Long-term Heat Storage using ThermoChemical Materials
Z. He WET 2007.14
Project Report August 2007 Committee Members prof.dr.ir. A.A. van Steenhoven (TU/e) dr.ir. C.C.M. Rindt (TU/e) dr.ir. R. Schuitema (ECN) dr.ir. V.M. van Essen (ECN) dr.ir. W.G.J. van Helden (ECN) Eindhoven University of Technology Department of Mechanical Engineering Division of Thermo Fluids Engineering Energy Technology Group
Content List of Figures
List of Tables
Abstract
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Chapter 1 Introduction
Chapter 2 Literature Review
2.1. Heat Storage
2.2. ThermoChemical Materials (TCM)
2.3. Reactor System
Chapter 3 Definition of Experiments
3.1. Raw Materials
3.2. Materials Processing
3.3. Materials Characterization
3.4. Experimental Variables
3.5. Result Analysis and Discussion
3.6 Further Approaches
Chapter 4 Concluding Remarks and Project Planning
References
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List of Figures Figure 1 Working principles of thermochemical materials
Figure 2 Crystal structure of MgSO4·H2O showing (a) the bulk unit cell, (b) side
view of the (100) surface along a direction, and (c) side view of the (100)
surface along b direction
Figure 3 SEM images of an epsomite crystal before (a and b) and after (c and d)
dehydration [6]
Figure 4 Schematic diagram of rehydration behavior
Figure 5 Basic TCM store model
Figure 6 System volume for (a) integrated and (b) separate material stores and
reactors
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List of Tables Table 1 Potential TCM candidates for seasonal heat storage
Table 2 Characterization methods for thermochemical materials
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Abstract
This report was written during the preparation phase of the collaborating project between
TU/e (Eindhoven University of Technology) and ECN (Energy research Center of the
Netherlands). The collaborating project, long-term heat storage using thermochemical
materials, is part of a much larger project, WAELS (Woningen Als Energie Leverend
Systeem; houses as energy supplying system), which is coordinated by ECN and financed
by SenterNovem.
Solar energy could provide durable heat for a domestic environment. However, it is most
effective in summer and not in winter when there is a high demand. To accommodate the
difference in time between energy production and energy demand, heat storage is
necessary. The basic idea behind heat storage is to provide a buffer to balance
fluctuations in supply and demand of thermal energy for heating and cooling.
Materials are the key issue for heat storage. There are a large number of materials which
can be used for heat storage. Thermochemical materials have the highest storage capacity
among all storage media. In this report, a literature review related to thermochemical
materials for heat storage is given, which covers the concept of heat storage, the review
of thermochemical materials, and the description on thermochemical reactor system.
Furthermore, the definition of an experiment on thermochemical materials is presented,
and also the concluding remarks and the future work are given.
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Chapter 1 Introduction
Today the spotlight in the world is on the increasing demand for alternative and
renewable energy sources. Solar energy is one of the most important sources, which
could provide durable heat for various applications.
The availability of efficient heat storage technologies is one of the key factors for the
success of several renewable energy technologies. In particular, a high penetration of
solar energy technologies will be hard to realize without the availability of
technologically and economically attractive heat storage systems due to the short- and
long-term variation of the available solar radiation.
The principal gain from heat storage is that heat and cold may be moved in space and
time to allow utilization of thermal energy that would otherwise be lost because it was
available at the wrong place and the wrong time. Thermal energy storage systems
themselves do not save energy. However, energy storage applications for energy
conservation enable the introduction of more efficient, integrated energy systems.
Thermal energy storage can consequently serve at least five different purposes:
1) Energy conservation utilizing new renewable energy sources;
2) Peak shaving both in electric grids and district heating systems;
3) Power conservation by running energy conversion machines, for instance, co-
generating plants and heat pumps, on full (optimal) load instead of part load. This
reduces power demand and increases efficiency;
4) Reduced emissions of greenhouse gases; and
5) Freeing high quality electric energy for industrial value adding purposes.
Generally, thermal systems are characterized by a broad range of parameters, such as
operation temperature and pressure, capacity, power level, and use of different heat
transfer fluids. Consequently, the development of efficient and economic thermal energy
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storage requires the coverage of a broad spectrum of storage techniques and materials as
well as thermal engineering issues, effective heat transfer, and system integration aspects.
Most of the currently available heat storage technologies still suffer from problems such
as excessive investment cost, insufficient energy density, limited efficiency and
reliability. These issues are restricting broad application and market penetration of heat
storage and, therefore, require more R&D efforts to achieve significant improvements in
the above-mentioned areas.
There are three main physical ways for thermal energy storage: sensible heat, phase
change reactions, and thermochemical reactions. Storage based on thermochemical
reactions has much higher thermal capacity than sensible heat. The development and use
of new materials offers great innovation potential in storage technology. New materials
have already demonstrated to have better properties than the previously used silica gel
and zeolite types. Therefore, further research into new materials for effective and
economic heat storage systems plays a significant role.
The aim of the present project is to gain more insight into the physics of compact heat
storage using so-called thermochemical materials. Stored energy densities up to 3 GJ/m3
can be achieved TCM can be used for seasonal heat storage in the built environment to
bridge the gap between solar energy supply in the summer and heat demand in the winter.
The present project is part of a much large project, WAELS (Woningen Als Energie
Leverend Systeem; House As Energy Supplying System), which is coordinated by the
Energy research Center of the Netherlands (ECN), and financed by SenterNovem. The
goal of WAELS is to make the first steps on the route towards an energy neutral built
environment in 2050.
The objectives of the post-doc project are to
Characterize the thermochemical properties of the material candidates for heat
storage;
Demonstrate the working principle of thermochemical materials;
Investigate the mechanisms of heat and mass transfer on molecular, grain, and
component level;
Design a concept of a reactor system for heat storage; and
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Develop a proposal for further research based on the obtained results.
The material investigated is magnesium sulfate hepta hydrate (MgSO4·7H2O), which is
one of the most potential thermochemical materials for solar energy storage. Other
candidates will also be investigated based on the project progress.
In chapter 2, a literature review related to thermochemical materials for heat storage will
be given, which covers the concept of heat storage, the review of thermochemical
materials, and the description on thermochemical reactor system. The definition of the
experiment will be presented in Chapter 3. Chapter 4 summarizes the concluding remarks
and the future work, respectively.
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Chapter 2
Literature Review
2.1. Heat Storage
The present concern about the increasing demand for energy and the high cost of oil and
natural gases has incited researchers to find better ways of using alternative and
renewable energy resources, such as fuel cell, solar cell, pneumatics, and animal manure.
The energy sources normally used for heating and cooling are oil, gas, coal, and
electricity. The energy consumption could be divided for industrial and domestic
applications. However, it is not entirely logical, nor efficient, to burn fossil fuels at
temperatures up to 1000 0C in order to create an indoor climate at 20 to 25 0C.
Furthermore, burning of fossil fuels emits greenhouse gases. Neither is it efficient to use
electric power, a form of highly processed energy, only for resistance heating [1].
Solar collectors could produce durable heat in a domestic environment. However, it is
most effective in summer and not in winter when there is a high demand. To
accommodate the difference in time between energy production and energy demand, heat
storage is necessary. The basic idea behind heat storage is to provide a buffer to balance
fluctuations in supply and demand of thermal energy for heating and cooling. The
demand fluctuates in cycles of 24 hour periods (day and night), intermediate periods (e.g.
one week), and according to seasons (spring, summer, autumn, and winter). Systems for
storing thermal energy should therefore reflect these cycles, with either short term,
medium term, or long term (seasonal) storage capacity.
When a heat storage need occurs, there are three main physical principles to provide a
thermal energy function: sensible heat storage, latent heat storage, and thermochemical
storage [2].
- Sensible heat storage – this is where thermal energy is stored or released as a
result of a change of the temperature of the materials. No change in phase (i.e.
remains as solid, liquid, or gas) is involved and the amount of energy stored is
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dependant on the specific heat capacity of the material, its mass, and the rise in
temperature.
- Latent heat storage – this is where thermal energy is stored and released as a
result in a change in a materials physical state (e.g. liquid to solid and vice versa).
Materials that are used to store latent heat are termed Phase Change Materials
(PCM).
- Thermochemical heat storage – this is when heat is applied to certain materials
and produces a reversible chemical reaction and thermal energy is stored and
released as the bonds are broken and reformed. Thermal energy is stored during
the forward reaction which is endothermic and released during the reverse
reaction which is exothermic. Materials that are used to store thermochemical
heat are termed ThermoChemical Materials (TCM).
2.2. ThermoChemical Materials (TCM)
There are a large number of materials which could be used for thermochemical heat
storage. The most common sensible heat medium is water. The classical example for
phase change materials is sodium sulfate. Thermochemical materials have the highest
storage capacity among all storage media. Solid silica gel has a storage capacity which is
4 times that of water. Some of the materials may even approach the storage density of
biomass.
The basic reaction process for solar energy storage using TCM is:
C (solid) + Q (heat)⇔ A (fluid/gas) +B (solid)
This reaction is considered in thermodynamic equilibrium, where there is no net heat
exchange between the reacting substances. The equilibrium temperature is termed as
turnover temperature. During summer, the solid C decomposes into the fluid or gas A and
the solid B by adding solar heat at a reaction temperature that is higher than the turnover
temperature. Materials A and B are stored separately until winter. In winter, A and B are
mixed to start the reverse reaction at a temperature that is lower than the turnover
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temperature, and the heat is released during the reaction. The schematic diagram of the
reaction process is shown in Figure 1.
The basic demands on TCM for solar heat storage are:
• Reversible reactions as required
• Energy storage density greater than 1-2 GJ/m3
• Reaction temperature 60 ºC-250 ºC
• Cost of the materials (abundance and easy to mine)
• Environmental impact and toxicity of the materials
• Corrosiveness at storage and/or reaction
There criteria are chosen to be as far as possible independent of each other.
Figure 1 Working principles of thermochemical materials
In a survey recently conducted by the Energy research Center of the Netherlands (ECN)
and the University of Utecht [3], a list of potential theromchemical materials for seasonal
storage of solar heat is shown in Table 1.
Among the candidates, magnesium sulfate (MgSO4) possesses the largest realization
potential for heat storage. The only common, naturally occurring members of the
MgSO4·nH2O series on the earth are epsomite (MgSO4·7H2O, 51 wt% water),
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hexahydrite (MgSO4·6H2O, 47 wt% water) and kieserite (MgSO4·H2O, 13 wt% water).
These three salts are believed to be the only members that occur on the earth as
thermodynamically stable minerals [4]. Rare, metastable minerals of the series include
pentahydrite (MgSO4·5H2O, 43 wt% water), starkeyite (MgSO4·4H2O, 37 wt% water),
and sanderite (MgSO4·2H2O, 23 wt% water). Other hydration states (n= 12, 3, 1.25) are
not recognized as minerals but can be synthesized. All of these salts consist of SO4
tetrahedra and Mg(O,H2O)6 octahedra. Some include extra-polyhedral water (water that
is not in octahedral coordination with Mg), see the crystal structure as an illustration
shown in Figure 2.
Table 1 Potential TCM candidates for seasonal heat storage
In 1618 a farmer at Epsom in England attempted to give his cows water, but they refused
to drink it due to its sour/bitter taste. However the farmer noticed that the water seemed
to heal scratches and rashes. The fame of Epsom salts then began to spread. Epsom salt
was originally prepared by boiling down mineral waters at Epsom, England, and later
prepared from sea water. It forms as a precipitation from vapors on limestone cave walls
and on the walls and timbers of deep-shaft mines. In modern times, these salts are
obtained from certain minerals such as epsomite. Magnesium oxide, as mined or
extracted from seawater, acts as the starting point for commercial production of
magnesium sulfate. The magnesium sulfate is produced via the reaction between MgO
and concentrated sulfuric acid on certain prescribed conditions, followed by heat
treatment. Epsomite transforms readily to hexahydrite by loss of extra-polyhedral water;
this transition is reversible and occurs at 50–55% relative humidity (RH) at 298 K and at
lower temperatures as the activity of water diminishes. Kieserite is more stable at lower
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RH and higher temperature; for example, at moderate heating rates in thermogravimetric
analysis the kieserite structure survives to 670 K, compared with 450 K for hexahydrite.
However, kieserite converts to hexahydrite or epsomite as humidity increases, yet these
phases do not easily revert to kieserite on desiccation. Metastability, kinetic effects and
pathway dependence are important factors in the MgSO4·nH2O system.
Figure 2 Crystal structure of MgSO4·H2O showing (a) the bulk unit cell, (b) side view of
the (100) surface along a direction, and (c) side view of the (100) surface along b
direction
Reversible reactions of dehydration and rehydration are well-suited processes for heat
storage using TCM. These reversible reactions take place under non-equilibrium
conditions imposed by a double constraint of temperature and pressure. Such phenomena
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are limited by mass transfer, by heat transfer, and by the chemical kinetics of the reactive
salt.
The concept of grain and porous compact is useful as it makes it possible to define two
characteristic dimensions in the reactive medium: the grain, which is the basic particle
where the reaction takes place, and the porous compact, which is composed of a
combination of the reactive particles with or without the presence of an inert binder [5].
In general, dehydration reactions proceed stepwise through a series of intermediate
reactions involving the decomposition of one phase and the formation of a new one [6]. If
the materials receive the radiated solar energy, the dehydration occurs when the
temperature is higher than the turnover temperature. The main steps of dehydration
include destruction of the reactant structure, water evaporation, and product nucleation
and growth. When the dehydration conditions are maintained, it is observed that crack
formation and propagation occurs due to the fact that strain associated with water
removal is greater than that which can be sustained by the product structure. Figure 3
shows the observed cracks of the dehydration of an epsomite crystal. Cracks provide
channels for water escape. Dehydration results in an overall increase in close packing and
density and reduction in volume.
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Figure 3 SEM images of an epsomite crystal before (a and b) and after (c and d)
dehydration [6]
The dehydration process is mainly limited by the reaction interface. Once a dehydrated
layer is formed on the surface of the grain, the progress of the reaction can be influenced
by the behavior of the dehydrated part of the crystal. Gradually, the reaction interface
moves toward the interior of the crystal [7].
When the anhydride is exposed to water vapor, rehydration reactions occur. Water
molecules are first adsorbed on the accessible surfaces of the grains. When the accessible
crystallites are rehydrated, the process of diffusion along channels to inner lattices
occurs. Vacancies are produced by the jump of water molecules at the interface to
adjacent sites in the lattices. Following the explanation of Mojaradi and Sahimi [8], the
reaction is an annihilation process. The progress of the reaction depends on the rate at
which diffusing water molecules encounter rehydration sites [9]. As one water molecule
diffuses along such a path and encounters the first reaction site, a second molecule
continues along the same path until it encounters the second reaction site and so on. The
distance covered by diffusing water molecules along such a pathway is proportional to
the number of sites encountered. The schematic diagram of rehydration behavior is
shown in Figure 4. The initial rehydration of a superficial layer proceeds rather easily,
while the subsequent bulk rehydration might be somewhat hindered by the presence of
such an outer layer. The rehydration process causes volume expansion of the crystal
structures due to the addition of molecules incorporated into lattices, and the heat is
released through the porous network to the environment.
Figure 4 Schematic diagram of rehydration behavior
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The progress of dehydration and rehydration is dependent on temperature and pressure.
Temperature is a very important factor in controlling physical and chemical reactions.
From the kinetic standpoint, increasing temperature increases the reaction rate
significantly. Thus, the reaction species could contact each other more completely and
effectively [10, 11]. The dehydration process is enhanced at low vapor pressure, while
rehydration process is enhanced at high vapor pressure.
Compared to dehydration, rehydration proceeds slower because of low mobility of water
vacancies in the lattices [12]. The hysteresis behavior between dehydration and
rehydration processes suggests that the rehydration rate of the hydrate is proportional to
t1/4, while the dehydration reaction is proportional to t [9]. To enhance the rehydration, it
must therefore provide the beneficial channels for water molecules moving to reaction
sites through networks, probably associated with grain boundaries and other defects
which can produce pathways of similar dimensions to those of a diffusing water
molecule.
As stated, thermochemical materials are key components for the construction of heat
storage reactor systems. Therefore, the performance of the material candidates is critical
information and has to be known. The literatures [13-22] related to materials
characterization on thermochemical properties were reported. With the state-of-the-art
characterization technologies, thermochemical materials could be investigated, and as a
result, the important results related to heat storage could be achieved. As a summary,
Table 2 gives a comprehensive list of characterization methods for thermochemical
materials.
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Table 2 Characterization methods for thermochemical materials
Facility-Technology Parameter-Behavior
Differential scanning calorimetry (DSC);
Solution calorimetry
Enthalpy of formation; Gibbs free energy;
Entropy; Energy storage density
Thermogravimetry (TG) Thermochemical stability
Thermogravimetry (TG) - Differential
scanning calorimetry (DSC); Sorption
isotherms
Dehydration and Rehydration
Differential scanning calorimetry (DSC) Heat flow rate; Heat capacity
Dilatometry Thermal expansion
Laser flash Thermal diffusivity
X-ray diffraction (XRD) Composition and Phase
Inductively coupled plasma - mass
spectrometer (ICP-MS), Energy dispersive
X-ray analysis (EDX)
Element
X-ray photoelectron spectroscopy (XPS) Valence
Fourier transform infrared spectroscopy
(FTIR) – Raman spectroscopy
Energy bonding
Densimeter Density
Particle sizer Particle size
Scanning electron microscopy (SEM),
Transmission electron microscopy (TEM)
Microstructure
Pressure sensor Vapor pressure
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2.3. Reactor System
The TCM storage system consists of two chemical reactors with heat exchangers for the
reaction C (solid) + Q (heat) A (fluid/gas) +B (solid) and a separate material buffer for
each of the three reactants, as depicted in Figure 5.
⇔
Figure 5 Basic TCM store model
The materials A, B and C are modeled by their enthalpy function at constant atmospheric
pressure, so that sensible heat as well as latent heat is taken into account. Also heat losses
are taken into account. The two reactors are thermally well insulated, and the three
material store are poorly insulated.
When solar radiation is added to the dissociation reactor, Material C is transported from
material store C to the dissociation reactor. In the reactor it is heated up to the reactor
temperature and partly dissociated into materials A and B. Next the hot materials A and B
and the remaining part of material C are transported back to their respective material
stores, where they are allowed to cool down.
When heat is extracted from the association reactor, Materials A and B are transported
from their material stores to the association reactor. In the reactor, the materials are
heated up to the reactor temperature and partly associate into material C. Next the hot
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material C and the remaining part of the materials A and B are transported back to their
respective material stores, where they are allowed to cool down.
Each material store is considered as a large material filled container with a fixed heat loss
coefficient of 100 W/K between the store and its surroundings. Its heat content is
calculated from its enthalpy function with respect to some reference temperature. Its
temperature is the result of inflowing and outgoing enthalpy flows. The volume needed
for a material store is calculated from the minimum amount of material needed in the
store, and the storage density of that material. The volume of a fluid or gas (material A) is
equal to its mass divided by its mass density. The volume of a solid (materials C and B)
however is not, because it is stored as granulate or fine powder. From commercial
abrasives (these are fine powders) it was found that on average the store volume is about
1.5 times the volume calculated from its pure material mass density.
The transportation of materials between the material stores and the reactor vessels costs
energy. For each material flow a characteristic value of 10 kJ/kg is used that was derived
from the energy consumption of a commercial feeder.
Reacted matter has to be stored as compact as possible. As in general it is not readily
available as a fine powder, it has to be grinded before feeding it back to the material
stores. For the energy consumption of grinding a characteristic value of 50 kJ/kg was
derived from the breaking and grinding of natural gypsum on an industrial scale.
The influence of the losses mentioned above on the effective energy storage density
cannot be avoided, but it can be decreased in some ways. One way is to decrease void
volume in the energy storage system. Choosing separate material stores and reactors
instead of integrated stores and reactors in the storage system can do this. This is
illustrated in Figure 6. The system with separate material stores and reactors has a much
smaller system volume because it does not need the reaction volume of the total material
mass present, but only a relatively small reaction volume associated with the amount of
material that is actually being converted in the chemical reaction.
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1
2
(b)
(a)
Figure 6 System volume for (a) integrated and (b) separate material stores and reactors
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Chapter 3
Definition of Experiments
Since the novel concept of solar energy storage using thermochemical materials is just
initiated, research outcome related to this field has been rarely reported so far. The
performance of thermochemical materials should be first assessed due to the key role of
TCM on heat storage system. The aim of the present project is to gain more significant
insight into the physical and chemical aspects on potential candidates of TCM.
To achieve the target, the design of experiments, especially for thermochemical
characterization, is necessary. It will cover the evaluation on basic parameters, the
investigation on thermodynamic and kinetic mechanisms for the two reversible reactions,
and the analysis of the effects of internal (grain size, porosity, mass) and external
(heating rate, cooling rate, holding time, humidity) factors on materials thermochemical
behavior.
3.1. Raw Materials
Commercially available magnesium sulfate hepta hydrate (MgSO4·7H2O) powders with
an average particle size of 38 µm are used as the initial materials.
3.2. Materials Processing
The mass of the powders is measured using a highly precise balance. For obtaining the
powders with different particle sizes, the grinding, milling, and sieving process is made
using mortar, pestle, and siever. Die pressing is applied for forming the powders into
compacts with different porosities.
3.3. Materials Characterization
The density of the compact is calculated by weight and geometry measurement. The
composition and phase of the material is characterized using X-ray diffraction (XRD).
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The microstructural observation and the elemental analysis are made using scanning
electron microscopy (SEM) and energy dispersive X-ray analysis (EDX).
To investigate the thermochemical processes of dehydration and rehydration, combined
thermogravimetry and differential scanning calorimetry (TG-DSC) technique is
employed. The materials are heated from the room temperature to 300 0C, held
isothermally, and then cooled down to room temperature. In case of the investigation on
cycling behavior, the process is repeated up to 3 times. The processing and
characterization facilities are available at Mechanical and Chemical departments of TU/e
and Energy Storage Laboratory of ECN.
3.4. Experimental Variables
It is expected that the thermochmical properties of the materials will be influenced by the
internal and external factors. Therefore, the experiment is designed using the combination
of different variables:
Mass: 10, 20, 50 mg
Grain size: 5, 15, 25, 35 µm
Porosity: 10, 20, 30%
Heating rate: 0.5, 1, 5, 10 0C/min
Holding time: 15 minutes to 20 hours
Cooling rate: 0.5, 1, 5, 10 0C/min
Humidity: 30, 50, 70%
3.5 Result Analysis and Discussion
With the obtained results from TG-DSC, the enthalpy of formation, the Gibbs free
energy, the entropy, and the energy storage density are evaluated. The influences of
heating rate, cooling rate, holding time, and humidity on dehydration and rehydration
processes are analyzed and discussed. The interpretation of the effects of mass, particle
size, and porosity on energy storage density and cycling behavior is made to understand
the nature of mass transfer and heat transfer during hydration processes on molecular,
grain, and compact level. Finally, the optimal conditions of MgSO4·7H2O as potential
thermochemical materials for solar energy storage are determined.
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3.6. Further Approaches
Based on the research progress, further approaches will also be considered to potentially
enhance the performance of thermochemical materials. The first approach is synthesis,
processing, and characterization of nano MgSO4·7H2O. It is originated from the idea that
nano particles have much higher surface energy and hence higher reaction activity to
increase the reaction efficiency. On the other hand, shorter diffusion path due to
nanostructures could improve the reaction rate of the hydration processes. The second
approach is formation of hetero-valence doping MgSO4·7H2O. The replacement of Al3+
or Na+ for Mg2+ in the lattices could introduce more defects and vacancies inside the
grains, which could provide more pathways for diffusing water molecules during
rehydration. The third approach is formation of MgSO4·7H2O, (Al)2(SO4)3·18H2O, and/or
CuSO4·5H2O composites. For single phase TCM, there are only several characteristic
temperatures at which the hydration reactions occurs. The incorporation of different
compositions into the composites could increase the overall characteristic temperatures,
extend the reaction temperature range, and if designed well, obtain more released heat.
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Chapter 4
Concluding Remarks and Project Planning
• Solar energy could provide durable heat for a domestic environment. However, it
is most effective in summer and not in winter when there is a high demand. To
accommodate the difference in time between energy production and energy
demand, heat storage is necessary. The basic idea behind heat storage is to
provide a buffer to balance fluctuations in supply and demand of thermal energy
for heating and cooling.
• Materials are the key issue for heat storage. There are a large number of materials
which can be used for heat storage. Thermochemical materials have the highest
storage capacity among all storage media.
• The design of the experiments provides more significant insight into the physical
and chemical aspects on potential candidates of TCM.
The project is planned to be accomplished in one year. In addition to the first-3-month
preparation phase, the remaining 9 months are for experimental implementation and
proposal development.
Months 4-9: Performing the detailed research work according to the design of
experiments, as presented in Chapter 3.
Months 10-12: Proposing a proposal for future research based on the obtained results.
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