Volume 3 solar thermal systems components and applications 3 07 – thermal energy storage

Volume 3 solar thermal systems components and applications 3 07 – thermal energy storage Volume 3 solar thermal systems components and applications 3 07 – thermal energy storage Volume 3 solar thermal systems components and applications 3 07 – thermal energy storage Volume 3 solar thermal systems components and applications 3 07 – thermal energy storage Volume 3 solar thermal systems components and applications 3 07 – thermal energy storage

LF Cabeza, GREA Innovació Concurrent, Universitat de Lleida, Lleida, Spain

© 2012 Elsevier Ltd All rights reserved

3.07.1.1 Definition of Thermal Energy Storage

3.07.1.2 TES and Solar Energy

3.07.1.3 Design of Storages

3.07.1.4 Integration of Storages into Systems

3.07.4.2 BTES in a UK Office Building

3.07.4.3 Molten Salts in High-Temperature Solar Power Plants

3.07.4.4 Concrete and Other Solid Materials in High-Temperature Solar Power Plants

3.07.4.5 PCM in Buildings as Passive Energy System

3.07.4.6 PCM in Buildings as Active Energy System

3.07.4.7 Seasonal Storage of Solar Energy

3.07.4.8 Open Absorption Systems for Air Conditioning

References

ATES In aquifer thermal energy storage (ATES) systems, phase and vice versa

groundwater is used to carry the thermal energy into and Sensible energy storage In sensible thermal energyout of an aquifer For connection to the aquifer, water storage, energy is stored by changing the temperature of

BTES Borehole thermal energy storage (BTES) systems bricks, concrete, or sand.

50–200 m deep Boreholes act as heat exchangers to the allows the storage of heat and cold for later use TES is also underground, usually the U-pipe borehole heat known as heat or cold storage.

Thermochemical

Latent energy storage When a material stores heat while with high heat of reaction can be used for TES if the phase transition, the heat is stored as latent heat products of the reaction can be stored and if the heat Phase change material Aphase change material (PCM) is stored during the reaction can be released when the

a substance with a high heat of fusion that (melting and reversible reaction takes place

solidifying at a certain temperature) is capable of storing UTES Underground thermal energy storage (UTES) uses

Comprehensive Renewable Energy, Volume 3 doi:10.1016/B978-0-08-087872-0.00307-3 211

different ways, depending on geological, hydrogeological, borehole heat exchangers (BTES) and cavern thermal and other site conditions The two most promising energy storage (CTES) by way of underground cavities is a options are storage in aquifers (ATES) and storage through technology rarely applied commercially

c specific heat of the bed material (J kg−1 K−1) Ts–n new storage tank temperature after the time

b

heat of

cp specific the storage material (J kg−1°C−1) intervalΔt (°C)

d

G air mass velocity per square meter of bed frontal (UA)s storage tank loss coefficient and area product

V volume of the adsorbent (m3

m mass of storage material (kg) x position along the bed in the flow direction (m)

m_ mass flow of the air(kg s−1) adsorbent (kgwater/kgads)

m_c charging fluid flow rate (kg s−1) Δh phase change enthalpy, also called melting

Qbind binding energy (W) ΔHads integrated differential heat of adsorption (kJ kg−1)

Qu rate of collected solar energy delivered to the ΔTlm logarithmic mean temperature difference (°C)

−3

Ql rate of energy removedfrom storage tankto ρ density of the storage material (kgm )

ρ density of the air (kg m−3

Qtl rate of energy loss from the storage tank (W) ρsorb density of the adsorbent (kg m )

To reference (dead-state temperature) temperature (K)

3.07.1 Introduction

3.07.1.1 Definition of Thermal Energy Storage

Thermal energy storage (TES) allows the storage of heat and cold for later use TES is also known as heat or cold storage [1] TES can aid in the efficient use and provision of thermal energy whenever there is a mismatch between energy generation and use This mismatch can be in terms of time, temperature, power, or site [2]

The potential advantages on the overall system performance are as follows [1]:

• Better economics – reducing investment and running costs

• Better efficiency – achieving a more efficient use of energy

• Less pollution of the environment and less CO2 emissions

• Better system performance and reliability

The basic principle is the same in all TES applications Energy is supplied to a storage system for removal and use at a later time [2]

A complete process involves three steps (Figure 1): (1) charging, (2) storing, and (3) discharging In practical systems, some of the steps may occur simultaneously, and each step can happen more than once in each storage cycle [3]

Several factors have to be taken into consideration when deciding on the type and the design of any thermal storage system, and

a key issue is its thermal capacity However, selection of an appropriate system depends on many factors, such as cost–benefit considerations, technical criteria, and environmental criteria [3]

The cost of a TES system mainly depends on the following items: the storage material itself, the heat exchanger for charging and discharging the system, and the cost of the space and/or enclosure for the TES

Charging Storing Discharging

Figure 1 Steps involved in a complete TES system: charging, storing, and discharging

From a technical point of view, the most important requirements are as follows:

• High energy density in the storage material (storage capacity)

• Good heat transfer between heat transfer fluid (HTF) and storage medium (efficiency)

• Mechanical and chemical stability of storage material (must support several charging–discharging cycles)

• Compatibility between HTF, heat exchanger, and/or storage medium (safety)

• Complete reversibility of a number of charging–discharging cycles (lifetime)

• Low thermal losses

• Easy control

And the most important design criteria from the point of view of technology are

• Operation strategy

• Maximum load

• Nominal temperature and specific enthalpy drop in load

• Integration into the whole application system

3.07.1.2 TES and Solar Energy

TES is important to the success of any intermittent energy source in meeting demand [2] This problem is especially severe for solar energy because it is usually needed most when solar availability is lowest, that is, during winter TES complicates solar energy systems in two main ways First, a TES subsystem must be large enough to permit the system to operate over periods of inadequate sunshine The alternative is to have a backup energy supply, which adds a capital cost and provides a unit that remains idle The second major complication imposed by TES is that the primary collecting system must be sufficiently large to build the supply of stored energy during periods of adequate insolation Thus, additional collecting area is needed

Examinations of typical sunshine records show that even in the desert, the periods of cloudy and clear weather are about equally spaced; a few days of one followed by a few days of the other Partly cloudy days can greatly affect performance and make the difference between practical and impractical energy storage If the total energy of a partly cloudy day can be collected, then the periods requiring energy storage are greatly reduced

Concentrating solar systems must cope with the intermittent nature of direct sunlight on a cloudy day Consequently, absorbers and boilers must be designed with care to avoid problems of burnout when the sun suddenly returns with full brilliance Nonconcentrating systems face the fundamental problem of trying to provide sufficiently high efficiency at medium temperatures

to yield energy output at reasonable cost

Most TES applications involve a diurnal storage cycle; however, weekly and/or seasonal storage is also used [2] Solar energy applications require storage of thermal energy for periods ranging from very short duration to annual storage Advantages of diurnal storage include low capital investments for storage and low energy losses, smaller devices, and not-so-critical sizing of storage systems Advantages of seasonal storage are lower heat losses due to lower surface-to-volume ratios, and elimination of backup systems because periods of adverse weather have little effect on the long-term thermal energy availability

3.07.1.3 Design of Storages

Figure 2 shows the basic working scheme of a heat storage: heat or cold supplied by a heat source is transferred to the heat storage, stored in the storage, and later transferred to a heat sink to cope with the demand [1]

Heat source

Heat sink Heat

Figure 2 Basic working scheme of a storage: heat or cold from a source is transferred to the storage, stored in the storage, and later transferred to a sink [1]

Every application sets a number of boundary conditions, which must be looked into carefully:

• From the temperature point of view, the supply temperature at the source has to be higher or equal to the temperature of the storage, and the storage to the sink

• From the power point of view, that is, the amount of heat transferred in a certain time must be the required in the charging and discharging

• In some applications, the HTF and its movement by free or forced convection has to be considered

There are three basic design options in storage systems [1] The first one is when heat is exchanged by heat transfer on the surface of the storage This becomes a typical heat transfer problem where heat transfer resistance on the surface of the storage tank is the main parameter Conduction and free or forced convection mechanism are to be considered here

Second, when a heat exchanger is used separating the HTF with the storage material, the surface of heat transfer increases significantly This surface can be increased even further with the use of fins

Finally, a third scheme is used when the heat storage medium is also the heat transfer medium An example is when a water tank

is discharged due to the demand of the shower, and cold water enters the tank replacing the hot one In this case, heat transfer is basically by convection

3.07.1.4 Integration of Storages into Systems

The main goal to integrate a heat or cold storage tank into a system is to supply heat or cold However, the different supply and demand situations have a great influence on the integration concept [1]

The first case to consider is when there is no overlap in time between loading from the supply and unloading to the demand In this case, the storage system can match different times of supply and demand; in many cases, the storage system can match different supply and demand power, and even supply and demand location, with transport of the storage medium

If there is a partial or total overlap in time, it is possible to smooth out fluctuations of the supply and/or the demand Thus, the typical goals of storage integration are temperature regulation and power matching

The basic goals of the storage are to match supply and demand regarding the amount of heat and cold and the heating or cooling power at the right time While the amount of heat or cold is determined by the size of the storage and the heating or cooling power, which depend mainly on the design of the storage, the integration concept has a large influence with respect to time

3.07.2 Methods for TES

3.07.2.1 Sensible Heat

3.07.2.1.1 Definition

In sensible TES, energy is stored by changing the temperature of a storage medium such as water, air, oil, rock beds, bricks, concrete,

or sand The amount of energy introduced to the storage system is proportional to the temperature lift, the mass of the storage medium, and the heat capacity of the storage medium Each medium or material has its own advantages and disadvantages, but usually its selection is based on the heat capacity and the available space for storage [2]

The amount of heat stored in a material, Q, can be expressed as

Table 1 Thermal capacity at 20 °C of some common materials used in sensible TES [2]

A sensible TES system consists of a storage medium, a container (commonly, tank), and inlet–outlet devices Tanks must retain the storage material and prevent losses of thermal energy The existence of a thermal gradient across storage is desirable [3] Sensible heat storage can be made from solid or liquid media Solid media are usually used in packed beds, requiring a fluid to exchange heat When the fluid is a liquid, the heat capacity of the solid in the packed bed is not negligible, and the system is called dual storage system

3.07.2.1.2 Air

In solar heating systems that use air as heat transport fluid, the packed bed is a convenient and attractive storage device because it is generally formed from low-cost materials and exhibits a large heat transfer surface-to- occupancy volume ratio; typically 400 m2 m−3 can be found in a bed of particles of 0.01 m diameter [4]

The packed or fixed bed is generally a random assemblage of solid particles, each in physical contact with its neighbors and held firm in a container as shown in Figure 3 In the charging mode, the hot air flowing in warms the storage material and leaves the bin cooler The ideal storage process is achieved when all the solid materials are at the inlet temperature of the fluid To withdraw energy from the storage, discharging mode, the direction of the flow is reversed and the incoming cool air is heated progressively along the matrix

Insulation

Rockbed Container

Air flow

Figure 3 Schematic representation of packed bed storage unit [4]



In packed bed storage units, charge and discharge happen alternatively and cannot happen at the same time In these storage units, stratification is easily maintained

3.07.2.1.2.1 Thermal analysis of air systems

In air–pebbles storage units, both the air and the rocks change temperature in the direction of the airflow and there are temperature differentials between the rocks and the air In the thermal analysis of these systems, the following assumptions are made [5]:

1 The forced airflow is one dimensional

2 The system properties are constant

3 The heat transfer conduction along the rocked bed is negligible

4 There is no heat loss to the ambient

The thermal behavior of the pebbles and air are described by

An empirical equation for the determination of the volumetric heat transfer coefficient (hv) is

0 :7

G

d where G is the air mass velocity per square meter of bed frontal area (kg s−1m−2) and d is the rock diameter (m)

If the energy storage capacity of the air within the bed is neglected, eqn [4] is reduced to

The dimensionless NTUs is given by

in domestic solar systems

For a water tank to be effective, stratification is a key issue Water stratification occurs when water of high and low temperatures (thermocline) forms layers that act as barriers to water mixing (Figure 4) A thermally naturally stratified storage tank has no inside partitions Warm water has low density and moves to the top of the tank, whereas cooler water with higher density sinks to the bottom

A thin and tall water tank is desirable to improve thermal stratification The water inlet and outlet should be installed in a manner so as to produce a uniform flow to avoid mixing The surfaces that are in contact with the storage water should be minimized, and the insulation should be optimized The velocity of the water flowing into and out of the tank should be low [2]

Hot water heat store with stratification

Figure 4 Stratified water tank

Another type of water storage systems is solar ponds A solar pond is simply a pool of saltwater that collects and stores solar thermal energy The saltwater naturally forms a vertical salinity gradient, also known as a ‘halocline’, in which low-salinity water floats on top of high-salinity water, introducing water stratification due to the different salinity of the water The layers of salt solutions increase in concentration (and therefore density) with depth Below a certain depth, the solution has a uniform and high salt concentration [2, 6] When solar energy is absorbed by the water, its temperature increases, causing thermal expansion and a reduction in density If the water is fresh, the low-density warm water would float to the surface, causing a convection current The temperature gradient alone causes a density gradient that decreases with depth However, the salinity gradient forms a density gradient that increases with depth, and this counteracts the temperature gradient, thus preventing heat in the lower layers from moving upwards by convection and leaving the pond This means that the temperature at the bottom of the pond will rise to over 90 °C, while the temperature at the top

of the pond is usually around 30 °C A natural example of these effects in a saline water body is the Solar Lake located in Sinai, Israel The heat trapped in the salty bottom layer can be used for many different purposes, such as heating of buildings, or for industrial hot water, or to drive an organic Rankine cycle turbine or Stirling engine for generating electricity

One can use two types of water storage for water systems: pressurized and unpressurized [5] Other differences include the use of

an external or internal heat exchanger and single- or multiple-tank configurations Water may be stored in copper, galvanized metal,

or concrete tanks Whatever storage vessel is selected, it should be well insulated, and large tanks should be provided with internal access for maintenance Recommended U-value is about 0.16 W m−2K−1

Pressurized storage is preferred for small service water heating systems and the typical storage size is about 40–80 l m−2 of collector area With pressurized storage, the heat exchanger is always located on the collector side of the tank Either internal or external heat exchanger configurations can be used The two principal types of internal heat exchanger are an immersed coil and a tube bundle (Figure 5)

Due to the required storage volume, more than one tank can be used instead of a large one Additional tanks offer increased heat exchanger surface and reduced pressure drop in the collection loop A multiple-tank configuration for pressurized storage is shown

in Figure 6

An external heat exchanger provides greater flexibility because the tank and the exchanger can be selected independently of other equipments (Figure 7) The disadvantage of this system is the parasitic energy consumption, in the form of electrical energy, due to the additional use of the pump

For small systems, an internal heat exchanger–tank arrangement is usually used, which has the advantage of preventing the water side of the heat exchanger from freezing However, the energy required to maintain the water temperature above freezing point is

Solar storage tank

T Internal coil

To collector controller From collector

From collector

To collector controller

To collector

To collector

Solar storage tank

T Tube bundle

Cold water supply Immersed coil heat exchanger Figure 5 Pressurized storage water tank with internal heat exchanger [5]

Storage tank

T

Cold water supply

PumpCollector pump

To collector

To collector sensor From collector

Collector heat exchanger

Hot water load

Cold water supply

Figure 6 Multiple-tank storage arrangement with internal heat exchangers [5]

Figure 7 Pressurized storage system with external heat exchanger [5]

extracted from storage; thus, the overall system performance is decreased With an external heat exchanger, a bypass can be used to divert the cold fluid around the heat exchanger until it has been heated to an acceptable level of about 25 °C When the HTF is warmed to this level, it can enter the heat exchanger without causing freezing or extraction of heat from storage If necessary, this arrangement can also be used with internal heat exchangers to improve performance [5]

For systems with sizes greater than about 30 m3, unpressurized storage is usually more cost-effective than the pressurized This system, however, can also be employed in small domestic flat-plate collector systems, and in this case, the make-up system water is usually supplied from a cold water storage tank located on top of the hot water cylinder

Unpressurized storage for water and space heating can be combined with the pressurized storage for city water supply This implies the use of a heat exchanger on the load side of the tank to isolate the high-pressure mains’ potable water loop from the low-pressure collector loop An unpressurized storage system with an external heat exchanger is shown in Figure 8 In this

Hot water load

Solar storage

Backup storage

Cold water supply

T

DTHeat

 

 

configuration, heat is extracted from the top of the solar storage tank and the cooled water is returned to the bottom of the tank so as

to not distract stratification For the same reason, on the load side of the heat exchanger, the water to be heated flows from the bottom of the backup storage tank, where relatively cold water remains, and heated water returns to the top Where an HTF is circulated in the collector loop, the heat exchanger may have a double-wall construction to protect the potable water supply from contamination A differential temperature controller controls the two pumps on either side of the heat exchanger When small pumps are used, both may be controlled by the same controller without overloading problems [5] The external heat exchanger shown in Figure 8 provides good system flexibility and freedom in component selection In some cases, system cost and parasitic power consumption may be reduced by an internal heat exchanger

3.07.2.1.3.1 Thermal analysis of water storage systems

For fully mixed or unstratified energy storage, the capacity (Qs) of a liquid storage unit at uniform temperature, operating over a finite temperature difference (ΔTs), is given by

where m is the mass of storage capacity (kg)

The temperature range over which such a unit operates is limited by the requirements of the process The upper limit is also determined by the vapor pressure of the liquid

An energy balance of the storage tank gives

dTs

dt where Qu is the rate of solar energy collected and delivered to the storage tank (W), Ql the rate of energy removed from storage tank

to load (W), and Qtl the rate of energy loss from the storage tank (W)

The rate of energy loss from the storage tank is given by

The above equation assumes that the heat losses are constant in the period Δt The most common time period for this estimation

is an hour, because the solar radiation data are also available on an hourly basis

3.07.2.1.4 Other materials

Concrete is chosen because of its low cost, availability, and easy processing [2, 3] Moreover, concrete is a material with high specific heat, good mechanical properties (e.g., compressive strength), thermal expansion coefficient similar to that of steel (pipe material), and high mechanical resistance to cyclic thermal loading

When concrete is heated, a number of reactions and transformations take place, which influence its strength and other physical properties Resistance to thermal cycling depends on the thermal expansion coefficients of the materials used in the concrete To minimize such problems, a basalt concrete is sometimes used Steel needles and reinforcements are sometimes added to the concrete to impede cracking At the same time, by doing so, the thermal conductivity is increased by about 15% at 100 °C and 10%

at 250 °C

For high-temperature TES, liquid media is the preferred choice Different materials that can be used as liquid media are molten salts (a eutectic of sodium and potassium nitrate), silicon and synthetic oils (very expensive materials), and nitrites in salts (with potential corrosion problems) [3]

3.07.2.1.5 Underground thermal energy storage

Underground thermal energy storage (UTES) uses underground reservoirs for storing heat and cold in different ways, depending on geological, hydrogeological, and other site conditions The two most promising options are storage in aquifers (ATES) and storage through borehole heat exchangers (BTES) [7] TES through underground cavities (CTES, cavern thermal energy storage) is a technology rarely applied commercially

Heat Heat

pump

Cold Excess heat

at summer Summer

Winter

Groundwater level

Aquifer

Figure 9 ATES configuration [7]

In ATES systems, groundwater is used to carry the thermal energy into and out of an aquifer [7] For the connection to the aquifer, water wells are used (Figure 9)

In ATES systems, the energy is partly stored in the groundwater, and partly also in the solid mass which forms the aquifer This will result in the development of a thermal front with different temperatures This front will move in a radial direction from the well during charging of the store and then turn back while discharging

There are several hundreds of these systems in operation, with the Netherlands and Sweden as dominating countries of implementation Practically, all systems are designed for low-temperature applications where both heat and cold are seasonally stored, but they are sometimes used for short-term storage

BTES systems consist of a number of closely spaced boreholes, normally 50–200 m deep (Figure 10) Boreholes act as heat exchangers to the underground, usually the U-pipe borehole heat exchangers [7]

In some countries, the boreholes are grouted after the installation of borehole heat exchangers; but in this case, the thermal efficiency will decrease even though the groundwater is protected

The HTF flows through the U-pipe introducing or extracting heat from the underground The storing process is mainly conductive, and the temperature change of the rock will be restricted to only a few meters around each of the individual boreholes These systems have been implemented in many countries with thousands of systems in operation The numbers of plants are steadily growing and more new countries are gradually starting to use these systems They are typically applied for combined heating and cooling, normally supported with heat pumps for a better use of the low temperature from the storage [7]

Any ATES realization is quite a complex procedure and has to follow a certain pattern to be properly developed [7] Typical designing steps are as follows:

• Prefeasibility studies describing the principal issues

• Feasibility studies giving the technical and economical feasibility and environmental impact compared to one or several reference systems

• First permit applications to local authorities

• Definition of hydrogeological conditions by means of complementary site investigations and measurements of loads and temperatures on the user’s side

• Evaluation of results and modeling used for technical, legal, and environmental purposes

• Final design used for tender documents

• Final permit applications for court procedures

The technical issues are general, but the permit procedure may vary from country to country

While designing borehole heat exchangers, accurate information on the soil thermal parameters, such as thermal conductivity, heat capacity, and temperature, is essential for an economically sized and well-functioning thermal energy store [8] Especially, the soil thermal conductivity is critical as it affects both total length of heat exchanger needed as well as optimum interborehole distances

Cooling

Heating

Heat pump

Brine loop

Borehole storage

Figure 10 BTES configuration [7]

Due to the importance of ground thermal conductivity, several geothermal response test methods have been developed to measure the effective thermal conductivity of the ground and the local thermal resistance of the borehole heat exchanger installation All these tests operate under the assumption that the principal heat transport mechanism is conduction and therefore there is a relation between the thermal power applied to a heat exchanger, the temperature development with time, and the thermal conductivity

of the material Other mechanisms of heat transfer are not taken into account, which may invalidate the analysis of results

Another UTES system used is energy piles Energy piles use the building foundation as ground heat exchangers [9] This technology allows great possibility of cost reduction in the construction of ground heat exchangers and nowadays attracts a lot of attention in some countries like Japan

The types of foundation piles are classified broadly into three categories First is the cast-in-place concrete pile Second is the precasting concrete pile, which has a hole in the center The final one is the steel foundation pile with a blade on the tip of the pile, which is screwed into the ground by a rotating burying machine

The steel foundation can be easily utilized as the ground heat exchanger just after filling water and inserting several sets of U-tubes in the pile There are two typical methods that enable the steel foundation pile to provide ground heat exchanging One is direct water circulation method and the other one is indirect method using U-tubes filled with water The latter one can take a closed circulating system, which is better in terms of maintenance for many years

The amount of heat stored can be calculated by

where Δh is the phase change enthalpy, also called as melting enthalpy or heat of fusion, and m is the mass of storage material Figure 12 shows the typical range of melting enthalpy and temperature of common material classes used as phase change materials (PCMs) [1] The best known and the mostly commonly used PCM is water, which has been used for cold storage since the

FluoridesCarbonates

NitratesWater-salt

0 –100 0 +100 +200 +300 +400 +500 +600 +700 +800

Figure 11 Heat storage as sensible and latent TES

Figure 12 Classes of materials that can be used as PCM and their typical range of melting temperature and melting enthalpy [1]

early times For temperatures below 0 °C, water salt solutions are the typically used materials For temperatures between 0 and

130 °C, paraffins, salt hydrates, fatty acids, and sugar alcohols are used For temperatures above 150 °C, salts and other inorganic materials are utilized

Many substances have been studied as potential PCMs, but only a few of them are commercialized [1, 10, 11] The selection of the material to be used in latent heat storage is not easy Availability and cost are usually the main drawbacks for the selection of a technically suitable material Still today, problems such as phase separation, subcooling, corrosion, long-term stability, and low heat conductivity have not been totally solved and are under research

Recently, storage concepts have been classified as active or passive systems [3] An active storage system is mainly characterized

by forced convection heat transfer into the storage material The storage medium itself circulates through a heat exchanger (the heat exchanger can also be a solar receiver or a steam generator) This system uses one or two tanks as storage media Active systems are subdivided into direct and indirect systems In a direct system, the HTF serves also as the storage medium, while in an indirect system, a second medium is used for storing the heat Passive storage systems are generally dual-medium storage systems: the HTF passes through the storage only for charging and discharging a solid material

3.07.2.2.2 Exergy analysis of a latent storage system

Accessible work potential is called the exergy, that is, the maximum amount of work that may be performed theoretically by bringing a resource into equilibrium with its surrounding through a reversible process [12] Exergy analysis is essentially a

T

The exergy balance and the lost work are given by

where W is the work and the superimposed dot shows the change of variable in time The terms in square brackets show the exergy accompanying mass, heat, and work, respectively Wlost represents the destruction of exergy If a system undergoes a spontaneous change to the dead state without a device to perform work, then exergy is completely destroyed Therefore, exergy is a function of both the physical properties of a resource and its environment

Figure 13 shows the charging and discharging operations with appropriate valves, and temperature profiles for countercurrent latent heat storage with subcooling and sensible heating An optimum latent heat storage system performs exergy storage and recovery operations by destroying as little as possible the supplied exergy

• Charging

A charging fluid heats PCM, which may initially be at a subcooled temperature Tsc and may eventually reach to a temperature Tsh after sensible heating Therefore, the latent heat storage system undergoes a temperature difference of Tsh − Tsc, as shown in Figure 13 The heat available for storage would be

where U is the overall heat transfer coefficient, A the heat transfer area, m_c the charging fluid flow rate, and ΔTlm the logarithmic mean temperature difference expressed by

where NTUc ¼ UA=m_c Cpc ¼ Tci −Tco =ΔTlm is the number of transfer units Equation [21] relates the value of NTU with temperature Heat lost by the charging fluid will be gained by the PCM

The exergy stored by the PCM is

where Ts is an average temperature of storage, which may be approximated by (Tsc – Tsh)/2

The first and second law efficiencies are

actual heat stored Tci T

ðTci − TcoÞ − Toln

The heat gained by the discharging fluid will be lost by the PCM and the net exergy change of the charging fluid would be

TΔXd ¼ ðXdi − XdoÞ ¼ mdCpd

do

It is important to find the appropriate reversible chemical reaction for the temperature range of subjected energy source

3.07.2.3.3 Sorption systems

TES can be realized by utilizing reversible chemical reactions [32] Here the process of adsorption on solid materials or absorption

on liquids is explained Adsorption means binding of a gaseous or liquid phase of a component on the inner surface of a porous

Table 2 Comparison of storage densities of different TES methods

Adapted from Mehling H and Cabeza LF (2008) Heat and Cold Storage with PCM: An Up to Date Introduction into Basics and Applications

Berlin, Heidelberg: Springer

material During the desorption step, heat is put into the sample The adsorbed component is removed from the inner surface As soon as the reverse reaction (adsorption) is started, the heat will be released The adsorption step represents the discharging process There are two types of sorption systems, closed and open storage systems In a ‘closed sorption system’, the heat is transferred to and from the adsorbent by a heat exchanger, usually called condenser/evaporator The heat has to be transported to the absorber at the same time when it is extracted from the condenser to keep the HTF, usually water, flowing from the adsorber to the condenser This flow of HTF is very important, because if the sorption process reaches equilibrium, the process stops

The energy density expected is lower than an open sorption system because the adsorptive fluid is part of the storage system and also has to be stored In the case of using zeolite or silica gel as adsorbent, this can be up to 30–40% of the weight of the storage material

The advantages of closed systems are that they can reach higher output temperatures for heating operations compared to open systems Furthermore, they can supply lower temperatures for cooling, and it is possible to produce ice in the evaporator

In an ‘open sorption storage system’, air transports water vapor and heat in and out of the packed bed of solid or liquid adsorbents In the desorption mode, hot air enters the packed bed, desorbs the water from the adsorbent, and leaves the bed cooler and saturated In the adsorption mode, the humidified cool air enters the desorbed packed bed The adsorbent adsorbs the water vapor and releases the heat of sorption The air that exits is warm and dry

If a solid adsorbent is used, very hot air can be obtained If a liquid adsorbent is used, the process becomes absorption, and the humidification of the air is the main purpose

TES is achieved by separating the desorption step (charging mode) from the adsorption step (discharging mode) After desorption, the adsorbent can theoretically stay in this desorbed state without any thermal losses until the adsorption or absorption process is activated

The most common classes of solid absorbents are zeolites and silica gels Zeolites have a crystalline structure and a certain pore size, while silica gels have a pore size distribution The chemical composition of two typically used zeolites is shown in Table 3, and their properties are presented in Table 4 Silica gel is composed of 99% SiO2, while the rest are OH groups together with changing amounts of integrated water The properties of silica gel are presented in Table 5 Concerning the application of these adsorbents as TES, the amount of water that can be adsorbed is the most important property

For the characterization of solid sorbents in thermal applications like heating, cooling, and TES, the criteria to be used are

• the possible temperature lift (and drop in humidity ratio),

• the breakthrough curves (responsible for the dynamics of the process),

• the thermal coefficient of performance, and

• the energy density referring to the volume of the adsorbent

Table 3 Chemical composition of zeolite [32]

Pore diameter

Table 4 Properties of zeolites [32]

Table 5 Properties of silica gel [32]

For liquid absorbents, a similar theory could be explained

The ‘temperature lift’ (ΔT) is defined as the temperature difference between the air outlet and the air inlet The possible temperature lift is crucial for the design of sorption systems for heating applications The temperature lift of each adsorbent can

be very different under the same adsorption conditions The temperature lift can be calculated from

ΔHads

where Δx is the humidity ratio difference

ΔHads is the integrated differential heat of adsorption ΔHd between Cads and Cdes, and Cp air is the heat capacity of air ΔC is the difference in water concentration of the adsorbent

Csorb eff is the effective heat capacity of the adsorbent

The time-dependent changes in the properties of the outlet air of an adsorber is called ‘breakthrough curve’ In most applications, it

is referring only to the changes in the water content, but for thermal applications, the temperature change is also important The shape of the breakthrough curve depends on the behavior of the so-called mass transfer zone (MTZ) Within the MTZ, the properties

of the incoming air change to the properties of the outlet air

The dimension of the MTZ within a packed bed can be constant, expanding, or shrinking The zeolite breakthrough curve is caused by a constant or slightly shrinking MTZ, whereas the silica gel curve is caused by an expanding MTZ With the expanding MTZ cooler, more humid air is reached at the end of the bed, leading to a decrease in the outlet temperature and increase in the water content as shown in Figure 14

The thermal ‘coefficient of performance’ (COP) in sorption systems is defined as

Qcond − Qads

Qdes The energies are defined per mass of adsorbent, and they can be calculated from the adsorption equilibrium:

where Qsens is the amount of sensible heat brought into the system to heat up the packed bed of adsorbent pellets:

Qcond is the condensation energy:

Qbind is the binding energy, caused by the adsorption forces:

C ads

C des where L(T) is the heat of evaporation for water vapour and (ΔF + TΔS) is the heat of binding taken from Dubinis theory of volume filling the water adsorption, which can be determined from the adsorption equilibrium

Qads depends on the actual application

For a heat pump, Qads = Qdes

For long-term TES, Qsens cannot be used due to thermal losses

For a desiccant cooling system, only Qcond can be used during adsorption

The ‘energy density’ is defined as

ðQcond þ QbindÞmsorb

Vsorb where msorb is the mass of the adsorbent, Vsorb the volume of the adsorbent, and ρsorb the density of the adsorbent

3.07.2.4 Comparison of Thermal Storage System Types

Comparison of different thermal storage techniques for solar space heating and hot water production applications is summarized in Table 6 [14]

The main problem with water storage systems is the corrosion in long operation periods Another disadvantage of water storage systems is that the volume of the storage may be very large for large heat storage requirements and therefore the whole system becomes very heavy With large storage units, there is also the stratification problem Scale formation is another problem with such systems With packed-bed storage systems, there is no corrosion or scale-forming problem, but the volume of the systems might be large with an increase in cost On the other hand, by the use of phase change storage systems, large volumes required by the other type are eliminated Because of the chemical interaction between the storage material and the container, storage material loses its energy storage characteristics after a period of time

On weight basis, and even on volume basis, chemical storage has a greater capacity than other systems High-pressure CO–H2 mixtures, for example, have a storage capacity of an order of magnitude higher than liquid water (though less than salt hydrates and much less than metal hydrides) Although adequate thermodynamic data exist for most of the chemical reactions of interest, the chemical kinetics data are very scarce even for simple systems like methane–water

3.07.3 Economics of TES

3.07.3.1 TES and Energy Savings

TES can be used to reduce energy consumption or to transfer an energy load from one period/place to another [15] The reduced energy consumption can be achieved by storing excess thermal energy that would normally be released as water, such as heat produced by equipment and appliances, by lighting, and even by occupants

Table 6 Comparison of different storage techniques for solar space heating and hot water production applications

Sensible heat storage

Latent heat thermal storage

Comparison between different heat storage media

of the material

improve the heat transfer rate

for small temperature differences

material

Comparison of heat transfer properties and life of different types of thermal storages

discharging

selection of heat exchanger

Adapted from Kakac S, Paykoc E, and Yener Y (1989) Storage of solar thermal energy In: Kilkis B and Kakac S (eds.) NATO ASI Series, Series E: Applied Sciences, Vol 167: Energy Storage Systems, pp 129–161 Dordrecht: Kluwer Academic Publishers

The main objective of most TES systems, which is to alter energy use patterns so that financial saving occurs, can be achieved in several ways as follows [15]:

• The consumption of purchased energy can be reduced by storing waste or surplus thermal energy available at certain times for use

at other times For example, solar energy can be stored during the day for heating at night

• The demand of purchased electrical energy can be reduced by storing electrically produced thermal energy during off-peak periods

to meet the thermal loads that occur during high-demand periods

• The use of TES can defer the need to purchase additional equipment for heating, cooling, or air-conditioning applications and reduce equipment sizing in new facilities The relevant equipment is operated when thermal loads are low to charge the TES and energy is withdrawn from storage to help meet the thermal loads that exceed equipment capacity

3.07.3.2 Thermoeconomics of TES

The motivation and challenges for storing energy are focused mainly on three important facts [16]:

1 Energy security/reliability using new energy technology

2 Environmentally friendly techniques for climate protection, hence, contribution to environmental conservation – commitment for reduction of CO2 – obligations of Convention on Climate Change, Kyoto Protocol

3 Economic feasibility using market principles

Developing and deploying more efficient and environmentally friendly energy technology is critical to achieving the objectives of Energy security, Environmental protection, Economic growth and social development known as three Es The mission is to implement an environmentally friendly energy system If we are to achieve sustainable development, we will need to display greater responsibility for energy, economy, and environment

Thermodynamic analysis (TA) identifies the sources of exergy losses due to irreversibilities in each process in a system This will not guarantee that economical process modifications would be generated [12] For that, relations between the energy efficiency and capital cost must be evaluated Sometimes, improved energy efficiency will require more investment TA is of considerable value




where an efficient energy conversion is important Optimization seeks the best solution under specific constraints, which usually determines the complexity of the problem In every nonequilibrium system, an entropy effect leading to energy dissipation either within or through the boundary of the system exists

Currently, TA has realized three main stages [12]:

1 First, the second-law analysis is mainly used in thermal engineering by combining the principles of thermodynamics with heat transfer and fluid mechanics to reduce entropy production

2 Second, the exergy analysis combined the principles of thermodynamic with heat and mass transfer, fluid mechanics, and chemical kinetics that are widely used in the design and optimization of physical, chemical, and biological systems

3 Finally, exergy analysis is combined with economic analysis, which is called thermoeconomics or exergoeconomics

Thermoeconomics combines exergy analysis with economic analysis and calculates the efficiencies based on exergy; it assigns costs

to exergy-related variables by using the ‘exergy cost theory’ and ‘exergy cost balances’ Thermoeconomics can unify all balances – mass, energy, exergy, and cost by a single formalism ‘Extended exergy accounting’ considers nonenergetic costs, such as financial, labor, and environmental remediation costs as functions of the technical and thermodynamic parameters of systems There are two main groups of thermoeconomic methods: (1) cost accounting methods, such as exergy cost theory for a rational price assessment, and (2) optimization by minimizing the overall cost, under a proper set of financial, environmental, and technical constraints to identify the optimum design and operating conditions

Structural theory facilitates the evaluation of exergy cost and incorporation of thermoeconomics functional analysis It is a common formulation for the various thermoeconomic methods providing the costing equations from a set of modeling equations for the components of a system The structural theory needs a productive structure displaying how the resource consumptions are distributed among the components of a system The flows entering a component in the productive structure are considered as fuels F and flows leaving a component are products P The components are subsystems with control volumes as well as mixers and splitters Therefore, the productive structure is a graphical representation of the fuel and product distribution All the flows are extensive properties, such as exergy For any component j, or a subsystem, the unit exergy consumption xc is expressed on a fuel–product basis by

Fj Fj

Pj Xj For linear modeling, the average costs of fuels and products are defined by

dCT

dNTU Thermoeconomics of latent heat storage systems involves the use of principles of thermodynamics, fluid mechanics, and heat transfer Therefore, thermoeconomics may be applied to both the use of those principles and materials, construction, mechanical design, and a part of conventional economic analysis The distinguished side of it comes from the ability to account the quality of energy and environmental impact of energy usage in economic considerations

As an example, the seasonal solar energy storage with paraffin as PCM is studied Figure 15 shows the following three basic components: (1) solar air heaters, (2) latent heat storage, and (3) greenhouse

1 System of packed bed solar air heaters: The system has a total solar heat collector area of 27 m2 consisting of 18 packed bed solar air heaters Each unit has 1.5 m2 absorber area with a length of 1.9 m and width of 0.9 m The Raschig ring type (traditionally used in distillation columns) of packing made of polyvinyl chloride with the characteristic diameter of 0.05 m is used within the airflow passage The packing enhances the wall-to-fluid heat transfer by increasing the radial and axial mixing, as well as reducing the wall resistance The volumetric flow rate of airflow is 600 m3 h−1

Figure 15 Productive structure with three components of the latent heat storage system representing exergy transformation [12]

2 Latent heat storage unit: A horizontal steel tank, 1.7 m long and 5.2 m wide, contains 6000 kg of technical grade of paraffin as PCM Paraffin primarily consists of straight-chain hydrocarbons and very little amount of branching The n-alkane content exceeds 75% Commercial waxes may have a range of about 8–15 carbon number Volume contraction is <12% during freezing The tank is insulated with 0.05 m of glass wool Inside the tank, there are two spiral coils made of perforated polyethylene pipes with a total length of 97 m and diameter of 0.1 m embedded into the PCM The coils carry the warm airflow pumped from solar air heaters Differential scanning calorimeter measurements show that the paraffin has a melting temperature range of 48–60 °C and ∼190 kJ kg−1 of latent heat of melting Paraffin wax freeze without subcooling and melt without segregation of components

3 Greenhouse: The greenhouse with an area of 180 m2 is covered by 0.35 mm thick polyethylene, and is aligned north to south The floor area is 12  15 m and the height is 3 m The latent heat storage tank carries 33.3 kg of paraffin wax per square meter of the greenhouse ground surface area Heat storage unit connects the solar air heater system to the greenhouse with appropriate fans, valves, and piping Whenever the temperature in the greenhouse drops below a set point, a fan circulates the air from greenhouse through the latent heat storage unit until the temperature reaches the required level

Costs are the amount of resources consumed to produce a flow or a product When exergy is added into a flow, the cost of flow leaving a component is equal to the cost of flow entering plus the fuel value of added exergy When, on the other hand, exergy is removed, the fuel value of exergy is subtracted The products and their average costs in the productive structure shown in Figure 15 are summarized below:

• Component 1: Solar air heater system

Added exergy provided by the solar air heater system can be expressed in terms of NTU and ΔTlm:

T1o

T1i The airflow leaving the solar air heaters adds exergy, therefore its cost is

where C1pf is the fuel value of the product leaving the solar air heating system

• Component 2: Latent heat storage system

Removed exergy by the latent heat storage system during charging is

Tco

Tci Cost of the product after charging is

CpT ¼ C1p þ Ccp þ Cdp þ C3p ¼ C1pf þ Ccpf þ Cdpf þ C3pf ½61 Equation [61] may be used in eqn [47] to find an optimum value of NTU to minimize the total cost of production Cost optimization basically depends on the tradeoffs between the cost of energy (fuel) and capital investment as seen in Figure 16 Working with compatible design and operating conditions, and new technologies, it is possible to recover more and more exergy in energy conversion systems Implementing pollution charges and incentives for environmentally friendly technologies may reduce the cost of exergy loss

Thermoeconomics of the latent heat storage system involves fixed capital investment, operational and maintenance cost, and exergy costs Total fixed capital investment consists of the following:

• Direct expenses, such as equipment cost, materials, and labor

• Indirect project expenses, such as freight, insurance, taxes, construction, and overhead

• Contingency and contractor fee

• Auxiliary facilities, such as site development and auxiliary buildings