Adiabatic Compressed Air Energy Storage with

packed bed thermal energy storage

Barbour, Edward; Mignard, Dimitri; Ding, Yulong; Li, Yongliang

DOI:
10.1016/j.apenergy.2015.06.019
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Barbour, E, Mignard, D, Ding, Y & Li, Y 2015, 'Adiabatic Compressed Air Energy Storage with packed bed
thermal energy storage', Applied Energy, vol. 155, pp. 804-815. https://doi.org/10.1016/j.apenergy.2015.06.019

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 Applied Energy 155 (2015) 804–815

Contents lists available at ScienceDirect

Applied Energy
journal homepage: www.elsevier.com/locate/apenergy

Adiabatic Compressed Air Energy Storage with packed bed thermal

energy storage
Edward Barbour a,⇑, Dimitri Mignard b, Yulong Ding a, Yongliang Li a,⇑
a
School of Chemical Engineering, University of Birmingham, United Kingdom
b
Institute for Energy Systems, University of Edinburgh, United Kingdom

h i g h l i g h t s

 The paper presents a thermodynamic analysis of A-CAES using packed bed regenerators.
 The packed beds are used to store the compression heat.
 A numerical model is developed, validated and used to simulate system operation.
 The simulated efficiencies are between 70.5% and 71.1% for continuous operation.
 Heat build-up in the beds reduces continuous cycle efficiency slightly.

a r t i c l e i n f o a b s t r a c t

Article history: The majority of articles on Adiabatic Compressed Air Energy Storage (A-CAES) so far have focussed on the
Received 13 November 2014 use of indirect-contact heat exchangers and a thermal fluid in which to store the compression heat. While
Received in revised form 2 April 2015 packed beds have been suggested, a detailed analysis of A-CAES with packed beds is lacking in the available
Accepted 14 June 2015
literature. This paper presents such an analysis. We develop a numerical model of an A-CAES system with
packed beds and validate it against analytical solutions. Our results suggest that an efficiency in excess of
70% should be achievable, which is higher than many of the previous estimates for A-CAES systems using
Keywords:
indirect-contact heat exchangers. We carry out an exergy analysis for a single charge–storage–discharge
Adiabatic Compressed Air Energy Storage
Packed beds
cycle to see where the main losses are likely to transpire and we find that the main losses occur in the
Thermal energy storage compressors and expanders (accounting for nearly 20% of the work input) rather than in the packed beds.
Thermodynamic analysis The system is then simulated for continuous cycling and it is found that the build-up of leftover heat from
previous cycles in the packed beds results in higher steady state temperature profiles of the packed beds.
This leads to a small reduction (<0.5%) in efficiency for continuous operation.
Ó 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://
creativecommons.org/licenses/by/4.0/).

1. Introduction interconnectivity [3,4]. Several articles suggest that there may be

significant benefits available from cost-effective small-scale energy
If humanity is to continue to meet its energy needs in a sustain- storage devices; in distribution networks [5], to tidal current energy
able future, it is likely that the renewable energy era must truly [6], and for applications in isolated island grids [7]. This article con-
come of age. Although the last 20 years has seen a considerable siders the construction of a 2 MW h A-CAES system with packed
increase in the global installed capacity of renewable energy gener- bed regenerators to act as the thermal stores.
ation, many renewable generators are intermittent and cannot Two conventional CAES plants have been in existence for more
completely replace conventional thermal generation. Effective than 20 years; Huntorf, Germany (since 1978) and McIntosh,
energy storage would provide one way to resolve this issue and sev- Alabama (since 1991) [8,9]. Conventional CAES plants are hybrid
eral academic articles have been written on this topic, i.e. [1,2]. It air-storage/gas-combustion plants, essentially using low-cost elec-
should be noted that in addition to energy storage, future energy tricity to run the compressor in a single cycle gas turbine. Typical
systems will need a mix of demand-side management and single cycle gas turbines (peaking plants) are 35–40% efficient, so
require 2.5–2.86 kW h of gas for each kWh of peak electricity pro-
duced. This can be compared to the McIntosh CAES plant which
⇑ Corresponding authors.
uses 0.69 kW h of off-peak electricity and 1.17 kW h of gas to pro-
E-mail addresses: edward.r.barbour@gmail.com (E. Barbour), y.li.1@bham.ac.uk
(Y. Li). duce 1 kW h of peak electricity [10]. There has been some recent

http://dx.doi.org/10.1016/j.apenergy.2015.06.019
0306-2619/Ó 2015 The Authors. Published by Elsevier Ltd.
This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
 E. Barbour et al. / Applied Energy 155 (2015) 804–815 805

Nomenclature

c ratio of specific heats of air (–) ĥ heat transfer coefficient (Wm2 K1)
e void fraction (–) ĥvol volumetric heat transfer coefficient (Wm3 K1)
g polytropic efficiency (–) L length (m)
k thermal conductivity (Wm1 K1) m mass (kg)
l dynamic viscosity (Pa s) n moles (mol)
q density (kg m3) p pressure (Pa)
s thickness (m) Q heat (J)
v hoop stress (Pa) R specific molar gas constant (J kg1 K1)
w shape factor (–) Rth thermal resistance (KW1)
A area (m2) r radius (m)
B exergy (J) T temperature (K)
c specific heat capacity (J kg1 K1) t time (s)
d diameter (m) V volume (m3)
G core mass velocity (kg m2 s1) v velocity (ms1)
g gravitational constant (ms2) W work (J)
h enthalpy (J) z height (m)

work regarding coupling conventional CAES with wind energy to efficiency. In A-CAES energy is stored in both the compression heat
provide dispatchable utility-scale electricity generation [11–13]. and the cool pressurised air – i.e. a thermal effectiveness of zero
The Adiabatic CAES (A-CAES) concept is different from conven- would not lead to 0% efficiency, as work would still be extractable
tional CAES because it functions without the combustion of natural from the compressed air. Kim et al. calculate an efficiency of 68%
gas, and as such does not require the availability and storage of this without any external heat input [28]. Grazzini and Milazzo discuss
fossil fuel. In A-CAES surplus energy is used to power compressors design criteria, emphasizing the importance of heat exchanger
which drive air into a high pressure store (this store could be arti- design [29]. Hartmann et al. [30] analyses a range of A-CAES
ficially manufactured or be a naturally occurring cavern). The ther- configurations, concluding that an efficiency of 60% is realistic,
mal energy generated by the compression is stored in Thermal however it should be noted that the configurations mostly involve
Energy Stores (TES’s) and then used to reheat the air before it is multiple compression stages and a single expansion stage. Since
expanded again. To generate electricity the air is reheated and thermodynamic work is path dependent these systems are intrin-
expanded through turbines which drive generators. Although, to sically inefficient; in order to minimise irreversibilities the expan-
the best of the authors’ knowledge, no A-CAES plant has ever been sion path should be a close match to the reverse of the
built, it is often cited as a storage option in articles comparing compression path. Their analysis of a system with a single
energy storage technologies [14–16], usually with an expected effi- compression stage and single expansion stage highlights that a
ciency of 70–75% [14,16]. Recent research in A-CAES includes the combination of a fixed temperature TES and a sliding compression
ongoing EU based ‘‘Project ADELE’’ being undertaken by RWE (in which the outlet temperature is constantly changing) leads to a
Power, General Electric, Züblin and DLR, which quotes the poor efficiency (52% in their analysis). Wolf and Budt [31] suggest
expected efficiency at 70% [17]. Garrison and Webber [18] present that with lower TES temperatures A-CAES may be more economi-
a novel design for an integrated wind-solar-A-CAES system which cal despite having a lower efficiency (56%), due to quicker
uses solar energy to re-heat the compressed air before expansion, start-up times allowing it to participate in energy reserve markets.
with an overall energy efficiency of 46%. Pimm et al. [19] describe We believe that one aspect of previous A-CAES analyses that has
a novel approach in which ‘‘bags’’ of compressed air are stored been largely overlooked is the effect of (or how to avoid) mixing
under the sea; the air storage is essentially isobaric as the pressure of thermal storage at different temperatures (when using
is determined by the depth. Garvey [20] presents an analysis of a indirect-contact heat exchangers) as the outlet temperatures of
large-scale integrated offshore-wind and A-CAES system using the compressors changes with the pressure of the stored air.
these energy bags. This approach is also being investigated by A related developing energy storage technology that uses ther-
Cheung et al. [21] in partnership with Hydrostor [22]. mal energy storage in packed beds is Pumped Thermal Electricity
Commercial companies Lightsail [23] and SustainX [24] are devel- Storage (PTES). Desrues et al. [32] analyses a PTES system which
oping near-isothermal CAES but their technologies are yet to reach uses electricity to pump heat between packed beds, before using
the market so details on the processes and performances are a heat engine to produce electricity at a later time. White et al.
scarce. [33] undertakes a detailed theoretical analysis of thermal front
Several articles have specifically analysed the A-CAES concept, propagation in packed beds for energy storage. Although the use
but most consider using indirect-contact heat exchangers and a of packed beds for heat storage in A-CAES has been suggested, a
separate thermal fluid to store the compression heat. Bullough detailed analysis of this type of system is hard to find in the liter-
et al. estimates an efficiency greater than 70% [25], Grazzini and ature. This article presents a thermodynamic analysis of an A-CAES
Milazzo model a 16,500 MJ (4.6 MW h) system and suggest an system using packed bed regenerators for the TES’s.
efficiency of 72% [26], while Pickard et al. suggest a practical effi-
ciency greater than 50% for a bulk A-CAES facility (1GWd) may 2. Thermodynamics
be hard to achieve [27]. This discrepancy is not easily explained,
but seems at least in part to come from Pickard et al. modelling 2.1. Compression and expansion
the cooling stages as isochoric rather than isobaric. We suggest this
is inappropriate as one purpose of cooling is to reduce the volume Reversible isothermal compression and expansion would pro-
of the air. We also disagree with the statement in this paper that a vide the ideal for CAES, as heat could theoretically be exchanged
thermal effectiveness of 0.8 imposes a ceiling of 64% upon the cycle with the environment at ambient temperature and separate
806 E. Barbour et al. / Applied Energy 155 (2015) 804–815

thermal energy storage would not be required. However, although Unless the High Pressure (HP) air store is isobaric (kept at con-
there is significant research into near-isothermal compression for stant pressure), the states described in the Eqs. (2) and (3) will be
CAES (by companies like Lightsail and SustainX), it is not yet com- constantly changing. Each increment of air, Dm, must be com-
mercially available and any currently available compression that pressed to a pressure just above the store pressure for air to flow
approaches reversible isothermal compression is too slow for into the store. Therefore, the final pressure p2 of the compression
industrial use [27,28] due to the impractically small temperature will increase as the pressure in the store increases from the initial
differences required. Therefore most commonly cited A-CAES storage pressure to the maximum storage pressure pstore,max, and
designs opt for a series of adiabatic or polytropic compressions, during expansion the initial pressure p1 will fall as the pressure
after each of which the air is cooled back to the ambient tempera- inside the store decreases.
ture in order to reduce the both the temperature and volume of the In order to model the compression phase we use a finite step
air. approach. The model considers an increment of air, Dm, which is
The compressor work per unit mass can be estimated by consid- compressed from the ambient pressure to a pressure above the
ering the conservation of energy for the compressor control vol- storage pressure (so that air flows into the store). The store pres-
ume (neglecting changes in potential and kinetic energy from sure is a function of the mass of air contained within the store,
inlet to outlet): hence pstore = pstore(m). The work required to compress this finite
amount of air, Dm, depends on how many compressions it must
_ cv Q_ cv
W undergo, with the work required for the last compression given by:
 ¼ h1  h2 ð1Þ
m_ m_ !
  c1
h is the specific enthalpy of the gas. A reasonable first approxima- pstore ðm þ DmÞ þ ploss gpol;comp c
W Dm ¼ Dmcp T 1 1 ð7Þ
tion for the compressor work is: p1
 gc1c !
_
W p2 pol Here, p1 and T1 are the respective compressor inlet pressure and
¼ cp T 1 1 ð2Þ
_
m p1 temperature, ploss is any pressure loss introduced before the air
reaches the HP air store (by the after-cooling heat exchanger for
where the polytropic efficiency, gpol, is added to account for irre- example) and pstore(m + Dm) is the storage pressure after Dm has
versibilities and heat transfer. Similarly the work available per unit been added to the HP store, pstore(m + Dm) > pstore(m). If Dm passes
mass from an expansion is; through more than one compression, then the work required for
0 1 any previous compressions where the inlet and outlet pressures
_  gpol ðcc1Þ
W p are constant is given by Eq. (2). After being compressed and cooled
¼ cp T 1 @ 2
 1A ð3Þ the air Dm is then added to the air store at temperature Tstore (= T0).
_
m p1
Similarly during the expansion process an amount of air, Dm, is
The temperature of the gas is then given by; expanded from the store pressure to the ambient pressure. The
work available depends on the number of expansions undergone;
 gc1c with the work available from the first expansion given by:
p pol
T2 ¼ T1  2 For a compression 0 1
p1  gpol;turbc ðc1Þ
ð4Þ p2
  c
gpol ðc1Þ
W Dm ¼ Dmcp T 1 @  1A ð8Þ
p pstore ðm  DmÞ  ploss
¼ T1  2 For an expansion
p1
c is the ratio of specific heats (=cp/cv) and gpol is the polytropic effi- Now, T1 is temperature before the expansion, p2 is the pressure after
ciency of the compressor or turbine. Isentropic efficiency is a sim- the expansion, ploss is the pressure loss through the previous heat
pler way to account for irreversibilities, but it is dependent on exchanger and pstore(m  Dm) is the pressure when Dm has been
compression ratio [34]. Hence it is erroneous to use it to compare extracted from the HP air store. To validate the numerical model
compressions/expansions with different compression ratios. The and as an interesting aside the analytical solution for the work
polytropic (also known as infinitesimal stage or small-stage) effi- required to fill a fixed volume constant temperature air store in
ciency does not depend on the compression ratio and thus allows which the pressure depends on the mass of air contained within
for a better comparison between compressions with different pres- the store is derived for the case in which there are no
sure ratios. For example, a compression with p2/p1 = 3 and a poly- inter-cooling pressure losses in the Appendix A. As seen in the
tropic efficiency of 85% would have an isentropic efficiency of Appendix the model result matches the analytical solution.
82.5%, whereas p2/p1 = 9 and the same polytropic efficiency yields
an isentropic efficiency of 80%. 2.2. Heat storage in packed beds
The exergy destruction associated with a compression or
expansion is calculated by considering Eq. (5) for the change in In order to avoid very high temperatures the compression is
exergy in a flow stream. staged, with inter-cooling between each compression and
B_ v2 v2 after-cooling before the air enters the store to reduce the volume
¼ h2  h1  T 0 ðs2  s1 Þ þ 2  1 þ gðz2  z1 Þ ð5Þ required for the HP air store.
m_ 2 2
There are two distinct classes of heat exchangers that could be
Here, T0 is the ambient (dead state) temperature. Neglecting the used in an A-CAES system: These are direct-contact and
changes in potential and kinetic energy and noting that (h2–h1) is indirect-contact exchangers. In indirect-contact exchangers the
the compression work, the exergy destruction in the compressor heat transfer occurs through a wall that separates the fluid
is given by the T0(s2–s1) term. Using dQ = Tds and integrating for streams, whereas in direct-contact exchangers the heat transfer
an ideal gas the exergy destruction in the compressor and turbine occurs via direct contact between two fluid streams or between a
can be calculated as: fluid and a solid in a packed bed regenerator. Direct-contact
  exchangers are less common than their indirect-contact counter-
B_ T2 p parts, and this is perhaps why information concerning their appli-
¼ T 0 cp ln  R ln 2 ð6Þ
m_ T1 p1 cation in A-CAES thus far remains scarce in available literature.
 E. Barbour et al. / Applied Energy 155 (2015) 804–815 807

Packed bed regenerators are columns of porous solid (or packed Eqs. (9) and (10) are the standard 1-d equations for the temper-
solid particulate matter with some space between the particles- ature profile of a packed bed exchanger. The case in which the con-
this space is called void fraction, voidage or porosity). They are duction in the solid is neglected (ks = 0) was first solved
extensively used for many processes in the chemical and food analytically by Schumann [37] in 1929, who solved for tempera-
industries, i.e. adsorption, desorption, and rectification. They can ture under the assumptions that; any given solid particle has a uni-
offer very high rates of heat transfer, have very good pressure form temperature at any given time; there is negligible heat
and temperature tolerances and offer relatively inexpensive con- conduction between the solid particles; there is negligible heat
struction. There has been significant recent research analysing conduction among the fluid particles; the fluid motion is uniform
packed beds for high temperature thermal energy storage for solar and only in the axial direction of the solid; and the solid has a con-
applications (i.e. [35,36]). Using packed beds in an A-CAES system stant void fraction (porosity) and negligible radial temperature
would replace both the indirect-contact exchangers and the sepa- gradient. More sophisticated analytical treatments of packed bed
rate thermal energy stores, forgoing the need for a separate ther- systems can be also be found, i.e. Villatoro et al. [38].
mal fluid. The volumetric heat transfer coefficient, ĥvol, depends on the
Fig. 1 depicts an incremental slice of the packed bed regenera- flow properties of the fluid (air), the surface area to volume ratio
tor. Equations for the temperature of the fluid and solid phases of the gravel and the packing geometry of the bed. Several empir-
in an incremental slice of the packed bed can be expressed using ical relationships to determine ĥvol exist, as outlined in Adeyanju
the conservation of energy. and Manohar [39]. We use the empirical relationship suggested
Eq. (9) shows the energy rate balance for the fluid phase in a by Coutier and Farber [40] when investigating the heat transfer
slice of height Dz of the packed bed. The thermal power exchanged between gravel and air:
between the fluid and the solid phase is given by the term
^ ¼ 700ðG=dp Þ0:76
h ð14Þ
ĥvol(Tf–Ts)D zA while the net heat input due to the flow of the fluid v ol
is given by vfAqfcf(Tf(z,t)–Tf(z + Dz,t)) = vfAqfcf dTf/dz Dz. G is the core mass velocity (kg m2 s1) of the fluid and dp is the
dT f dT f average particle size (m). This correlation is also used by
eADzqf cf ¼ v f Aqf cf ^ ADzðT  T s Þ
Dz  h ð9Þ
v ol f Zanganeh et al. [41] to analyse a packed bed system for heat stor-
dt dz
age. The Biot number, Bi, gives a measure of the ratio of resistance
The energy rate balance for the solid phase is given by Eq. (10), to heat transfer via conduction to the resistance of heat transfer via
where the term A(d/dz)ks(dTs/dz) is due to the lengthwise (in the convection:
z-direction) conduction of heat through the solid in the packed bed.
  ^ c h
hL ^ dp
dT s v ol
ð1  eÞqs cs ^ ðT s  T Þ  A d ks dT s
¼ h ð10Þ Bi ¼ ¼ ð15Þ
dt
v ol f
dz dz ks 2kp ap

In Eqs. (9) and (10) cf and cs are the fluid and solid specific heat Lc is the characteristic length scale for heat transfer, dp is the particle
capacities (J kg1 K1), vf is the superficial velocity of the fluid mov- diameter, ks (=kp) is the solid particle thermal conductivity
ing through the bed (= volumetric flow rate/bed cross sectional (Wm1 K1) and ap is the ratio of surface area to volume. If
area, ms1) and ĥvol is the volumetric heat transfer coefficient Bi << 1, then the temperature of the particle can be approximated
(Wm3 K1). The void fraction is denoted e, hence the mass of as uniform, for example a gravel particle diameter of 10 mm leads
the fluid and the solid in a slice Dz are given by Eqs. (11) and (12). to a Biot number around 0.01. Hence we assume that the tempera-
ture within the solid gravel particulate is constant.
mf ¼ qf eADz ð11Þ
3. Details of the numerical A-CAES model with packed beds
ms ¼ qs ð1  eÞADz ð12Þ
Conservation of mass means the rate of change of fluid density The model adopts a finite step approach, considering a mass
in a slice is equal to the difference between mass flow rate across increment, Dm, of air passed through the compressors and packed
the slice. beds and added to the HP air store. The inlet temperatures to the
packed beds are calculated from Eq. (4), and discretised Eqs. 9,
dqf dðv f qf Þ 10 and 13 are solved for each slice of the packed beds. It should
¼ ð13Þ
dt dz be noted that Dm changes between the compressors as the pres-
sure and temperature profile of each packed bed changes.

Fig. 2. A schematic of an A-CAES system with packed bed heat exchangers. PB1
provides cooling between the compressions while PB2 cools the air entering the
Fig. 1. A depiction of a slice of height Dz in a packed bed regenerator. store. This reduces the required volume of the store.
808 E. Barbour et al. / Applied Energy 155 (2015) 804–815

 
A schematic of the model system is shown in Fig. 2. The maxi- T0
dBheat loss ¼ 1  dQ ð20Þ
mum storage pressure is 80 atm (8.106 MPa) and the minimum T
storage pressure is 20 atm (2.027 MPa). These pressures are chosen
Assuming that the packed bed has a constant specific heat
as a trade-off between minimising the range of pressures encoun-
capacity, dQ can be written as mcdT where c is the specific heat
tered and minimising the volume of the HP air store, as well as
capacity of the packed bed. Integrating this to get the exergy loss
allowing the HP air store to be either a HP tank or a rock cavern.
associated with heat flow as the bed cools from T1 to T2 yields:
The maximum storage pressure at the McIntosh CAES facility  
(which uses a solution mined salt cavern) is 7.93 MPa [42]. T1 T2 T1
Bheat loss ¼ mcT 0   ln ð21Þ
In the model the maximum pressure ratio, r, is the same for T0 T0 T2
each compression. To calculate r an estimate of the pressure loss Pressure losses in the packed beds are accounted for using the
that each cooling stage introduces is used; the pressure after the Ergun equation. The Ergun equation [44] provides one method of
nth cooling stage is given by: estimating the pressure drop through a packed bed and is generally
regarded as suitable for a first estimate, providing the void fraction
X
n
pn ¼ rn p0  r n1 ploss ð16Þ is in the range 0.33 < e < 0.55, the bed is made up of similar sized
1 particles and the flow rates are moderate [45]. It is an empirical
relationship, although du Plessis and Woudberg [46] has provided
With a final pressure of 8.106 MPa, an initial pressure of
some theoretical validation. The Ergun equation states:
101.3 kPa, 2 compression stages (therefore p2 = 8.106 MPa) and
assuming each packed bed introduces a pressure drop of 5 kPa, DP 150l ð1  eÞ2 1:75qf ð1  eÞ 2
¼ 2 2 vf þ vf ð22Þ
the pressure ratio r is 8.97. With 3 stages this decreases to 4.33. L w dp e3 wdp e3
In this first analysis the intermediate expansion pressures are the
dp is the particle diameter, qf is the fluid density, vf is the superficial
same as those for the respective compression stage.
bed velocity (the velocity that the fluid would have through an
In the finite step model the solid conductivity in the lengthwise
equivalent empty tube, given by volumetric flowrate divided by
direction of the packed beds is accounted for as well as thermal
cross sectional area), l is the dynamic viscosity of the fluid and e
power losses due to imperfect insulation of the regenerators. The
is the void fraction of the packed bed. w is the shape factor to
insulation losses are approximated by calculating the thermal
correct for the granitic gravel pieces not being spherical. The shape
resistance of a slice of insulating cylindrical layer.
factor is defined in Eq. (23). Vp is the volume of a single particle and
To calculate the thermal resistance we model each slice (as
Ap its surface area. The product (wdp) is the equivalent spherical
shown in Fig. 1) of the packed bed as a cylinder at Thot with radius
particle diameter:
ri, contained within a hollow insulation cylinder of inner radius ri
and outer radius ro (ro–ri is the insulation thickness). If the heat 6V p
w¼ ð23Þ
transfer rate is slow then temperature within the insulation layer Ap dp
(ri < r < ro) approximately satisfies Laplace’s equation. Solving this The overall efficiency of a single cycle is given by:
yields:
W discharge
T hot  T 0 g¼ ð24Þ
T ¼ T hot þ lnðr=r i Þ ð17Þ W charge
lnðr i =r o Þ
where Wcharge is the total work input required to run the compres-
Applying Fourier’s heat law in integral form gives the thermal sion and Wdischarge is the total useful work released by the expan-
power loss and allows the thermal resistance (Q_ = (Thot–T0)/Rth) to sion. The exergy balance for the system is given by:
be calculated, where Dz is the height of the slice and k is the ther-
mal conductivity of the insulation material.
W charge ¼ W discharge þ Bd;comp þ Bd;exp þ Blost;exit þ Blost;PB þ Bd;PB ð25Þ
Bd,comp is the exergy destroyed in the compressor and Bd,exp is the
lnðr o =ri Þ
Rth ¼ ð18Þ exergy destroyed in the expanders, which are estimated by the
2pDzk
model using Eq. (6). Blost,exit is the exergy remaining in the exhaust
The thermal resistance of the cylinder ends are also approxi- gas exiting the final expansion stage and is estimated using Eq. (5)
mated for the end slices of the packed beds. In this way the thermal in the model. Blost,PB is the exergy lost from the packed beds as heat,
power loss is calculated for each slice of the bed in the model. including heat remaining in the beds after the cycle has finished,
We also estimate the exergy loss associated with heat flow out estimated using Eq. (21). Finally Bd,PB is the exergy destroyed in
of the packed bed. We assume that all of the available work the packed from pressure losses and lengthwise conduction of heat
(exergy) lost from the bed is transferred to the environment, at along the bed and accounts for the remainder of the charge work.
temperature T0, and moreover we assume that work could have
been generated from this heat reversibly. A more involved treat- 3.1. Model specifics
ment recognises that work can only be generated irreversibly;
therefore during the work generation process heat will be trans-  The polytropic efficiencies of the expanders and compressors
ferred to parts of the system other than the environment, having are assumed at 85%. The turbines at the McIntosh CAES facility
temperatures other than T0. In this manner not all the exergy must have isentropic efficiencies of 87.4–89.1% [18], which given that
be lost to the environment. A detailed explanation is available in the plant has 4 stages, and a high pressure between 60 and
Appendix A of [43]. Under our assumptions in which all the avail- 80 bar, suggests a polytropic efficiency of 86%.
able work is lost to the environment, the exergy loss associated  Heat losses from the packed beds and the air store to the envi-
with a flow of heat from temperature T to the ambient environ- ronment depend on the driving temperature difference and the
ment (with temperature T0) is given by: insulation properties. A thermal conductivity of 0.3 Wm1 K1
  is assumed for the packed bed insulation layer, as insulation
T0 _
B_ heat loss ¼ 1  Q ð19Þ materials with this thermal conductivity are easily available
T
(fibreglass typically has a thermal conductivity less than
As heat flows out of the bed its temperature decreases, so Eq. 0.1 Wm1 K1), and the insulation is assigned a thickness of
(19) becomes: 0.2 m.
 E. Barbour et al. / Applied Energy 155 (2015) 804–815 809

 The PBHE is a cylinder containing uniformly sized granitic bed regenerators is initially at the ambient throughout the whole
gravel particles. The gravel particles in the packed beds have a length of the bed. Although no system is anticipated to use 100
diameter of 0.01 m, a specific heat capacity of 1 kJ kg1 K1 stages the extrapolation serves as a useful check to compare
and the effective thermal conductivity through the bed is against isothermal operation.
4 Wm1 K1 (the solid thermal conductivity of gravel is around The energy density is decreased as the number of compression
2 Wm1 K1). stages is increased and the HP air store must be larger to store the
 It is assumed that the specific heat capacity of the air is constant same amount of energy, as heat is stored in the packed beds at a
and equal to 1.01 kJ K1. In the temperature range encountered lower temperature. The model is further validated by noting that
the specific heat varies by <5%. We also assume that the specific as the number of stages gets very large the compression work
heat of the gravel is constant in the encountered temperature required (and hence the volume required to store the desired
range. amount of work) tends towards the isothermal value. This is calcu-
 Fluid flow is assumed uniform throughout the regenerators. lated by replacing Eq. (7) in the model with Eq. (23) below.
 The thermal inertia of the packed bed container is neglected.
 There is no change in volume of the solid with temperature and pðm þ DmÞ
W Dm ¼ DmRT 1 ln ð26Þ
the fluid and solid heat capacities are constant. p1
 The rate of heat transfer between the fluid and the solid bed is
The system temperatures achieved are of course lower with
proportional to the temperature difference between them.
more compression stages. Packed bed regenerators will allow for
 Each of the individual solid particulates have uniform tempera-
higher system temperatures than conventional heat exchangers
ture, i.e. Bi << 1.
as there is no requirement for a thermal fluid which must remain
 Leakage of compressed air has been neglected.
liquid and stable throughout the range of temperatures encoun-
tered (as in the indirect-contact designs). However, it is unlikely
For interest and for validation the full MATLAB code for the
that a final pressure of 80 atm will be practical in one compression
numerical A-CAES model is available at www.energystorage-
stage. Hence we present results for modelled systems with 2, 3 and
sense.com/downloads [47].
4 compression stages to reach the final storage pressure, with the
main focus on a 2-stage A-CAES system.
4. Results
4.2. Single cycle exergy analysis
Results for the simulated 2 MW h 500 kW A-CAES system are
presented. Firstly consideration is given as to the effect of the
In this subsection we use the model developed to perform an
number of compression/expansion stages. Secondly a single
exergy analysis of a single charge/discharge cycle of the 2-stage
charge/discharge cycle is analysed to see where the main losses
system in order to illustrate where the main exergy destruction
occur. Finally continuous charging and discharging is simulated
in the system occurs. The system takes 4 h to charge, remains idle
to predict how the system may operate under continuous cycling.
for 10 h and then is discharged for 4 h. The exergy balance is given
by Eq. (25). Initially the temperature in both the packed beds is
4.1. Number of compression stages uniform and ambient. Fig. 4 shows the results of the exergy
analysis.
The system depicted in Fig. 2 (based on the usual A-CAES design The simulated efficiency is 71.3% (obtained from Eq. (24)). The
– see [25,26] – but replacing the indirect-contact exchangers with results show that the biggest loss (nearly 20% of the work input)
direct-contact regenerators) has 2 compression and expansion occurs in the compressors and expanders. Thermal losses from
stages. Fig. 3 shows how the volume of the high pressure air store the packed beds account for a further 7% of the exergy loss. Exit
varies as the number of compression stages is varied, for one losses from the turbine, heat left in the packed beds, conduction
charge/discharge cycle in which the temperature of the packed losses in the packed beds and pressure losses through the packed
beds make up the rest (2%). This illustrates that maintaining high

Fig. 3. Graph showing how the HP (80 atm) storage volume and maximum
temperature achieved in the compression depends on the number of compression
stages. These results represent the initial cycle, with the regenerators starting at Fig. 4. Results of the exergy analysis performed on the 2-stage system. Losses are
ambient temperature. ordered from largest to smallest. ‘‘Packed Beds’’ is abbreviated to ‘‘PBs’’ in the figure.
810 E. Barbour et al. / Applied Energy 155 (2015) 804–815

Fig. 5. (a) the energy stored and the energy released over the first 50 cycles of the 2-stage system. (b) The efficiency of the first 50 cycles of the 2-stage system.

compressor and expander efficiencies throughout the system oper- 4. Pressure losses result in a smaller pressure ratio during dis-
ation is the most important challenge for A-CAES. The exergy lost charge (than that during charge) which tends to increase the
as heat flows from the packed bed regenerators to the surround- expander outlet temperatures. Therefore the air entering the
ings is also a significant loss. This could be reduced by increasing second packed bed during discharge has higher than ambient
insulation thickness; however this would increase the continuous temperature (PB1 in Fig. 2) and this regenerator is not cooled
cycling temperatures. back to the ambient temperature. This effect is predominant
One particularly interesting loss is the heat that is left in the in the early and middle part of the expansion and explains
regenerators after the expansion process has been completed. the central peak in the temperature profile of the second packed
This becomes particularly important when considering system bed at the end of the discharge (Fig. 6a and g).
operation under continuous cycling, as this heat leftover in the 5. Due to the larger heat loss from the ends of the beds (as the end
packed beds will affect the performance of the next cycle. of the regenerator has a higher surface-area-to-volume ratio –
see Fig. 6c and d and Fig. 6e and f), once the thermal front gets
4.3. System operation under continuous cycling close to the end and there is little heat left stored in the regen-
erator, the air exiting is heated less. This causes the first expan-
As shown in [48] it is likely that any market driven energy stor- der outlet temperature to drop towards the end of the discharge
age system would operate over a daily cycle to exploit the daily and explains why the temperature profile of the second expan-
electricity price differentials. To illustrate how the system may sion regenerator drops off after the central peak (Fig. 6g and a).
operate under continuous use we simulate the storage charging 6. During the idle time between discharge and the charge of the
for 4 h early in the morning (2 am–6 am), remaining fully charged next cycle the temperature of the beds does tend towards the
throughout the day until 4 pm when it discharges until 8 pm ambient, however the insulation to stop the stored compression
(4 pm–8 pm discharging), then remaining idle until 2am and the heat escaping between charge and discharge means this process
start of the next cycle. This equates to 4 h charging, 10 h idle is slow, and hence the temperature profile of the regenerators
fully-charged, 4 h discharging and then 6 h idle empty. Thermal doesn’t change much between the discharge of the previous
conduction in the packed beds and heat losses occur throughout cycle and the charge of the next (transition from Fig. 6g and h
the entire multi-cycle duration, including the idle periods. Fig. 5a to Fig. 6a and b). The ends of the bed tend towards the ambient
shows the energy stored and the energy returned over 50 succes- faster as they have a larger surface-area to volume ratio.
sive cycles for the 2-stage system and Fig. 5b shows the resulting
efficiency of each cycle. Fig. 6 shows how the temperature profiles of the regenerators in
We see that transient effects mostly die out after around the 2-stage system (PB1 in Fig. 2) evolve with continuous cycling. It
20 cycles. The initial cycles are different due to differing tempera- can be seen that the temperature profile in the packed beds
ture profiles in the packed beds at the start (of the cycle) – at the changes significantly compared to the initial cycle.
start of the first cycle the packed bed regenerators were at the Table 1 shows the main results of the simulations for A-CAES
ambient temperature throughout their length. However there are systems with 2 stages, 3 stages and 4 stages of compression and
several interplaying effects that mean that the temperature pro- expansion.
files of the beds at the start of the next cycle are different:
5. Cost estimates
1. Thermal conductivity along the length of the packed bed tends
to collapse the thermal front, spreading out the heat stored in Costs for prototype mechanical are notoriously difficult to esti-
the packed bed. Therefore when the air is reheated it reaches mate, however a set of very simple cost estimates for the High
a lower temperature and when the expansion is finished there Pressure (HP) air tank, the regenerators and the compressors and
is some heat remaining in the bed. expanders is given. The HP air tank and packed beds are cost by
2. Pressure losses mean less air can be usefully removed from the volume of steel and the compressors and the expanders from
HP store during discharge. The result is that not all the heat in tables of existing costs. Although these can only be regarded as
the packed beds is used for re-heating and this (as with point 1) ‘‘ballpark’’ estimates, they are useful to at least gain an order of
explains the peak in the temperature profile at the end of both magnitude cost for the system.
of the packed beds after the discharge has finished (i.e.
Figs. 6a and g). 5.1. The HP air tank
3. Heat loss from the beds and thermal conductivity along the
beds tend to decrease the temperatures reached during dis- Assuming the HP air tank is cylindrical, with hemispherical
charge compared to those during charge. ends and the thickness of the walls, sw, is constant and much
 E. Barbour et al. / Applied Energy 155 (2015) 804–815 811

Fig. 6. The figure shows the evolution of temperature profiles of the packed beds for the 2-stage system when the system is used continuously on a daily cycle with 4 h
charge, 10 h idle, 4 h discharge, 6 h idle as described. (a) First packed bed at the beginning of each cycle (b) second bed at the beginning of each cycle (c) first packed bed at the
end of the charge (d) second packed bed at the end of the charge (e) first packed bed at the beginning of the discharge (f) second packed bed at the beginning of the discharge
(g) first packed bed at the end of the discharge (f) second packed bed at the end of the discharge.
812 E. Barbour et al. / Applied Energy 155 (2015) 804–815

Table 1
Simulations results for continuous cycling.

2-stage system 3-stage system 4-stage system

Charging energy (first cycle) 2034 kW h 2033 kW h 2031 kW h
Discharging energy (first cycle) 1451 kW h 1446 kW h 1440 kW h
Charging energy (steady state) 2193 kW h 2186 kW h 2156 kW h
Discharging energy (steady state) 1559 kW h 1547 kW h 1520 kW h
Efficiency (first cycle) 71.3% 71.1% 70.9%
Efficiency (steady state) 71.1% 70.8% 70.5%
HP air store volume 182 m3 204 m3 216 m3
Compressor/expander polytropic efficiency (isentropic 85 % 85% 85%
efficiency will vary)
Max. operating pressure 80 atm (= 8.106 MPa) 80 atm (= 8.106 MPa) 80 atm (= 8.106 MPa)
Min. operating pressure 20 atm (= 2.027 MPa) 20 atm (= 2.027 MPa) 20 atm (= 2.027 MPa)
Regenerator dimensions 3 Regenerators with radius 0.6 m, 3 Regenerators with radius 0.6 m, 4 regenerators with radius 0.6 m,
length 12 m length 12 m length 12 m
Max packed bed temperature (first cycle) 605 K 474 K 419 K
Max packed bed temperature (steady state) 713 K 556 K 469 K

smaller than the radius (r >> sw), the volume of material required 5.4. Turbines
can be approximated as:
Without the ability to attain manufacturer quotes it is simply
V mat ¼ 2prsw L þ 4pr 2 sw ð27Þ assumed that the air turbines cost will be broadly similar to the
cost of the compressors. A cost of £140,000 for 500 kW equates
where r is the internal radius and L is the length of the cylinder. The to 440 $/kW. This is not dissimilar to costs per kW for large gas
hoop stress on the cylinder walls is: turbines (see [50]). Air turbines should also be easier to manufac-
ture in the long term as they have only to withstand temperatures
pr less than 1000 K, as opposed to gas turbines which work with high
v¼ ð28Þ temperatures around 2200 K, and the air turbines will not have to
sw
work simultaneously with the compressors (unlike a modern gas
The ratio of the material volume to internal volume of the tank turbine).
is: Summing these costs comes to $720 k. This is anticipated to
constitute the majority of the capital costs, but does not include
V mat 2sw L þ 4r sw costs for pipes, valves, the packed bed particulates, filters, pumps
¼ ð29Þ
V rL þ 4r 2 =3 and insulation. Another recent article [53] by Mignard has also
Assuming a HP air store geometry in which the length is 5 times attempted to estimate A-CAES costs.
the radius (L = 5r), then: An A-CAES system on the scale considered here will have to
compete with the other storage technologies; one notable technol-
42pV ogy in the capacity and power range modelled here (2 MW h
V mat ¼ ð30Þ 500 kW) being NaS (Sodium Sulphur) battery systems. These
19v
systems have efficiencies in excess of 80% over the time range
Allowing a maximum steel stress of 100 MPa, the 182 m3 HP air modelled [51]. However, with current cost estimates at 1000–
store (max pressure 8.106 MPa) would require 310 tonnes of 1400 $/kW h [52] equating to $2–2.8 million for a 2 MW h NaS
steel, assuming a density of 7800 kg m3. At $800/tonne this would system, with significant operating cost and a limited cycle life it
cost $250,000. may not be unreasonable to expect that a similar size A-CAES plant
will be significantly cheaper in the long term.

5.2. The packed beds

6. Discussions
The main cost in the PBHE’s will be the pressure vessel housing.
We again use Eq. (29) and apply the geometry specified in Table 1 The paper has presented a first analysis of an A-CAES system
to calculate the volume of material. In the 2-stage system we using packed bed regenerators. Despite some limitations the
require that the low pressure regenerator must be able to with- authors believe that the work is a useful contribution to the fields
stand pressures up to 1 MPa, while the high pressure regenerator of A-CAES and energy storage. Using packed bed regenerators
must withstand pressures up to 10 MPa. The LP regenerator then appears to have a number of advantages over conventional
requires 3 tonnes of steel while the HP requires 25 tonnes, indirect-contact heat exchangers for A-CAES. Compared to a sys-
yielding costs of $2400 and $20,000 respectively. tem with indirect-contact heat exchangers, the packed bed regen-
erator based system has no thermal fluid requirements, and hence
offers a simple solution for maintaining a large degree of the tem-
5.3. Compressors perature stratification of the thermal energy stores. This is not sim-
ply achievable using indirect-contact exchangers and a thermal
The compression train is required to produce air at 80 atm, at a fluid, as mixing of the thermal fluid would destroy stratification
power of around 500 kW. Referring to page 77 of [49], delivering and results in a significantly lower efficiency, as demonstrated by
air at 80 atm could just be achieved using a horizontal compressor the analysis of Hartmann et al. [30]. Packed beds should also offer
at a cost of 34.7 £/m3 h1. In terms of Free Air Delivery (FAD), the higher heat transfer coefficients, have good temperature and pres-
system would require about 4000 m3 h1. The total cost of the sure tolerances and offer simpler construction. A cost comparison
compression is then estimated at £140,000. between the two systems is an area of future work. The packed
 E. Barbour et al. / Applied Energy 155 (2015) 804–815 813

bed system not only removes the need for indirect-contact any exotic materials, suggest that further investigation is
exchangers, thermal energy stores and a suitable thermal fluid worthwhile.
but also is likely to require fewer compression and expansions Future detailed analysis of both packed bed and conventional
stages as the beds will tolerate much higher temperatures. heat exchanger based systems with sophisticated compression
Furthermore as there is no liquid coolant required, there is no and expansion modelling would be of value, accounting for the
pump required to move the thermal fluid around the system. variations in specific heat capacity and including a very rigorous
The simulations described in the present analysis are a simpli- packed bed model. However, should funding be available, the most
fied representation of how the real system may operate. informative next step may be the construction of a small-scale pro-
However, even in this simple model the many different interac- totype system, developing the necessary air compression and
tions lead to some complicated results – as shown by the evolution expansion technology and comparing the use of packed beds
of the temperature profiles of the packed beds through successive against conventional heat exchangers.
charge/discharge cycles. Loss estimates have attempted to be con- On a final note, A-CAES is a thermo-mechanical storage system
servative and it may be possible to increase performance slightly and this paper has studied its mechanical–mechanical turnaround
via optimisation (i.e. by optimisation of the intermediate expan- efficiency. An alternative strategy for using A-CAES would be to use
sion pressures). However some losses have also been omitted, i.e. the compression heat and the cold compressed air separately, for
leakages, pipe losses and span-wise conduction in the regenera- example by using the stored heat for hot water and the cool com-
tors. Fouling and flow channelling in the regenerators may require pressed air for simultaneous power and cooling. Investigation into
additional filtration and a specially designed nozzle manifold for this type of use is worthwhile and may turn out to have more
the injection of air respectively, introducing additional pressure favourable economics.
losses. Hence the losses in the real system may also turn out to
be more costly. On balance these effects are likely to have some
Acknowledgements
cancellation effect.
Conventionally, compressions are designed close to isothermal
This work was supported by the Engineering and Physical
to minimise the work required for a desired output pressure.
Sciences Research Council under the grants EP/K002252/1
However for an A-CAES system this is not necessarily the case as
(Energy Storage for Low Carbon Grids) and EP/L014211/1 (Next
minimising the compression work reduces the energy density. In
Generation Grid Scale Thermal Energy Storage Technologies).
A-CAES the expansion process should be the exact reverse of the
compression process in order to make the cycle as reversible as
possible. Therefore regarding the number of stages we suggest that Appendix A. Validation of numerical compressor model
fewer is better, to maximise energy density, reduce pressure losses,
reduce the number of components required and allow the air This appendix derives the analytical solution for the work
expanders to work with higher inlet temperatures and higher pres- required to change the pressure in a constant volume constant
sure ratios. It is important to realise that the systems outlined here temperature store from some initial pressure to a final pressure
store energy in two parts – partly in compressed gas and partly as pstore,max when there are no pressure losses in the after-cooling heat
heat; it is only the effective recombination of these parts that will exchanger. The after cooling heat exchanger cools the air from the
lead to a successful A-CAES system. Hence another important dif- exit temperature of the compressor to the storage (= ambient)
ference with conventional compressors and those used for temperature. The results match the numerical model outlined by
A-CAES is the need to store the heat of compression, so the Eqs. (7) and (8) and so serve to provide some validation. The
A-CAES compressors should minimise cooling during compression derivation is as follows:
allowing the maximum possible heat to be stored. Consider compressing an infinitesimal amount of gas, dm, from
Accordingly it is likely that the progression of A-CAES will be the ambient pressure p0 to the storage pressure pstore, then cooling
aided by the development of specialised compressors designed to it back to the ambient temperature with no pressure loss, and then
minimise any heat loss and output high temperature air while adding it to a store at the same temperature. Eq. (2) becomes Eq.
maximising reversibility. This equipment should be simple in that (A1) for an infinitesimal amount of gas.
no inter-cooling will be required – however it will also need to be !
able to withstand higher temperatures. These compressors should
  c1
pstore gpol c
provide a far better match to the reverse of modern gas turbines dW ¼ dmcp T 0 1 ðA1Þ
p0
which operate with high pressure ratios.
We now substitute dm = Mg dn, where n is the amount of moles
compressed and Mg is the molar mass of the gas. To simplify we
7. Conclusions also substitute x = (c–1)/(cgpol), and Eq. (A1) can be written as:
 x 
We conclude that an A-CAES system based on direct-contact pstore
dW ¼ dnM g cp T 0 1 ðA2Þ
heat exchangers (packed beds) is a better preliminary design than p0
a system based on indirect-contact heat exchangers. We anticipate
that a continuous cycling efficiency in excess of 70% should be Using the ideal gas law pV ¼ nRT (where R is the universal gas
achievable using packed beds, as stratification of heat stored at constant) and substituting dnT 0 ¼ dp0 V 0 =R yields:
different temperatures can be effectively preserved. In terms of  x 
M g cp V 0 pstore
efficiency the most important aspect is maintaining high compres- dW ¼ dp0 1 ðA3Þ
R p0
sor and expander efficiencies throughout the cycle.
A-CAES has potential as an energy storage medium. Although The store temperature Tstore is constant and equal to the ambi-
the work here suggests that it may struggle to match emerging ent temperature T0 (which is the initial temperature of the gas)
battery technologies in terms of efficiency, the current high costs and the gas is isobarically cooled back to ambient after it is
for battery storage, its problems with cycle life and depth of dis- compressed. Therefore, p0V0 = pstoreVstore and hence
charge, and the fact that an A-CAES system should not require dp0 = dpstore(Vstore/V0). Therefore it is possible to write:
814 E. Barbour et al. / Applied Energy 155 (2015) 804–815

 x 
cp V store pstore model (Eq. (7)) using different mass increments of air (blue line).
dW ¼ dpstore 1 ðA4Þ
R p0 It can be seen that the finite step method becomes a very good
approximation for the work required when using mass increments
where R is replaced by the specific gas constant R ¼ R=M g . Now the equal to or less than 102 kg. Hence a mass increment of 102 kg is
total work required to change the storage pressure pstore from the used throughout for the numerical model.
ambient pressure p0 to some maximum storage pressure pstore,max
can then be found by integrating Eq. (A4): Appendix B. Supplementary material
Z Z pstore;max  x 
cp V store pstore
dW ¼  1 dpstore ðA5Þ Supplementary data associated with this article can be found, in
R p0 p0
the online version, at http://dx.doi.org/10.1016/j.apenergy.2015.
Putting in limits of p0 and pstore,max, and re-substituting back in 06.019.
x = (c–1)/(cgpol) leads to the expression for the work required to
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