C. Danga, E. Hiharab, In-tube cooling heat transfer of supercritical carbon dioxide.

Part 1. Experimental measurement, International Journal of Refrigeration 27 (2004)

736747.

[12] S.M. Liao, T.S. Zhao, An experimental investigation of convection heat transfer to

supercritical carbon dioxide in miniature tubes, International Journal of Heat and Mass

Transfer 45 (2002) 50255034.

[13] P.C. Simoes, J. Fernandes, J.P. Mota, Dynamic model of a supercritical carbon

dioxide heat exchanger, J. of Supercritical Fluids 35 (2005) 167173.

[14] M. Mukhopadhyay, Natural Extracts using Supercritical Carbon Dioxide, CRC

Press, Florida, 2000.

[15] M. van der Kraan, M.M.W. Peeters, M.V. Fernandez Cid, G.F. Woerlee, W.J.T.

Veugelers, G.J. Witkamp, The influence of variable physical properties and buoyancy

on heat exchanger design for near- and supercritical conditions, J. of Supercritical

Fluids 34 (2005) 99-105.

Page


18/29

Ac

cepted

Manu

script

17

[16] P. Joshi, K.D.P. Nigam, E. Bruce Nauman, The Kenics static mixer: new data and

proposed correlations, Chem. Eng. J. 59 (1995) 265-271.

Table 1. Range of values obtained for the physical properties used in this work.

Pressure (MPa) 8.0 9.0 15.0 21.0

Gas temperature at outlet (C) 24 - 43 32 - 47 25 - 52 26 - 53

Density (kg m-3) 563 - 904 368 - 910 679 - 945 782 - 967

Viscosity (105 Pa s) 2.11 - 9.27 2.73 - 9.41 5.4 - 10.5 6.84 - 11.1

Specific Heat (J g-1

K-1

) 2.5 - 19.1 2.4 - 10.3 2.1 - 3.2 2.0 - 2.3

Thermal conductivity

(102 W m-1 K-1)

4.05 - 10.6 5.24 - 10.7 7.34 - 11.6 8.69 - 12.0

Page


19/29

Ac

cepted

Manu

script

18

Figure Captions

Fig. 1a. Mixing elements of the Kenics-type static mixer.

Fig. 1b. Schematic diagram of the experimental apparatus. SM: static mixer; P: pumps;

MFM: mass flow meters; dP: differential pressure meter; EV: expansion valve; PI and

TI: pressure and temperature indicators or controllers.

Fig. 2. Heat transfer coefficient, hG, as a function of gas phase Reynolds number and

inlet pressure. Wall temperature is equal to 313K.

Fig. 3. Heat transfer coefficient, hG, as a function of the outlet bulk temperature of

carbon dioxide at 8.0 MPa. Wall temperature is equal to 353K.

Fig. 4. Heat flux, Q/Ai, as a function of the gas phase Reynolds number and wall

temperature for two types of heat exchangers. Pressure is equal to 21.0 MPa.

313K; 333K; 353K. Closed symbols: the actual static mixer; open symbols:

double-pipe tube-in-tube counterflow exchanger [13].

Fig. 5. Amount of heat, Q/Ai, transferred to the fluid per unit surface area over a

residence time, , for the static mixer and tube-in-tube heat exchangers.

Fig. 6. Pressure drop of static mixer as a function of the carbon dioxide mass flowrate

and inlet pressure.

Fig. 7. Grb/Reb2

ratio against the Reynolds number at CO2 bulk conditions.

Fig. 8. Parity plot of calculated and experimental heat transfer coefficients of gas for

several operating conditions.

Page


20/29

Ac

cepted

Manu

script

ure 1a

Page


21/29

Ac

cepted

Manu

script

ure 1b

Page
http://ees.elsevier.com/supflu/download.aspx?id=18850&guid=ca0dd7d3-8bfb-4abf-ac15-52c384578346&scheme=1


22/29

Ac

cepted

Manu

script

ure 2

Page
http://ees.elsevier.com/supflu/download.aspx?id=18851&guid=942caecb-bcf9-45b0-98ef-f019863e72f1&scheme=1


23/29

Ac

cepted

Manu

script

ure 3

Page
http://ees.elsevier.com/supflu/download.aspx?id=18852&guid=6213a8a5-1a4f-4873-aff4-ddb2c6c60297&scheme=1


24/29

Ac

cepted

Manu

script

ure 4

Page
http://ees.elsevier.com/supflu/download.aspx?id=18854&guid=abdc1d91-e5e0-4ab7-880a-9349574f0279&scheme=1


25/29

Ac

cepted

Manu

script

ure 5

Page
http://ees.elsevier.com/supflu/download.aspx?id=18855&guid=f0b8889c-541c-4003-bb15-289de90b17e1&scheme=1


26/29

Ac

cepted

Manu

script

ure 6

Page
http://ees.elsevier.com/supflu/download.aspx?id=18856&guid=e9900584-96a7-4cce-ae10-f16ed948fcc1&scheme=1


27/29

Ac

cepted

Manu

script

ure 7

Page
http://ees.elsevier.com/supflu/download.aspx?id=18857&guid=652fdf50-9ee1-4405-bb04-2021167c37e5&scheme=1


28/29

Ac

cepted

Manu

script

ure 8

Page
http://ees.elsevier.com/supflu/download.aspx?id=18858&guid=70f67c63-ac85-4556-aefb-40ff7d05dd7f&scheme=1


29/29

Ac

cepted

Manu

script

ure 9
http://ees.elsevier.com/supflu/download.aspx?id=18859&guid=05f4f750-2bad-409c-9da1-538236509323&scheme=1

static mixers as heat exchangers in supercritical fluid extraction processes.pdf

Documents