isobaric, isochoric and supercritical thermal

Proceedings of the ASME 2013 International Mechanical Engineering Congress and Exposition
IMECE 2013
November 15-21, 2013, San Diego, CA, USA
IMECE2013-64947
ISOBARIC, ISOCHORIC AND SUPERCRITICAL THERMAL ENERGY STORAGE IN R134a
Benjamin I. Furst
Mechanical and Aerospace Engineering Dept.
University of California, Los Angeles
Los Angeles, CA,USA
Adrienne S. Lavine
Mechanical and Aerospace Engineering Dept.
University of California, Los Angeles
Los Angeles, CA,USA
Reza Baghaei Lakeh
Mechanical and Aerospace Engineering Dept.
University of California, Los Angeles
Los Angeles, CA,USA
Richard E. Wirz
Mechanical and Aerospace Engineering Dept.
University of California, Los Angeles
Los Angeles, CA,USA
ABSTRACT
The effective thermal energy density of R134a subjected to
an isobaric or isochoric process is determined and evaluated in
the two-phase and supercritical regimes. The results are
qualitatively extended to other fluids via the principle of
corresponding states. It is shown that substantial increases in
volumetric energy density can be realized in the critical region
for isobaric processes. Also, for isobaric processes which utilize
the full enthalpy of vaporization at a given pressure, there exists
a pressure at which the volumetric energy density is a
maximum. For isochoric processes (supercritical and twophase), it is found that there is no appreciable increase in
volumetric energy density over sensible liquid heat storage; the
effective specific heat can be enhanced in the two-phase,
isochoric regime, but only with a significant reduction in
volumetric energy density.
e
enthalpy for CPTES or internal energy for CVTES
(kJ kg-1)
h
enthalpy (kJ kg-1)
hfg
enthalpy of vaporization (kJ kg-1)
ufg,eff
effective latent heat for an isochoric process (kJ kg-1)
T
temperature (K)
u
internal energy (kJ kg-1)
∆( )
signifies a change in quantity ( )

average fluid density (kg m-3)
NOMENCLATURE
INTRODUCTION
The goal of this paper is to explore and evaluate the
Thermal Energy Storage (TES) potential of isobaric and
isochoric processes, using R134a as an example fluid. The
focus is placed on the energy density that can be obtained in a
TES system using these processes. The motivation for
investigating isobaric and isochoric processes is twofold.
Firstly, by utilizing an isobaric or isochoric process, energy can
be stored under the dome in the two-phase regime where the
latent heat of vaporization is available. Secondly, these
processes can both be used to store energy near the critical
point, where large enhancements in specific heat have been
measured [1]. Both of these regimes (under the dome and in the
CPTES constant pressure thermal energy storage
CVTES constant volume thermal energy storage
cp
specific heat at constant pressure (kJ kg-1 K-1)
cv
specific heat at constant volume (kJ kg-1 K-1)
ceff
effective specific heat (kJ kg-1 K-1)
cvol,eff
effective volumetric energy density (kJ m-3 K-1)
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Copyright © 2013 by ASME
critical region) have been identified as having potentially high
energy densities [2], which may offset their disadvantages.
Isobaric and isochoric TES under the dome and in the
critical region appears to not have been thoroughly studied in
the literature. In TES reviews, the liquid-vapor phase change is
mentioned only in passing (if at all) when discussing latent heat
TES [3]. This is understandable considering that isobaric
processes require possibly impractical changes in volume—as a
fluid changes from liquid to vapor at constant pressure its
volume can change by several orders of magnitude.
Additionally, the pressure in such a system could be high,
depending on where the dome is crossed. In principle isochoric
systems have been studied, but not in the same way proposed
here. The case often studied in literature is the one where a
liquid (e.g. water) is contained in a pressurized vessel in order
to enable the liquid to store sensible heat at elevated
temperatures without completely vaporizing [4]. In this paper a
more general analysis is done to see if the energy density of an
isochoric TES system can be increased by using the latent heat
of vaporization.
The TES characteristics of R134a were investigated using
the highly accessible and accurate data from NIST REFPROP
[5]. This program facilitated a systematic graphical and
numerical evaluation of pertinent thermodynamic data. All
graphs and thermodynamic values in this paper were derived
from NIST REFPROP unless otherwise noted. R134a has a
critical temperature, pressure and density of 101°C, 4.06 MPa
and 512 kg/m3 respectively.
The evaluation of isobaric and isochoric TES with a
particular fluid (R134a) has been done with the idea that using
real properties for an actual fluid would elucidate the TES
potential of these thermodynamic regimes in general, via the
well-established principle of corresponding states, which
somewhat unifies the thermodynamic behavior of all fluids [6].
The trends seen for this particular fluid would then qualitatively
apply to other fluids as well.
In a Constant Volume Thermal Energy Storage (CVTES)
or isochoric system, a fixed mass of fluid would be loaded into
a fixed volume (container). With the addition of heat, the
temperature and pressure of the fluid would increase while the
average density would remain constant and would depend on
the initial quantity of mass and container size. Such a system
would follow a vertical line on a P-v diagram, and fluid could
exist as a liquid, vapor or two-phase mixture (Figure 1). To pass
through the critical point the fluid needs to be loaded at its
critical density.
In a Constant Pressure Thermal Energy Storage (CPTES)
or isobaric system, a fixed mass of fluid would be loaded into a
distensible volume. As heat was added to the fluid, the
container would adjust its size such that the pressure would
remain constant. Perhaps the simplest version of such a system
would be the prototypical, vertical piston/cylinder configuration
where the pressure exerted on the fluid in the cylinder is due to
the force acting on the piston (its weight and the surrounding
pressure). The piston would be allowed to move and thus
accommodate the changes in volume of the fluid while
maintaining a constant pressure. Such a system would traverse
a horizontal line on the P-v diagram (Figure 1).
The overall optimization and feasibility of both a CPTES
and CVTES system are beyond the scope of this paper,
although there are clearly important implementation issues for
each. For example, in a CVTES system the pressure can
increase substantially with temperature, while a CPTES system
would likely require some sort of robust, distensible volume.
The larger optimization problem has been investigated
elsewhere for the case of a high temperature (~400°C) CVTES
system with encouraging results [7]. Here, the focus is purely
on the energy density potential of different thermodynamic
regimes.
Figure 1 – P-v diagram for R134a with isotherms
[5].
RESULTS
There are a few subtleties involved in quantifying TES.
Generally the quantities of interest are the energy stored per
degree temperature change per unit mass or unit volume.
Temperature change is not a pertinent parameter for a purely
latent heat process. When there is a change in temperature (∆T)
involved, it is useful to use an effective specific heat value (ceff)
defined as the change in specific energy (∆e) that occurs over
the change in temperature divided by that change in
temperature:
𝑐𝑒𝑓𝑓 =
∆𝑒
∆𝑇
𝑘𝐽
[
]
𝑘𝑔 𝐾
Note that ∆e is enthalpy for a CPTES and internal energy for
CVTES. Another useful quantity is the effective volumetric
energy density, defined as:
𝑐𝑣𝑜𝑙,𝑒𝑓𝑓 =
∆𝑒 ∙ 𝜌𝑚𝑖𝑛
∆𝑇
𝑘𝐽
[ 3 ]
𝑚 𝐾
where 𝜌𝑚𝑖𝑛 is the minimum density that occurs in the process-this is appropriate when dealing with CPTES systems where the
volume (and thus average density) changes, as it corresponds to
the largest volume of the system.
These quantities facilitate convenient comparisons between
TES in different regimes and other materials, but must be used
with care. The effective values are only valid for the specific
conditions under which they were derived, namely the specified
change in energy and temperature. They should not be
extrapolated to use with another ∆T without great care. For
example, in a CPTES system an extremely high effective
specific heat can be calculated along the critical isobar if ∆T is
made small enough, however this value of ceff is only valid for
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Copyright © 2013 by ASME
the given ∆T and the given enthalpy change, and using a
different ∆T with that ceff would not make sense. (See the
section on supercritical CPTES). This is emphasized since it
contrasts with the familiar case of the specific heat being
relatively independent of temperature (e.g. for liquids and
solids).
CPTES
An overview of CPTES in R134a is given by the h-T
diagram in Figure 2. This graph suggests that there are 3 main
CPTES regions: 1) under the two-phase dome where a large
change in enthalpy occurs at a fixed temperature (the enthalpy
of vaporization); 2) outside the dome far from the critical
region where enthalpy is approximately linearly dependent on
temperature; and 3) in the critical region where enthalpy is nonlinearly related to temperature. From a TES perspective the
regions of interest are the critical region and under the dome,
where there are relatively large changes in enthalpy over small
(or no) changes in temperature. These two regions are discussed
in more detail below.
Figure 3 – The enthalpy of vaporization, saturated vapor
density and volumetric energy density versus pressure for
R134a.
SUPERCRITICAL CPTES
A CPTES system has the potential to exploit the large
increase in cp that occurs near the critical point. Figure 4 shows
these spikes in cp for several pressures in the supercritical
region. The critical temperature and pressure of R134a are
101°C and 4.06 MPa. The energy storage potential of this
region depends on what pressure is selected (which spike), and
the size and location of the ∆T at this pressure. It is clarifying to
compare Figures 2 and 4: pressures at which the spike is more
pronounced in Figure 4 correspond to the enthalpy versus
temperature isobar being more vertical in the critical region in
Figure 2. Clearly the greatest TES is obtained for a given spike
when the ∆T is centered on the maximum. It is also clear from
Figure 2 that for a given pressure, a larger ∆T yields a larger
∆h, and that the largest ∆h per ∆T occurs at the critical pressure.
Figure 2 – An enthalpy versus temperature diagram for
R134a [5]. The two-phase dome and lines of constant
pressure are shown.
SUBCRITICAL CPTES
Below the critical pressure the most energetically
interesting region is under the dome where large excursions in h
exist for isothermal processes. This is the realm of the familiar
latent heat of vaporization at constant pressure. The TES
characteristics of this region are succinctly contained in the
enthalpy of vaporization at a given pressure. These values are
plotted in Figure 3. The enthalpy of vaporization monotonically
decreases with increasing pressure. The saturated vapor density
(ρmin in this case) is also included in Figure 3 for the
corresponding pressure; it increases as the enthalpy of
vaporization decreases. The product of density and enthalpy of
vaporization is the volumetric energy density (Figure 3). There
is a maximum volumetric energy density at about 3.31 MPa.
Figure 4 – The specific heat at constant pressure versus
temperature for several isobars [5]. At the critical point (4.06
MPa) this quantity dramatically increases; for pressures
above and close to the critical point the spike diminishes. A
subcritical pressure (2 MPa) is included for reference--the
discontinuity occurs at the liquid/vapor phase change.
These observations are quantified in Figures 5 and 6.
Figure 5 shows the effective specific heat and effective
volumetric energy density at different supercritical pressures for
a ∆T of 5 °C centered on the location of the cp maximum for
each pressure. As expected ceff and cvol,eff increase as the
pressure is reduced towards the critical pressure. Note that the
∆T range was chosen so that it captured most of the elevated cp
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along the critical isobar. This choice is somewhat arbitrary, but
also unimportant since the same basic trend would be seen
whatever the chosen ∆T was. Figure 6 shows the effective
specific heat and effective volumetric energy density as a
function of ∆T at the critical pressure. The ∆T is centered on the
maximum in each case. As expected, the effective specific heat
diverges as the ∆T decreases; in the limit of zero ∆T, ceff
approaches cp. Note that while ceff and cvol,eff increases
dramatically as ∆T is reduced, the total energy that can be
stored at this high ceff decreases. This trend can also be seen in
Figure 2. The values for cvol,eff were obtained by multiplying ceff
by the density at the upper value of the temperature interval,
which is the minimum density for the process.
CVTES
An overview of CVTES is provided by Figure 7. In this
graph the internal energy is plotted against temperature for a
characteristic sample of isochores. The dome (saturated liquid
and vapor values) is also shown. Outside of the dome all of the
isochores have approximately the same slope implying that the
effective specific heat (and cv) in this region is practically
independent of density and temperature. Inside the two-phase
dome there is a non-linear relation between u and T along the
isochores. In particular there are larger slopes under the dome,
indicating enhanced ceff. Furthermore, as the density gets
lower, portions of the u versus T slope are greater, indicating
local regions of enhanced ceff. This improved effective specific
heat under the dome should be expected since latent heat effects
are present.
Figure 5 – The effective specific heat and effective volumetric
energy density at different supercritical pressures for a ∆T of 5
°C centered on the cp maxima.
Figure 7 – Internal energy versus temperature for lines of
constant density [5]. The two-phase dome is also shown. The
3
critical density is 512 kg/m .
Note that there is no special TES phenomenon near the
critical point. Unlike lines of constant pressure in an h versus T
diagram, here the lines of constant density do not approach
being vertical near the critical point. This is reinforced by
looking at a cv versus T diagram (Figure 8)—the increase in
specific heat at constant volume near the critical point is
modest, increasing about 25% over the nearby saturated liquid
values.
Figure 6 – The effective specific heat and effective volumetric
energy density at the critical pressure as a function of
decreasing ∆T. The associated enthalpy change available at this
ceff/cvol,eff is also included. The ∆T is centered on the location of
the maximum in cp. As the effective specific heat increases, the
available enthalpy decreases.
Figure 8 – Specific heat at constant volume versus
temperature for lines of constant density [5]. Note that the
increase near the critical point is very modest.
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Copyright © 2013 by ASME
Figure 7 establishes that under the dome is the most
valuable region from the perspective of effective specific heat
(best ∆𝑢/∆𝑇). In order to further explore the potential of this
region, the change in internal energy that occurs under the
dome was looked at for a range of densities. Note that an
analog to the latent heat of vaporization does not have an
obvious definition here, as it does in the case of constant
pressure, since for an isochoric process the fluid can start out
being two-phase (imagine a P-v diagram with lines of constant
volume). However, Figure 7 suggests that all the densities do
converge to the same value of internal energy at low
temperatures (about -100°C). Then a metric for quantifying the
latent heat changes in a constant volume process for R134a can
be defined as the difference in internal energy between the
reference temperature of -100°C and the point where the
isochores leave the two-phase region. These effective isochoric
latent heat values (ufg,eff) are shown in Figure 9 for a range of
densities. This metric shows the same trend that is seen in
Figure 7: smaller densities under the dome have larger changes
in internal energy per unit mass.
Figure 9 – The effective isochoric latent heat (ufg,eff) for
different densities. ufg,eff is defined as the change in internal
energy along an isochore between -100°C and the point
where the isochore leaves the dome.
Unlike in a constant pressure process, the temperature
changes during an isochoric liquid/vapor phase change. This
suggests that an effective specific heat can be defined for this
process by dividing ufg,eff by the ∆T that is associated with it.
This quantity is shown in Figure 10. As expected from Figure 7,
lower densities have higher effective specific heats.
Figure 10 – The effective specific heat for ufg,eff and the
optimal case (∆T of 5 °C) as a function of density.
The volumetric effective specific isochoric latent heat is
also of interest. This quantity can be determined by multiplying
the effective specific isochoric latent heat by the associated
density. These effective volumetric densities are shown in
Figure 11; they monotonically increase with density.
Figure 11 – The effective volumetric energy density for ufg,eff
and the optimal case (∆T of 5 °C) as a function of density.
It is important to keep in mind that the ∆T associated with
each isochoric latent heat is different and that even though the
∆T may be larger for a given 𝜌 it may have a smaller ufg,eff than
another 𝜌 with a smaller ∆T. This can be seen in Figure 7 where
the lowest density clearly has the smallest ∆T and a relatively
large ufg,eff.
While the definition adopted for ufg,eff provides a
convenient metric for CVTES under the dome, it does not
provide a comprehensive picture. As in the case of CPTES near
the critical point the values of ceff and cvol,eff are strongly
dependent on the ∆T chosen. In particular if a ∆T is judiciously
chosen, higher values of ceff can be realized. In Figure 7 it can
be seen that the highest values of ceff along a given isochore
occur just before the isochore intersects the saturation dome
(the slope is steepest). Then the best achievable (optimal) ceff
and cvol,eff for a given isochore occurs when the ∆T is chosen to
be just inside the dome. These values are shown in Figures 10
and 11 using a ∆T of 5°C, where the upper value of the ∆T
interval is the saturation point for the given isochore. In accord
with Figure 7, the values for ceff and cvol,eff are larger for the
small ∆T just inside the dome at all densities shown except the
highest, where the values converge with those calculated for
ufg,eff. The hump-type feature that occurs for the case of a 5°C
∆T is due to the shape of the dome, and it is only visible for a
small ∆T. The upper values provide an upper bound to the
achievable ceff and cvol,eff in this domain
DISCUSSION
TES can be divided into two classes: that involving a ∆T,
and that not involving a ∆T (pure phase change process). For
TES processes that involve a ∆T, the metrics of ceff and cvol,eff
provide a convenient basis for comparison. In fact these
parameters can be seen as figures of merit since they lump the
important TES parameters together in the appropriate way: the
ideal TES system has a large energy capacity (numerator) over
a small ∆T and in a small volume/mass (denominator). Note
that as far as practical TES is concerned, volumetric energy
density (represented by cvol,eff) is probably the most important
metric—it is generally of greatest interest to have a small
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Copyright © 2013 by ASME
volume with a large capacity. Another important aspect to keep
in mind while evaluating TES is the ∆T, since ceff and cvol,eff
generally depend on ∆T.
Table 1 compares the TES potential of the thermodynamic
regions explored in the previous section for processes involving
a ∆T: CPTES in the critical region and CVTES in the twophase region. To facilitate the comparison, the largest values of
ceff and cvol,eff available in each thermodynamic region are listed
for the case of a ∆T of 5°C; the quantity of energy stored in this
interval is also included. For CPTES, energy is equal to
enthalpy; for CVTES, energy is internal energy. Values for the
sensible heat TES of R134a and water at 20°C have been
included for reference. (Note that isobaric and isochoric
sensible heat changes in this interval differ by about 1%).
The most prominent features of Table 1 are that the
sensible heat of water is hard to beat (which is well known),
and that CPTES in the critical region can perform very well.
For a ∆T of 5°C, R134a CPTES along the critical isobar can
have an effective specific heat about three times larger than
water and an effective volumetric energy density rivaling water
(only 8% smaller). These values depend on the ∆T, and as the
∆T is reduced, critical CPTES only improves; the trade-off is
that less and less energy can be stored at the high values of ceff
and cvol,eff. The second entry in Table 1 (critical CPTES with a
∆T of 0.5°C) illustrates this.
An evaluation of CVTES is slightly more complex. In
order to evaluate the potential for TES in this region, values
from the “optimal” case were used, where the ∆T is taken to be
just inside the two-phase dome. These represent the best
possible performance in this region (see previous section). As
can be seen from Figures 15 and 16, ceff and cvol,eff have opposite
trends: ceff decreases with increasing density while cvol,eff
increases with increasing density. To bound the TES potential
of this region, values for the lowest and highest densities are
used in rows three and four of Table 1. As can be seen, for low
density an appreciable increase in ceff over saturated liquid can
be obtained (170% larger). However, this is accompanied by a
79% reduction in the volumetric storage capacity (cvol,eff)
compared to sensible heat TES in R134a at 20°C. At the other
end of the spectrum (high density CVTES), the values of ceff
and cvol,eff approach the saturated liquid values at 20°C. This is
expected from Figure 10, where the high density isochores
practically follow the saturated liquid line. The cvol,eff of sensible
TES in liquid cannot be substantially improved upon by a
CVTES system.
Evaluating the latent enthalpy of vaporization is somewhat
more elusive since it cannot be directly compared to sensible
modes of TES due to there being no ∆T involved. It would
probably be most appropriate to compare this mode of TES to
other latent heat storage (melting/freezing); however data for
the latent heat of fusion for R134a could not be found in the
literature. The most noteworthy aspect of this regime found
here is the maximum in volumetric energy storage that occurs
for a pressure of about 3.31 MPa. To compensate for the lack of
data for R134a, the optimal volumetric energy density of water
and ammonia in isobaric processes were compared to their
latent heat of fusion. It was found that the volumetric energy
density of the latent heat of fusion is 3.2 times greater than the
optimal isobaric process for water, and 5.2 times greater for
ammonia.
Table 1—Summary of results
ceff
cv ol,eff
(kJ/kg/K) (MJ/m^3/K)
∆T
(K)
∆e
∆e*ρ min
(kJ/kg) (MJ/m^3)
Modality
Region
CPTES
along critical
isobar
12.8
3.85
5
63.4
19.2
CPTES
along critical
isobar
65.8
25.2
0.5
32.9
12.6
CVTES
(optimal)
under dome -lowest
density
3.8
0.38
5
18.8
1.9
CVTES
(optimal)
under dome -highest
density
1.2
1.8
5
6.03
9.0
sensible
(R134a)
saturated
liquid at 20 C
1.4
1.7
5
7.1
8.5
sensible
(water)
saturated
water at 20 C
4.2
4.2
5
20.9
20.8
CONCLUSION
A preliminary evaluation of isobaric and isochoric TES in
R134a has been conducted. The TES potential of the liquid,
two-phase and supercritical regions were compared using
thermal energy density metrics. The investigated TES processes
were divided into two classes: those involving a ∆T, and those
not involving a ∆T. Only CPTES in the two-phase regime fell
under the latter category. In this regime it was found that there
is an optimum pressure of about 3.31 MPa where the enthalpy
stored per unit volume reaches a maximum of 18 MJ/m3.
For processes involving a ∆T, the TES capacity of different
regimes was compared to the TES capacity of saturated liquid
R134a at 20°C with a 5°C ∆T. The metrics of comparison were
the effective specific heat (ceff) and the effective volumetric
energy density (cvol,eff) over a 5°C ∆T. The greatest values from
each regime were selected for comparison.
It was found that a CVTES system was unable to achieve
substantial gains in cvol,eff over the reference sensible TES liquid
values. Values of ceff could be increased by 170% over the
sensible heat TES values, but only at the expense of a dramatic
reduction in volumetric energy density (down 79% from the
sensible heat TES reference). This implies that a CVTES
system is unable to practically improve upon the energy density
of sensible TES in saturated liquid.
In the supercritical regime it was found that substantial
benefits over sensible liquid TES can be realized in a CPTES
system. For a ∆T of 5°C, a cvol,eff of 19.2 MJ/m3 can be obtained
(1.3 times larger than the sensible liquid TES reference); the
effective specific heat in this region is 12.8 kJ kg-1 K-1 (8.1
times larger than the saturated liquid sensible TES value).
These values can be improved by reducing the ∆T; increasing
the ∆T diminishes the advantage. No significant advantages
were apparent for CVTES in the supercritical region.
While the quantitative conclusions above solely apply to
R134a, the general trends observed can be expected to apply to
other fluids as well via thermodynamic similarity (the principle
of corresponding states [6]). These more general trends are
summarized below:
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Copyright © 2013 by ASME
1) For a CVTES system operating in the two-phase
regime, the volumetric energy density (cvol,eff) cannot
be substantially improved over values available in
sensible liquid TES.
2) A CVTES system in the two-phase regime can
significantly increase the effective specific heat over
sensible heat storage in liquid, however volumetric
energy density decreases substantially.
3) There is practically no TES benefit in the supercritical
region for a CVTES system.
4) A CPTES system operating in the critical region can
substantially increase the volumetric energy density
and effective specific heat over sensible liquid TES
values. The increase in ceff and cvol,eff decreases with
increasing ∆T.
5) For a CPTES system exploiting the entire enthalpy of
vaporization, there is a pressure at which the
volumetric energy density is a maximum.
It should be emphasized that the conclusions drawn here
only pertain to energy density. Energy density is only one
aspect of a practical TES system, and other considerations
could be important such as pressure, cost and containment. For
example, although a CVTES system cannot yield substantially
higher energy densities than sensible liquid TES, it does have
other advantages. Given a specified ∆T, a CVTES system will
always incur less of a pressure increase than a pure liquid
sensible heat TES system traversing the same ∆T (compare
lines of constant density on a P-v diagram inside the dome and
in sub-cooled liquid). In fact CVTES systems are currently
being explored [2, 7, 8], and have shown promise. Conversely,
regions that have been shown here to have a very high energy
density (e.g. the critical region) may not be practically
accessible in many situations.
The main value of this study is the trends highlighted
above that are expected to hold for other fluids. These provide a
guide of what relative energy densities are to be expected in a
fluid undergoing an isobaric or isochoric processes.
[4] Medrano, M., et al. "State of the art on high-temperature
thermal energy storage for power generation. Part 2—Case
studies." Renewable and Sustainable Energy Reviews, 14.1
(2010): 56-72.
[5] NIST Reference Fluid Thermodynamic and Transport
Properties—REFPROP, Version 9.0. Thermophysical
Properties Division National Institute of Standards and
Technology. Boulder, Colorado 80305.
[6] Leland, T. W., Chappelear, P. S. "The corresponding states
principle—a review of current theory and practice." Industrial
& Engineering Chemistry 60.7 (1968): 15-43.
[7] Tse, L. A., Ganapathi, G. B., Wirz, R. E., Lavine, A. S.
2012. “System modeling for a supercritical thermal energy
storage system”. Proceedings of the ASME 2012 6th
International Conference on Energy Sustainability & 10th Fuel
Cell Science, Engineering and Technology Conference.
[8] Ganapathi, G. B., Berisford, D., Furst, B., Bame, D.,
Pauken, M., Wirz, R.”A 5 kWh Lab Scale Demonstration of a
Novel Thermal Energy Storage Concept with Supercritical
Fluids”. ASME 7th International Conference on Energy
Sustainability, Jul 14-19, 2013, Minneapolis, MN, USA.
ACKNOWLEDGEMENTS
This effort was supported by ARPA-E Award DE-AR0000140
and Grant No. 5660021607 from the Southern California Gas
Company.
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