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 1.1 Thesis outline ...... 2

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 19 4.1 Simplified Model for Highly Permeable Packed Beds ...... 19 4.1.1 Governing Equations ...... 19 4.1.2 Boundary & Initial Conditions ...... 22 4.1.3 Simulation Results ...... 24 4.2 Extended Model for Poorly Permeable Beds ...... 36 4.2.1 Extended System of Governing Equations ...... 37 4.2.2 Boundary & Initial Conditions ...... 38 4.2.3 Simulation Results ...... 38

iv Contents

4.3 Design Suggestion for a Plate Heat Exchanger Reactor ...... 44

5 Conclusion & Prospects 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 Schematic of an Andasol-type solar thermal power plant ...... 4 2.2 Schematic of a proposed storage concept for direct steam generation 5 2.3 Typical T,h-diagram of a pure substance ...... 6 2.4 Plot of the van’t Hoff equation for the reversible reaction system of

Ca(OH)2 – CaO ...... 13 2.5 Principle of heat transformation in the system of Ca(OH)2 – CaO . . 14

3.1 Schematic of reactor with direct heat transfer ...... 16 3.2 Schematic of reactor with indirect heat transfer ...... 16 3.3 Schematic of a shell and tube heat exchanger reactor ...... 17 3.4 Heat transfer coefficient and heat transfer area over inner diameter for pipe flow ...... 17 3.5 Schematic of a plate heat exchanger reactor for energy storage . . . . 18

4.1 Schematic of the implemented geometric model with corresponding boundaries and domains ...... 23 4.2 Temperature profile of the reaction bed for various bed dimensions at t = 30 min...... 27 4.3 Conversion profile of the reaction bed for various bed dimensions at t = 30 min...... 27 4.4 Transferred heat per flow channel over time for various reaction bed dimensions ...... 28 4.5 Average HTF outlet temperature over time for various reaction bed dimensions ...... 28 4.6 Averaged conversion over time for various reaction bed dimensions 29 4.7 Temperature profile of the reaction bed for various HTF inlet velocities at t = 60 min ...... 31 4.8 Conversion profile of the reaction bed for various HTF inlet velocities at t = 60 min ...... 31

vi List of Figures

4.9 Transferred heat per flow channel over time for various HTF inlet velocities ...... 32 4.10 Average HTF outlet temperature over time for various HTF inlet velo- cities ...... 32 4.11 Averaged conversion over time for various HTF inlet velocities . . . 33 4.12 Volumetric energy density at rated power as a function of HTF inlet velocity and reaction bed width ...... 35 4.13 Conversion at rated power as a function of HTF inlet velocity and reaction bed width ...... 35 4.14 Effective volumetric energy density at rated power as a function of HTF inlet velocity and reaction bed width ...... 36 4.15 Conversion after 15 min versus bed permeability ...... 39 4.16 Characteristic temperatures along the boundary of reaction bed and flow channel ...... 41 4.17 Average HTF outlet temperature over time for countercurrent flow configuration ...... 42 4.18 Conversion profile across the reaction bed in countercurrent flow at various times ...... 43 4.19 Temperature profile across the reaction bed in countercurrent flow at various times ...... 43 4.20 Schematic of a horizontal reaction bed ...... 44 4.21 Average HTF outlet temperature over time for various design parame- ters of a horizontal reaction bed ...... 46 4.22 Transferred heat per flow channel over time for various design para- meters 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 Boundary conditions of the simplified model ...... 25 4.2 Initial conditions of the simplified model ...... 25 4.3 Reactor key data for various reaction bed dimensions ...... 30 4.4 Reactor key data for various HTF inlet velocities ...... 33 4.5 Additional boundary & initial conditions for the extended model . . 38 4.6 Key data of a reactor with vertical reaction bed for various design parameters ...... 45 4.7 Key data of a reactor with horizontal reaction bed for various design parameters ...... 47

viii 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 [J/(mol · K)] q˙ Heat flux [W/m2] cp Specific heat capacity at constant pressure [J/(kg · K)] d Diameter [m]

E Energy content [kWh] h Height [m] h Specific enthalpy [J/kg]

K Equilibrium constant [-]

K Permeability [m2]

ix Nomenclature k Reaction rate constant [1/s]

M Molar mass [kg/mol] m Mass [kg] n Number [-]

Nu Nusselt number [-] p Pressure [Pa] pv Volumetric power density [kW/m3]

Pr Prandtl number [-]

Q Heat [J]

R Gas constant [J/(mol · K)] r Reaction rate [mol/(m3 · s)]

Rth Thermal resistance [K/W]

Re Reynolds number [-] s Thickness [m]

W 3 SQ˙ Heat source/sink [ /m ]

Sm Mass source/sink [kg/(m3 · s)]

T Temperature [K] t Time [s]

U Overall heat transfer coefficient [W/(m2 · K)] ug Velocity of gaseous phase [m/s] uv Volumetric energy density [kWh/m3]

V Volume [m3] v Velocity [m/s]

x Nomenclature w Width [m]

X Conversion [-]

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 coun- tries. 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 rene- wable 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 electri- city 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 cp of the storage medium, and the storage size in terms of mass m and is defined as

Q = m · cp · ∆T. (2.1)

It becomes evident that for a high volumetric energy density uv of the storage, the volumetric heat capacity (ρ · cp) 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 The first parabolic trough power plants in Europe – the world’s largest solar power plants: Andasol 1 to 3

Water availability Solar field transforms solar radiation into heat energy The power plant’s site is unique in Spain for its comparatively above-average water availability. An Andasol power plant has a solar field that The Sierra Nevada mountain range which sur- covers 510,120 square meters. The parabolic rounds the site is the primary source. The Andasol troughs are set up in 312 collector rows which are power plant’s annual water needs are about connected by pipes. The rows are set up on a equal to the water which would be needed for the north-south axis and follow the course of the sun cultivation of crops such as wheat on the power from east to west. One row is made up of two plant’s site. The plant requires about 870,000 m2 collector units. Every collector unit has its own of water per year, which is mainly used for cool- solar sensors and hydraulic drives, which allow ing the steam circuit, i.e. from the vaporization of the mirrors to track the position of the sun. The water in the cooling towers. The water needs are collector units each have 12 collectors, which are primarily met with ground water extracted from 12 m long and 6 m wide. Every collector has 28 wells on the site. mirrors and 3 absorption pipes. An Andasol power plant requires 7,488 collectors. Specialists assemble Technical description and check these collectors photogrammetrically In parabolic trough power plants, trough-shaped to determine their precision in specially-con- 2.1 Sensible Heat Storagemirrors in the solar field concentrate the suns structed factory buildings before the collectors rays by a factor of 80 onto an absorption pipe in are brought to the field and anchored. the focal line of the collector. In the pipes, a heat low thermal conductivitytransfer and fluid their circulates high in specifica closed circuit costs which (Herrmann is and Kearney, 2002). As oils decompose atheated temperatures to 400 degrees of Celsius around by 400the concentrated◦C, they are notEfficiency applicable for solar solar radiation. The heated fluid is then pumped Solar field power tower plants.into a centrally located power block and flows through a heat exchanger. In this way, steam is Peak efficiency ca. 70% Even though somegenerated molten which salts (similar can be to aggressive conventional and power corrosive,Annual they average show benefi- ca. 50% plants) powers the turbine using an electric Turbine circuit 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 ca. 40% low cost medium withthe power operating plant to parameters function at full that capacity match both those ofAnnual modern average steam tur- ca. 30% on overcast days and at night. The Andasol power bines. The specific storage capacity of nitrate salts is higher than thatEntire plant of oils at lower plants each consist of a solar field, a thermal Peak efficiency ca. 28% specific costs (Herrmannstorage tank, and and Kearney, a conventional 2002). power In addition, plant experience in handling molten salts has alreadysection. been gained in chemical and metal industries.Annual average Andasol-type ca. 15% 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

2 1 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,12 2008) 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. Du- ring 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 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 C B Evaporation / condensation unit, liquid water C Evaporation / condensation unit, steam steam D Superheating unit, live steam drum from solar field

to solar field D B A sensible heat storage unit: latent heat storage unit: sensible heat storage unit: from to power preheating / cooling of evaporation / condensation superheating / cooling of steam block power condensate 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 embeddedet al., aggregates. 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 challenging, the project resources for concrete storage were losses of the aggregates and the concrete depending on the allocated completely to a superheating module. This mod- temperature profile were examined. The oven tests lasted ule is also suitable for preheating. The test-loop being for several thousand hours. Results show that the mass installed for this purpose at the power plant Litoral of of the aggregate and concrete samples stabilizes at Endesa in Carboneras, Spain, is described in more detail 500 °C. Mass losses were from 1.5 to 3.5 wt.% for the 5 in Eck et al. (2009). aggregates and about 5.3 wt.% for the concrete samples. The dominating mechanism of the mass loss is evaporable 3.2. Storage technology for preheating water and for water in the concrete. Also, the impact of temperature on superheating steam the strength of the concrete was tested. Detailed results of material investigations related to the thermal stability 3.2.1. Concept and design of the concrete storage test module of concrete up to 500 °C are presented in Laing et al. (in The design parameters for the test module are: press). Overall, oven experiments and strength measure- ments up to 500 °C show that mass loss and strength values  Heat transfer fluid: water/steam. of the concrete stabilize after a period of time and a num-  Maximum internal pressure: 128 bar. ber of thermal cycles. Hence, the utilization of high-tem-  Temperature: up to 400 °C. perature concrete as sensible heat storage up to 500 °C seems feasible. The concrete storage module is principally composed of a tube register and storage concrete. The tube register is 3. Pilot-scale storage combining PCM and concrete modules used for transporting and distributing the heat transfer medium while sustaining the fluid pressure; the storage 3.1. Background concrete stores the thermal energy as sensible heat. A dura- ble and safe construction is achieved by this division of the

In 2008, not only was the laboratory scale NaNO3 PCM functions. test module described above tested, but also a 20 m3 con- A special focus was set on the mismatch of the thermal crete storage test module was built in Stuttgart and has expansion between concrete and tubing. In previous lab been successfully operated up to 400 °C(Laing et al., tests, the coefficients of thermal expansion of the concrete 2008). These experiences using heating/cooling circuits and the tubes were determined. In a temperature range of with thermal oil as the heat carrier lay the foundation for 100–350 °C, the values were estimated with aT = 0.90– À5 À1 the development of the concrete storage technology with 1.20 Â 10 K for concrete and aT = 1.35–1.50 Â À5 À1 the pressure and temperature conditions as they occur in 10 K for tubing. Without additional measures, this a DSG power plant with main steam parameters of mismatch would lead to longitudinal and radial stresses 110 bar/400 °C. in the tubing as well as in the concrete. To limit the stresses The combined storage system to be tested in autumn to an acceptable level, a special interface material was 2009 has a total storage capacity of approx. 1 MW h and installed. This special material reduces the friction between comprises of a PCM storage module for evaporation of tubing and concrete and is compressible to allow a slight water and a concrete storage module for superheating deformation to reduce the stresses without reduction of steam. A separate concrete module for preheating liquid thermal transmission. 2.2 Latent Heat Storage and superheat steam.

2.2 Latent Heat Storage

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 ∆hpc 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 Sensible Heat of Heat of Heat Solid Fusion Liquid Vaporization Gas Temperature

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 (N2CO3) 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 di- sadvantage. 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. Additio- nally, 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

θ θ ∆rG = ∆r H − T · ∆rS + R · T · ln(K), (2.2)

θ θ where ∆r H represents changes in standard enthalpy of reaction, ∆rS 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, ∆rG 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

θ θ ∆r H(p ,Teq) − Teq · ∆rS(p ,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 ∆rS and assumed that the activity of all reactants and products is equal to one, which results in K = 1. These considerations lead to

∆ Hθ = r Teq θ , (2.4) ∆rS 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. Tempera- tures 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 θ means that a reaction must absorb large amounts of energy ∆r H . To assure that θ Teq is within practical limits, ∆rS 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 com- ponents 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 concer- ning 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, ∆rS 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 sto- rage (Tamme, 2002)

Type of reaction Reaction Temperature range [◦C]

2 NH3 )* N2 + 3 H2 400 – 500 Catalytic dissociation 2 SO3 )* 2 SO2 + O2 500 – 900

Mg(OH)2 )* MgO + H2O 250 – 350 Dehydration of metal Ca(OH) )* CaO + H O 450 – 550 hydroxides 2 2 Ba(OH)2 )* BaO + H2O 700 – 800

Decarboxylation of metal MgCO3 )* MgO + CO2 350 – 450 carbonates CaCO3 )* CaO + CO2 850 – 950

Thermal deoxygenation of 2 BaO2 )* 2 BaO + O2 750 – 850 metal oxides 4 KO2 )* 2 K2O + 3 O2 600 – 800

CH4 + H2O )* CO + 3 H2 700 – 1000 Reforming processes CH4 + CO2 )* 2 CO + 2 H2 700 – 1000

Thermal dehydrogenation MgH2 )* Mg + H2 200 – 400 of metal hydrides Mg2NiH4 )* Mg2Ni + 2 H2 150 – 300

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) + H2O (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:

 p νi p = i = H2O K ∏ θ θ . (2.7) i p p

For the considered reaction system, the general expression, middle term in eq. (2.7), p θ reduces to H2O/p 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

 p  ∆ H(pθ,T) 1 ∆ S(pθ,T) ln H2O = − r · + r . (2.8) pθ R T R

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

 p  1000 ln H2O = −12.72 K · + 16.03. (2.9) bar T

12 2.3 Chemical Heat Storage

10 CaO (s) + H O (g)  Ca(OH) (s) 2 2

1.0 [bar])

O 0.1 2 H

ln (p Ca(OH) (s)  CaO (s) + H O (g) 2 2 0.01

0.001 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1000/T [1000/K]

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 pH2O,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 tem- perature. 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 domi- nant. 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

Q˙ out % 1.0 ↑  p H O Q˙ in 2

[bar]) ↓ .

O 0.1 2 H ln (p

0.01

←−  T −→

0.001 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1000/T [1000/K]

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 (dp ≈ 5 µm) of the currently available material, which leads to enormous parasitic losses.

15 3 Motivation & Focus

H2O H2O

H2O & Heat H2O & Heat Heat transfer fluidHeat transfer fluid transfer fluid transfer fluid

Figure 3.1: Schematic of reactor with Figure 3.2: Schematic of reactor with direct heat transfer 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 3 Motivation & Focus

Heat transfer area

Heat transfer coefficient Tube diameter Heat transfer coefficient Heat transfer area

Figure 3.3: Schematic of a shell and Figure 3.4: Heat transfer coefficient tube heat exchanger reac- and heat transfer area tor over inner diameter for pipe flow 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

Q˙ ht

λwall

αHTF

λHTF

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

∂T (c · ρ) · bed = −∇ · (−λ · ∇T ) + S , (4.1) p bed ∂t bed bed Q˙ ,r

19 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 (cp · ρ)bed, which in turn is the sum of storage capacities of the bed’s constituents:

(cp · ρ)bed = (1 − ε) · cp,s · ρs + ε · cp,g · ρg. (4.2)

Since the solid material of the bed changes during reaction, the corresponding mate- rial properties have to be evaluated accordingly. Taking into account the conversion

XH during hydration, the solid density ρs and specific heat capacity cp,s can both be estimated using the following approximations:

= ( − ) + ρs 1 XH · ρCaO XH · ρCa(OH)2 , (4.3)

= ( − ) + cp,s 1 XH · cp,CaO XH · cp,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 cp 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

J J cp,CaO = 0.16495 · · Ts + 798.64700 · (4.5) kg · K2 kg · K and

J J c ( ) = 0.38612 · · Ts + 1217.29416 · . (4.6) p,Ca OH 2 kg · K2 kg · K

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 XH the gaseous phase accounts for less than 1 % of the value of (cp · 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 (cp · 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 · λg. (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 SQ˙ ,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:

SQ˙ ,r = −(1 − ε) · r · ∆r H. (4.8)

Besides the porosity ε and the enthalpy of reaction ∆r H, the value of SQ˙ ,r is determi- ned by the reaction rate r, which accounts for the solid material that reacts per unit volume per time interval. It is defined as

ρ dX r = s,r · H , (4.9) Ms,r dt where XH accounts for the fraction of solid material which has already been hydrated. dXH Hence, 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

dXH Tbed − Teq = (1 − XH) · k · . (4.10) dt Teq

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 (uHTF, pHTF, 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 10 13

5 8 11

Figure 4.1: Schematic of the implemented geometric model with corresponding boun- daries and domains is defined as

q˙ht = −U · (Tbed − THTF), (4.11) where the overall heat transfer coefficient U itself is given as

1 1 s 1 = + wall + . (4.12) U αbed λwall αHTF

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 2 packed bed and wall, αbed can be assumed with 800 W/(m · 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, αHTF is evaluated by applying basic Nusselt number correlations for parallel plates at constant temperature in accordance with Gnielinski (2006). Thereby,

αHTF is defined as

Num · λHTF αHTF = , (4.13) dh

23 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

3 3 3 1/3 Num = (Nu1 + Nu2 + Nu3) , (4.14) with

Nu1 = 7.541, (4.15a)

s 3 dh Nu2 = 1.841 · Re · Pr · , (4.15b) h f c

 1/6 !1/2 2 dh Nu3 = · Re · Pr · . (4.15c) 1 + 22 · Pr h f c

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 eva- luated with the well-known correlations for these dimensionless quantities. All temperature dependent material properties of the heat transfer fluid, used to de- termine αHTF, are taken from the COMSOL material library at a mean temperature 1 THTF,m = 2 · (THTF,in + THTF,out).

Whereas the inlet velocity of the heat transfer fluid vHTF,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

vHTF,y = 0 m/s 7, 10

vHTF,in 5, 11 5 pHTF,out = 10 Pa 6, 12

Heat transfer in heat transfer fluid

Symmetry 4, 13 −n · (−λ · ∇T) = 0 6, 12 ◦ THTF,in = 400 C 5, 11

q˙ht 7, 10

Heat transfer in reaction bed

−n · (−λ · ∇T) = 0 8, 9

−q˙ht 7, 10

Table 4.2: Initial conditions of the simplified model

Condition Domain

Laminar flow in heat transfer fluid

vHTF,init = vHTF,in 1, 3 5 pHTF,init = 10 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 cor- responding rate. Thus, the amount of transferred heat Q˙ ht decreases at a significantly higher rate for decreasing wbed (Fig. 4.4).

Under the consideration of a constant heat capacity rate (m˙ · cp)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 Q˙ ht, cf. Fig. 4.4 and 4.5.

A measure of the depth of discharge is the conversion XH, 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 dXH conversion rate 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

500

400 [W] ht 300 · Q

200

100

0 0 30 60 90 120 150 180 210 240 270 300 t [min]

w = 0.01 m w = 0.02 m w = 0.03 m w = 0.04 m w = 0.05 m bed bed bed bed bed

Figure 4.4: Transferred heat per flow channel over time for various reaction bed dimen- sions

540

520

500

480

T [°C] 460

440

420

400 0 30 60 90 120 150 180 210 240 270 300 t [min]

w = 0.01 m w = 0.02 m w = 0.03 m w = 0.04 m w = 0.05 m bed bed bed bed bed

Figure 4.5: Average HTF outlet temperature over time for various reaction bed dimen- sions

28 4.1 Simplified Model for Highly Permeable Packed Beds

1

0.9

0.8

0.7

0.6

[-] 0.5 H X 0.4

0.3

0.2

0.1

0 0 30 60 90 120 150 180 210 240 270 300 t [min]

w = 0.01 m w = 0.02 m w = 0.03 m w = 0.04 m w = 0.05 m bed bed bed bed bed

Figure 4.6: Averaged conversion over time for various reaction bed dimensions

To summarize and compare the investigated bed dimensions, the simulation re- sults 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 Q˙ ht,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 Q˙ ht,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 drasti- cally. The aforementioned different reaction front characteristics affect the ratio of t operation time to reaction time rp/t95% and the conversion Xrp, where a reaction front perpendicular to the HTF flow direction, leads to better results in terms of discharge t 56 177 performance. Values for rp/t95% and Xrp drop from /85 to /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 3 Vreactor [m ] 0.069 0.119 0.269

Vbed/Vreactor [-] 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

HTF Inlet Velocity

For variation of the HTF inlet velocity vHTF,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 (m˙ · cp)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. Conse- quently, the temperature difference between reaction bed and heat transfer fluid decreases, which, in turn, leads to a decrease in Q˙ ht. This drop is more pronounced for increasing values of vHTF,in.

Higher inlet velocities reduce the residence time of the heat transfer fluid in the reac- tor. This overcompensates the improved heat transfer so that in total the maximum

HTF outlet temperature decreases with increasing vHTF,in (Fig. 4.10). Futhermore,

30 4.1 Simplified Model for Highly Permeable Packed Beds

(a) vHTF,in = 5 m/s (b) vHTF,in = 15 m/s

Figure 4.7: Temperature profile of the reaction bed for various HTF inlet velocities at t = 60 min

(a) vHTF,in = 5 m/s (b) vHTF,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 su- perimpose 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 dXH conversion rate 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

600

500 [W]

ht 400

· Q

300

200

100

0 0 30 60 90 120 150 180 210 240 270 300 t [min]

v = 5.0 m/s v = 7.5 m/s v = 10.0 m/s v = 12.5 m/s v = 15.0 m/s in in in in in

Figure 4.9: Transferred heat per flow channel over time for various HTF inlet velocities

540

520

500

480

T [°C] 460

440

420

400 0 30 60 90 120 150 180 210 240 270 300 t [min]

v = 5.0 m/s v = 7.5 m/s v = 10.0 m/s v = 12.5 m/s v = 15.0 m/s in in in in 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

0.6

[-] 0.5 H X 0.4

0.3

0.2

0.1

0 0 30 60 90 120 150 180 210 240 270 300 t [min]

v = 5.0 m/s v = 7.5 m/s v = 10.0 m/s v = 12.5 m/s v = 15.0 m/s in in in in 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 tem- perature 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

vHTF,in = 5 m/s vHTF,in = 10 m/s vHTF,in = 15 m/s

n f c [-] 37 19 13

wreactor [m] 0.908 0.476 0.332 3 Vreactor [m ] 0.227 0.119 0.083

Vbed/Vreactor [-] 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

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 t volume. The ratio of operational time to reaction time rp/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 vHTF,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 (m˙ · cp)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 in- let 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 vHTF,in at rated power, volumetric energy density and achieved conversion at

34 4.1 Simplified Model for Highly Permeable Packed Beds

320

] 300 3

280

260 [kWh/m v

u 240

220 0.05 0.04 15.0 0.03 12.5 10.0 0.02 w [m] 7.5 v [m/s] bed 0.01 5.0 in

Figure 4.12: Volumetric energy density at rated power as a function of HTF inlet velo- city and reaction bed width

1.0

0.8

0.6 [-]

rp 0.4 X

0.2

0.0 0.01 0.02 5.0 0.03 7.5 10.0 0.04 w [m] 12.5 v [m/s] bed 0.05 15.0 in

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

250 ] 3 200

150 [kWh/m

100 v,eff u

50 0.01 0.02 5.0 0.03 7.5 10.0 0.04 w [m] 12.5 v [m/s] bed 0.05 15.0 in

Figure 4.14: Effective volumetric energy density at rated power as a function of HTF inlet velocity and reaction bed width

kWh 3 effective volumetric energy density uv,e f f based on CaO ranges between 71 /m 3 and 242 kWh/m , with its peak at wbed = 0.03 m and vHTF,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 phe- nomena 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 · ρg) = −∇(ρ · u ) + S . (4.16) ∂t g g m,g,r

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, ug designates the velocity of the gas, which depends on the bed permeability K, the dynamic viscosity ηg of the gas and the pressure gradient ∇pg. Darcy’s law defines the relation between these quantities for Re < 1 as

K ug = − · ∇pg. (4.17) ηg

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

∂T (c · ρ) · bed = −c · ρ · ∇T · u − ∇ · (−λ · ∇T ) + Q˙ , (4.19) p bed ∂t p,g g bed g bed bed r where Darcy’s law, eq. (4.17), is used to obtain the velocity ug 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 7, 9, 10 5 pg,in = 10 Pa 8

Initial Condition

pg,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

2 3 dp · ε K = , (4.20) 180 · (1 − ε)2 where dp 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 (m˙ · cp)HTF and, thereafter, the changes in conversion after 15 min are determined (Fig. 4.15). For

0.16

0.14

0.12

0.1 Limited Limited 0.08 gas heat transport transfer @ 15 min [-] 0.06 H X

0.04

0.02

0 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 10 10 10 10 10 10 10 10 10 10 K [m2] d = 5µm,  = 0.8 d = 10µm,  = 0.8 p p

Figure 4.15: Conversion after 15 min versus bed permeability; wbed = 0.02 m, 5 vHTF,in = 10 m/s, pg,init = 5691 Pa, pg,in = 10 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 −14 2 −10 2 dp ≤ 375 nm. Increasing conversion in the interval 10 m < K < 10 m indicates that the limitation in gas transport decreases with increasing permeability. −10 2 The increase in XH levels out and remains constant at around 0.1560 for K ≥ 10 m . 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 dp ≥ 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 dp = 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 dXH of the highest gradients 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 dp = 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 pg 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 4.2 Extended Model for Poorly Permeable Beds

540 540

520 520

500 500

480 480

460 460 T [°C] T [°C] 440 440

420 420

400 400 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 h [m] h [m] T T T T T T eq bed htf eq bed htf (a) t = 1 min (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 (m˙ · cp)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 maxi- mum 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

450

440 T [°C] 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 confi- guration 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 pg 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 Q˙ ht 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 (m˙ · cp)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 Figure 4.19: Temperature profile across the reaction bed across the reaction bed in countercurrent flow in countercurrent flow at various times 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 pg,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 fin- dings 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 t 49 of Xrp and rp/t95% are with 0.2293 and /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 parame- ters

vHTF,in = 5 m/s; vHTF,in = 5 m/s; vHTF,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 3 Vreactor [m ] 0.132 0.322 0.188

Vbed/Vreactor [-] 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

energy density at rated power of 71 kWh/m3, the system is in the range of conven- tional 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 t Xrp and rp/t95%. These values are the higher, the lower vHTF,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 vHTF,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 vHTF,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 t increase the ratio rp/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

500

480

T [°C] 460

440

420

400 0 60 120 180 240 300 360 420 480 540 600 660 t [min]

v = 5.0 m/s; h = 0.01 m v = 5.0 m/s; h = 0.03 m v = 1.0 m/s; h = 0.01 m in bed in bed in bed

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%.

t Besides the value of rp/t95%, the lower heat capacity rate (m˙ · cp)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 Q˙ ht, 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 t power plants, the required high values for uv, rp/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

250

200 [W] ht 150 · Q

100

50

0 0 60 120 180 240 300 360 420 480 540 600 660 t [min]

v = 5.0 m/s; h = 0.01 m v = 5.0 m/s; h = 0.03 m v = 1.0 m/s; h = 0.01 m in bed in bed in bed

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 para- meters

vHTF,in = 5 m/s; vHTF,in = 5 m/s; vHTF,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 3 Vreactor [m ] 0.119 0.298 0.560

Vbed/Vreactor [-] 0.7143 0.8824 0.7143

mCaO [kg] 57.29 171.87 269.60 E [kWh] 28.24 84.71 132.88

uv [kWh/m3] 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

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 in- direct 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 parame- ters were carried out in order to identify limiting factors with regard to the reactor performance. From these studies, knowledge about the characteristics of the iden- tified 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 (m˙ · cp)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 appli- cations 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

ANXIONNAZ,Z.,CABASSUD,M.,GOURDON,C.,TOCHON, P., 2008. Heat exchan- ger/reactors (HEX reactors): Concepts, technologies: State-of-the-art. Chemical Engineering and Processing: Process Intensification, 47(12), pp.2029–2050.

BARIN,I. AND PLATZKI, G., 1995. Thermochemical data of pure substances. 3rd ed. Weinheim: VCH.

BAUMANN, T. AND LUCHT, G., 2011. Discussion on the gap width of plate heat exchangers. [conversation] (Personal communication, 19 April 2011).

BAYÓN,R.,ROJAS,E.,VALENZUELA,L.,ZARZA,E.,LEÓN, 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.

GIL,A.,MEDRANO,M.,MARTORELL,I.,LÁZARO,A.,DOLADO, P., ZALBA,B., CABEZA, 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.

GNIELINKSI, 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.

HERRMANN,U. AND KEARNEY, D.W., 2002. Survey of thermal energy storage for parabolic trough power plants. Journal of Solar Energy Engineering, 124(2), pp.145–152.

HOSHI,A.,MILLS,D.R.,BITTAR,A.,SAITOH, 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.

INTERNATIONAL ENERGY AGENCY, 2009. World Energy Outlook 2009. Paris: Orga- nisation for Economic Co-operation and Development / International Energy Agency.

50 5 Conclusion & Prospects

LAING,D.,STEINMANN, W.-D., TAMME,R.,RICHTER, C., 2006. Solid media thermal storage for parabolic trough power plants. Solar Energy, 80(10), pp.1283–1289.

LAING,D.,STEINMANN, W.-D., VIEBAHN, P., GRÄTER, F., BAHL, C., 2010. Eco- nomic analysis and life cycle assessment of concrete thermal energy storage for parabolic trough power plants. Journal of Solar Energy Engineering, 132(4), p.041013.

LAING,D.,BAHL,C.,BAUER, T., LEHMANN,D.,STEINMANN, W.-D., 2011. Thermal energy storage for direct steam generation. Solar Energy, 85(4), pp.627–633.

LINDER, M., 2011. Discussion on reaction bed properties. [conversation] (Personal communication, 5 April 2011).

MEDRANO,M.,GIL,A.,MARTORELL,I.,POTAU,X.,CABEZA, 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.

MICHELS,H. AND PITZ-PAAL, R., 2007. Cascaded latent heat storage for parabolic trough solar power plants. Solar Energy, 81(6), pp.829–837.

ROYAL DUTCH SHELL, 2008. Sustainability Report 2008. [online] Available at: www. shell.com/annualreport [Accessed 18 August 2011].

SCHAUBE, F., 2011. Discussion on average particle diameter of calcium odxide and hydroxide. [conversation] (Personal communication, 15 May 2011).

SCHAUBE, F., (in press) Untersuchungen zur Nutzung des CaO/Ca(OH)2-Reaktionssystems für die thermochemische Wärmespeicherung. Ph.D. thesis, University of Stuttgart.

SOLAR MILLENNIUM 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].

STEINMANN, W.-D., LAING,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.

TRIEB, F., SCHILLINGS,C.,O’SULLIVAN,M.,PREGGER, T., HOYER-KLICK, C., 2009. Global potential of concentrating solar power. 15th SolarPaces Conference. Berlin, Germany 15–18 September 2009.

UTZ, I., 2011. Discussion on heat transfer in packed beds. [conversation] (Personal communication, 7 April 2011).

WENTWORTH, W. E., CHEN, 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 H2O

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 H2O

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 Cp 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 vHTF,in = 5.0 m/s

vHTF,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

Q˙ ht,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 3 Vf c [m ] 0.037 0.037 0.037 0.037 0.037 3 Vbed [m ] 0.095 0.190 0.285 0.380 0.475 3 Vreactor [m ] 0.132 0.227 0.322 0.417 0.512

Vbed/Vreactor [-] 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

uv [kWh/m3] 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

55 Appendix B

Table B.2: Reactor data for vHTF,in = 7.5 m/s

vHTF,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

Q˙ ht,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 3 Vf c [m ] 0.025 0.025 0.025 0.025 0.025 3 Vbed [m ] 0.065 0.130 0.195 0.260 0.325 3 Vreactor [m ] 0.090 0.155 0.220 0.285 0.350

Vbed/Vreactor [-] 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 [kW/m3] 113.16 65.61 46.37 35.80 29.20

Xrp [-] 0.7897 0.7730 0.7355 0.6962 0.6531

56 Appendix B

Table B.3: Reactor data for vHTF,in = 10.0 m/s

vHTF,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

Q˙ ht,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 3 Vf c [m ] 0.019 0.019 0.019 0.019 0.019 3 Vbed [m ] 0.050 0.100 0.150 0.200 0.250 3 Vreactor [m ] 0.069 0.119 0.169 0.219 0.269

Vbed/Vreactor [-] 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 [kW/m3] 150.09 86.98 61.33 47.30 38.50

Xrp [-] 0.7224 0.6949 0.6462 0.5802 0.4815

57 Appendix B

Table B.4: Reactor data for vHTF,in = 12.5 m/s

vHTF,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

Q˙ ht,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 3 Vf c [m ] 0.015 0.015 0.015 0.015 0.015 3 Vbed [m ] 0.040 0.080 0.120 0.160 0.200 3 Vreactor [m ] 0.055 0.095 0.135 0.175 0.215

Vbed/Vreactor [-] 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 [kW/m3] 185.96 107.88 75.79 58.41 47.54

Xrp [-] 0.6545 0.6134 0.5119 0.4031 0.3351

58 Appendix B

Table B.5: Reactor data for vHTF,in = 15.0 m/s

vHTF,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

Q˙ ht,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 3 Vf c [m ] 0.013 0.013 0.013 0.013 0.013 3 Vbed [m ] 0.035 0.070 0.105 0.140 0.175 3 Vreactor [m ] 0.048 0.083 0.118 0.153 0.188

Vbed/Vreactor [-] 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 [kW/m3] 222.02 128.40 90.29 69.64 56.67

Xrp [-] 0.5699 0.4703 0.3402 0.2709 0.2293

59