On the Design of a Reactor for High
Temperature Heat Storage by Means
of Reversible Chemical Reactions
Patrick Schmidt
Master of Science Thesis
KTH School of Industrial Engineering and Management
Energy Technology EGI-2011-117MSC EKV 862
Division of Energy Technology
SE-100 44 STOCKHOLM
Abstract
This work aims on the investigation of factors influencing the discharge characteristics
of a heat storage system, which is based on the reversible reaction system of Ca(OH)2
and CaO. As storage, a packed bed reactor with embedded plate heat exchanger for
indirect heat transfer is considered. The storage system was studied theoretically by
means of finite element analysis of a corresponding mathematical model. Parametric
studies were carried out to determine the influence of reactor design and operational
mode on storage discharge. Analysis showed that heat and gas transport through
the reaction bed as well as the heat capacity rate of the heat transfer fluid affect the
discharge characteristics to a great extent. To obtain favourable characteristics in
terms of the fraction of energy which can be extracted at rated power, a reaction front
perpendicular to the flow direction of the heat transfer fluid has to develop. Such a
front arises for small bed dimensions in the main direction of heat transport within
the bed and for low heat capacity rates of the heat transfer fluid. Depending on the
design parameters, volumetric energy densities of up to 309 kWh/m3 were calculated
for a storage system with 10 kW rated power output and a temperature increase of
the heat transfer fluid of 100 K. Given these findings, this study is the basis for the
dimensioning and design of a pilot scale heat exchanger reactor and will help to
evaluate the technical feasibility of thermo-chemical heat storage systems.
ii
Acknowledgement
With these lines I want to express my gratitude to all the people who supported me
in the last couple of months.
First and foremost I want to thank my advisor Marc Linder. The joy and enthusiasm
he has for research was contagious and motivational for me. I appreciate all the
effort, time, and ideas he contributed to support my work. Thanks to his patience
and guidance my time at DLR was a valuable experience. I also owe Inga Utz a debt
of gratitude for her advice and patience with which she has helped setting up and
mending the modelling part of this thesis. Also, I would like to thank Victoria Martin
for her support at Kungliga Tekniska högskolan in Stockholm.
Thanks goes also to the many people that became a part of my life over the last
months. You have made sure that I still had a life besides this thesis. For the
enjoyable time spent together I am grateful.
Finally, I want to thank my family for their unconditional support throughout my
life.
iii
Contents
Abstract
ii
Ackowledgement
iii
List of Figures
vi
List of Tables
viii
Nomenclature
ix
1
Introduction
1.1 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
Thermal Energy Storage: State of the Art
3
2.1 Sensible Heat Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
2.2 Latent Heat Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
2.3 Chemical Heat Storage . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
2.3.1 Reversible chemical reactions: thermodynamic considerations
8
2.3.2 Calcium Hydroxide – Calcium Oxide System . . . . . . . . . . . 11
2.3.3 Principle of Le Chatelier and Process Control . . . . . . . . . .
13
3
Motivation & Focus
15
4
Plate Heat Exchanger Reactor as Chemical Heat Storage
4.1 Simplified Model for Highly Permeable Packed Beds
4.1.1 Governing Equations . . . . . . . . . . . . . . .
4.1.2 Boundary & Initial Conditions . . . . . . . . .
4.1.3 Simulation Results . . . . . . . . . . . . . . . .
4.2 Extended Model for Poorly Permeable Beds . . . . . .
4.2.1 Extended System of Governing Equations . . .
4.2.2 Boundary & Initial Conditions . . . . . . . . .
4.2.3 Simulation Results . . . . . . . . . . . . . . . .
19
19
19
22
24
36
37
38
38
iv
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1
2
Contents
4.3
5
Design Suggestion for a Plate Heat Exchanger Reactor . . . . . . . . .
Conclusion & Prospects
44
48
References
50
A Thermophysical Properties of the reactants of the Calcium Hydroxide –
Calcium Oxide System
53
A.1 Enthalpy and Entropy of Formation . . . . . . . . . . . . . . . . . . .
53
A.2 Molar heat capacity at constant pressure . . . . . . . . . . . . . . . . .
54
B Results of Parametric Study
55
v
List of Figures
2.1
2.2
2.3
2.4
2.5
3.1
3.2
3.3
3.4
3.5
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
Schematic of an Andasol-type solar thermal power plant . . . . . . .
Schematic of a proposed storage concept for direct steam generation
Typical T,h-diagram of a pure substance . . . . . . . . . . . . . . . . .
Plot of the van’t Hoff equation for the reversible reaction system of
Ca(OH)2 – CaO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Principle of heat transformation in the system of Ca(OH)2 – CaO . .
Schematic of reactor with direct heat transfer . . . . . . . . . . . . . .
Schematic of reactor with indirect heat transfer . . . . . . . . . . . . .
Schematic of a shell and tube heat exchanger reactor . . . . . . . . . .
Heat transfer coefficient and heat transfer area over inner diameter for
pipe flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Schematic of a plate heat exchanger reactor for energy storage . . . .
4
5
6
13
14
16
16
17
17
18
Schematic of the implemented geometric model with corresponding
boundaries and domains . . . . . . . . . . . . . . . . . . . . . . . . . .
23
Temperature profile of the reaction bed for various bed dimensions at
t = 30 min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
Conversion profile of the reaction bed for various bed dimensions at
t = 30 min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
Transferred heat per flow channel over time for various reaction bed
dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
Average HTF outlet temperature over time for various reaction bed
dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
Averaged conversion over time for various reaction bed dimensions
29
Temperature profile of the reaction bed for various HTF inlet velocities
at t = 60 min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Conversion profile of the reaction bed for various HTF inlet velocities
at t = 60 min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
vi
List of Figures
4.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17
4.18
4.19
4.20
4.21
4.22
Transferred heat per flow channel over time for various HTF inlet
velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
Average HTF outlet temperature over time for various HTF inlet velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
Averaged conversion over time for various HTF inlet velocities . . .
33
Volumetric energy density at rated power as a function of HTF inlet
velocity and reaction bed width . . . . . . . . . . . . . . . . . . . . . .
35
Conversion at rated power as a function of HTF inlet velocity and
reaction bed width . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
Effective volumetric energy density at rated power as a function of
HTF inlet velocity and reaction bed width . . . . . . . . . . . . . . . .
36
Conversion after 15 min versus bed permeability . . . . . . . . . . . .
39
Characteristic temperatures along the boundary of reaction bed and
flow channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Average HTF outlet temperature over time for countercurrent flow
configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
Conversion profile across the reaction bed in countercurrent flow at
various times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
Temperature profile across the reaction bed in countercurrent flow at
various times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
Schematic of a horizontal reaction bed . . . . . . . . . . . . . . . . . .
44
Average HTF outlet temperature over time for various design parameters of a horizontal reaction bed . . . . . . . . . . . . . . . . . . . . . .
46
Transferred heat per flow channel over time for various design parameters of a horizontal reaction bed . . . . . . . . . . . . . . . . . . . .
47
vii
List of Tables
2.1
Selection of reversible reactions proposed for high temperature energy
storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.1
4.2
4.3
4.4
4.5
4.6
Boundary conditions of the simplified model . . . . . . . . . . . . . .
Initial conditions of the simplified model . . . . . . . . . . . . . . . .
Reactor key data for various reaction bed dimensions . . . . . . . . .
Reactor key data for various HTF inlet velocities . . . . . . . . . . . .
Additional boundary & initial conditions for the extended model . .
Key data of a reactor with vertical reaction bed for various design
parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Key data of a reactor with horizontal reaction bed for various design
parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7
viii
25
25
30
33
38
45
47
Nomenclature
Acronyms
CSP
Concentrating Solar Power
DLR
Deutsches Zentrum für Luft- und Raumfahrt
HEX
Heat exchanger
HTF
Heat transfer fluid
NIST
National Insitute of Standards and Technology
PCM
Phase change material
SEGS
Solar Energy Generating System
Latin Letters
∆rG
Change in Gibbs free energy of reaction
[J/mol]
∆r H
Enthalpy of reaction
[J/mol]
∆rS
Entropy of reaction
q̇
Heat flux
cp
Specific heat capacity at constant pressure
d
Diameter
E
Energy content
h
Height
h
Specific enthalpy
K
Equilibrium constant
K
Permeability
[J/(mol · K)]
[W/m2 ]
[J/(kg · K)]
[m]
[kWh]
[m]
[J/kg]
[-]
[m2 ]
ix
Nomenclature
k
Reaction rate constant
M
Molar mass
m
Mass
n
Number
[-]
Nu
Nusselt number
[-]
p
Pressure
pv
Volumetric power density
Pr
Prandtl number
[-]
Q
Heat
[J]
R
Gas constant
[J/(mol · K)]
r
Reaction rate
[mol/(m3 · s)]
Rth
Thermal resistance
Re
Reynolds number
s
Thickness
SQ̇
Heat source/sink
[W/m3 ]
Sm
Mass source/sink
[kg/(m3 · s)]
T
Temperature
t
Time
U
Overall heat transfer coefficient
ug
Velocity of gaseous phase
uv
Volumetric energy density
V
Volume
[m3 ]
v
Velocity
[m/s]
[1/s]
[kg/mol]
[kg]
[Pa]
[kW/m3 ]
[K/W]
[-]
[m]
[K]
[s]
[W/(m2 · K)]
[m/s]
[kWh/m3 ]
x
Nomenclature
w
Width
X
Conversion
[m]
[-]
Greek Letters
α
Heat transfer coefficient
[W/(m2 · K)]
ε
Porosity
η
Dynamic viscosity
[kg/(m · s)]
λ
Thermal conductivity
[W/(m · K)]
ν
Stoichiometric coeffient
ρ
Density
[-]
[-]
[kg/m3 ]
Subscripts
95%
Conversion of 95%
bed
Reaction bed
eff
Effective
eq
Equilibrium
fc
Flow channel
g
Gaseous phase
H
Hydration
h
Hydraulic
ht
Heat transfer
HTF
Heat transfer fluid
in
Inlet
init
Initial
m
Mean
xi
Nomenclature
out
Outlet
p
Particle
pc
Phase change
r
Reaction, reactant
rp
Rated power
s
Solid phase
y
y-direction in coordinate system
Superscripts
θ
Standard condition
xii
CHAPTER 1
Introduction
Economic growth and the quality of life in the developed world depend
critically on reliable, affordable energy. It drives industrial production
and the information economy. Access to it is also vital for lifting people
out of poverty.
This quote from Royal Dutch Shell (2008) emphasizes the importance of energy for
today’s world. Modern lifestyle is highly dependent on the various forms of energy:
transportation demands liquid fuels, recent means of communication need electrical
power, industrial processes require mechanical or thermal energy. Beyond this, access
to affordable energy also offers the possibility to reduce and ultimately overcome
poverty. However, the energy supply, especially by means of conventional methods,
will become increasingly challenging in the future.
One concern that the world has to face in the next decades is the growing energy
demand. The International Energy Agency (2009, p.76) projects the world’s primary
energy demand to rise by 40 % between 2007 and 2030. This increase is caused by
rising population and economic growth, which mainly takes place in emerging countries. India and China together will account for more than half (53 %) of the projected
increase. However, the actual challenge arises from supplying the increasing demand.
Today’s energy demand is predominantly supplied by fossil fuels such as oil, gas,
and coal. Since these resources are limited, energy prices will rise in the future,
especially in the context of the projected increase in demand. As a consequence,
access to affordable energy becomes more and more restricted. In order to avoid such
a scenario, energy sources other than fossil fuels must increasingly be utilized.
With rising awareness for sustainable use of energy, large scale utilization of renewable energy sources has begun in recent years. As these resources are unlimited per
definition, their potential to cover a substantial amount of the world’s energy demand
is tremendous. Considering concentrating solar power only, the estimated global
1
1.1 Thesis outline
technical potential of around 3000 PWh/y is considerably larger than the global electricity consumption of 18 PWh/y (Trieb et al., 2009). For other renewable energy sources,
such as biomass or wind, a comparatively large potential is estimated. Nonetheless,
market penetration of technologies utilizing these sources is still rather poor. This is
mainly due to their higher levelised cost of energy and the intermittent availability.
Both factors lead to a lower competitiveness compared to conventional means of
energy supply. With technology improvements, mass production, economies of scale,
and improved operation and maintenance future cost of energy from renewable
sources will be reduced. To increase the dispatchability, large scale energy storage
systems are required. However, the development of such systems, regardless of its
type, is still in an early stage and comprehensive research is needed. The Institute of
Technical Thermodynamics at the German Aerospace Center in Stuttgart contributes
to the research on sensible, latent, and chemical heat storage systems for power plant
applications and industrial processes.
1.1 Thesis outline
The following list outlines the content of the main chapters of this thesis:
• Chapter 2 gives an overview of the state of the art of thermal energy storage
systems. Different principles of heat storage and their thermodynamic basics
are briefly discussed.
• Motivation and focus as well as the aims of this work are outlined in chapter 3.
• The mathematical model which is used to investigate the performance of a
reactor for chemical heat storage is discussed in chapter 4. Moreover, the results
of parametric studies, which were obtained by means of finite element analysis,
are presented and analysed. Finally, a design for a reactor in pilot plant scale is
suggested based on the findings of the conducted studies.
2
CHAPTER 2
Thermal Energy Storage: State of the Art
Basically, thermal energy can be stored in three different ways: as sensible heat, latent
heat of fusion, and in form of reaction enthalpy in reversible chemical reactions. The
former two alternatives are already in use in various technical applications whereas
the latter type of heat storage is still under development. This chapter will shortly
discuss the basic principles of the different heat storage concepts. Furthermore, a
brief overview of the state of the art will be given.
2.1 Sensible Heat Storage
A rather straightforward way of storing thermal energy is in form of sensible heat.
Increasing the temperature of a storage medium will absorb thermal energy, which in
turn can be released by lowering its temperature. The amount of energy that can be
stored in this way depends on the temperature increase ∆T, the specific heat capacity
c p of the storage medium, and the storage size in terms of mass m and is defined as
Q = m · c p · ∆T.
(2.1)
It becomes evident that for a high volumetric energy density uv of the storage, the
volumetric heat capacity (ρ · c p ) of the storage material should be as high as possible.
For technical applications, both solid and liquid storage materials are in use.
Generally, liquids have a higher heat capacity than solids but the temperature range
they can be used in is limited due to low evaporation or decomposition temperatures.
Within the temperature limits of 300 ◦ C and 400 ◦ C, which are typical for SEGS-type
parabolic trough power plants, oils and molten salts are feasible liquid storage media.
Synthetic oils pose some potential due to favourable volumetric storage capacities
but may be classified hazardous. By comparison, silicone oils are non-hazardous at
only slightly lower storage capacities. Common for both kinds of oils is the rather
3
primarily met with ground water extracted from
wells on the site.
Technical description
12 m long and 6 m wide. Every collector has 2
mirrors and 3 absorption pipes. An Andasol p
plant requires 7,488 collectors. Specialists asse
and check these collectors photogrammetric
to determine their precision in specially-con
structed factory buildings before the collecto
are brought to the field and anchored.
In parabolic trough power plants, trough-shaped
mirrors in the solar field concentrate the suns
2.1 Sensible Heat Storage
rays by a factor of 80 onto an absorption pipe in
the focal line of the collector. In the pipes, a heat
transferand
fluidtheir
circulates
a closed circuit
is
low thermal conductivity
highinspecific
costswhich
(Herrmann
and Kearney, 2002).
heated to 400 degrees Celsius by the concentrated
Efficiency
As oils decompose at temperatures of around 400 ◦ C, they are not
applicable for solar
solar radiation. The heated fluid is then pumped
Solar field
power tower plants.into a centrally located power block and flows
Peak efficiency
through a heat exchanger. In this way, steam is
average
generated
conventionaland
power
Even though some
moltenwhich
salts (similar
can betoaggressive
corrosive,Annual
they
show benefiTurbine circuit
plants) powers the turbine using an electric
cial properties for the use as storage media. Gil et al. (2010) see them as an efficient,
generator. The integration of a heat storage allows
Peak efficiency
low cost medium with
operating
that
match
those of Annual
modern
steam turthe power
plant toparameters
function at full
capacity
both
average
on overcast
days andofatnitrate
night. The
Andasol
power than that
bines. The specific storage
capacity
salts
is higher
of oils at lower
Entire plant
plants each consist of a solar field, a thermal
Peak efficiency
specific costs (Herrmann
and Kearney, 2002). In addition, experience
in handling
storage tank, and a conventional power plant
Annual average
molten salts has already
been gained in chemical and metal industries. Andasol-type
section.
solar thermal power plants incorporate a indirect two-tank thermal energy storage
system to store heat equivalent to 7.5 h of nominal operation (Fig. 2.1). The system
4
1
2
3
5
1. Solar field, 2. Storage, 3. Heat exchanger, 4. Steam turbine and generator, 5. Condenser
Figure 2.1: Schematic of an Andasol-type solar thermal power plant (Solar Millennium
AG,122008)
is based on a binary salt mixture consisting of 60 % sodium nitrate (NaNO3 ) and
40 % potassium nitrate (KNO3 ) and operates at temperature of 290 ◦ C to 390 ◦ C. During charging/discharging, the salt is pumped from one storage tank to the other
while heat is absorbed/released. Using this system, a volumetric energy density uv
of about 71 kWh/m3 has been realized (Solar Millennium AG, 2008; Medrano et al.,
2010). Such indirect two-tank molten salt thermal energy storage systems are today’s
benchmark for parabolic trough solar power plants. In order to use molten salt at a
higher temperature level, it has to be used as heat transfer medium as well since heat
4
ca. 70%
ca. 50%
ca. 40%
ca. 30%
ca. 28%
ca. 15%
2.1 Sensible Heat Storage
transfer oils decompose above 400 ◦ C. Efforts are being made to develop new salts or
salt mixtures, which will be applicable and favourable as heat transfer and storage
medium at those temperatures.
Although solid storage materials have a worse specific heat capacity than liquids,
they pose an alternative to molten salt due to a higher thermal conductivity and lower
costs per kWh/m3 . Herrmann and Kearney (2002) contemplated a variety of solid
materials for sensible heat storage but concluded that reinforced concrete and NaCl
are the most favourable. Laing et al. (2006) considered and analysed two composites
as storage material: high temperature concrete and a castable ceramic. In general,
both materials are feasible for sensible heat storage. Nonetheless, concrete seems to
be more favourable due to lower specific costs, higher strength of material and easier
handling even though the castable ceramic shows better thermo-physical properties.
For both materials, storage units with embedded tubular heat exchangers were tested
at Plataforma Solar de Almería and reached temperatures up to 325 ◦ C. During
testing, high power levels were obtained and high temperature differences between
heat transfer fluid and storage have been handled without any problems. After 60
charge/discharge cycles no degradation of heat transfer was observed. Regarding
integration of the storage system, modular operation concepts have been evaluated
and seem to be economically beneficial. In addition, environmental impact of a
Andasol-type solar power plant could be reduced by 7 %, considering 1 kWh supply
to the grid, using a concrete instead of a molten salt storage system (Laing et al.,
2010). Also, Laing et al. (2011) suggest the use of concrete based storage modules for
direct steam generation (Fig. 2.2). In that case, the modules are used to preheat water
D. Laing et al. / Solar Energy 85 (2011) 627–633
629
Capital letters designate inlet / outlet of
A Preheating unit, feed water
B Evaporation / condensation unit, liquid water
C Evaporation / condensation unit, steam
D Superheating unit, live steam
C
steam
drum
from solar
field
to solar
field
D
B
A
from
power
block
sensible heat storage unit:
preheating / cooling of
condensate
latent heat storage unit:
evaporation / condensation
sensible heat storage unit:
superheating / cooling of steam
to power
block
Fig. 2. Overview of a three-part thermal energy storage system for DSG combining sensible and latent heat storage.
Figure 2.2: Schematic of a proposed storage concept for direct steam generation (Laing
with the embedded
aggregates.
et al.,
2011) The stability of the cement water is not installed. Since the superheating step is more
paste has a decisive impact on the concrete strength. Mass
losses of the aggregates and the concrete depending on the
temperature profile were examined. The oven tests lasted
for several thousand hours. Results show that the mass
of the aggregate and concrete samples stabilizes at
500 °C. Mass losses were from 1.5 to 3.5 wt.% for the
aggregates and about 5.3 wt.% for the concrete samples.
The dominating mechanism of the mass loss is evaporable
water in the concrete. Also, the impact of temperature on
the strength of the concrete was tested. Detailed results
of material investigations related to the thermal stability
of concrete up to 500 °C are presented in Laing et al. (in
press). Overall, oven experiments and strength measure-
5
challenging, the project resources for concrete storage were
allocated completely to a superheating module. This module is also suitable for preheating. The test-loop being
installed for this purpose at the power plant Litoral of
Endesa in Carboneras, Spain, is described in more detail
in Eck et al. (2009).
3.2. Storage technology for preheating water and for
superheating steam
3.2.1. Concept and design of the concrete storage test module
The design parameters for the test module are:
2.2 Latent Heat Storage
and superheat steam.
2.2 Latent Heat Storage
Temperature
Besides sensible heat, thermal energy can also be stored as latent heat during phase
change of a substance. Each phase transition leads to changes in enthalpy ∆h pc of
the respective substance. This enthalpy change is comparatively large whereas the
temperature of the substance remains constant during transition (Fig. 2.3). This cha-
Sensible Heat Sensible
Heat
of
Heat
Solid Fusion Liquid
Heat
of
Vaporization
Sensible
Heat
Gas
Enthalpy
Figure 2.3: Typical T,h-diagram of a pure substance
racteristic can be used to store thermal energy isothermically with a high volumetric
energy density. Despite liquid–gas transition causing the highest enthalpy change,
solid–liquid phase change is the most suitable for technical applications due to the
considerably lower volume change between these two phases.
In contrast to sensible heat storage, material selection is more difficult for systems
based on latent heat as the melting temperature of the material has to match the
operational temperature of the associated process. Hoshi et al. (2005) screened high
melting point phase change materials (PCM) for a possible use in solar thermal power
plants. Their material selection is primarily based on a trade-off between melting
temperature, theoretical storage capacity, specific costs, and thermal conductivity.
6
2.2 Latent Heat Storage
While storage capacity and specific costs are important from an economic point of
view, thermal conductivity of the considered material is vital for the performance
of the storage system. The authors conclude that sodium nitrate (NaNO3 ) would be
suitable for medium temperature systems, e.g. Compact Linear Fresnel Reflector or
parabolic trough, and sodium carbonate (N2 CO3 ) for high temperature applications
operating with Brayton cycle turbines. Furthermore, heat transfer design is more
difficult for latent heat storage systems due to the low thermal conductivity of phase
change materials, which is in accordance with Herrmann and Kearney (2002) and
Michels and Pitz-Paal (2007). To overcome this issue, a so-called sandwich concept
has been found to be the most promising option (Steinmann et al., 2010). Thereby,
graphite fins are attached perpendicular to the axis of the heat exchanger tubes,
which enhances heat transfer within the PCM. This, in turn, reduces the number
of heat exchanger tubes embedded in the phase change material and is therefore
more cost-effective. After the concept has been proven through lab-scale testing, a
prototype storage for direct steam generation using the eutectic mixture of KNO3 –
NaNO3 was designed. The prototype has been tested under real conditions at the
Plataforma Solar de Almería, where some problems with the design, such as deficient
insulation, inefficient storage/supply of thermal energy due to excess PCM mass,
and uneven steam production, have been observed (Bayón et al., 2010). Despite these
problems, basic functionality and feasibility were proven. Since the eutectic mixture
of KNO3 –NaNO3 already melts at 221 ◦ C, Laing et al. (2011) developed a pilot-scale
storage based on NaNO3 with a capacity of about 680 kWh. Pure sodium nitrate
melts at a temperature of 306 ◦ C and is, therefore, suitable for a live steam pressure
of around 100 bar. This latent heat storage is part of a modular system proposed
for direct steam generation and will provide/absorb the energy needed/released
during the phase transition of water (Fig. 2.2). An approach to utilize the high storage
capacity of PCMs with sensible heat transfer media in an exergy efficient way is
proposed by Michels and Pitz-Paal (2007). They suggest to cascade phase change
materials with different melting temperatures in order to meet the characteristic
of the heat transfer fluid. Advantageous would be the more uniform temperature
distribution, which leads to higher charge/discharge rates, and the higher portion of
PCM undergoing a phase transition. On the other hand, material selection becomes
even more difficult.
7
2.3 Chemical Heat Storage
2.3 Chemical Heat Storage
Both previously discussed options for thermal energy storage have a principle disadvantage. The enthalpy change per mole for heating or melting of a substance
or fluid is low. Especially for electrical power generation this leads to large storage
volumes of the respective medium as large quantities of heat are required. Additionally, the storage tanks need to be costly insulated in order to minimize heat losses.
An alternative to partially avoid these downsides is the storage of thermal energy in
form of reaction enthalpy using reversible chemical reactions. While the endothermic
forward reaction proceeds, energy is absorbed and stored as chemical potential. This
potential is used to release energy during the exothermic backward reaction. As there
is a huge variety of reversible reactions, basic thermodynamic considerations are
used to establish criteria that help in the selection of possible reaction systems for
high temperature thermal energy storage.
2.3.1 Reversible chemical reactions: thermodynamic considerations
To determine whether a reversible reaction might be suitable for thermal energy
storage, the state of equilibrium has to be evaluated. The equilibrium constant K
provides information about which side of the reaction is favoured. It is defined
as the ratio of forward reaction rate to backward reaction rate. In case K > 1, the
forward reaction is dominant, whereas the backward reaction is favoured if K < 1.
Further, K can be associated with changes in Gibbs free energy of reaction at a given
temperature. This relation is given as
∆ r G = ∆ r H θ − T · ∆ r Sθ + R · T · ln(K ),
(2.2)
where ∆ r H θ represents changes in standard enthalpy of reaction, ∆ r Sθ changes in
standard entropy of reaction, and R is the gas constant. In general, changes in Gibbs
free energy can be seen as the potential amount of energy which can be extracted from
a closed thermodynamic system at a given temperature and pressure. In chemical
equilibrium, ∆ r G must be zero as the driving force of the reaction vanishes since
forward and backward reaction rate are equal. Under this condition, eq. (2.2) results
8
2.3 Chemical Heat Storage
in
∆ r H ( pθ ,Teq ) − Teq · ∆ r S( pθ ,Teq ) + R · Teq · ln(Keq ) = 0,
(2.3)
which determines all reaction parameters for the state of equilibrium. Calculating
Teq from eq. (2.3) might be rather difficult. A viable simplification was proposed by
Wentworth and Chen (1976). They neglected the temperature dependency of ∆ r H
and ∆ r S and assumed that the activity of all reactants and products is equal to one,
which results in K = 1. These considerations lead to
Teq =
∆ r Hθ
,
∆ r Sθ
(2.4)
which can be used to roughly estimate the equilibrium temperature of a reversible
reaction. Teq is of importance since it must comply with the considered application.
Moreover, it indicates the direction of the reaction for a given temperature. Temperatures above Teq favour the forward reaction while for T < Teq the backward reaction
proceeds, see chapter 2.3.3. For storage systems to be economical, it is necessary that
they have a large specific storage capacity. In terms of thermo-chemical storage, this
means that a reaction must absorb large amounts of energy ∆ r H θ . To assure that
Teq is within practical limits, ∆ r Sθ has to be correspondingly high. Reactions which
show high changes in entropy and are suitable for high temperature applications
are primarily dissociation reactions in which reactants and products are present in
heterogenous phases. Formally, reactions of this kind can be written as
AB (s,l) + ∆ r H *
) A (s,l) + B (g).
(2.5)
During forward reaction the compound AB dissociates endothermically to the components A and B. Since these components are present in different phases, they can
be separated easily in order to prevent backward reaction. As soon as A and B
are brought together again, the exothermic backward reaction takes place and the
chemically stored energy is released.
In addition to these thermodynamic considerations other important criteria concerning selection of a suitable reaction must be taken into acount:
• full reversibility of the reaction over a large number of cycles
9
2.3 Chemical Heat Storage
• no occurring side reactions
• fast kinetics of the reaction in order to ensure a high charge/discharge power
• high catalyst durability and activity in case of catalytic reactions
• good heat transfer properties
• low temperature difference between charge and discharge to minimize exergy
losses
• availability of compounds in sufficient quantities at low cost
• involved compounds can preferably be handled with known technology
• little or no safety risk
Given this variety of criteria, it becomes obvious that compromises in the selection of
a reaction and its technical implementation have to be made.
Over the past decades, numerous reaction systems have been investigated and
proposed for solar thermal energy storage. Wentworth and Chen (1976) evaluated
dissociation reactions based on hydroxides, carbonates, sulfates, and oxides of Group
1 and 2 elements. They found that within the Groups, ∆ r S remains approximately
constant for the respective class of compounds. Reason for this is the similarity of
reaction equations within a Group of elements for a given compound class. However,
with exception of oxides all investigated compound classes show an increase in
enthalpy of reaction ∆ r H with increasing atomic number. This means that for similar
reactions, higher storage capacities are obtained for systems proceeding at higher
temperatures, cf. eq. (2.4). In Table 2.1, further types of reactions that are suitable
for solar thermal energy storage from a thermodynamic point of view are listed.
According to Tamme (2002), the development status of most of these reaction types
is at the level of studies and fundamental investigations. So far, catalytic dissociation
of sulfur trioxide (SO3 ), steam and CO2 reforming, and thermal dehydrogenation of
metal hydrides are the only reactions for which pilot plants have been installed.
10
2.3 Chemical Heat Storage
Table 2.1: Selection of reversible reactions proposed for high temperature energy storage (Tamme, 2002)
Reaction
Temperature range [◦ C]
2 NH3 *
) N2 + 3 H 2
400 – 500
2 SO3 *
) 2 SO2 + O2
500 – 900
Mg(OH)2 *
) MgO + H2 O
250 – 350
Ca(OH)2 *
) CaO + H2 O
450 – 550
Ba(OH)2 *
) BaO + H2 O
700 – 800
Decarboxylation of metal
carbonates
MgCO3 *
) MgO + CO2
350 – 450
CaCO3 *
) CaO + CO2
850 – 950
Thermal deoxygenation of
metal oxides
2 BaO2 *
) 2 BaO + O2
750 – 850
4 KO2 *
) 2 K2 O + 3 O2
600 – 800
CH4 + H2 O *
) CO + 3 H2
700 – 1000
CH4 + CO2 *
) 2 CO + 2 H2
700 – 1000
MgH2 *
) Mg + H2
200 – 400
Mg2 NiH4 *
) Mg2 Ni + 2 H2
150 – 300
Type of reaction
Catalytic dissociation
Dehydration of metal
hydroxides
Reforming processes
Thermal dehydrogenation
of metal hydrides
2.3.2 Calcium Hydroxide – Calcium Oxide System
Applying the selection criteria stated in chatper 2.3.1 on Table 2.1, the hydroxide
system based on calcium shows the highest potential for utilization as heat storage
systems in medium temperature CSP applications. This reaction system has been
thoroughly investigated at DLR in Stuttgart in recent years. Schaube (in press)
carried out cycling tests, which showed no significant decrease in maximum reaction
yield. In addition, she investigated and quanitified the reaction kinetics of both the
formation and decomposition.
The heterogenous gas–solid reaction of the calcium hydoxide and calcium oxide
system is formulated as
Ca(OH)2 (s) + ∆ r H *
) CaO (s) + H2 O (g).
(2.6)
Based on data from Barin and Platzki (1995), standard reaction enthalpy accounts
11
2.3 Chemical Heat Storage
for 109.17 kJ/mol. This results in a theoretical volumetric energy density of around
365 kWh/m3 based on CaO at a bed porosity of ε = 0.8 and shows that chemical
reactions have a tremendous potential for the storage of thermal energy. Another
positive aspect of this reaction system is the fact that water vapour is used as reaction
gas. Since steam is often used in industrial processes, a Ca(OH)2 – CaO based energy
storage system could readily be integrated. In both industrial and solar thermal
applications, the storage systems would ideally be operated at atmospheric pressure
in order to avoid parasitic losses in form of compression work of the reaction gas.
Under these conditions, low pressure and high temperature, the gaseous phase
behaves like an ideal gas. Thus, the equilibrium constant can be expressed in terms
of the partial pressures of the involved gaseous species:
K=
∏
i
pi
pθ
νi
=
p H2 O
.
pθ
(2.7)
For the considered reaction system, the general expression, middle term in eq. (2.7),
reduces to p H2 O/pθ as water vapour is the only gaseous species and the respective
stoichiometric coeffient is one, cf. eq. (2.6). Substituting eq. (2.7) in eq. (2.3) results in
ln
p H2 O
pθ
=−
∆ r H ( pθ ,T ) 1 ∆ r S( pθ ,T )
· +
.
R
T
R
(2.8)
This form of the van’t Hoff equation relates gas pressure and reaction temperature in
chemical equilibrium. Plotting the natural logarithm of the gas pressure against the
inverse reaction temperature is a convenient way to graphically illustrate the relation
given in eq. (2.8). In such a plot, the negative change in enthalpy of reaction divided
by the gas constant determines the slope of the curve and thereby the pressure change
due to temperature change. With data taken from the National Insitute of Standards
and Technology (NIST) and Barin and Platzki (1995), eq. (2.8) has been evaluated for
temperatures within a range of 298 K to 1000 K (Appendix A.1). Figure 2.4 shows the
relevant interval between 600 K and 900 K. Applying a linear regression model based
on ordinary least squares the full intervall can be approximated by
ln
p
H2 O
bar
= −12.72 K ·
12
1000
+ 16.03.
T
(2.9)
2.3 Chemical Heat Storage
10
CaO (s) + H2O (g)  Ca(OH)2 (s)
0.1
ln (pH
2
O
[bar])
1.0
0.01
0.001
1.0
Ca(OH)2 (s)  CaO (s) + H2O (g)
1.1
1.2
1.3
1.4
1000/T [1000/K]
1.5
1.6
1.7
Figure 2.4: Plot of the van’t Hoff equation for the reversible reaction system of
Ca(OH)2 – CaO
This equation can be used to calculate the equilibrium pressure p H2 O,eq for a given
temperature T or vice versa.
2.3.3 Principle of Le Chatelier and Process Control
The equilibrium of reversible gas–solid reactions depends on gas pressure and temperature. For a given state of equilibrium, changes in either pressure or temperature
shift the equilibirum along the curve in Fig. 2.4. The equilibrium shifts in such a
way that it counteracts the imposed change according to Le Chatelier’s principle. An
increase in pressure at a given temperature causes the exothermic hydration reaction
to proceed until the corresponding equilibrium temperature is reached and vice
versa. A similar shift in equilibrium occurs with temperature changes. Endothermic
dehydration of calcium hydroxide will counterbalance a temperature increase at
given gas pressure whereas a temperature decrease is counteracted by the exothermic
hydration of calcium oxide. Considering the principle of Le Chatelier, Fig. 2.4 can
be divided into two domains in which either of the reactions in eq. (2.6) is dominant. Dehydration is dominant in the region below the fitted curve, hydration for
13
2.3 Chemical Heat Storage
the region above. This indicates conditions under which the storage system can be
charged or discharged from a chemical point of view. Only for temperatures above
equilibrium temperature, storage can be charged at a given pressure. The same
applies analogously to the discharge.
Additionally, the relation between gas pressure and temperature can be used
to transform heat from one temperature level to another, similar to heat pumps.
Lowering the pressure during charging, thermal energy at a lower temperature level
can be stored as the equilibrium temperature decreases, cf. eq. (2.9). In reverse,
energy is released at a higher temperature level when storage discharge takes place
at a pressure level higher than the charging pressure level. For the Ca(OH)2 – CaO
system a temperature difference of around 100 K can theoretically be obtained by
increasing the vapour pressure from 0.1 bar to 1.0 bar during charge and discharge,
respectively (Fig. 2.5).
10
%
↑
 pH
0.1
↓
Q̇in
O
2
.
ln (pH
2
O
[bar])
1.0
Q̇out
0.01
←−  T −→
0.001
1.0
1.1
1.2
1.3
1.4
1000/T [1000/K]
1.5
1.6
1.7
Figure 2.5: Principle of heat transformation in the system of Ca(OH)2 – CaO
14
CHAPTER 3
Motivation & Focus
As discussed in the previous chapter, the reaction system of Ca(OH)2 – CaO has
an enormous potential for heat storage applications due to the high amount of
energy that is absorbed or released during reaction. Further positive aspects of
this reaction system are the manageable saftey risks and the high availability of the
reaction materials. Both, calcium hydroxide and oxide are inexpensive materials
and widely used in various industries. Schaube (in press) showed that both the
formation and decomposition reaction is reversible for numerous reaction cycles. In
addition, reaction kinetics are sufficiently fast to assure reasonable charge/discharge
times. These promising findings provide the basis for further investigations of the
Ca(OH)2 – CaO system with focus on a heat exchanger reactor in the lower kilowatt
range.
In her work, Schaube (in press) used a reactor with direct heat transfer. In this direct
case, a gaseous heat transfer fluid passes, together with the reaction gas, through the
reaction bed. Therefore, the heat transfer fluid is in direct contact with the reaction
material (Fig. 3.1). This is favourable for the heat input and output since the heat
transfer area, which is the surface area of all particles, is very large. Concerning the
selection of the heat transfer fluid, inert gases are to be preferred as undesired side
reactions are avoided this way. Although this concept offers advantages regarding
the heat transfer, it is technologically difficult to implement. To assure a constant
temperature level during charge and discharge, the partial pressure of water vapour
must be kept constant during reaction. Admixing and extracting the right amount
of water vapour into or out of the heat transfer fluid is difficult, particularly from a
metrological and energetic point of view. Another disadvantage of the direct heat
transfer concept is the high pressure drop across the reaction bed due to the small
particle size (d p ≈ 5 µm) of the currently available material, which leads to enormous
parasitic losses.
15
3 Motivation & Focus
H 2O
H2O & Heat H2O & Heat
transfer fluid transfer fluid
H 2O
Heat transfer fluid
Heat transfer fluid
Figure 3.1: Schematic of reactor with
direct heat transfer
Figure 3.2: Schematic of reactor with
indirect heat transfer
One way to avoid these drawbacks is to separate the reaction gas from the heat
transfer fluid. In this concept only the reaction gas passes directly through the bed
whereas the HTF flows through channels embedded in the reaction bed (Fig. 3.2). The
separation leads to a limited heat transfer, which is the main downside of this concept.
Since the thermal conductivity of the reaction material is rather low, heat conduction
in the reaction bed becomes an important factor for the thermal performance of
the storage system. Hence, it is necessary to adapt the reactor design on the heat
transport characteristics of the reaction bed. The focus of this work is, therefore,
upon the investigation of design parameters and their influence on the thermal
performance of the reactor by means of finite element analysis.
Basically, two types of heat exchangers can be used as a reactor for chemical heat
storage: shell and tube heat exchangers and plate heat exchangers. The first type of
heat exchanger is schematically shown in Fig. 3.3 and can itself be implemented in
two different ways. One configuration is to place the reaction bed inside the tubes
while the heat transfer fluid passes through the tube bundle in cross flow. Main
drawback of this configuration is the more complex dimensioning and design. For
finite element analysis of the reactor performance, a three-dimensional mathematical
model has to be solved, which is rather time and resource consuming. Interchanging
the position of reaction bed and heat transfer fluid leads to the second possible
16
Heat transfer area
Heat transfer coefficient
3 Motivation & Focus
Tube diameter
Heat transfer coefficient
Heat transfer area
Figure 3.4: Heat transfer coefficient
and heat transfer area
over inner diameter for
pipe flow
Figure 3.3: Schematic of a shell and
tube heat exchanger reactor
configuration for a shell and tube heat exchanger reactor. In this case, both the
heat and gas transport through the reaction bed can be modelled in a 2D domain.
However, the heat transfer from bed to HTF is limited since heat transfer coefficient
and heat transfer area are related inversely with increasing tube diameter (Fig. 3.4).
Due to this limitation, a large number of tubes is required for storage systems with
a charge/discharge power in the lower kilowatt range already. At this point, plate
heat exchangers offer clear advantages since they obtain higher volumetric power
densities (Anxionnaz et al., 2008). Heat transfer coefficient and heat transfer area
can be adjusted indepentently, which results in a maximized heat transfer. A plate
heat exchanger integrated into a packed bed chemical reactor could be implemented
as shown in Fig. 3.5. In this proposed design, reaction material and heat transfer
fluid are located alternately between the plates. To attain the highest possible heat
transfer coefficient at a given flow rate, the gap on the HTF side should be as small
as possible. In contrast, the reaction–side gap should be as large as possible in order
to maximize the volumetric storage density of the storage system. The heat transfer
area can be adapted easily by resizing the plates. In addition to the improved heat
transfer characteristics, a plate heat exchanger reactor can be extended more easily
compared to a shell and tube heat exchanger. Based on these considerations a reactor
with integrated plate heat exchanger is investigated within the scope of this work.
Based on the work of Schaube (in press), it can be assumed that the intrinsic reaction
kinetics of formation and decomposition of calcium hydroxide are sufficiently fast.
17
3 Motivation & Focus
λbed
αbed
Q̇ht
λwall
α HTF
λ HTF
Flow channel HTF
Reaction bed
Figure 3.5: Schematic of a plate heat exchanger reactor for energy storage
Therefore, charging and discharging characterisitcs depend on extrinsic reaction
parameters such as heat and mass transfer, which are comparable for both reaction
directions. In this work, the exothermic formation reaction will be investigated only.
The objectives of this work are defined as follows:
• implementation of a finite element based simulation tool for a storage reactor
with embedded plate heat exchanger for indirect heat transfer
• identification of critical parameters concerning heat and gas transport
• identification of favourable design parameters and suggestion of a design
concept for a pilot plant heat storage system utilizing commercially available
reaction material
• estimation of characterisitc data such as volumetric energy and power density.
18
CHAPTER 4
Plate Heat Exchanger Reactor as Chemical Heat Storage
It has been discussed in chapter 3 that a plate heat exchanger reactor is a favourable
design concept for a chemical heat storage system. The lack of experience designing
such systems, together with their high complexity, demands an investigation into
the influence of crucial design parameters on the performance of the proposed heat
exchanger reactor. For that purpose, the considered system has been simulated using
the finite element based, commercially available software COMSOL Multiphysics ® .
The mathematical model describing the system as well as the obtained simulation
results are summarized and presented in this chapter.
4.1 Simplified Model for Highly Permeable Packed Beds
To begin with, the gas transport inside the reaction bed is assumed to be unrestricted,
which is the case for a bed permeability K above a certain threshold. This reduces
the complexity of the system since the reaction is not limited, due to a possible lack
of reaction gas. Thus, the influence of design parameters on the thermal performance
of the reactor can be investigated directly.
4.1.1 Governing Equations
Under the condition of high permeability, K > 1 · 10−10 m2 , the change in pressure,
due to gas reacting with solid material will be compensated immediately. From
this consideration follows that only the energy balance is necessary to describe the
reaction system. Conservation of energy can be written as
(c p · ρ)bed ·
∂Tbed
= −∇ · (−λbed · ∇ Tbed ) + SQ̇,r ,
∂t
19
(4.1)
4.1 Simplified Model for Highly Permeable Packed Beds
where the left-hand side of the equation accounts for the rate of accumulation of
energy within the system. This term is characterised by the energy storage capacity
of the bed (c p · ρ)bed , which in turn is the sum of storage capacities of the bed’s
constituents:
(c p · ρ)bed = (1 − ε) · c p,s · ρs + ε · c p,g · ρ g .
(4.2)
Since the solid material of the bed changes during reaction, the corresponding material properties have to be evaluated accordingly. Taking into account the conversion
X H during hydration, the solid density ρs and specific heat capacity c p,s can both be
estimated using the following approximations:
ρs = (1 − X H ) · ρCaO + X H · ρCa(OH )2 ,
(4.3)
c p,s = (1 − X H ) · c p,CaO + X H · c p,Ca(OH )2 .
(4.4)
In addition to the dependency on the composition of the bed, the material properties
are also dependent on temperature. Whereas the density can be considered constant,
the c p for both CaO and Ca(OH)2 is approximated for a temperature range of 500 K
to 1000 K using linear regression models based on ordinary least squares. With data
taken from NIST (Appendix A.2) these models can be written as
c p,CaO = 0.16495 ·
J
J
· Ts + 798.64700 ·
2
kg · K
kg · K
(4.5)
and
c p,Ca(OH )2 = 0.38612 ·
J
J
· Ts + 1217.29416 ·
.
2
kg · K
kg · K
(4.6)
Calculating the energy storage capacity at 450 °C according to the equations (4.2)
to (4.6), it can be seen that for any value of X H the gaseous phase accounts for less
than 1 % of the value of (c p · ρ)bed . This phase will therefore not be considered in
eq. (4.2) any further. Beyond that, the solid, gas, and bed temperature can be set
equal due to the low energy storage capacity (c p · ρ) g of the gaseous phase.
The first term on the right-hand side of eq. (4.1) describes heat conduction within
the reaction bed. Analogous to the energy storage capacity, cf. eq. (4.2), the thermal
20
4.1 Simplified Model for Highly Permeable Packed Beds
conductivity of the bed can be written as
λbed = (1 − ε) · λs + ε · λ g .
(4.7)
The fact that the solid material is used as a powder makes it difficult to determine an
adequate value for λs . Hence, the thermal conductivity λbed is set equal to 0.3 W/(m · K)
within the prevalent temperature range, and for a porosity of ε = 0.8 in accordance
with (Linder, 2011).
Energy changes due to chemical reaction are represented by SQ̇,r in eq. (4.1). This
term accounts for the amount of energy that is released during the hydration of the
solid material and is estimated as follows:
SQ̇,r = −(1 − ε) · r · ∆ r H.
(4.8)
Besides the porosity ε and the enthalpy of reaction ∆ r H, the value of SQ̇,r is determined by the reaction rate r, which accounts for the solid material that reacts per unit
volume per time interval. It is defined as
r=
ρs,r dX H
,
·
Ms,r dt
(4.9)
where X H accounts for the fraction of solid material which has already been hydrated.
H
Hence, dX
dt is the rate at which the solid material reacts per time interval. This rate, as
well as the conversion, can be estimated by solving the ordinary differential equation
Tbed − Teq
dX H
= (1 − X H ) · k ·
.
dt
Teq
(4.10)
As eq. 4.10 shows, the speed at which the solid reactant is hydrated depends on the
current state of conversion, the rate constant k, and the temperature difference from
thermal equilibrium. Basically, k is evaluated by means of the Arrhenius equation
and is therefore temperature dependent. In this work, however, a representative rate
constant of -0.05 1/s is used in accordance with (reference). In order for the reaction
to proceed and to obtain a sufficiently high reaction rate, a temperature difference
Tbed − Teq has to be maintained, cf. chapter 2.3.
Due to the low thermal resistance and heat capacity of the separating metal wall
21
4.1 Simplified Model for Highly Permeable Packed Beds
between reaction bed and heat transfer fluid, the wall temperature is assumed to be
equal to the bed temperature at any point. It is therefore not necessary to consider
the wall energy equation in this model.
Regarding the type of flow of the heat transfer fluid, it can be shown that for the
given conditions (medium, temperature range, flow channel geometry) the flow
remains laminar at all times of this study. Standard COMSOL modules are used
to implement conservation of energy and momentum for laminar flow. Thereby,
only the boundary and initial conditions are adjusted to meet the conditions on the
reaction side. The necessary interrelation between fluid flow and energy transport is
established by using the output (u HTF , p HTF , THTF ) of each module as input for the
other.
Even though only the hydration of calcium oxide is analysed in this work, the
above presented governing equations are in principle valid for the dehydration as
well.
4.1.2 Boundary & Initial Conditions
Finite element analyis is used to solve the system of ordinary and partial differential
equations numerically. Therefore, a corresponding geometry model which represents
the considered HEX reactor is needed. This model is set up in a 2D domain using
symmetry wherever applicable, in order to minimize the number of elements and
reduce the computing time and needed computation resources. Figure 4.1 shows a
schematic of the implemented geometric model indicating its domains and boudaries.
The model represents a section of the entire reactor consisting of a reaction bed (2)
and the two adjacent flow channels (1, 3). Due to symmetry reasons, only a half of
each flow channel is implemented. In this study, the reactor height is set to 0.5 m
whereas the width of the reaction bed is varied. For the flow channel, a width of
2 mm is used as suggested by Baumann and Lucht (2011).
One boundary condition that plays a major role in the investigated system is the
heat transferred across the boundary of the reaction bed during cooling of the bed.
This heat flow is expressed and incorporated by means of an outward heat flux that
22
4.1 Simplified Model for Highly Permeable Packed Beds
6
9
12
1
2
3
4
7
5
10
8
13
11
Figure 4.1: Schematic of the implemented geometric model with corresponding boundaries and domains
is defined as
q̇ht = −U · ( Tbed − THTF ),
(4.11)
where the overall heat transfer coefficient U itself is given as
1
1
s
1
=
.
+ wall +
U
αbed λwall
α HTF
(4.12)
For evaluation of the thermal resistance of the separating wall between reaction
bed and heat transfer fluid, a wall thickness swall of 0.001 m and a constant thermal
conductivity λwall of 14 W/(m · K) are assumed. Regarding the heat transfer between
packed bed and wall, αbed can be assumed with 800 W/(m2 · K) according to Utz (2011).
Even though this value is rather conservative, it is not a limiting factor for the overall
heat transfer and, hence, sufficiently accurate. For the heat transfer from wall to heat
transfer fluid, α HTF is evaluated by applying basic Nusselt number correlations for
parallel plates at constant temperature in accordance with Gnielinski (2006). Thereby,
α HTF is defined as
α HTF =
Num · λ HTF
,
dh
23
(4.13)
4.1 Simplified Model for Highly Permeable Packed Beds
where dh , the hydraulic diameter, is twice the width of the gap between the plates.
For laminar flow, the Nusselt number in eq. (4.13) can be written as
Num = ( Nu31 + Nu32 + Nu33 )1/3 ,
(4.14)
Nu1 = 7.541,
(4.15a)
with
s
Nu2 = 1.841 ·
Nu3 =
2
1 + 22 · Pr
3
Re · Pr ·
dh
,
hfc
1/6
·
Re · Pr ·
dh
hfc
(4.15b)
!1/2
.
(4.15c)
Equations (4.15a) – (4.15c) represent the Nusselt numbers for different domains
of the flow, cf. (Gnielinski, 2006). Reynolds number Re and Prandtl number Pr,
needed to estimate the Nusselt number used in eq. (4.15b) and (4.15c) are evaluated with the well-known correlations for these dimensionless quantities. All
temperature dependent material properties of the heat transfer fluid, used to determine α HTF , are taken from the COMSOL material library at a mean temperature
THTF,m = 21 · ( THTF,in + THTF,out ).
Whereas the inlet velocity of the heat transfer fluid v HTF,in is varied, the HTF
inlet temperature THTF,in and the initial bed temperature Tbed,init are set equal to
400 ◦ C throughout this study. The remaining boundary conditions as well as initial
conditions applied to the simplified model are listed in Table 4.1 and 4.2.
4.1.3 Simulation Results
Basically, there are three parameters regarding the design and operation of the
proposed reactor that can be chosen freely: flow channel width, width of the reaction
bed, and inlet velocity of the heat transfer fluid. Even though a reduction of the gap
between the plates is favourable for the overall heat tranfser coefficient U, it can not
24
4.1 Simplified Model for Highly Permeable Packed Beds
Table 4.1: Boundary conditions of the simplified model
Condition
Boundary
Laminar flow in heat transfer fluid
Symmetry
4, 13
v HTF,y = 0 m/s
7, 10
v HTF,in
5, 11
p HTF,out =
105 Pa
6, 12
Heat transfer in heat transfer fluid
Symmetry
4, 13
−n · (−λ · ∇ T ) = 0
6, 12
THTF,in = 400 ◦ C
5, 11
q̇ht
7, 10
Heat transfer in reaction bed
−n · (−λ · ∇ T ) = 0
8, 9
−q̇ht
7, 10
Table 4.2: Initial conditions of the simplified model
Condition
Domain
Laminar flow in heat transfer fluid
v HTF,init = v HTF,in
1, 3
p HTF,init = 105 Pa
1, 3
Heat transfer in heat transfer fluid
THTF,init = THTF,in
1, 3
Heat transfer in reaction bed
Tbed,init = THTF,in
2
25
4.1 Simplified Model for Highly Permeable Packed Beds
be reduced arbitrarily due to technical reasons. In accordance with Baumann and
Lucht (2011) it is, therefore, set to 2 mm. The influence of the remaining parameters
on the performance of the proposed heat exchanger reactor has been investigated
with the above described simplified model.
Reaction Bed Dimension
The width of the reaction bed wbed has been varied between 0.01 m and 0.05 m and
the system has been simulated accordingly with a constant inlet velocity of the heat
transfer fluid of 10 m/s. By definition, the maximum thermal resistance Rth of the
bed increases with increasing bed width (Rth ∝ wbed ). Due to this, heat is sufficiently
removed from the core region for small reactor geometries whilst the heat transfer
away from that region is strongly limited for wider beds. The resulting accumulation
of heat (Fig. 4.2b) causes the reaction in the respective parts of the bed to slow down
significantly (Fig. 4.3b). A reaction front, which moves from the edges to the centre
of the bed is the consequence. In contrast, reaction takes place across the entire width
of small beds, with a reaction front perpendicular to HTF flow direction, since heat is
removed sufficiently from the centre (Fig. 4.3a and 4.2a).
Considering that the bed temperature reaches equilibrium temperature in most
parts of the bed, regardless of its width shortly after beginning of the reaction, the
observed average bed temperatures after 30 min suggest a higher rate of decrease of
Tbed for smaller beds (Fig. 4.2). Consequently, the temperature difference between
bed and HTF, which represents the driving force for heat transfer, decreases at a corresponding rate. Thus, the amount of transferred heat Q̇ht decreases at a significantly
higher rate for decreasing wbed (Fig. 4.4).
Under the consideration of a constant heat capacity rate (ṁ · c p ) HTF follows that
the temperature difference ∆THTF between inlet and outlet of the HTF is directly
proporational to the transferred heat. Hence, the outlet temperature of the heat
transfer fluid decreases during storage discharge with a rate corresponding to Q̇ht ,
cf. Fig. 4.4 and 4.5.
A measure of the depth of discharge is the conversion X H , which accounts for
the amount CaO that has been hydrated to Ca(OH)2 . For smaller beds the driving
force of the reaction, the temperature difference ( Tbed − Teq ), is higher than for wider
26
4.1 Simplified Model for Highly Permeable Packed Beds
(a) wbed = 0.01 m
(b) wbed = 0.05 m
Figure 4.2: Temperature profile of the reaction bed for various bed dimensions at
t = 30 min
(a) wbed = 0.01 m
(b) wbed = 0.05 m
Figure 4.3: Conversion profile of the reaction bed for various bed dimensions at
t = 30 min
beds as the average bed temperature decreases faster. This, in turn, leads to a higher
H
conversion rate dX
dt (Fig. 4.6). The rapid increase in conversion at the beginning
of the reaction indicates sufficient availability of reaction gas due to an assumed
high bed permeability for the simplified model. Moreover, it can be seen that for a
given ∆THTF the achieved conversion decreases with incresing bed width, cf. Fig. 4.5
and 4.6.
27
4.1 Simplified Model for Highly Permeable Packed Beds
700
600
Qht [W]
500
·
400
300
200
100
0
0
30
w
bed
60
= 0.01 m
90
w
bed
120
= 0.02 m
150
t [min]
w
bed
180
= 0.03 m
210
w
bed
240
270
300
= 0.04 m
w
= 0.05 m
bed
Figure 4.4: Transferred heat per flow channel over time for various reaction bed dimensions
540
520
T [°C]
500
480
460
440
420
400
0
30
w
bed
= 0.01 m
60
90
w
bed
120
= 0.02 m
150
t [min]
w
bed
180
= 0.03 m
210
w
bed
240
270
300
= 0.04 m
w
= 0.05 m
bed
Figure 4.5: Average HTF outlet temperature over time for various reaction bed dimensions
28
4.1 Simplified Model for Highly Permeable Packed Beds
1
0.9
0.8
0.7
XH [-]
0.6
0.5
0.4
0.3
0.2
0.1
0
0
30
w
bed
= 0.01 m
60
90
w
bed
120
= 0.02 m
150
t [min]
w
bed
180
= 0.03 m
210
w
bed
240
270
300
= 0.04 m
w
= 0.05 m
bed
Figure 4.6: Averaged conversion over time for various reaction bed dimensions
To summarize and compare the investigated bed dimensions, the simulation results have been used to estimate the characteristics and performance of a reactor
with a rated power of 10 kW at a temperature increase of the heat transfer fluid
∆THTF of 100 K. For this purpose the transferred heat per flow channel Q̇ht,rp at
a HTF outlet temperature of 500 °C was identified and, thereafter, the number of
needed flow channels was determined to meet the rated power output. Comparing
Fig. 4.4 and 4.5, it can be seen that Q̇ht,rp is equal for all investigated bed dimensions,
which leads to a constant number of flow channels (Table 4.3). On the other hand,
the volume of the reaction bed increases with increasing bed width, and with it the
fraction of bed volume to total volume. This, in turn, leads to a higher volumetric
energy density uv whereas the volumetric power density pv will be lowered drastically. The aforementioned different reaction front characteristics affect the ratio of
operation time to reaction time trp/t95% and the conversion Xrp , where a reaction front
perpendicular to the HTF flow direction, leads to better results in terms of discharge
performance. Values for trp/t95% and Xrp drop from 56/85 to 177/491 and from 0.7211 to
0.5276 , respectively, by widening the bed from 0.01 m to 0.05 m. This means that a
considerable part of the energy stored in wide beds can not provide the rated power
of 10 kW at 500 ◦ C.
29
4.1 Simplified Model for Highly Permeable Packed Beds
Table 4.3: Reactor key data for various reaction bed dimensions
wbed = 0.01 m
wbed = 0.02 m
wbed = 0.05 m
n f c [-]
19
19
19
wreactor [m]
0.276
0.476
1.076
Vreactor [m3 ]
0.069
0.119
0.269
0.7246
0.8403
0.9294
mCaO [kg]
33.70
67.40
168.50
E [kWh]
16.61
33.22
83.05
uv [kWh/m3 ]
240.72
279.16
308.73
pv [kW/m3 ]
150.09
86.98
38.50
trp [min] / t95% [min]
56 / 85
107 / 173
177 / 491
Xrp [-]
0.7224
0.6949
0.4815
Vbed/Vreactor
[-]
HTF Inlet Velocity
For variation of the HTF inlet velocity v HTF,in the bed width has been kept constant at
0.02 m. Hence, heat transport characteristics of the bed are equal for all investigated
velocities. Despite the existing limitation in heat transport, which is indicated by the
V-shaped temperature profile, it can be seen that heat is removed across the entire
bed width regardless of the HTF inlet velocity (Fig. 4.7). The exact shape, however,
depends on the heat capacity rate (ṁ · c p ) HTF of the heat transfer fluid. With higher
rates more heat is removed from the bed, which, in turn, leads to a more stretched
reaction zone, cf. Fig. 4.8a and 4.8b.
At the beginning of the discharge phase, the heat capacity rate determines the
amount of heat transferred from reaction bed to HTF (Fig. 4.9). As heat is removed
by the HTF, the average bed temperature decreases during storage discharge. Consequently, the temperature difference between reaction bed and heat transfer fluid
decreases, which, in turn, leads to a decrease in Q̇ht . This drop is more pronounced
for increasing values of v HTF,in .
Higher inlet velocities reduce the residence time of the heat transfer fluid in the reactor. This overcompensates the improved heat transfer so that in total the maximum
HTF outlet temperature decreases with increasing v HTF,in (Fig. 4.10). Futhermore,
30
4.1 Simplified Model for Highly Permeable Packed Beds
(a) v HTF,in = 5 m/s
(b) v HTF,in = 15 m/s
Figure 4.7: Temperature profile of the reaction bed for various HTF inlet velocities at
t = 60 min
(a) v HTF,in = 5 m/s
(b) v HTF,in = 15 m/s
Figure 4.8: Conversion profile of the reaction bed for various HTF inlet velocities at
t = 60 min
the effects of reducing residence time and decreasing amount of transferred heat superimpose each other and lead to an increasing decline of the HTF oulet temperature
with increasing inlet velocity.
Since heat is removed from a larger region of the reaction bed for higher HTF
inlet velocities more material is converted, cf. Fig. 4.8a and 4.8b, and, thus, a higher
H
conversion rate dX
dt is obtained (Fig. 4.11). However, at a given ∆THTF a higher
conversion can be reached for low inlet velocities of the heat transfer fluid.
31
4.1 Simplified Model for Highly Permeable Packed Beds
900
800
700
Qht [W]
600
·
500
400
300
200
100
0
0
30
60
v = 5.0 m/s
90
120
v = 7.5 m/s
in
150
t [min]
180
v = 10.0 m/s
in
in
210
240
v = 12.5 m/s
in
270
300
v = 15.0 m/s
in
Figure 4.9: Transferred heat per flow channel over time for various HTF inlet velocities
540
520
T [°C]
500
480
460
440
420
400
0
30
v = 5.0 m/s
in
60
90
v = 7.5 m/s
in
120
150
t [min]
180
v = 10.0 m/s
in
210
240
v = 12.5 m/s
in
270
300
v = 15.0 m/s
in
Figure 4.10: Average HTF outlet temperature over time for various HTF inlet velocities
32
4.1 Simplified Model for Highly Permeable Packed Beds
1
0.9
0.8
0.7
XH [-]
0.6
0.5
0.4
0.3
0.2
0.1
0
0
30
60
v = 5.0 m/s
in
90
120
v = 7.5 m/s
150
t [min]
180
v = 10.0 m/s
in
in
210
240
v = 12.5 m/s
in
270
300
v = 15.0 m/s
in
Figure 4.11: Averaged conversion over time for various HTF inlet velocities
Similar to the variation of wbed , the obtained results have been used to determine
the performance of a reactor with 10 kW rated power output at a HTF outlet temperature of 500 °C. Key data for various HTF inlet velocities are summarized and
compared in Table 4.4. It can be seen that the overall volume of the reactor increases
Table 4.4: Reactor key data for various HTF inlet velocities
v HTF,in = 5 m/s
v HTF,in = 10 m/s
v HTF,in = 15 m/s
n f c [-]
37
19
13
wreactor [m]
0.908
0.476
0.332
[m3 ]
0.227
0.119
0.083
0.8370
0.8403
0.8434
mCaO [kg]
128.06
67.40
47.18
E [kWh]
63.12
33.22
23.25
uv [kWh/m3 ]
278.05
279.16
280.17
pv [kW/m3 ]
44.18
86.98
128.40
trp [min] / t95% [min]
259 / 307
107 / 173
48 / 130
Xrp [-]
0.8480
0.6949
0.4703
Vreactor
Vbed/Vreactor
[-]
33
4.1 Simplified Model for Highly Permeable Packed Beds
considerably with decreasing inlet velocity due to the higher number of required flow
channels. The ratio between bed volume and reactor volume, however, decreases
only marginally, which is due to the unequal number of flow channels and reaction
beds in the reactor, see Fig. 3.5. Since this ratio remains practically constant, the
volumetric energy density uv does not change for the investigated velocity range. In
contrast, the volumetric power density pv decreases due to the rise in total reactor
volume. The ratio of operational time to reaction time trp/t95% and the conversion at
rated power Xrp are enhanced significantly with decreasing inlet velocity. Under
these conditions, a reaction front perpendicular to the HTF flow direction develops
and leads to the improved discharge characteristics (Table 4.4).
Influence of Design Parameter on Performance
To determine favourable design and operational parameters for a HEX reactor for
chemical heat storage systems, the results of both parametric studies are combined
to estimate the total impact on the performance of the system. Therefore, volumetric
energy density uv and conversion Xrp , which represent key criteria for a packed
bed reactor, are plotted against reaction bed width wbed and HTF inlet velocity
v HTF,in . As already discussed, the bed width has a strong influence on the volumetric
energy density whereas the inlet velocity of the heat transfer fluid has practically no
impact (Fig. 4.12). For the investigated parameters uv ranges between 239 kWh/m3 and
309 kWh/m3 , based on CaO. Towards wide reaction beds and high HTF inlet velocities,
the achieved conversion at rated power Xrp decreases considerably (Fig. 4.13). This is
caused by the increasing limitation of heat transport in the bed combined with high
heat capacity rates (ṁ · c p ) HTF . Under these conditions, the HTF outlet temperature
drops below 500 °C before an acceptable depth of discharge is reached. In general,
changes in inlet velocity have a larger influence on the achievable conversion than
changes in bed width. The attained conversion at rated power Xrp ranges between
0.2293 and 0.8614 for the studied parameters.
Comparing Fig. 4.12 and 4.13, it becomes obvious that bed width and HTF inlet velocity have an entirely opposed influence on volumetric energy density and
conversion. Highest uv is obtained at high bed width and inlet velocity whereas
Xrp is lowest for these conditions. In order to identify the optimum setting of wbed
and v HTF,in at rated power, volumetric energy density and achieved conversion at
34
4.1 Simplified Model for Highly Permeable Packed Beds
320
3
uv [kWh/m ]
300
280
260
240
220
0.05
15.0
0.04
12.5
0.03
wbed [m]
10.0
0.02
0.01
7.5
5.0
vin [m/s]
Figure 4.12: Volumetric energy density at rated power as a function of HTF inlet velocity and reaction bed width
1.0
Xrp [-]
0.8
0.6
0.4
0.2
0.0
0.01
5.0
0.02
7.5
0.03
wbed [m]
10.0
0.04
0.05
12.5
15.0
vin [m/s]
Figure 4.13: Conversion at rated power as a function of HTF inlet velocity and reaction
bed width
35
4.2 Extended Model for Poorly Permeable Beds
this point are multiplied. This leads to the effective amount of energy that can be
extracted per unit volume for a given thermal power, respectively (Fig. 4.14). The
3
uv,eff [kWh/m ]
250
200
150
100
50
0.01
5.0
0.02
7.5
0.03
wbed [m]
10.0
0.04
0.05
12.5
15.0
vin [m/s]
Figure 4.14: Effective volumetric energy density at rated power as a function of HTF
inlet velocity and reaction bed width
effective volumetric energy density uv,e f f based on CaO ranges between 71 kWh/m3
and 242 kWh/m3 , with its peak at wbed = 0.03 m and v HTF,in = 5 m/s. Largest changes in
uv,e f f can be observed for wide reaction beds, the lowest at low inlet velocities.
4.2 Extended Model for Poorly Permeable Beds
After investigating the influence of design parameters on the thermal performance
of a reactor with 10 kW rated power output, the mathematical model is extended
to incorporate the transport of reaction gas through the reaction bed. With this
extension, effects of gas transport on the design and performance of a plate heat
exchanger reactor for heat storage can be investigated.
36
4.2 Extended Model for Poorly Permeable Beds
4.2.1 Extended System of Governing Equations
In addition to the energy transport, the extended model considers transport phenomena of the reaction gas inside the reaction bed. Thus, it becomes necessary to
include the conservation of mass in the system of governing equations. Regarding
the gas density, mass conservation can be written as
∂(ε · ρ g )
= −∇(ρ g · u g ) + Sm,g,r .
∂t
(4.16)
Similar to the conservation of energy in the reaction bed, cf. eq. (4.1), the left-hand
side of eq. (4.16) represents the rate of accumulation of mass with respect to the void
fraction of the bed.
The first term on the right-hand side describes changes in mass per unit volume
per time interval due to gas transport. In this term, u g designates the velocity of
the gas, which depends on the bed permeability K, the dynamic viscosity ηg of the
gas and the pressure gradient ∇ p g . Darcy’s law defines the relation between these
quantities for Re < 1 as
ug = −
K
· ∇ pg .
ηg
(4.17)
Production of reaction gas in terms of mass per unit volume per time interval due
to reaction is incorporated by the second term on the right-hand side of eq. (4.16) and
is given as
Sm,g,r = −(1 − ε) · r · Mg ,
(4.18)
where r is the reaction rate as defined in eq. (4.9) and Mg the molar mass of the gas.
Since the stoichiometric coefficients of reacting solid and gas are equal, the reaction
rate of eq. (4.9) can readily be used in eq. (4.18).
The gas passing through the reaction bed carries along energy which has to be
accounted for in the conservation of energy. Incorporating this convective energy
37
4.2 Extended Model for Poorly Permeable Beds
transport, the extended conservation equation can be written as
(c p · ρ)bed ·
∂Tbed
= −c p,g · ρ g · ∇ Tbed · u g − ∇ · (−λbed · ∇ Tbed ) + Q̇r ,
∂t
(4.19)
where Darcy’s law, eq. (4.17), is used to obtain the velocity u g of the gas.
4.2.2 Boundary & Initial Conditions
The additional set of equations implemented in the extended model require boundary
and inital conditions supplementary to those listed in Table 4.1 and 4.2. These
additional conditions are specified in Table 4.5.
Table 4.5: Additional boundary & initial conditions for the extended model
Condition
Boundary/Domain
Boundary Condition
No flow
p g,in =
7, 9, 10
105 Pa
8
Initial Condition
p g,init = peq ( Tbed,init )
2
4.2.3 Simulation Results
Gas transport through the bed plays an important role for the course of reaction.
Variables that influence the transport of reaction gas are the bed permeability and the
gas inlet compared to the inlet of the heat transfer fluid. Both parameters are varied
and their influence on the discharge behaviour of the reactor is analysed.
Variation of Bed Permeability
The ease with which fluids pass through porous media is determined by the media’s
permeability K. Thus, it affects the transport of reaction gas through the reaction bed.
38
4.2 Extended Model for Poorly Permeable Beds
According to the Carman-Kozeny equation, K can be written as
K=
d2p · ε3
180 · (1 − ε)2
,
(4.20)
where d p describes the average particle diameter. To identify the influence of the
gas transport on the reaction during storage discharge, the permeability is varied by
several orders of magnitude at a sufficiently high HTF heat capacity rate (ṁ · c p ) HTF
and, thereafter, the changes in conversion after 15 min are determined (Fig. 4.15). For
0.16
0.14
XH @ 15 min [-]
0.12
0.1
0.08
0.06
Limited
gas
transport
Limited
heat
transfer
0.04
0.02
0 -16
10
10
-15
-14
10
-13
10
10
-12
10
-11
K [m2]
d = 5µm,  = 0.8
p
10
-10
-9
10
-8
10
10
-7
d = 10µm,  = 0.8
p
Figure 4.15: Conversion after 15 min versus bed permeability; wbed = 0.02 m,
v HTF,in = 10 m/s, p g,init = 5691 Pa, p g,in = 105 Pa, ε = 0.8
values of K ≤ 10−14 m2 there is virtually no conversion of reaction material. This is
due to a lack of reaction gas caused by low permeability of the reaction bed. Applying
eq. (4.20) with a porosity of ε = 0.8, this limitation occurs for particle diameters of
d p ≤ 375 nm. Increasing conversion in the interval 10−14 m2 < K < 10−10 m2
indicates that the limitation in gas transport decreases with increasing permeability.
The increase in X H levels out and remains constant at around 0.1560 for K ≥ 10−10 m2 .
In this domain of K the gas transport through the reaction bed is not the limiting
factor anymore. However, reaction is still inhibited due to limited heat transfer
through the reaction bed. Particle diameters of d p ≥ 37.5 µm correspond to this
39
4.2 Extended Model for Poorly Permeable Beds
domain of K.
Calcium oxide and hydroxide, the substances that are used as reaction material,
have an average particle diameter of d p = 5 µm (Schaube, 2011). The corresponding
premeability of 1.778 · 10−12 m2 and the resulting conversion of 0.0887 after 15 min
are shown in Fig. 4.15. It can be seen that under these conditions, K is in the domain
H
of the highest gradients dX
dK . This means that rather small increases in permeability
enhance the achievable conversion considerably. As the bed porosity (ε = 0.8) can
hardly be increased any further, the permeability can only be increased by enlarging
the particle size of the used substances, cf. eq. (4.20). A doubling of the particle
diameter to d p = 10 µm would lead to an increase in conversion by 47 % (Fig. 4.15).
Variation of Reaction Gas Inlet
With respect to the inlet of the reaction gas, different configurations are possible.
It can be introduced into the reactor on the bottom side, the top side or at several
positions of the bed at the same time. Regarding the inlet of the heat transfer fluid,
the former two options result in a cocurrent and countercurrent flow configuration,
respectively, whereas the latter one approaches the unlimited gas transport discussed
in chapter 4.1. Initially, the reaction bed is in the state of chemical equilibrium at
400 ◦ C with a corresponding gas pressure of 5691 Pa. In cocurrent flow, both the
reaction gas and heat transfer fluid pass through the reactor from bottom to top. At
the beginning of storage discharge, the gas pressure p g close to the inlet increases
immediately. This results in a significant rise in equilibrium temperature Teq and in
hydration of calcium oxide due to the temperature difference ( Teq − Tbed ) (Fig. 4.16a).
The comparatively low bed permeability, leads to a rather small reaction zone in
which the equilibrium temperature is above the temperature of the reaction bed.
Only within the first 0.09 m of the bed, released heat of reaction is absorbed by the
heat transfer fluid, cf. Fig. 4.16a. During its passage through the reactor, the heated
HTF passes the upper part of the reactor, which has a temperature slightly above
inital temperature. Consequently, the heat flow is reversed so that the reaction bed
is heated by the HTF. This effect, combined with a low equilibrium temperature in
this part of the reactor due to limited gas transport, results in conditions that favour
dehydration instead of hydration. As there is no calcium hydroxide available for
decomposition, no reaction takes place in regions of the bed where Teq ≤ Tbed . After
40
540
540
520
520
500
500
T [°C]
T [°C]
4.2 Extended Model for Poorly Permeable Beds
480
460
480
460
440
440
420
420
400
0
0.1
0.2
0.3
0.4
h [m]
Teq
Tbed
400
0
0.5
Thtf
0.1
0.2
Teq
(a) t = 1 min
0.3
0.4
h [m]
Tbed
0.5
Thtf
(b) t = 25 min
Figure 4.16: Characteristic temperatures along the boundary of reaction bed and flow
channel
reaching a temperature maximum of around 450 ◦ C at the boundary (x = ±0.01 m),
the HTF leaves the reactor at about 403 ◦ C at the beginning of the discharge phase
(Fig. 4.16a). The amount of energy that corresponds to the temperature difference is
transferred back to the reaction bed. In the course of the discharge phase, the pressure
of reaction gas and with it the equilibrium temperature Teq rise across the reaction
bed. The region with conditions favourable for the hydration reaction ( Teq > Tbed )
expands towards the upper end of the reactor. At around 25 min the temperatures
are arranged in a way that CaO reacts to Ca(OH)2 and heat is transferred from bed to
HTF over the entire height of the reactor (Fig. 4.16b). Thereby, the zone of significant
reaction rates has expanded to around 0.25 m. Comparing Fig. 4.5 and 4.16b, it can
be seen that the limited gas transport reduces the maximum HTF outlet temperature
for a heat capacity rate (ṁ · c p ) HTF corresponding to an inlet velocity of 10 m/s by
around 40 K. Lowering the heat capacity rate enhances the outlet temperature, but
at the cost of longer reaction times. Considering these discharge characteristics, the
conclusion can be drawn that, under the here discussed conditions, the cocurrent
flow configuration is unfavourable for technical applications.
Another configuration in which the reaction gas and heat transfer fluid can be
introduced into the reactor is in countercurrent flow. In this setup, the reaction gas
inlet is located at the top side of the reactor, whereas the inlet for the heat transfer
fluid is at the bottom side. Investigations of the discharge phase reveal similar maximum outlet temperatures of the HTF as in cocurrent flow (Fig. 4.17). Generally, the
41
4.2 Extended Model for Poorly Permeable Beds
480
470
460
T [°C]
450
440
430
420
410
400
0
30
60
90
120 150 180 210 240 270 300 330 360 390 420 450 480
t [min]
Cocurrent
Countercurrent
Figure 4.17: Average HTF outlet temperature over time for countercurrent flow configuration
temperature profiles of both inlet configurations are quite alike with the exception of
a significant drop of around 20 K between 120 min and 160 min for the countercurrent
flow and the reversed heat flow within the first 25 min in cocurrent flow, cf. Fig 4.16.
During the first stage of discharge (t ≤ 120 min), reaction proceeds in the upper half
of the reactor only, cf. Fig. 4.18a. Thereby, the bed temperature decreases towards
the bottom of the reactor since the reaction gas pressure p g decreases due to limited
gas transport (Fig. 4.19a). As soon as all calcium oxide is hydrated in the upper part,
the reaction zone decreases significantly as can be seen in Fig. 4.18a through 4.18c.
With this decrease, the amount of transferred heat Q̇ht also reduces to a lower level,
which, in turn leads to a considerable drop in HTF outlet temperature within the
interval 120 min < t < 160 min. For the last stage of the discharge phase (t ≥ 160 min),
the reaction zone remains rather small, which results in a moderately elevated outlet
temperature of the heat transfer fluid (Fig. 4.17). The considerations regarding heat
capacity rate (ṁ · c p ) HTF and HTF outlet temperature discussed for cocurrent flow
apply for the countercurrent flow configuration as well. Even though the temperature
drop can be reduced by lowering the heat capacity rate, the thereby significantly
extended reaction time is not acceptable.
42
4.2 Extended Model for Poorly Permeable Beds
(a) t = 120 min
(a) t = 120 min
(b) t = 140 min
(b) t = 140 min
(c) t = 160 min
(c) t = 160 min
Figure 4.18: Conversion profile
across the reaction bed
in countercurrent flow
at various times
Figure 4.19: Temperature profile
across the reaction bed
in countercurrent flow
at various times
43
4.3 Design Suggestion for a Plate Heat Exchanger Reactor
4.3 Design Suggestion for a Plate Heat Exchanger Reactor
The results discussed in chapter 4.2.3 show that the gas transport characteristics of
the reaction bed consisting of commercially available material have adverse effects
on the performance of the reactor. Hence, the reactor should be designed in such a
way that the transport of reaction gas through the bed is not the limiting factor. This
can be achieved by horizontal alignment of the reaction bed, where the reaction gas
inlet is located on the top side of the bed (Fig. 4.20). Since the passage of reaction gas
Reaction gas inlet
Flow channel HTF
Reaction bed
Figure 4.20: Schematic of a horizontal reaction bed
through the bed is reduced to several centimetre, the gas pressure reaches the level
of inlet pressure p g,in almost instantaneously after the beginning of discharge. In
order to supply the reaction gas from the top side a gap has to be introduced, which
separates the reaction bed from the adjacent flow channel. In principle, this brings
along two adverse effects: the bed is cooled from only one side and heat is transferred
from HTF to reaction gas. However, the heat loss to the reaction gas is limited due
to its low velocity and the reduced cooling of the bed can be counteracted to some
extent by choosing the bed height appropriately.
As the gas transport is not the limiting factor for this reactor geometry, the findings from chapter 4.1.3 can be applied on the horizontal bed design to determine
the parameters for a final design suggestion. Therefore, the identified maxima for
volumetric energy density uv , achieved conversion at rated power Xrp , and effective
volumetric energy density at rated power uv,e f f are the most promising geometries
(Fig. 4.12 – 4.14, Table 4.6). Comparing the key data of these sets of parameters, it
becomes apparent that the investigated configuration with high HTF inlet velocitiy
and wide reaction bed is unfavourable for technical applications. Even though this
setting leads to a high volumetric energy density of around 309 kWh/m3 , the values
of Xrp and trp/t95% are with 0.2293 and 49/390 fairly low. With an effective volumetric
44
4.3 Design Suggestion for a Plate Heat Exchanger Reactor
Table 4.6: Key data of a reactor with vertical reaction bed for various design parameters
v HTF,in = 5 m/s;
v HTF,in = 5 m/s;
v HTF,in = 15 m/s;
wbed = 0.01 m
wbed = 0.03 m
wbed = 0.05 m
n f c [-]
37
37
13
wreactor [m]
0.528
1.288
0.752
Vreactor [m3 ]
0.132
0.322
0.188
0.7197
0.8851
0.9309
mCaO [kg]
64.03
192.09
117.95
E [kWh]
31.56
94.68
58.13
uv [kWh/m3 ]
239.08
294.03
309.23
pv [kW/m3 ]
76.04
31.23
56.67
trp [min] / t95% [min]
132 / 152
376 / 468
49 / 390
Xrp [-]
0.8614
0.8240
0.2293
Vbed/Vreactor
[-]
energy density at rated power of 71 kWh/m3 , the system is in the range of conventional thermal energy storage systems and therefore not considered any further. In
contrast, a low inlet velocity of the heat transfer fluid is beneficial with respect to
Xrp and trp/t95% . These values are the higher, the lower v HTF,in is chosen. Hence, the
configurations for the inlet velocity of 5 m/s listed in Table 4.6 are transferred to the
horizontal bed design and analysed regarding reactor performance.
Looking at the HTF outlet temperatures at v HTF,in = 5 m/s, it can be seen that the
peak is lower for the horizontally aligned reaction bed, compare Fig. 4.10 and 4.21.
Since the heat transfer fluid is heated from only one side in this layout, the maximum
outlet temperature is lowered by around 16 K compared to the vertical reaction bed.
Beyond that, the time trp after which the temperature drops below 500 ◦ C is reduced
to about 56 min for both investigated bed dimensions at v HTF,in = 5 m/s compared to
132 min and 376 min, respectively, for the vertical bed. This effect is caused by the
limited heat transport through the reaction bed. Considering the same thickness of
material, the distance of heat transfer is twice as long for the horizontal bed as only
one flow channel is in contact with the reaction bed, cf. Fig. 3.5 and 4.20. In order to
increase the ratio trp/t95% , it is more effective to decrease the HTF inlet velocity rather
than the bed height, see chapter 4.1.3. Hence, thermal performance of the reactor is
45
4.3 Design Suggestion for a Plate Heat Exchanger Reactor
540
520
T [°C]
500
480
460
440
420
400
0
60
120
v = 5.0 m/s; h
in
bed
180
= 0.01 m
240
300
360
t [min]
v = 5.0 m/s; h
in
bed
420
= 0.03 m
480
540
600
v = 1.0 m/s; h
in
bed
660
= 0.01 m
Figure 4.21: Average HTF outlet temperature over time for various design parameters
of a horizontal reaction bed
studied at a lowered inlet velocity of 1 m/s. A bed height of 0.01 m is chosen to ensure
a reasonable reaction time t95% .
Besides the value of trp/t95% , the lower heat capacity rate (ṁ · c p ) HTF also has a
positive effect on the HTF outlet temperature (Fig. 4.21). Drawback of the decreased
heat capacity rate is the significantly reduced transferred heat per flow channel Q̇ht ,
which can be seen in Fig. 4.22. This results in a considerably increased number
of channels that are required to meet the rated power of 10 kW (Table 4.7). For
storage applications with constant power output over long periods, e.g., in base load
power plants, the required high values for uv , trp/t95% , and Xrp may be realized by
using a HEX reactor with a bed height of 0.01 m and a HTF inlet velocity of 1 m/s.
However, industrial batch processes, for instance, demand systems with different
characteristics, i.e, high power density for only short periods of time. Hence, it has to
be concluded that the design parameters of the HEX reactor depend strongly on the
specifics of the respective heat storage application.
46
4.3 Design Suggestion for a Plate Heat Exchanger Reactor
350
300
Qht [W]
250
·
200
150
100
50
0
0
60
120
v = 5.0 m/s; h
in
bed
180
240
= 0.01 m
300
360
t [min]
v = 5.0 m/s; h
in
bed
420
480
= 0.03 m
540
600
v = 1.0 m/s; h
in
660
bed
= 0.01 m
Figure 4.22: Transferred heat per flow channel over time for various design parameters
of a horizontal reaction bed
Table 4.7: Key data of a reactor with horizontal reaction bed for various design parameters
v HTF,in = 5 m/s;
v HTF,in = 5 m/s;
v HTF,in = 1 m/s;
wbed = 0.01 m
wbed = 0.03 m
wbed = 0.01 m
n f c [-]
34
34
160
hreactor [m]
0.476
1.156
2.240
Vreactor [m3 ]
0.119
0.298
0.560
0.7143
0.8824
0.7143
mCaO [kg]
57.29
171.87
269.60
E [kWh]
28.24
84.71
132.88
uv [kWh/
237.28
293.11
237.28
pv [kW/m3 ]
85.99
35.43
17.94
trp [min] / t95% [min]
56 / 178
56 / 637
496 / 509
Xrp [-]
0.4061
0.1774
0.9358
Vbed/Vreactor
[-]
m3 ]
47
CHAPTER 5
Conclusion & Prospects
In this work, the design of a plate heat exchanger reactor for thermo-chemical heat
storage was investigated. Thereby, the focus was to estimate the influence of design
parameters on the reactor performance. The studies were conducted on a theoretical
basis by means of finite element analysis.
A mathematical model of a reactor with embedded plate heat exchanger for indirect heat transfer was developed and implemented in COMSOL Multiphysics ® ,
a commercially available simulation software. The model incorporates both heat
and mass transport through a fixed bed of reaction material. Even though the model
has not yet been validated, the obtained results can be used to identify correlations
between individual parameters of the reactor. Parametric studies on design parameters were carried out in order to identify limiting factors with regard to the reactor
performance. From these studies, knowledge about the characteristics of the identified limiting factors as well as the influence of design parameters on the reactor
performance was deduced.
The investigations showed that three limiting factors exist: gas and heat transport
through the reaction bed, and a limited heat capacity rate. Reason for the limitation
in gas transport is the low bed permeability, which results from the small particle
diameter of the used reaction material. Since the reaction should proceed at constant
reaction gas pressure, sufficient gas transport must be assured. This can be realized
by implementing small bed dimensions in the main direction of reaction gas flow.
The second limiting factor, heat transport through the reaction bed, is caused by the
low thermal conductivity of the bed. However, this factor is only limiting at high
heat capacity rates of the heat transfer fluid. Under this condition, insufficient heat is
provided, which leads to outlet temperatures well below equilibrium temperature
and a rapid temperature decrease of the HTF over time. Reducing the thermal
resistance of the reaction bed decreases this limiting effect, which, again, can be
48
5 Conclusion & Prospects
realized by small bed dimensions in the main direction of heat flow. Yet, small bed
dimensions result in lower volumetric energy densities. Depending on operational
parameters, such as HTF inlet velocity, the heat capacity rate of the HTF might be
another limiting factor. This is primarily caused by the use of a gaseous heat transfer
fluid for the temperature range above 400 ◦ C. A limitation of the reactor performance
through a low heat capacity rate (ṁ · c p ) HTF extends the time of reaction and lowers
the volumetric power density. On the other hand, the outlet temperature of the heat
transfer fluid would remain at a higher level for a longer fraction of the reaction time.
Concluding the characterization of identified limiting factors, it is worth mentioning
that the first two depend on the reactor design for a given reaction material, whereas
the latter factor can be influenced by adjusting operational parameters.
With knowledge about the characteristics of the limiting factors, optimal design
parameters for a storage reactor can be determined. However, since these parameters
have a different and partly conflicting influence on the performance of the reactor,
they strongly depend on actual area of application of the storage system. For applications in base load power plants where constant power output over a long period
of time is required, small bed dimensions and a moderate heat capacity rate are
the parameters of choice. In contrast, a high heat capacity rate at moderate bed
dimensions is preferred for applications in which high volumetric power densities
are required. This could be the case for buffer storages that are incorporated in
industrial processes.
For the actual design of a reactor for chemical heat storage in pilot plant scale,
further investigations need to be carried out subsequent to this work. Primarily, the
model which was developed in this work needs to be validated in order to allow more
accurate predictions of the reactor behaviour during charge/discharge. Therefore,
the theoretical studies of this work should be complemented by design and test
bench constraints. In this context, it could be reasonable to drop the idea of a cubic
reactor and use e. g. an ashlar-shaped reactor design. This would offer additional
vapour supply options. Concerning the heat transfer limitation, methods to increase
the effective thermal conductivity of the bed, such as embedded heat conducting
structures, should be studied. And finally, possibilities of increasing the particle
diameter by means of material modification to improve the transport of reaction gas
is another promising starting point for improvements of the reactor performance.
49
References
A NXIONNAZ , Z., C ABASSUD , M., G OURDON , C., T OCHON , P., 2008. Heat exchanger/reactors (HEX reactors): Concepts, technologies: State-of-the-art. Chemical
Engineering and Processing: Process Intensification, 47(12), pp.2029–2050.
B ARIN , I. AND P LATZKI , G., 1995. Thermochemical data of pure substances. 3rd ed.
Weinheim: VCH.
B AUMANN , T. AND L UCHT, G., 2011. Discussion on the gap width of plate heat exchangers.
[conversation] (Personal communication, 19 April 2011).
B AYÓN , R., R OJAS , E., VALENZUELA , L., Z ARZA , E., L EÓN , J., 2010. Analysis of
the experimental behaviour of a 100 kWth latent heat storage system for direct
steam generation in solar thermal power plants. Applied Thermal Engineering,
30(17–18), pp.2643–2651.
G IL , A., M EDRANO , M., M ARTORELL , I., L ÁZARO , A., D OLADO , P., Z ALBA , B.,
C ABEZA , L.F., 2010. State of the art on high temperature thermal energy storage
for power generation. Part 1 – Concepts, materials and modellization. Renewable
and Sustainable Energy Reviews, 14(1), pp.31–55.
G NIELINKSI , V., 2006. Wärmeübertragung im konzentrischen Ringspalt und im
ebenen Spalt. In: Verein Deutscher Ingenieute, ed. 2002. VDI Wärmeatlas.
Berlin; Heidelberg; New York: Springer-Verlag. Ch. Gb7.
H ERRMANN , U. AND K EARNEY, D.W., 2002. Survey of thermal energy storage
for parabolic trough power plants. Journal of Solar Energy Engineering, 124(2),
pp.145–152.
H OSHI , A., M ILLS , D.R., B ITTAR , A., S AITOH , T.S., 2005. Screening of high melting
point phase change materials (PCM) in solar thermal concentrating technology
based on CLFR. Solar Energy, 79(3), pp.332–339.
I NTERNATIONAL E NERGY A GENCY, 2009. World Energy Outlook 2009. Paris: Organisation for Economic Co-operation and Development / International Energy
Agency.
50
5 Conclusion & Prospects
L AING , D., S TEINMANN , W.-D., TAMME , R., R ICHTER , C., 2006. Solid media thermal
storage for parabolic trough power plants. Solar Energy, 80(10), pp.1283–1289.
L AING , D., S TEINMANN , W.-D., V IEBAHN , P., G RÄTER , F., B AHL , C., 2010. Economic analysis and life cycle assessment of concrete thermal energy storage
for parabolic trough power plants. Journal of Solar Energy Engineering, 132(4),
p.041013.
L AING , D., B AHL , C., B AUER , T., L EHMANN , D., S TEINMANN , W.-D., 2011. Thermal
energy storage for direct steam generation. Solar Energy, 85(4), pp.627–633.
L INDER , M., 2011. Discussion on reaction bed properties. [conversation] (Personal
communication, 5 April 2011).
M EDRANO , M., G IL , A., M ARTORELL , I., P OTAU , X., C ABEZA , L.F., 2010. State
of the art on high temperature thermal energy storage for power generation.
Part 2 – Case Studies. Renewable and Sustainable Energy Reviews, 14(1), pp.56–72.
M ICHELS , H. AND P ITZ -PAAL , R., 2007. Cascaded latent heat storage for parabolic
trough solar power plants. Solar Energy, 81(6), pp.829–837.
R OYAL D UTCH S HELL, 2008. Sustainability Report 2008. [online] Available at: www.
shell.com/annualreport [Accessed 18 August 2011].
S CHAUBE , F., 2011. Discussion on average particle diameter of calcium odxide and hydroxide.
[conversation] (Personal communication, 15 May 2011).
S CHAUBE , F., (in press) Untersuchungen zur Nutzung des CaO/Ca(OH)2 -Reaktionssystems
für die thermochemische Wärmespeicherung. Ph.D. thesis, University of Stuttgart.
S OLAR M ILLENNIUM AG, 2008. The parabolic trough power plants Andasol 1 to 3. The
largest solar power plants in the world – Technology premiere in Europe. [online]
Available at: http://www.solarmillennium.de/upload/Download/
Technologie/eng/Andasol1-3engl.pdf [Accessed 09 July 2011].
S TEINMANN , W.-D., L AING , D., TAMME , R., 2010. Latent heat storage systems for
solar thermal power plants and process heat applications. Journal of Solar Energy
Engineering, 132(2), p.021003.
51
5 Conclusion & Prospects
TAMME , R., 2002. Speichern von Energie. In: E. Rebhan, ed. 2002. Energiehandbuch:
Gewinnung, Nutzung und Wandlung von Energie. Berlin; Heidelberg; New York:
Springer-Verlag. Ch. 4.1.
T RIEB , F., S CHILLINGS , C., O’S ULLIVAN , M., P REGGER , T., H OYER -K LICK , C., 2009.
Global potential of concentrating solar power. 15th SolarPaces Conference. Berlin,
Germany 15–18 September 2009.
U TZ , I., 2011. Discussion on heat transfer in packed beds. [conversation] (Personal
communication, 7 April 2011).
W ENTWORTH , W. E., C HEN , E., 1976. Simple thermal decomposition reactions for
storge of solar thermal energy. Solar Energy, 18(3), pp.205–214.
52
APPENDIX A
Thermophysical Properties of the reactants of the Calcium
Hydroxide – Calcium Oxide System
A.1 Enthalpy and Entropy of Formation
The values for calcium hydroxide and calcium oxide in Table A.1 and A.2 are taken
from the National Institute of Standards and Technology, the values for water are
taken from Barin and Platzki (1995).
Table A.1: Enthalpy of formation for various temperatures
Ca(OH)2
CaO
H2 O
T
∆H
∆H
∆H
[K]
[kJ/mol]
[kJ/mol]
[kJ/mol]
298
-986.105
-635.099
-241.826
300
-985.935
-635.019
-241.764
400
-976.545
-630.539
-238.375
500
-966.415
-625.749
-234.902
600
-955.835
-620.769
-231.326
700
-944.925
-615.669
-227.635
800
-933.705
-610.469
-223.825
900
-922.225
-605.199
-219.889
1000
-910.525
-599.859
-215.827
53
Appendix A
Table A.2: Entropy of formation for various temperatures
Ca(OH)2
CaO
H2 O
T
∆S
∆S
∆S
[K]
[kJ/(mol · K)]
[kJ/(mol · K)]
[kJ/(mol · K)]
298
83.310
38.170
188.959
300
83.900
38.450
189.167
400
110.800
51.290
198.910
500
133.400
61.990
206.656
600
152.700
71.060
213.174
700
169.500
78.930
218.860
800
184.500
85.860
223.947
900
198.000
92.070
228.580
1000
210.300
97.700
232.860
A.2 Molar heat capacity at constant pressure
To obtain the specific heat capacity of the listed reactants, the values given in Table A.3
have to be divided by the repective molar mass.
Table A.3: Molar heat capacity at constant pressure C p for various temperatures
Ca(OH)2
CaO
T
Cp
Cp
[K]
[J/(mol · K)]
[J/(mol · K)]
500
103.8
49.02
600
107.5
50.48
700
110.7
51.54
800
113.5
52.37
900
116.0
53.08
1000
118.0
53.71
54
APPENDIX B
Results of Parametric Study
Table B.1: Reactor data for v HTF,in = 5.0 m/s
v HTF,in = 5.0 m/s
wbed
0.01 m
0.02 m
0.03 m
0.04 m
0.05 m
trp [min]
132
259
376
484
581
t95% [min]
152
307
468
636
812
Q̇ht,rp [W]
271.28
271.04
271.79
271.26
271.69
n f c [-]
37
37
37
37
37
wreactor [m]
0.528
0.908
1.288
1.668
2.048
Vf c [m3 ]
0.037
0.037
0.037
0.037
0.037
[m3 ]
0.095
0.190
0.285
0.380
0.475
0.132
0.227
0.322
0.417
0.512
0.7197
0.8370
0.8851
0.9113
0.9277
mCaO [kg]
64.03
128.06
192.09
256.12
320.15
E [kWh]
31.56
63.12
94.68
126.23
157.79
]
239.08
278.05
294.03
302.72
308.19
pv [kW/m3 ]
76.04
44.18
31.23
24.07
19.63
Xrp [-]
0.8614
0.8480
0.8240
0.7983
0.7700
Vbed
Vreactor [m3 ]
Vbed/Vreactor
uv [
[-]
kWh m3
/
55
Appendix B
Table B.2: Reactor data for v HTF,in = 7.5 m/s
v HTF,in = 7.5 m/s
wbed
0.01 m
0.02 m
0.03 m
0.04 m
0.05 m
trp [min]
81
158
224
281
327
t95% [min]
107
217
335
461
596
Q̇ht,rp [W]
407.38
406.80
408.05
408.07
408.87
n f c [-]
25
25
25
25
25
wreactor [m]
0.360
0.620
0.880
1.140
1.400
[m3 ]
0.025
0.025
0.025
0.025
0.025
Vbed [m3 ]
0.065
0.130
0.195
0.260
0.325
0.090
0.155
0.220
0.285
0.350
0.7222
0.8387
0.8864
0.9123
0.9286
mCaO [kg]
43.81
87.60
131.40
175.20
219.05
E [kWh]
21.59
43.19
94.78
86.37
107.96
uv [kWh/m3 ]
239.92
278.62
294.45
303.06
308.47
pv [
113.16
65.61
46.37
35.80
29.20
0.7897
0.7730
0.7355
0.6962
0.6531
Vf c
Vreactor
[m3 ]
Vbed/Vreactor
kW m3
/
Xrp [-]
[-]
]
56
Appendix B
Table B.3: Reactor data for v HTF,in = 10.0 m/s
v HTF,in = 10.0 m/s
wbed
0.01 m
0.02 m
0.03 m
0.04 m
0.05 m
trp [min]
56
107
148
175
177
t95% [min]
85
173
270
375
491
Q̇ht,rp [W]
545.06
544.74
545.48
545.19
545.06
n f c [-]
19
19
19
19
19
wreactor [m]
0.276
0.476
0.676
0.876
1.076
[m3 ]
0.019
0.019
0.019
0.019
0.019
Vbed [m3 ]
0.050
0.100
0.150
0.200
0.250
0.069
0.119
0.169
0.219
0.269
0.7246
0.8403
0.8876
0.9132
0.9294
mCaO [kg]
33.70
67.40
101.10
134.80
168.50
E [kWh]
16.61
33.22
49.83
66.44
83.05
uv [kWh/m3 ]
240.72
279.16
294.85
303.38
308.73
pv [
150.09
86.98
61.33
47.30
38.50
0.7224
0.6949
0.6462
0.5802
0.4815
Vf c
Vreactor
[m3 ]
Vbed/Vreactor
kW m3
/
Xrp [-]
[-]
]
57
Appendix B
Table B.4: Reactor data for v HTF,in = 12.5 m/s
v HTF,in = 12.5 m/s
wbed
0.01 m
0.02 m
0.03 m
0.04 m
0.05 m
trp [min]
41
76
93
94
94
t95% [min]
72
147
231
325
430
Q̇ht,rp [W]
681.84
683.26
682.07
681.42
681.42
n f c [-]
15
15
15
15
15
wreactor [m]
0.220
0.380
0.540
0.700
0.860
[m3 ]
0.015
0.015
0.015
0.015
0.015
Vbed [m3 ]
0.040
0.080
0.120
0.160
0.200
0.055
0.095
0.135
0.175
0.215
0.7273
0.8421
0.8889
0.9143
0.9302
mCaO [kg]
26.96
53.90
80.90
107.80
134.80
E [kWh]
13.29
26.58
39.86
53.15
66.44
uv [kWh/m3 ]
241.60
279.74
295.29
303.72
309.02
pv [
185.96
107.88
75.79
58.41
47.54
0.6545
0.6134
0.5119
0.4031
0.3351
Vf c
Vreactor
[m3 ]
Vbed/Vreactor
kW m3
/
Xrp [-]
[-]
]
58
Appendix B
Table B.5: Reactor data for v HTF,in = 15.0 m/s
v HTF,in = 15.0 m/s
wbed
0.01 m
0.02 m
0.03 m
0.04 m
0.05 m
trp [min]
30
48
49
49
49
t95% [min]
63
130
207
293
390
Q̇ht,rp [W]
819.77
819.76
819.54
819.56
819.55
n f c [-]
13
13
13
13
13
wreactor [m]
0.192
0.332
0.472
0.612
0.752
[m3 ]
0.013
0.013
0.013
0.013
0.013
Vbed [m3 ]
0.035
0.070
0.105
0.140
0.175
0.048
0.083
0.118
0.153
0.188
0.7292
0.8434
0.8898
0.9150
0.9309
mCaO [kg]
23.59
47.18
70.80
94.40
117.95
E [kWh]
11.63
23.25
34.88
46.51
58.13
uv [kWh/m3 ]
242.23
280.17
295.60
303.97
309.23
pv [
222.02
128.40
90.29
69.64
56.67
0.5699
0.4703
0.3402
0.2709
0.2293
Vf c
Vreactor
[m3 ]
Vbed/Vreactor
kW m3
/
Xrp [-]
[-]
]
59