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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
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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
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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
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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
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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.
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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.
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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
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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
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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
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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
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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,
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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
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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].
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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
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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
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out carbon dioxide conditions at outlet of static mixer
G gas phase
pc pseudo critical condition
w property evaluated at the wall temperature
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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.
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[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
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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.
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