isobaric, isochoric and supercritical thermal …

1 Copyright © 2013 by ASME

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.


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.


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 two-

phase), 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.

NOMENCLATURE

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

)

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

)

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


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

𝑚3 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


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 non-

linearly 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 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 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.

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

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.


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.

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 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.

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 7 – Internal energy versus temperature for lines of

constant density [5]. The two-phase dome is also shown. The critical density is 512 kg/m

3.

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 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.


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.

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.

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

Figure 10 – The effective specific heat for ufg,eff and the

optimal case (∆T of 5 °C) as a function of density.

Figure 11 – The effective volumetric energy density for ufg,eff

and the optimal case (∆T of 5 °C) as a function of density.


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 two-

phase 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

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:

Modality Regionceff

(kJ/kg/K)

cv ol,eff

(MJ/m^3/K)

∆T

(K)

∆e

(kJ/kg)

∆e*ρ min

(MJ/m^3)

CPTESalong critical

isobar12.8 3.85 5 63.4 19.2

CPTESalong critical

isobar65.8 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 C1.4 1.7 5 7.1 8.5

sensible

(water)

saturated

water at 20 C4.2 4.2 5 20.9 20.8


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.

ACKNOWLEDGEMENTS This effort was supported by ARPA-E Award DE-AR0000140

and Grant No. 5660021607 from the Southern California Gas

Company.

REFERENCES [1] Sengers, J. M. H. Levelt. “Supercritical Fluids: Their

Properties and Applications.” Supercritical Fluids:

Fundamentals and Applications. Springer Science+Business

Media, 2000.

[2] Ganapathi, G. B., Wirz, R. E. “High density Thermal

Energy Storage with Supercritical Fluids,” ASME 6th

International Conference on Energy Sustainability, Jul 23-26,

2012, San Diego, CA, USA

[3] Hasnain, S. M. "Review on sustainable thermal energy

storage technologies, part I: heat storage materials and

techniques." Energy Conversion and Management, 39.11

(1998): 1127-1138.

[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.

isobaric, isochoric and supercritical thermal …

Documents