On the Design of a Reactor for High Temperature Heat ...457217/FULLTEXT01.pdf · As storage, a...

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

On the Design of a Reactor for High Temperature Heat Storage by Means

of Reversible Chemical Reactions

Patrick Schmidt

Abstract

This work aims on the investigation of factors influencing the discharge characteristicsof 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 forindirect heat transfer is considered. The storage system was studied theoretically bymeans of finite element analysis of a corresponding mathematical model. Parametricstudies were carried out to determine the influence of reactor design and operationalmode on storage discharge. Analysis showed that heat and gas transport throughthe reaction bed as well as the heat capacity rate of the heat transfer fluid affect thedischarge characteristics to a great extent. To obtain favourable characteristics interms of the fraction of energy which can be extracted at rated power, a reaction frontperpendicular to the flow direction of the heat transfer fluid has to develop. Such afront arises for small bed dimensions in the main direction of heat transport withinthe bed and for low heat capacity rates of the heat transfer fluid. Depending on thedesign parameters, volumetric energy densities of up to 309 kWh/m3 were calculatedfor a storage system with 10 kW rated power output and a temperature increase ofthe heat transfer fluid of 100 K. Given these findings, this study is the basis for thedimensioning and design of a pilot scale heat exchanger reactor and will help toevaluate 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 mein the last couple of months.

First and foremost I want to thank my advisor Marc Linder. The joy and enthusiasmhe has for research was contagious and motivational for me. I appreciate all theeffort, time, and ideas he contributed to support my work. Thanks to his patienceand guidance my time at DLR was a valuable experience. I also owe Inga Utz a debtof gratitude for her advice and patience with which she has helped setting up andmending the modelling part of this thesis. Also, I would like to thank Victoria Martinfor her support at Kungliga Tekniska högskolan in Stockholm.

Thanks goes also to the many people that became a part of my life over the lastmonths. You have made sure that I still had a life besides this thesis. For theenjoyable time spent together I am grateful.

Finally, I want to thank my family for their unconditional support throughout mylife.

iii

Contents

Abstract ii

Ackowledgement iii

List of Figures vi

List of Tables viii

Nomenclature ix

1 Introduction 11.1 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Thermal Energy Storage: State of the Art 32.1 Sensible Heat Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Latent Heat Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.3 Chemical Heat Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3.1 Reversible chemical reactions: thermodynamic considerations 82.3.2 Calcium Hydroxide – Calcium Oxide System . . . . . . . . . . . 112.3.3 Principle of Le Chatelier and Process Control . . . . . . . . . . 13

3 Motivation & Focus 15

4 Plate Heat Exchanger Reactor as Chemical Heat Storage 194.1 Simplified Model for Highly Permeable Packed Beds . . . . . . . . . 19

4.1.1 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . 194.1.2 Boundary & Initial Conditions . . . . . . . . . . . . . . . . . . 224.1.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.2 Extended Model for Poorly Permeable Beds . . . . . . . . . . . . . . . 364.2.1 Extended System of Governing Equations . . . . . . . . . . . . 374.2.2 Boundary & Initial Conditions . . . . . . . . . . . . . . . . . . 384.2.3 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 53A.1 Enthalpy and Entropy of Formation . . . . . . . . . . . . . . . . . . . 53A.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 . . . . . . . 42.2 Schematic of a proposed storage concept for direct steam generation 52.3 Typical T,h-diagram of a pure substance . . . . . . . . . . . . . . . . . 62.4 Plot of the van’t Hoff equation for the reversible reaction system of

Ca(OH)2 – CaO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.5 Principle of heat transformation in the system of Ca(OH)2 – CaO . . 14

3.1 Schematic of reactor with direct heat transfer . . . . . . . . . . . . . . 163.2 Schematic of reactor with indirect heat transfer . . . . . . . . . . . . . 163.3 Schematic of a shell and tube heat exchanger reactor . . . . . . . . . . 173.4 Heat transfer coefficient and heat transfer area over inner diameter for

pipe flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.5 Schematic of a plate heat exchanger reactor for energy storage . . . . 18

4.1 Schematic of the implemented geometric model with correspondingboundaries and domains . . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.2 Temperature profile of the reaction bed for various bed dimensions att = 30 min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.3 Conversion profile of the reaction bed for various bed dimensions att = 30 min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.4 Transferred heat per flow channel over time for various reaction beddimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.5 Average HTF outlet temperature over time for various reaction beddimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.6 Averaged conversion over time for various reaction bed dimensions 294.7 Temperature profile of the reaction bed for various HTF inlet velocities

at t = 60 min . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.8 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 inletvelocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 . . . 334.12 Volumetric energy density at rated power as a function of HTF inlet

velocity and reaction bed width . . . . . . . . . . . . . . . . . . . . . . 354.13 Conversion at rated power as a function of HTF inlet velocity and

reaction bed width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.14 Effective volumetric energy density at rated power as a function of

HTF inlet velocity and reaction bed width . . . . . . . . . . . . . . . . 364.15 Conversion after 15 min versus bed permeability . . . . . . . . . . . . 394.16 Characteristic temperatures along the boundary of reaction bed and

flow channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.17 Average HTF outlet temperature over time for countercurrent flow

configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.18 Conversion profile across the reaction bed in countercurrent flow at

various times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.19 Temperature profile across the reaction bed in countercurrent flow at

various times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.20 Schematic of a horizontal reaction bed . . . . . . . . . . . . . . . . . . 444.21 Average HTF outlet temperature over time for various design parame-

ters of a horizontal reaction bed . . . . . . . . . . . . . . . . . . . . . . 464.22 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 energystorage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4.1 Boundary conditions of the simplified model . . . . . . . . . . . . . . 254.2 Initial conditions of the simplified model . . . . . . . . . . . . . . . . 254.3 Reactor key data for various reaction bed dimensions . . . . . . . . . 304.4 Reactor key data for various HTF inlet velocities . . . . . . . . . . . . 334.5 Additional boundary & initial conditions for the extended model . . 384.6 Key data of a reactor with vertical reaction bed for various design

parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.7 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]

∆rH 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]

SQ Heat source/sink [W/m3]

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 dependcritically on reliable, affordable energy. It drives industrial productionand the information economy. Access to it is also vital for lifting peopleout of poverty.

This quote from Royal Dutch Shell (2008) emphasizes the importance of energy fortoday’s world. Modern lifestyle is highly dependent on the various forms of energy:transportation demands liquid fuels, recent means of communication need electricalpower, industrial processes require mechanical or thermal energy. Beyond this, accessto affordable energy also offers the possibility to reduce and ultimately overcomepoverty. 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 energydemand. The International Energy Agency (2009, p.76) projects the world’s primaryenergy demand to rise by 40 % between 2007 and 2030. This increase is caused byrising 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 projectedincrease. 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 sucha 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 perdefinition, their potential to cover a substantial amount of the world’s energy demandis 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 ismainly due to their higher levelised cost of energy and the intermittent availability.Both factors lead to a lower competitiveness compared to conventional means ofenergy supply. With technology improvements, mass production, economies of scale,and improved operation and maintenance future cost of energy from renewablesources will be reduced. To increase the dispatchability, large scale energy storagesystems are required. However, the development of such systems, regardless of itstype, is still in an early stage and comprehensive research is needed. The Institute ofTechnical Thermodynamics at the German Aerospace Center in Stuttgart contributesto the research on sensible, latent, and chemical heat storage systems for power plantapplications 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 storagesystems. Different principles of heat storage and their thermodynamic basicsare 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 areactor for chemical heat storage is discussed in chapter 4. Moreover, the resultsof 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 issuggested 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, latentheat of fusion, and in form of reaction enthalpy in reversible chemical reactions. Theformer two alternatives are already in use in various technical applications whereasthe latter type of heat storage is still under development. This chapter will shortlydiscuss the basic principles of the different heat storage concepts. Furthermore, abrief 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 inturn can be released by lowering its temperature. The amount of energy that can bestored in this way depends on the temperature increase ∆T, the specific heat capacitycp 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, thevolumetric 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 rangethey 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-typeparabolic trough power plants, oils and molten salts are feasible liquid storage media.Synthetic oils pose some potential due to favourable volumetric storage capacitiesbut may be classified hazardous. By comparison, silicone oils are non-hazardous atonly slightly lower storage capacities. Common for both kinds of oils is the rather

3


low thermal conductivity and their high specific costs (Herrmann and Kearney, 2002).As oils decompose at temperatures of around 400 ◦C, they are not applicable for solarpower tower plants.

Even though some molten salts can be aggressive and corrosive, they show benefi-cial properties for the use as storage media. Gil et al. (2010) see them as an efficient,low cost medium with operating parameters that match those of modern steam tur-bines. The specific storage capacity of nitrate salts is higher than that of oils at lowerspecific costs (Herrmann and Kearney, 2002). In addition, experience in handlingmolten salts has already been gained in chemical and metal industries. Andasol-typesolar thermal power plants incorporate a indirect two-tank thermal energy storagesystem to store heat equivalent to 7.5 h of nominal operation (Fig. 2.1). The system

12

The first parabolic trough power plants in Europe – the world’s largest solar power plants: Andasol 1 to 3

Water availability

The power plant’s site is unique in Spain for itscomparatively above-average water availability.The Sierra Nevada mountain range which sur-rounds the site is the primary source. The Andasolpower plant’s annual water needs are aboutequal to the water which would be needed for thecultivation of crops such as wheat on the powerplant’s site. The plant requires about 870,000 m2

of water per year, which is mainly used for cool-ing the steam circuit, i.e. from the vaporization ofwater in the cooling towers. The water needs areprimarily met with ground water extracted fromwells on the site.

Technical description

In parabolic trough power plants, trough-shapedmirrors in the solar field concentrate the sunsrays by a factor of 80 onto an absorption pipe inthe focal line of the collector. In the pipes, a heattransfer fluid circulates in a closed circuit which isheated to 400 degrees Celsius by the concentratedsolar radiation. The heated fluid is then pumpedinto a centrally located power block and flowsthrough a heat exchanger. In this way, steam isgenerated which (similar to conventional powerplants) powers the turbine using an electricgenerator. The integration of a heat storage allowsthe power plant to function at full capacity bothon overcast days and at night. The Andasol powerplants each consist of a solar field, a thermalstorage tank, and a conventional power plantsection.

Solar field transforms solar radiation into heat energy

An Andasol power plant has a solar field thatcovers 510,120 square meters. The parabolictroughs are set up in 312 collector rows which areconnected by pipes. The rows are set up on anorth-south axis and follow the course of the sunfrom east to west. One row is made up of twocollector units. Every collector unit has its ownsolar sensors and hydraulic drives, which allowthe mirrors to track the position of the sun. Thecollector units each have 12 collectors, which are12 m long and 6 m wide. Every collector has 28mirrors and 3 absorption pipes. An Andasol powerplant requires 7,488 collectors. Specialists assembleand check these collectors photogrammetricallyto determine their precision in specially-con-structed factory buildings before the collectorsare brought to the field and anchored.

1. Solar field, 2. Storage, 3. Heat exchanger, 4. Steam turbine and generator, 5. Condenser

23

4

5

1

Efficiency

Solar field

Peak efficiency ca. 70%

Annual average ca. 50%

Turbine circuit



Entire plant



Figure 2.1: Schematic of an Andasol-type solar thermal power plant (Solar MillenniumAG, 2008)

is based on a binary salt mixture consisting of 60 % sodium nitrate (NaNO3) and40 % 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 otherwhile 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’sbenchmark for parabolic trough solar power plants. In order to use molten salt at ahigher temperature level, it has to be used as heat transfer medium as well since heat

4


transfer oils decompose above 400 ◦C. Efforts are being made to develop new salts orsalt mixtures, which will be applicable and favourable as heat transfer and storagemedium 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 lowercosts per kWh/m3. Herrmann and Kearney (2002) contemplated a variety of solidmaterials for sensible heat storage but concluded that reinforced concrete and NaClare the most favourable. Laing et al. (2006) considered and analysed two compositesas storage material: high temperature concrete and a castable ceramic. In general,both materials are feasible for sensible heat storage. Nonetheless, concrete seems tobe more favourable due to lower specific costs, higher strength of material and easierhandling even though the castable ceramic shows better thermo-physical properties.For both materials, storage units with embedded tubular heat exchangers were testedat Plataforma Solar de Almería and reached temperatures up to 325 ◦C. Duringtesting, high power levels were obtained and high temperature differences betweenheat transfer fluid and storage have been handled without any problems. After 60charge/discharge cycles no degradation of heat transfer was observed. Regardingintegration of the storage system, modular operation concepts have been evaluatedand seem to be economically beneficial. In addition, environmental impact of aAndasol-type solar power plant could be reduced by 7 %, considering 1 kWh supplyto 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 fordirect steam generation (Fig. 2.2). In that case, the modules are used to preheat water

with the embedded aggregates. The stability of the cementpaste has a decisive impact on the concrete strength. Masslosses of the aggregates and the concrete depending on thetemperature profile were examined. The oven tests lastedfor several thousand hours. Results show that the massof the aggregate and concrete samples stabilizes at500 �C. Mass losses were from 1.5 to 3.5 wt.% for theaggregates and about 5.3 wt.% for the concrete samples.The dominating mechanism of the mass loss is evaporablewater in the concrete. Also, the impact of temperature onthe strength of the concrete was tested. Detailed resultsof material investigations related to the thermal stabilityof concrete up to 500 �C are presented in Laing et al. (inpress). Overall, oven experiments and strength measure-ments up to 500 �C show that mass loss and strength valuesof the concrete stabilize after a period of time and a num-ber of thermal cycles. Hence, the utilization of high-tem-perature concrete as sensible heat storage up to 500 �Cseems feasible.

3. Pilot-scale storage combining PCM and concrete modules

3.1. Background

In 2008, not only was the laboratory scale NaNO3 PCMtest module described above tested, but also a 20 m3 con-crete storage test module was built in Stuttgart and hasbeen successfully operated up to 400 �C (Laing et al.,2008). These experiences using heating/cooling circuitswith thermal oil as the heat carrier lay the foundation forthe development of the concrete storage technology withthe pressure and temperature conditions as they occur ina DSG power plant with main steam parameters of110 bar/400 �C.

The combined storage system to be tested in autumn2009 has a total storage capacity of approx. 1 MW h andcomprises of a PCM storage module for evaporation ofwater and a concrete storage module for superheatingsteam. A separate concrete module for preheating liquid

water is not installed. Since the superheating step is morechallenging, the project resources for concrete storage wereallocated completely to a superheating module. This mod-ule is also suitable for preheating. The test-loop beinginstalled for this purpose at the power plant Litoral ofEndesa in Carboneras, Spain, is described in more detailin Eck et al. (2009).

3.2. Storage technology for preheating water and for

superheating steam

3.2.1. Concept and design of the concrete storage test module

The design parameters for the test module are:

� Heat transfer fluid: water/steam.� Maximum internal pressure: 128 bar.� Temperature: up to 400 �C.

The concrete storage module is principally composed ofa tube register and storage concrete. The tube register isused for transporting and distributing the heat transfermedium while sustaining the fluid pressure; the storageconcrete stores the thermal energy as sensible heat. A dura-ble and safe construction is achieved by this division of thefunctions.

A special focus was set on the mismatch of the thermalexpansion between concrete and tubing. In previous labtests, the coefficients of thermal expansion of the concreteand the tubes were determined. In a temperature range of100–350 �C, the values were estimated with aT = 0.90–1.20 � 10�5 K�1 for concrete and aT = 1.35–1.50 �10�5 K�1 for tubing. Without additional measures, thismismatch would lead to longitudinal and radial stressesin the tubing as well as in the concrete. To limit the stressesto an acceptable level, a special interface material wasinstalled. This special material reduces the friction betweentubing and concrete and is compressible to allow a slightdeformation to reduce the stresses without reduction ofthermal transmission.

from solarfield

to power block

from power block

to solar field

sensible heat storage unit:preheating / cooling of

condensate

latent heat storage unit: evaporation / condensation

sensible heat storage unit:superheating / cooling of steam

steamdrum

A

BB

CC

DD

Capital letters designate inlet / outlet ofA Preheating unit, feed waterB Evaporation / condensation unit, liquid waterC Evaporation / condensation unit, steamD Superheating unit, live steam

Fig. 2. Overview of a three-part thermal energy storage system for DSG combining sensible and latent heat storage.

D. Laing et al. / Solar Energy 85 (2011) 627–633 629

Figure 2.2: Schematic of a proposed storage concept for direct steam generation (Lainget al., 2011)

5

2.2 Latent Heat Storage

and superheat steam.


Besides sensible heat, thermal energy can also be stored as latent heat during phasechange of a substance. Each phase transition leads to changes in enthalpy ∆hpc ofthe respective substance. This enthalpy change is comparatively large whereas thetemperature of the substance remains constant during transition (Fig. 2.3). This cha-

Tem

pera

ture

Enthalpy

SensibleHeatSolid

Heatof

Fusion

SensibleHeat

Liquid

Heatof

Vaporization

SensibleHeatGas

Figure 2.3: Typical T,h-diagram of a pure substance

racteristic can be used to store thermal energy isothermically with a high volumetricenergy density. Despite liquid–gas transition causing the highest enthalpy change,solid–liquid phase change is the most suitable for technical applications due to theconsiderably lower volume change between these two phases.

In contrast to sensible heat storage, material selection is more difficult for systemsbased on latent heat as the melting temperature of the material has to match theoperational temperature of the associated process. Hoshi et al. (2005) screened highmelting point phase change materials (PCM) for a possible use in solar thermal powerplants. Their material selection is primarily based on a trade-off between meltingtemperature, theoretical storage capacity, specific costs, and thermal conductivity.

6


While storage capacity and specific costs are important from an economic point ofview, thermal conductivity of the considered material is vital for the performanceof the storage system. The authors conclude that sodium nitrate (NaNO3) would besuitable for medium temperature systems, e.g. Compact Linear Fresnel Reflector orparabolic trough, and sodium carbonate (N2CO3) for high temperature applicationsoperating with Brayton cycle turbines. Furthermore, heat transfer design is moredifficult for latent heat storage systems due to the low thermal conductivity of phasechange materials, which is in accordance with Herrmann and Kearney (2002) andMichels and Pitz-Paal (2007). To overcome this issue, a so-called sandwich concepthas 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 numberof heat exchanger tubes embedded in the phase change material and is thereforemore cost-effective. After the concept has been proven through lab-scale testing, aprototype storage for direct steam generation using the eutectic mixture of KNO3–NaNO3 was designed. The prototype has been tested under real conditions at thePlataforma Solar de Almería, where some problems with the design, such as deficientinsulation, inefficient storage/supply of thermal energy due to excess PCM mass,and uneven steam production, have been observed (Bayón et al., 2010). Despite theseproblems, basic functionality and feasibility were proven. Since the eutectic mixtureof KNO3–NaNO3 already melts at 221 ◦C, Laing et al. (2011) developed a pilot-scalestorage based on NaNO3 with a capacity of about 680 kWh. Pure sodium nitratemelts at a temperature of 306 ◦C and is, therefore, suitable for a live steam pressureof around 100 bar. This latent heat storage is part of a modular system proposedfor direct steam generation and will provide/absorb the energy needed/releasedduring the phase transition of water (Fig. 2.2). An approach to utilize the high storagecapacity of PCMs with sensible heat transfer media in an exergy efficient way isproposed by Michels and Pitz-Paal (2007). They suggest to cascade phase changematerials with different melting temperatures in order to meet the characteristicof the heat transfer fluid. Advantageous would be the more uniform temperaturedistribution, which leads to higher charge/discharge rates, and the higher portion ofPCM undergoing a phase transition. On the other hand, material selection becomeseven more difficult.

7

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 substanceor fluid is low. Especially for electrical power generation this leads to large storagevolumes 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 inform of reaction enthalpy using reversible chemical reactions. While the endothermicforward reaction proceeds, energy is absorbed and stored as chemical potential. Thispotential is used to release energy during the exothermic backward reaction. As thereis a huge variety of reversible reactions, basic thermodynamic considerations areused to establish criteria that help in the selection of possible reaction systems forhigh temperature thermal energy storage.

2.3.1 Reversible chemical reactions: thermodynamic considerations

To determine whether a reversible reaction might be suitable for thermal energystorage, the state of equilibrium has to be evaluated. The equilibrium constant Kprovides information about which side of the reaction is favoured. It is definedas the ratio of forward reaction rate to backward reaction rate. In case K > 1, theforward 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 giventemperature. This relation is given as

∆rG = ∆rHθ − T · ∆rSθ + R · T · ln(K), (2.2)

where ∆rHθ represents changes in standard enthalpy of reaction, ∆rSθ changes instandard entropy of reaction, and R is the gas constant. In general, changes in Gibbsfree energy can be seen as the potential amount of energy which can be extracted froma closed thermodynamic system at a given temperature and pressure. In chemicalequilibrium, ∆rG must be zero as the driving force of the reaction vanishes sinceforward and backward reaction rate are equal. Under this condition, eq. (2.2) results

8


in

∆rH(pθ,Teq)− Teq · ∆rS(pθ,Teq) + R · Teq · ln(Keq) = 0, (2.3)

which determines all reaction parameters for the state of equilibrium. CalculatingTeq from eq. (2.3) might be rather difficult. A viable simplification was proposed byWentworth and Chen (1976). They neglected the temperature dependency of ∆rHand ∆rS and assumed that the activity of all reactants and products is equal to one,which results in K = 1. These considerations lead to

Teq =∆rHθ

∆rSθ, (2.4)

which can be used to roughly estimate the equilibrium temperature of a reversiblereaction. 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 reactionproceeds, see chapter 2.3.3. For storage systems to be economical, it is necessary thatthey have a large specific storage capacity. In terms of thermo-chemical storage, thismeans that a reaction must absorb large amounts of energy ∆rHθ. To assure thatTeq is within practical limits, ∆rSθ has to be correspondingly high. Reactions whichshow high changes in entropy and are suitable for high temperature applicationsare primarily dissociation reactions in which reactants and products are present inheterogenous phases. Formally, reactions of this kind can be written as

AB (s,l) + ∆rH ⇀↽ 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 canbe separated easily in order to prevent backward reaction. As soon as A and Bare brought together again, the exothermic backward reaction takes place and thechemically 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


• 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 exergylosses

• 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 ofa reaction and its technical implementation have to be made.

Over the past decades, numerous reaction systems have been investigated andproposed for solar thermal energy storage. Wentworth and Chen (1976) evaluateddissociation reactions based on hydroxides, carbonates, sulfates, and oxides of Group1 and 2 elements. They found that within the Groups, ∆rS remains approximatelyconstant for the respective class of compounds. Reason for this is the similarity ofreaction equations within a Group of elements for a given compound class. However,with exception of oxides all investigated compound classes show an increase inenthalpy of reaction ∆rH with increasing atomic number. This means that for similarreactions, higher storage capacities are obtained for systems proceeding at highertemperatures, cf. eq. (2.4). In Table 2.1, further types of reactions that are suitablefor solar thermal energy storage from a thermodynamic point of view are listed.According to Tamme (2002), the development status of most of these reaction typesis at the level of studies and fundamental investigations. So far, catalytic dissociationof sulfur trioxide (SO3), steam and CO2 reforming, and thermal dehydrogenation ofmetal hydrides are the only reactions for which pilot plants have been installed.

10


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 – 500Catalytic dissociation

2 SO3 ⇀↽ 2 SO2 + O2 500 – 900

Mg(OH)2 ⇀↽ MgO + H2O 250 – 350

Ca(OH)2 ⇀↽ CaO + H2O 450 – 550Dehydration of metal

hydroxidesBa(OH)2 ⇀↽ BaO + H2O 700 – 800

MgCO3 ⇀↽ MgO + CO2 350 – 450Decarboxylation of metalcarbonates CaCO3 ⇀↽ CaO + CO2 850 – 950

2 BaO2 ⇀↽ 2 BaO + O2 750 – 850Thermal deoxygenation ofmetal oxides 4 KO2 ⇀↽ 2 K2O + 3 O2 600 – 800

CH4 + H2O ⇀↽ CO + 3 H2 700 – 1000Reforming processes

CH4 + CO2 ⇀↽ 2 CO + 2 H2 700 – 1000

MgH2 ⇀↽ Mg + H2 200 – 400Thermal dehydrogenationof 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 hydroxidesystem based on calcium shows the highest potential for utilization as heat storagesystems in medium temperature CSP applications. This reaction system has beenthoroughly investigated at DLR in Stuttgart in recent years. Schaube (in press)carried out cycling tests, which showed no significant decrease in maximum reactionyield. In addition, she investigated and quanitified the reaction kinetics of both theformation and decomposition.

The heterogenous gas–solid reaction of the calcium hydoxide and calcium oxidesystem is formulated as

Ca(OH)2 (s) + ∆rH ⇀↽ CaO (s) + H2O (g). (2.6)

Based on data from Barin and Platzki (1995), standard reaction enthalpy accounts

11


for 109.17 kJ/mol. This results in a theoretical volumetric energy density of around365 kWh/m3 based on CaO at a bed porosity of ε = 0.8 and shows that chemicalreactions have a tremendous potential for the storage of thermal energy. Anotherpositive aspect of this reaction system is the fact that water vapour is used as reactiongas. Since steam is often used in industrial processes, a Ca(OH)2 – CaO based energystorage system could readily be integrated. In both industrial and solar thermalapplications, the storage systems would ideally be operated at atmospheric pressurein order to avoid parasitic losses in form of compression work of the reaction gas.Under these conditions, low pressure and high temperature, the gaseous phasebehaves like an ideal gas. Thus, the equilibrium constant can be expressed in termsof the partial pressures of the involved gaseous species:

K = ∏i

(pi

pθ

)νi

=pH2O

pθ. (2.7)

For the considered reaction system, the general expression, middle term in eq. (2.7),reduces to pH2O/pθ as water vapour is the only gaseous species and the respectivestoichiometric coeffient is one, cf. eq. (2.6). Substituting eq. (2.7) in eq. (2.3) results in

ln(

pH2O

pθ

)= −∆rH(pθ,T)

R·

1T+

∆rS(pθ,T)R

. (2.8)

This form of the van’t Hoff equation relates gas pressure and reaction temperature inchemical equilibrium. Plotting the natural logarithm of the gas pressure against theinverse reaction temperature is a convenient way to graphically illustrate the relationgiven in eq. (2.8). In such a plot, the negative change in enthalpy of reaction dividedby the gas constant determines the slope of the curve and thereby the pressure changedue to temperature change. With data taken from the National Insitute of Standardsand Technology (NIST) and Barin and Platzki (1995), eq. (2.8) has been evaluated fortemperatures within a range of 298 K to 1000 K (Appendix A.1). Figure 2.4 shows therelevant interval between 600 K and 900 K. Applying a linear regression model basedon ordinary least squares the full intervall can be approximated by

ln( pH2O

bar

)= −12.72 K ·

1000T

+ 16.03. (2.9)

12


1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.70.001

0.01

0.1

1.0

10ln

(pH

2O [b

ar])

1000/T [1000/K]

Ca(OH)2 (s) CaO (s) + H2O (g)

CaO (s) + H2O (g) Ca(OH)2 (s)

Figure 2.4: Plot of the van’t Hoff equation for the reversible reaction system ofCa(OH)2 – CaO

This equation can be used to calculate the equilibrium pressure pH2O,eq for a giventemperature 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 temperatureshift the equilibirum along the curve in Fig. 2.4. The equilibrium shifts in such away that it counteracts the imposed change according to Le Chatelier’s principle. Anincrease in pressure at a given temperature causes the exothermic hydration reactionto proceed until the corresponding equilibrium temperature is reached and viceversa. A similar shift in equilibrium occurs with temperature changes. Endothermicdehydration of calcium hydroxide will counterbalance a temperature increase atgiven gas pressure whereas a temperature decrease is counteracted by the exothermichydration of calcium oxide. Considering the principle of Le Chatelier, Fig. 2.4 canbe 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


the region above. This indicates conditions under which the storage system can becharged or discharged from a chemical point of view. Only for temperatures aboveequilibrium temperature, storage can be charged at a given pressure. The sameapplies analogously to the discharge.

Additionally, the relation between gas pressure and temperature can be usedto transform heat from one temperature level to another, similar to heat pumps.Lowering the pressure during charging, thermal energy at a lower temperature levelcan 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 placeat a pressure level higher than the charging pressure level. For the Ca(OH)2 – CaOsystem a temperature difference of around 100 K can theoretically be obtained byincreasing the vapour pressure from 0.1 bar to 1.0 bar during charge and discharge,respectively (Fig. 2.5).

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.70.001

0.01

0.1

1.0

10

ln (p

H2O

[bar

])

1000/T [1000/K]

pH2O

T

↑

↓

↗

←− −→

↙

Qout

Qin

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 hasan enormous potential for heat storage applications due to the high amount ofenergy that is absorbed or released during reaction. Further positive aspects ofthis reaction system are the manageable saftey risks and the high availability of thereaction materials. Both, calcium hydroxide and oxide are inexpensive materialsand widely used in various industries. Schaube (in press) showed that both theformation and decomposition reaction is reversible for numerous reaction cycles. Inaddition, reaction kinetics are sufficiently fast to assure reasonable charge/dischargetimes. These promising findings provide the basis for further investigations of theCa(OH)2 – CaO system with focus on a heat exchanger reactor in the lower kilowattrange.

In her work, Schaube (in press) used a reactor with direct heat transfer. In this directcase, a gaseous heat transfer fluid passes, together with the reaction gas, through thereaction bed. Therefore, the heat transfer fluid is in direct contact with the reactionmaterial (Fig. 3.1). This is favourable for the heat input and output since the heattransfer area, which is the surface area of all particles, is very large. Concerning theselection of the heat transfer fluid, inert gases are to be preferred as undesired sidereactions are avoided this way. Although this concept offers advantages regardingthe heat transfer, it is technologically difficult to implement. To assure a constanttemperature level during charge and discharge, the partial pressure of water vapourmust be kept constant during reaction. Admixing and extracting the right amountof water vapour into or out of the heat transfer fluid is difficult, particularly from ametrological and energetic point of view. Another disadvantage of the direct heattransfer concept is the high pressure drop across the reaction bed due to the smallparticle size (dp ≈ 5 µm) of the currently available material, which leads to enormousparasitic losses.

15

3 Motivation & Focus

H2O & Heat transfer fluid

Heat transfer fluid

H2O

Figure 3.1: Schematic of reactor withdirect heat transfer

H2O & Heat transfer fluid

Heat transfer fluid

H2O

Figure 3.2: Schematic of reactor withindirect heat transfer

One way to avoid these drawbacks is to separate the reaction gas from the heattransfer fluid. In this concept only the reaction gas passes directly through the bedwhereas the HTF flows through channels embedded in the reaction bed (Fig. 3.2). Theseparation 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 conductionin the reaction bed becomes an important factor for the thermal performance ofthe storage system. Hence, it is necessary to adapt the reactor design on the heattransport characteristics of the reaction bed. The focus of this work is, therefore,upon the investigation of design parameters and their influence on the thermalperformance of the reactor by means of finite element analysis.

Basically, two types of heat exchangers can be used as a reactor for chemical heatstorage: shell and tube heat exchangers and plate heat exchangers. The first type ofheat exchanger is schematically shown in Fig. 3.3 and can itself be implemented intwo different ways. One configuration is to place the reaction bed inside the tubeswhile the heat transfer fluid passes through the tube bundle in cross flow. Maindrawback of this configuration is the more complex dimensioning and design. Forfinite element analysis of the reactor performance, a three-dimensional mathematicalmodel has to be solved, which is rather time and resource consuming. Interchangingthe position of reaction bed and heat transfer fluid leads to the second possible

16


Figure 3.3: Schematic of a shell andtube heat exchanger reac-tor

Hea

t tra

nsfe

r coe

ffici

ent

Tube diameter

Hea

t tra

nsfe

r are

a

Heat transfer coefficient Heat transfer area

Figure 3.4: Heat transfer coefficientand heat transfer areaover inner diameter forpipe flow

configuration for a shell and tube heat exchanger reactor. In this case, both theheat 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 coefficientand 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 witha charge/discharge power in the lower kilowatt range already. At this point, plateheat exchangers offer clear advantages since they obtain higher volumetric powerdensities (Anxionnaz et al., 2008). Heat transfer coefficient and heat transfer areacan be adjusted indepentently, which results in a maximized heat transfer. A plateheat exchanger integrated into a packed bed chemical reactor could be implementedas shown in Fig. 3.5. In this proposed design, reaction material and heat transferfluid are located alternately between the plates. To attain the highest possible heattransfer coefficient at a given flow rate, the gap on the HTF side should be as smallas possible. In contrast, the reaction–side gap should be as large as possible in orderto maximize the volumetric storage density of the storage system. The heat transferarea can be adapted easily by resizing the plates. In addition to the improved heattransfer characteristics, a plate heat exchanger reactor can be extended more easilycompared to a shell and tube heat exchanger. Based on these considerations a reactorwith 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 reactionkinetics of formation and decomposition of calcium hydroxide are sufficiently fast.

17


Flow channel HTF Reaction bed

λbed

αbed

Qht

λwall

αHTF

λHTF

Figure 3.5: Schematic of a plate heat exchanger reactor for energy storage

Therefore, charging and discharging characterisitcs depend on extrinsic reactionparameters such as heat and mass transfer, which are comparable for both reactiondirections. 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 reactorwith 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 designconcept for a pilot plant heat storage system utilizing commercially availablereaction 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 favourabledesign concept for a chemical heat storage system. The lack of experience designingsuch systems, together with their high complexity, demands an investigation intothe influence of crucial design parameters on the performance of the proposed heatexchanger reactor. For that purpose, the considered system has been simulated usingthe finite element based, commercially available software COMSOL Multiphysics ®.The mathematical model describing the system as well as the obtained simulationresults 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 reducesthe complexity of the system since the reaction is not limited, due to a possible lackof reaction gas. Thus, the influence of design parameters on the thermal performanceof 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. Fromthis consideration follows that only the energy balance is necessary to describe thereaction system. Conservation of energy can be written as

(cp · ρ)bed ·∂Tbed

∂t= −∇ · (−λbed ·∇Tbed) + SQ,r, (4.1)

19


where the left-hand side of the equation accounts for the rate of accumulation ofenergy within the system. This term is characterised by the energy storage capacityof the bed (cp · ρ)bed, which in turn is the sum of storage capacities of the bed’sconstituents:

(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 conversionXH during hydration, the solid density ρs and specific heat capacity cp,s can both beestimated 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 propertiesare 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 Kto 1000 K using linear regression models based on ordinary least squares. With datataken from NIST (Appendix A.2) these models can be written as

cp,CaO = 0.16495 ·J

kg · K2 · Ts + 798.64700 ·J

kg · K(4.5)

and

cp,Ca(OH)2= 0.38612 ·

Jkg · K2 · Ts + 1217.29416 ·

Jkg · K

. (4.6)

Calculating the energy storage capacity at 450 °C according to the equations (4.2)to (4.6), it can be seen that for any value of XH the gaseous phase accounts for lessthan 1 % of the value of (cp · ρ)bed. This phase will therefore not be considered ineq. (4.2) any further. Beyond that, the solid, gas, and bed temperature can be setequal 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 withinthe reaction bed. Analogous to the energy storage capacity, cf. eq. (4.2), the thermal

20


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 anadequate 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 accordancewith (Linder, 2011).

Energy changes due to chemical reaction are represented by SQ,r in eq. (4.1). Thisterm accounts for the amount of energy that is released during the hydration of thesolid material and is estimated as follows:

SQ,r = −(1− ε) · r · ∆rH. (4.8)

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

r =ρs,r

Ms,r·

dXH

dt, (4.9)

where XH accounts for the fraction of solid material which has already been hydrated.Hence, dXH

dt is the rate at which the solid material reacts per time interval. This rate, aswell as the conversion, can be estimated by solving the ordinary differential equation

dXH

dt= (1− XH) · k ·

Tbed − Teq

Teq. (4.10)

As eq. 4.10 shows, the speed at which the solid reactant is hydrated depends on thecurrent state of conversion, the rate constant k, and the temperature difference fromthermal equilibrium. Basically, k is evaluated by means of the Arrhenius equationand is therefore temperature dependent. In this work, however, a representative rateconstant of -0.05 1/s is used in accordance with (reference). In order for the reactionto proceed and to obtain a sufficiently high reaction rate, a temperature differenceTbed − Teq has to be maintained, cf. chapter 2.3.

Due to the low thermal resistance and heat capacity of the separating metal wall

21


between reaction bed and heat transfer fluid, the wall temperature is assumed to beequal to the bed temperature at any point. It is therefore not necessary to considerthe wall energy equation in this model.

Regarding the type of flow of the heat transfer fluid, it can be shown that for thegiven conditions (medium, temperature range, flow channel geometry) the flowremains laminar at all times of this study. Standard COMSOL modules are usedto implement conservation of energy and momentum for laminar flow. Thereby,only the boundary and initial conditions are adjusted to meet the conditions on thereaction side. The necessary interrelation between fluid flow and energy transport isestablished by using the output (uHTF, pHTF, THTF) of each module as input for theother.

Even though only the hydration of calcium oxide is analysed in this work, theabove presented governing equations are in principle valid for the dehydration aswell.

4.1.2 Boundary & Initial Conditions

Finite element analyis is used to solve the system of ordinary and partial differentialequations numerically. Therefore, a corresponding geometry model which representsthe considered HEX reactor is needed. This model is set up in a 2D domain usingsymmetry wherever applicable, in order to minimize the number of elements andreduce the computing time and needed computation resources. Figure 4.1 shows aschematic 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 ofeach flow channel is implemented. In this study, the reactor height is set to 0.5 mwhereas the width of the reaction bed is varied. For the flow channel, a width of2 mm is used as suggested by Baumann and Lucht (2011).

One boundary condition that plays a major role in the investigated system is theheat 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


2 31

8

4

5

6

7

9

10

11

12

13

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

is defined as

qht = −U · (Tbed − THTF), (4.11)

where the overall heat transfer coefficient U itself is given as

1U

=1

αbed+

swallλwall

+1

αHTF. (4.12)

For evaluation of the thermal resistance of the separating wall between reactionbed and heat transfer fluid, a wall thickness swall of 0.001 m and a constant thermalconductivity λwall of 14 W/(m · K) are assumed. Regarding the heat transfer betweenpacked bed and wall, αbed can be assumed with 800 W/(m2 · K) according to Utz (2011).Even though this value is rather conservative, it is not a limiting factor for the overallheat transfer and, hence, sufficiently accurate. For the heat transfer from wall to heattransfer fluid, αHTF is evaluated by applying basic Nusselt number correlations forparallel plates at constant temperature in accordance with Gnielinski (2006). Thereby,αHTF is defined as

αHTF =Num · λHTF

dh, (4.13)

23


where dh, the hydraulic diameter, is twice the width of the gap between the plates.For laminar flow, the Nusselt number in eq. (4.13) can be written as

Num = (Nu31 + Nu3

2 + Nu33)

1/3, (4.14)

with

Nu1 = 7.541, (4.15a)

Nu2 = 1.841 · 3

√Re · Pr ·

dhh f c

, (4.15b)

Nu3 =

(2

1 + 22 · Pr

)1/6

·

(Re · Pr ·

dhh f c

)1/2

. (4.15c)

Equations (4.15a) – (4.15c) represent the Nusselt numbers for different domainsof 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. Alltemperature dependent material properties of the heat transfer fluid, used to de-termine αHTF, are taken from the COMSOL material library at a mean temperatureTHTF,m = 1

2 · (THTF,in + THTF,out).

Whereas the inlet velocity of the heat transfer fluid vHTF,in is varied, the HTFinlet temperature THTF,in and the initial bed temperature Tbed,init are set equal to400 ◦C throughout this study. The remaining boundary conditions as well as initialconditions 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 theproposed reactor that can be chosen freely: flow channel width, width of the reactionbed, and inlet velocity of the heat transfer fluid. Even though a reduction of the gapbetween the plates is favourable for the overall heat tranfser coefficient U, it can not

24


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

pHTF,out = 105 Pa 6, 12

Heat transfer in heat transfer fluid

Symmetry 4, 13

−n · (−λ ·∇T) = 0 6, 12

THTF,in = 400 ◦C 5, 11

qht 7, 10

Heat transfer in reaction bed

−n · (−λ ·∇T) = 0 8, 9

−qht 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

pHTF,init = 105 Pa 1, 3

Heat transfer in heat transfer fluid

THTF,init = THTF,in 1, 3

Heat transfer in reaction bed

Tbed,init = THTF,in 2

25


be reduced arbitrarily due to technical reasons. In accordance with Baumann andLucht (2011) it is, therefore, set to 2 mm. The influence of the remaining parameterson the performance of the proposed heat exchanger reactor has been investigatedwith 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 andthe system has been simulated accordingly with a constant inlet velocity of the heattransfer fluid of 10 m/s. By definition, the maximum thermal resistance Rth of thebed increases with increasing bed width (Rth ∝ wbed). Due to this, heat is sufficientlyremoved from the core region for small reactor geometries whilst the heat transferaway from that region is strongly limited for wider beds. The resulting accumulationof heat (Fig. 4.2b) causes the reaction in the respective parts of the bed to slow downsignificantly (Fig. 4.3b). A reaction front, which moves from the edges to the centreof the bed is the consequence. In contrast, reaction takes place across the entire widthof small beds, with a reaction front perpendicular to HTF flow direction, since heat isremoved sufficiently from the centre (Fig. 4.3a and 4.2a).

Considering that the bed temperature reaches equilibrium temperature in mostparts of the bed, regardless of its width shortly after beginning of the reaction, theobserved average bed temperatures after 30 min suggest a higher rate of decrease ofTbed for smaller beds (Fig. 4.2). Consequently, the temperature difference betweenbed and HTF, which represents the driving force for heat transfer, decreases at a cor-responding rate. Thus, the amount of transferred heat Qht decreases at a significantlyhigher rate for decreasing wbed (Fig. 4.4).

Under the consideration of a constant heat capacity rate (m · cp)HTF follows thatthe temperature difference ∆THTF between inlet and outlet of the HTF is directlyproporational to the transferred heat. Hence, the outlet temperature of the heattransfer fluid decreases during storage discharge with a rate corresponding to Qht,cf. Fig. 4.4 and 4.5.

A measure of the depth of discharge is the conversion XH, which accounts forthe amount CaO that has been hydrated to Ca(OH)2. For smaller beds the drivingforce of the reaction, the temperature difference (Tbed − Teq), is higher than for wider

26


(a) wbed = 0.01 m (b) wbed = 0.05 m

Figure 4.2: Temperature profile of the reaction bed for various bed dimensions att = 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 att = 30 min

beds as the average bed temperature decreases faster. This, in turn, leads to a higherconversion rate dXH

dt (Fig. 4.6). The rapid increase in conversion at the beginningof the reaction indicates sufficient availability of reaction gas due to an assumedhigh bed permeability for the simplified model. Moreover, it can be seen that for agiven ∆THTF the achieved conversion decreases with incresing bed width, cf. Fig. 4.5and 4.6.

27


0 30 60 90 120 150 180 210 240 270 3000

100

200

300

400

500

600

700

Qht

[W]

t [min]

wbed = 0.01 m wbed = 0.02 m wbed = 0.03 m wbed = 0.04 m wbed = 0.05 m

·

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

0 30 60 90 120 150 180 210 240 270 300400

420

440

460

480

500

520

540

T [°

C]

t [min]


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

28


0 30 60 90 120 150 180 210 240 270 3000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

X H [-

]

t [min]


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 reactorwith 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 Qht,rp ata HTF outlet temperature of 500 °C was identified and, thereafter, the number ofneeded flow channels was determined to meet the rated power output. ComparingFig. 4.4 and 4.5, it can be seen that Qht,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 thefraction of bed volume to total volume. This, in turn, leads to a higher volumetricenergy density uv whereas the volumetric power density pv will be lowered drasti-cally. The aforementioned different reaction front characteristics affect the ratio ofoperation time to reaction time trp/t95% and the conversion Xrp, where a reaction frontperpendicular to the HTF flow direction, leads to better results in terms of dischargeperformance. Values for trp/t95% and Xrp drop from 56/85 to 177/491 and from 0.7211 to0.5276 , respectively, by widening the bed from 0.01 m to 0.05 m. This means that aconsiderable part of the energy stored in wide beds can not provide the rated powerof 10 kW at 500 ◦C.

29


Table 4.3: Reactor key data for various reaction bed dimensions

wbed = 0.01 m wbed = 0.02 m wbed = 0.05 m

n f c [-] 19 19 19

wreactor [m] 0.276 0.476 1.076

Vreactor [m3] 0.069 0.119 0.269

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 at0.02 m. Hence, heat transport characteristics of the bed are equal for all investigatedvelocities. Despite the existing limitation in heat transport, which is indicated by theV-shaped temperature profile, it can be seen that heat is removed across the entirebed 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 higherrates more heat is removed from the bed, which, in turn, leads to a more stretchedreaction zone, cf. Fig. 4.8a and 4.8b.

At the beginning of the discharge phase, the heat capacity rate determines theamount of heat transferred from reaction bed to HTF (Fig. 4.9). As heat is removedby the HTF, the average bed temperature decreases during storage discharge. Conse-quently, the temperature difference between reaction bed and heat transfer fluiddecreases, which, in turn, leads to a decrease in Qht. This drop is more pronouncedfor 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 maximumHTF outlet temperature decreases with increasing vHTF,in (Fig. 4.10). Futhermore,

30


(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 att = 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 att = 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 temperaturewith increasing inlet velocity.

Since heat is removed from a larger region of the reaction bed for higher HTFinlet velocities more material is converted, cf. Fig. 4.8a and 4.8b, and, thus, a higherconversion rate dXH

dt is obtained (Fig. 4.11). However, at a given ∆THTF a higherconversion can be reached for low inlet velocities of the heat transfer fluid.

31


0 30 60 90 120 150 180 210 240 270 3000

100

200

300

400

500

600

700

800

900

Qht

[W]

t [min]

vin = 5.0 m/s vin = 7.5 m/s vin = 10.0 m/s vin = 12.5 m/s vin = 15.0 m/s

·

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

0 30 60 90 120 150 180 210 240 270 300400

420

440

460

480

500

520

540

T [°

C]

t [min]


Figure 4.10: Average HTF outlet temperature over time for various HTF inlet velocities

32


0 30 60 90 120 150 180 210 240 270 3000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

X H [-

]

t [min]


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 determinethe 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 andcompared 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

Vreactor [m3] 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


considerably with decreasing inlet velocity due to the higher number of required flowchannels. The ratio between bed volume and reactor volume, however, decreasesonly marginally, which is due to the unequal number of flow channels and reactionbeds in the reactor, see Fig. 3.5. Since this ratio remains practically constant, thevolumetric energy density uv does not change for the investigated velocity range. Incontrast, the volumetric power density pv decreases due to the rise in total reactorvolume. The ratio of operational time to reaction time trp/t95% and the conversion atrated power Xrp are enhanced significantly with decreasing inlet velocity. Underthese conditions, a reaction front perpendicular to the HTF flow direction developsand 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 forchemical heat storage systems, the results of both parametric studies are combinedto estimate the total impact on the performance of the system. Therefore, volumetricenergy density uv and conversion Xrp, which represent key criteria for a packedbed reactor, are plotted against reaction bed width wbed and HTF inlet velocityvHTF,in. As already discussed, the bed width has a strong influence on the volumetricenergy density whereas the inlet velocity of the heat transfer fluid has practically noimpact (Fig. 4.12). For the investigated parameters uv ranges between 239 kWh/m3 and309 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 iscaused by the increasing limitation of heat transport in the bed combined with highheat capacity rates (m · cp)HTF. Under these conditions, the HTF outlet temperaturedrops 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 thanchanges in bed width. The attained conversion at rated power Xrp ranges between0.2293 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 andconversion. Highest uv is obtained at high bed width and inlet velocity whereasXrp 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


5.07.5

10.012.5

15.0

0.01

0.02

0.03

0.04

0.05220

240

260

280

300

320

vin[m/s]w

bed[m]

u v[kWh/m3 ]

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

5.07.5

10.012.5

15.0

0.01

0.02

0.03

0.04

0.05

0.0

0.2

0.4

0.6

0.8

1.0

vin[m/s]w

bed[m]

Xrp[-]

Figure 4.13: Conversion at rated power as a function of HTF inlet velocity and reactionbed width

35

4.2 Extended Model for Poorly Permeable Beds

this point are multiplied. This leads to the effective amount of energy that can beextracted per unit volume for a given thermal power, respectively (Fig. 4.14). The

5.07.5

10.012.5

15.0

0.01

0.02

0.03

0.04

0.05

50

100

150

200

250

vin[m/s]w

bed[m]

uv,eff[kWh/m3 ]

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

effective volumetric energy density uv,e f f based on CaO ranges between 71 kWh/m3

and 242 kWh/m3, with its peak at wbed = 0.03 m and vHTF,in = 5 m/s. Largest changes inuv,e f f can be observed for wide reaction beds, the lowest at low inlet velocities.


After investigating the influence of design parameters on the thermal performanceof a reactor with 10 kW rated power output, the mathematical model is extendedto incorporate the transport of reaction gas through the reaction bed. With thisextension, effects of gas transport on the design and performance of a plate heatexchanger reactor for heat storage can be investigated.

36


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 toinclude the conservation of mass in the system of governing equations. Regardingthe gas density, mass conservation can be written as

∂(ε · ρg)

∂t= −∇(ρg · ug) + Sm,g,r. (4.16)

Similar to the conservation of energy in the reaction bed, cf. eq. (4.1), the left-handside of eq. (4.16) represents the rate of accumulation of mass with respect to the voidfraction of the bed.

The first term on the right-hand side describes changes in mass per unit volumeper time interval due to gas transport. In this term, ug designates the velocity ofthe gas, which depends on the bed permeability K, the dynamic viscosity ηg of thegas and the pressure gradient ∇pg. Darcy’s law defines the relation between thesequantities for Re < 1 as

ug = − Kηg

·∇pg. (4.17)

Production of reaction gas in terms of mass per unit volume per time interval dueto reaction is incorporated by the second term on the right-hand side of eq. (4.16) andis 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 reactionrate 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 beaccounted for in the conservation of energy. Incorporating this convective energy

37


transport, the extended conservation equation can be written as

(cp · ρ)bed ·∂Tbed

∂t= −cp,g · ρg ·∇Tbed · ug −∇ · (−λbed ·∇Tbed) + Qr, (4.19)

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 boundaryand inital conditions supplementary to those listed in Table 4.1 and 4.2. Theseadditional 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

pg,in = 105 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 thegas inlet compared to the inlet of the heat transfer fluid. Both parameters are variedand 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’spermeability K. Thus, it affects the transport of reaction gas through the reaction bed.

38


According to the Carman-Kozeny equation, K can be written as

K =d2

p · ε3

180 · (1− ε)2 , (4.20)

where dp describes the average particle diameter. To identify the influence of thegas transport on the reaction during storage discharge, the permeability is varied byseveral 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

10-16 10-15 10-14 10-13 10-12 10-11 10-10 10-9 10-8 10-70

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

X H @

15

min

[-]

K [m2]

dp = 5µm, = 0.8 dp = 10µm, = 0.8

Limitedgas

transport

Limitedheat

transfer

Figure 4.15: Conversion after 15 min versus bed permeability; wbed = 0.02 m,vHTF,in = 10 m/s, pg,init = 5691 Pa, pg,in = 105 Pa, ε = 0.8

values of K ≤ 10−14 m2 there is virtually no conversion of reaction material. This isdue to a lack of reaction gas caused by low permeability of the reaction bed. Applyingeq. (4.20) with a porosity of ε = 0.8, this limitation occurs for particle diameters ofdp ≤ 375 nm. Increasing conversion in the interval 10−14 m2 < K < 10−10 m2

indicates that the limitation in gas transport decreases with increasing permeability.The increase in XH levels out and remains constant at around 0.1560 for K ≥ 10−10 m2.In this domain of K the gas transport through the reaction bed is not the limitingfactor anymore. However, reaction is still inhibited due to limited heat transferthrough the reaction bed. Particle diameters of dp ≥ 37.5 µm correspond to this

39


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 correspondingpremeability of 1.778 · 10−12 m2 and the resulting conversion of 0.0887 after 15 minare shown in Fig. 4.15. It can be seen that under these conditions, K is in the domainof the highest gradients dXH

dK . This means that rather small increases in permeabilityenhance the achievable conversion considerably. As the bed porosity (ε = 0.8) canhardly be increased any further, the permeability can only be increased by enlargingthe particle size of the used substances, cf. eq. (4.20). A doubling of the particlediameter 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 severalpositions 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 discussedin chapter 4.1. Initially, the reaction bed is in the state of chemical equilibrium at400 ◦C with a corresponding gas pressure of 5691 Pa. In cocurrent flow, both thereaction gas and heat transfer fluid pass through the reactor from bottom to top. Atthe beginning of storage discharge, the gas pressure pg close to the inlet increasesimmediately. This results in a significant rise in equilibrium temperature Teq and inhydration 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 inwhich 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 theheat transfer fluid, cf. Fig. 4.16a. During its passage through the reactor, the heatedHTF passes the upper part of the reactor, which has a temperature slightly aboveinital temperature. Consequently, the heat flow is reversed so that the reaction bedis heated by the HTF. This effect, combined with a low equilibrium temperature inthis part of the reactor due to limited gas transport, results in conditions that favourdehydration instead of hydration. As there is no calcium hydroxide available fordecomposition, no reaction takes place in regions of the bed where Teq ≤ Tbed. After

40


0 0.1 0.2 0.3 0.4 0.5400

420

440

460

480

500

520

540

T [°

C]

h [m]

Teq Tbed Thtf

(a) t = 1 min

0 0.1 0.2 0.3 0.4 0.5400

420

440

460

480

500

520

540

T [°

C]

h [m]

Teq Tbed Thtf

(b) t = 25 min

Figure 4.16: Characteristic temperatures along the boundary of reaction bed and flowchannel

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 istransferred back to the reaction bed. In the course of the discharge phase, the pressureof reaction gas and with it the equilibrium temperature Teq rise across the reactionbed. The region with conditions favourable for the hydration reaction (Teq > Tbed)

expands towards the upper end of the reactor. At around 25 min the temperaturesare arranged in a way that CaO reacts to Ca(OH)2 and heat is transferred from bed toHTF over the entire height of the reactor (Fig. 4.16b). Thereby, the zone of significantreaction rates has expanded to around 0.25 m. Comparing Fig. 4.5 and 4.16b, it canbe seen that the limited gas transport reduces the maximum HTF outlet temperaturefor a heat capacity rate (m · cp)HTF corresponding to an inlet velocity of 10 m/s byaround 40 K. Lowering the heat capacity rate enhances the outlet temperature, butat the cost of longer reaction times. Considering these discharge characteristics, theconclusion can be drawn that, under the here discussed conditions, the cocurrentflow configuration is unfavourable for technical applications.

Another configuration in which the reaction gas and heat transfer fluid can beintroduced into the reactor is in countercurrent flow. In this setup, the reaction gasinlet is located at the top side of the reactor, whereas the inlet for the heat transferfluid 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


0 30 60 90 120 150 180 210 240 270 300 330 360 390 420 450 480400

410

420

430

440

450

460

470

480

T [°

C]

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 ofa significant drop of around 20 K between 120 min and 160 min for the countercurrentflow 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 halfof the reactor only, cf. Fig. 4.18a. Thereby, the bed temperature decreases towardsthe bottom of the reactor since the reaction gas pressure pg decreases due to limitedgas 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 Qht also reduces to a lower level,which, in turn leads to a considerable drop in HTF outlet temperature within theinterval 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 outlettemperature of the heat transfer fluid (Fig. 4.17). The considerations regarding heatcapacity rate (m · cp)HTF and HTF outlet temperature discussed for cocurrent flowapply for the countercurrent flow configuration as well. Even though the temperaturedrop can be reduced by lowering the heat capacity rate, the thereby significantlyextended reaction time is not acceptable.

42


(a) t = 120 min

(b) t = 140 min

(c) t = 160 min

Figure 4.18: Conversion profileacross the reaction bedin countercurrent flowat various times

(a) t = 120 min

(b) t = 140 min

(c) t = 160 min

Figure 4.19: Temperature profileacross the reaction bedin countercurrent flowat various times

43

4.3 Design Suggestion for a Plate Heat Exchanger Reactor


The results discussed in chapter 4.2.3 show that the gas transport characteristics ofthe reaction bed consisting of commercially available material have adverse effectson the performance of the reactor. Hence, the reactor should be designed in such away that the transport of reaction gas through the bed is not the limiting factor. Thiscan be achieved by horizontal alignment of the reaction bed, where the reaction gasinlet is located on the top side of the bed (Fig. 4.20). Since the passage of reaction gas

Flow channel HTF Reaction bed

Reaction gas inlet

Figure 4.20: Schematic of a horizontal reaction bed

through the bed is reduced to several centimetre, the gas pressure reaches the levelof inlet pressure pg,in almost instantaneously after the beginning of discharge. Inorder to supply the reaction gas from the top side a gap has to be introduced, whichseparates the reaction bed from the adjacent flow channel. In principle, this bringsalong two adverse effects: the bed is cooled from only one side and heat is transferredfrom HTF to reaction gas. However, the heat loss to the reaction gas is limited dueto its low velocity and the reduced cooling of the bed can be counteracted to someextent 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 determinethe parameters for a final design suggestion. Therefore, the identified maxima forvolumetric energy density uv, achieved conversion at rated power Xrp, and effectivevolumetric 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, itbecomes apparent that the investigated configuration with high HTF inlet velocitiyand wide reaction bed is unfavourable for technical applications. Even though thissetting leads to a high volumetric energy density of around 309 kWh/m3, the valuesof Xrp and trp/t95% are with 0.2293 and 49/390 fairly low. With an effective volumetric

44


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;


n f c [-] 37 37 13

wreactor [m] 0.528 1.288 0.752

Vreactor [m3] 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. Incontrast, a low inlet velocity of the heat transfer fluid is beneficial with respect toXrp and trp/t95%. These values are the higher, the lower vHTF,in is chosen. Hence, theconfigurations for the inlet velocity of 5 m/s listed in Table 4.6 are transferred to thehorizontal bed design and analysed regarding reactor performance.

Looking at the HTF outlet temperatures at vHTF,in = 5 m/s, it can be seen that thepeak 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 maximumoutlet 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 reducedto about 56 min for both investigated bed dimensions at vHTF,in = 5 m/s compared to132 min and 376 min, respectively, for the vertical bed. This effect is caused by thelimited heat transport through the reaction bed. Considering the same thickness ofmaterial, the distance of heat transfer is twice as long for the horizontal bed as onlyone flow channel is in contact with the reaction bed, cf. Fig. 3.5 and 4.20. In order toincrease the ratio trp/t95%, it is more effective to decrease the HTF inlet velocity ratherthan the bed height, see chapter 4.1.3. Hence, thermal performance of the reactor is

45


0 60 120 180 240 300 360 420 480 540 600 660400

420

440

460

480

500

520

540

T [°

C]

t [min]

vin = 5.0 m/s; hbed = 0.01 m vin = 5.0 m/s; hbed = 0.03 m vin = 1.0 m/s; hbed = 0.01 m

Figure 4.21: Average HTF outlet temperature over time for various design parametersof a horizontal reaction bed

studied at a lowered inlet velocity of 1 m/s. A bed height of 0.01 m is chosen to ensurea reasonable reaction time t95%.

Besides the value of trp/t95%, the lower heat capacity rate (m · cp)HTF also has apositive effect on the HTF outlet temperature (Fig. 4.21). Drawback of the decreasedheat capacity rate is the significantly reduced transferred heat per flow channel Qht,which can be seen in Fig. 4.22. This results in a considerably increased numberof channels that are required to meet the rated power of 10 kW (Table 4.7). Forstorage applications with constant power output over long periods, e.g., in base loadpower plants, the required high values for uv, trp/t95%, and Xrp may be realized byusing 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 differentcharacteristics, i.e, high power density for only short periods of time. Hence, it has tobe concluded that the design parameters of the HEX reactor depend strongly on thespecifics of the respective heat storage application.

46


0 60 120 180 240 300 360 420 480 540 600 6600

50

100

150

200

250

300

350

Qht

[W]

t [min]

vin = 5.0 m/s; hbed = 0.01 m vin = 5.0 m/s; hbed = 0.03 m vin = 1.0 m/s; hbed = 0.01 m

·

Figure 4.22: Transferred heat per flow channel over time for various design parametersof 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;


n f c [-] 34 34 160

hreactor [m] 0.476 1.156 2.240

Vreactor [m3] 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 heatstorage was investigated. Thereby, the focus was to estimate the influence of designparameters on the reactor performance. The studies were conducted on a theoreticalbasis 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 heatand mass transport through a fixed bed of reaction material. Even though the modelhas not yet been validated, the obtained results can be used to identify correlationsbetween individual parameters of the reactor. Parametric studies on design parame-ters were carried out in order to identify limiting factors with regard to the reactorperformance. From these studies, knowledge about the characteristics of the iden-tified limiting factors as well as the influence of design parameters on the reactorperformance was deduced.

The investigations showed that three limiting factors exist: gas and heat transportthrough the reaction bed, and a limited heat capacity rate. Reason for the limitationin gas transport is the low bed permeability, which results from the small particlediameter of the used reaction material. Since the reaction should proceed at constantreaction gas pressure, sufficient gas transport must be assured. This can be realizedby 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 thelow thermal conductivity of the bed. However, this factor is only limiting at highheat capacity rates of the heat transfer fluid. Under this condition, insufficient heat isprovided, which leads to outlet temperatures well below equilibrium temperatureand a rapid temperature decrease of the HTF over time. Reducing the thermalresistance 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 beddimensions result in lower volumetric energy densities. Depending on operationalparameters, such as HTF inlet velocity, the heat capacity rate of the HTF might beanother limiting factor. This is primarily caused by the use of a gaseous heat transferfluid for the temperature range above 400 ◦C. A limitation of the reactor performancethrough a low heat capacity rate (m · cp)HTF extends the time of reaction and lowersthe volumetric power density. On the other hand, the outlet temperature of the heattransfer 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 mentioningthat the first two depend on the reactor design for a given reaction material, whereasthe latter factor can be influenced by adjusting operational parameters.

With knowledge about the characteristics of the limiting factors, optimal designparameters for a storage reactor can be determined. However, since these parametershave 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 periodof time is required, small bed dimensions and a moderate heat capacity rate arethe parameters of choice. In contrast, a high heat capacity rate at moderate beddimensions is preferred for applications in which high volumetric power densitiesare required. This could be the case for buffer storages that are incorporated inindustrial 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, themodel which was developed in this work needs to be validated in order to allow moreaccurate predictions of the reactor behaviour during charge/discharge. Therefore,the theoretical studies of this work should be complemented by design and testbench constraints. In this context, it could be reasonable to drop the idea of a cubicreactor and use e. g. an ashlar-shaped reactor design. This would offer additionalvapour supply options. Concerning the heat transfer limitation, methods to increasethe effective thermal conductivity of the bed, such as embedded heat conductingstructures, should be studied. And finally, possibilities of increasing the particlediameter by means of material modification to improve the transport of reaction gasis 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. ChemicalEngineering 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 ofthe experimental behaviour of a 100 kWth latent heat storage system for directsteam 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 storagefor power generation. Part 1 – Concepts, materials and modellization. Renewableand Sustainable Energy Reviews, 14(1), pp.31–55.

GNIELINKSI, V., 2006. Wärmeübertragung im konzentrischen Ringspalt und imebenen 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 storagefor 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 meltingpoint phase change materials (PCM) in solar thermal concentrating technologybased 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 EnergyAgency.

50


LAING, D., STEINMANN, W.-D., TAMME, R., RICHTER, C., 2006. Solid media thermalstorage 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 storagefor 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. Thermalenergy storage for direct steam generation. Solar Energy, 85(4), pp.627–633.

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

MEDRANO, M., GIL, A., MARTORELL, I., POTAU, X., CABEZA, L.F., 2010. Stateof 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 parabolictrough 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-Reaktionssystemsfür die thermochemische Wärmespeicherung. Ph.D. thesis, University of Stuttgart.

SOLAR MILLENNIUM AG, 2008. The parabolic trough power plants Andasol 1 to 3. Thelargest 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 forsolar thermal power plants and process heat applications. Journal of Solar EnergyEngineering, 132(2), p.021003.

51

www.shell.com/annualreport

www.shell.com/annualreport

http://www.solarmillennium.de/upload/Download/Technologie/eng/Andasol1-3engl.pdf

http://www.solarmillennium.de/upload/Download/Technologie/eng/Andasol1-3engl.pdf


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] (Personalcommunication, 7 April 2011).

WENTWORTH, W. E., CHEN, E., 1976. Simple thermal decomposition reactions forstorge of solar thermal energy. Solar Energy, 18(3), pp.205–214.

52

APPENDIX AThermophysical Properties of the reactants of the CalciumHydroxide – Calcium Oxide System

A.1 Enthalpy and Entropy of FormationThe values for calcium hydroxide and calcium oxide in Table A.1 and A.2 are takenfrom the National Institute of Standards and Technology, the values for water aretaken 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 pressureTo obtain the specific heat capacity of the listed reactants, the values given in Table A.3have 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 BResults 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

Qht,rp [W] 271.28 271.04 271.79 271.26 271.69

n f c [-] 37 37 37 37 37

wreactor [m] 0.528 0.908 1.288 1.668 2.048

Vf c [m3] 0.037 0.037 0.037 0.037 0.037

Vbed [m3] 0.095 0.190 0.285 0.380 0.475

Vreactor [m3] 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


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

Qht,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

Vf c [m3] 0.025 0.025 0.025 0.025 0.025

Vbed [m3] 0.065 0.130 0.195 0.260 0.325

Vreactor [m3] 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


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

Qht,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

Vf c [m3] 0.019 0.019 0.019 0.019 0.019

Vbed [m3] 0.050 0.100 0.150 0.200 0.250

Vreactor [m3] 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


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

Qht,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

Vf c [m3] 0.015 0.015 0.015 0.015 0.015

Vbed [m3] 0.040 0.080 0.120 0.160 0.200

Vreactor [m3] 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


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

Qht,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

Vf c [m3] 0.013 0.013 0.013 0.013 0.013

Vbed [m3] 0.035 0.070 0.105 0.140 0.175

Vreactor [m3] 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

On the Design of a Reactor for High Temperature Heat ...457217/FULLTEXT01.pdf · As storage, a...

Documents

Transcript of On the Design of a Reactor for High Temperature Heat ...457217/FULLTEXT01.pdf · As storage, a...