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Technische Universität Berlin
Fakultät III Prozesswissenschaften
Institut für Energietechnik
Lehrstuhl Prof. Ziegler
1st Workshop
Development and Progress in Sorption Technologies
Characteristic Equation Method
In cooperation with
1st Workshop
Development and Progress in Sorption Technologies – Characteristic Equation Method
Date 27. – 28. Februar 2012
Organisation Dipl.-Ing. Jan Albers Technische Universität Berlin Fakultät III - Prozesswissenschaften Institut für Energietechnik Fachgebiet Maschinen u. Energieanlagentechnik Marchstraße 18, 10587 Berlin
jan.albers@tu-berlin.de
Co-Organisation Prof. Alberto Coronas Universitat Rovira i Virgili CREVER- Dep. Enginyeria Mecanica Avda Països Catalans 26 43007 Tarragona (Espanya)
1
Dedicated to all the “almost constants” in the world.
2
Summary
Idea of the workshop
The workshop series Development and Progress in Sorption Technologies is planned as an annually research workshop of the chair for Energy Conversion Technologies at the Institute of Energy Engineering at TU Berlin with an alternating specific topic mainly attributed to absorption chillers, heat pumps and heat transformers.
In addition the idea of the first workshop about the “Characteristic equation method” was to get international researchers from the UNIVERSITAT ROVIRA I VIRGILI (Tarragona, Spain) and the TECHNISCHE UNIVERSITÄT BERLIN together, to give them a structured possibility to present their results achieved so far and to discuss problems and ideas for their future work.
Characteristic equation method
The characteristic equation method is a method to describe the performance of an apparatus, which consists of at least two heat exchangers with phase change dominated heat transfer in a closed or open thermodynamic cycle by a small set of simple algebraic equations but based on thermodynamic fundamentals.
In the 1980th the characteristic equation method has been developed for heat transformers first. Since then several modifications and improvements have been carried out by a relatively small number of researchers. Although the method facilitates a considerable simplification of the thermodynamic description of e.g. absorption chillers, heat pumps and heat transformers, its application is far from being rampant.
Results and future work
From the given presentations at the workshop it turned out that future research work may focus on the following three topics:
1. Review and examination of allowed fit-parameters in multi regression methods and alternative modeling approaches (e.g. like artificial neural networks, non-linear multivariable regression etc.) in order to achieve improvements in accuracy on the one hand side but to ensure physical boundaries on the other hand.
2. Application of improved heat transfer calculation to multi stage cycles and reversible heat pumps of type 1 (chillers, heat pumps) and type 2 (heat transformers) in connection with new working pairs were the higher ratio of sensible heat to latent heat (i.e. higher Stefan number) may lead to problems in the validity of some method inherent assumptions.
3. Generalization of the method to non-sorptive heat pump technologies, like mechanical vapor compression systems and jet-ejector cycles.
3
Presentations
1. Felix Ziegler: Review of the characteristic equation method
2. Juan Carles Bruno: Application of characteristic equation to absorption chillers in CREVER-URV projects
3. Jan Albers: Deduction and Application of an improved Characteristic Equation Method
4. Andrés Montero: Application of the characteristic equation method to double-effect absorption chillers
5. Falk Cudok: Application of the Characteristic Equation Method to heat transformers
6. Dereje S. Ayou: Performance analysis of Absorption Heat Transformers using Ionic Liquids with 2,2,2-Trifluoroethanol as working fluid pairs
7. Tobias Zegenhagen, Felix Ziegler: Application of the Characteristic Equation Method to vapor jet-ejector cycles
8. David Martinez: Integration of the characteristic equation in complete data treatment and modeling approaches of absorption chillers
1
F. Ziegler • Review of the characteristic equation method
Technische Universität Berlin • Department of Energy Engineering
Review of the characteristic equation method
Felix Ziegler
1. The Japanese start 2. The Munich-Berlin adaptation 3. A proposal for generalization
2
F. Ziegler • Review of the characteristic equation method
Technische Universität Berlin • Department of Energy Engineering
The Japanese start: Takada, Furukawa, Sonoda
3
F. Ziegler • Review of the characteristic equation method
Technische Universität Berlin • Department of Energy Engineering
4
F. Ziegler • Review of the characteristic equation method
Technische Universität Berlin • Department of Energy Engineering
Enthalpy balance across each main component:
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F. Ziegler • Review of the characteristic equation method
Technische Universität Berlin • Department of Energy Engineering
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F. Ziegler • Review of the characteristic equation method
Technische Universität Berlin • Department of Energy Engineering
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F. Ziegler • Review of the characteristic equation method
Technische Universität Berlin • Department of Energy Engineering
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F. Ziegler • Review of the characteristic equation method
Technische Universität Berlin • Department of Energy Engineering
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9
F. Ziegler • Review of the characteristic equation method
Technische Universität Berlin • Department of Energy Engineering
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10
F. Ziegler • Review of the characteristic equation method
Technische Universität Berlin • Department of Energy Engineering
11
F. Ziegler • Review of the characteristic equation method
Technische Universität Berlin • Department of Energy Engineering
12
F. Ziegler • Review of the characteristic equation method
Technische Universität Berlin • Department of Energy Engineering
Variable Constant (almost)
Enthalpy balance across each main component:
? „Solution heat exchanger loss“
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The Munich-Berlin adaptation: Alefeld, Kern, Riesch, Scharfe, Ziegler et al….
13
F. Ziegler • Review of the characteristic equation method
Technische Universität Berlin • Department of Energy Engineering
Heat transfer across each main component:
Mean temperatures
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14
F. Ziegler • Review of the characteristic equation method
Technische Universität Berlin • Department of Energy Engineering
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15
F. Ziegler • Review of the characteristic equation method
Technische Universität Berlin • Department of Energy Engineering
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16
F. Ziegler • Review of the characteristic equation method
Technische Universität Berlin • Department of Energy Engineering
02468
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Characteristic temperature function � � t [K]
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17
F. Ziegler • Review of the characteristic equation method
Technische Universität Berlin • Department of Energy Engineering
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0 5 10 15 20 25 30 35 40 45Adapted characteristic temperature function ��t' [K]
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18
F. Ziegler • Review of the characteristic equation method
Technische Universität Berlin • Department of Energy Engineering
.
A proposal for generalization
Conversion process with n (main) heat exchangers yields: n energy balances with n unknown heat flows and m different unknown internal mass flow rates n heat transfer equations with n known external temperatures and n unknown internal temperatures
2n equations with 2n+m unknowns Therefore: m additional equations are required which give information about mass flows or temperatures
19
F. Ziegler • Review of the characteristic equation method
Technische Universität Berlin • Department of Energy Engineering
Or: for each mass flow rate an additional restriction for temperatures or mass flow is necessary
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Approximated
Application of the Characteristic Equation Method to absorption chillers in CREVER – URV projects
Joan Carles BrunoUniversitat Rovira i Virgili (Spain),CREVER – Research Group on Applied Thermal Engineeringjuancarlos.bruno@urv.cat
1st Workshop
Development and Progress in Sorption Technologies
Characteristic Equation MethodBerlin (Germany) – February 2012
TABLE OF CONTENT
J. C. Bruno – 1st Workshop on Development and Progress in Sorption Technologies – Berlin, 2012 1
1
2
3
5
Objectives
Review of the Characteristic Equation Method
Comparison of the different approaches
Examples of applications at CREVER-URV
– First approach– Second approach
6 Conclusions and perspectives
4 Modification of the second approach
1 – OBJECTIVES
2J. C. Bruno – 1st Workshop on Development and Progress in Sorption Technologies – Berlin, 2012
The idea behind the use of the Characteristic Equation Method at theCREVER-URV projects is to have a simple but rigorous method toestimated the performance of absorption systems at partial load.
The aim is to integrate the final characteristic equations into morecomplete and complex simulation and optimisation environmentsfor Polygeneration of energy systems including conventional and renewable energy technologies. These modelling environments are mainly TRNSYS, GAMS, Aspen Plus, etc.
The interaction between complete thermodynamic models (developedIn EES for example) and these complex modelling environments is notvery robust.
2 – REVIEW OF THE CHARACTERISTIC EQUATION METHOD
3J. C. Bruno – 1st Workshop on Development and Progress in Sorption Technologies – Berlin, 2012
At CREVER–URV the Characteristic Equation Method has been reviewed:
Puig-Arnavat, M.; López-Villada, J.; Bruno, J.C.; Coronas, A. (2010) Analysis and parameter identification for characteristic equations of single and double effect absorption chillers by means of multivariable regression. International Journal of Refrigeration, 33: 70-78.
and the main findings are presented here.
In this study two approaches to obtain the Characteristic Equation methodwere identified and a modification of the second approach was proposed.
2 – REVIEW OF THE CHARACTERISTIC EQUATION METHOD
4J. C. Bruno – 1st Workshop on Development and Progress in Sorption Technologies – Berlin, 2012
2.1 – Basics of the Characteristic Equation Method
The heat transfer equations (which implicitly also include the internal mass transfer) in the four major components relate the transferred heat loads to the driving temperature differences (Hellmann et al, 1999):
� is the logarithmic mean temperature difference divided by the arithmeticmean temperature difference
� is the internal arithmetic mean temperature
[Eq 1]
2 – REVIEW OF THE CHARACTERISTIC EQUATION METHOD
5J. C. Bruno – 1st Workshop on Development and Progress in Sorption Technologies – Berlin, 2012
2.1 – Basics of the Characteristic Equation Method
The internal temperatures of the four heat exchangers can be combined using Dühring’s rule:
[Eq 2]
Combining Eq. 1 and Eq. 2, it is possible to find a relation between the external temperatures:
[Eq 3]
[Eq 4]
2 – REVIEW OF THE CHARACTERISTIC EQUATION METHOD
6J. C. Bruno – 1st Workshop on Development and Progress in Sorption Technologies – Berlin, 2012
2.1 – Basics of the Characteristic Equation MethodTo eliminate the heat loads of the generator, absorber and condenser from Eq. 3, the energy balances of the four major components are introduced:
[Eq 5]
where Qhex stands for the heat exchanged in the solution heat exchanger between the strong and the weak solution streams that reduce the heat loads at the absorber and generator.
2 – REVIEW OF THE CHARACTERISTIC EQUATION METHOD
7J. C. Bruno – 1st Workshop on Development and Progress in Sorption Technologies – Berlin, 2012
2.1 – Basics of the Characteristic Equation MethodThe heat loads of the condenser, absorber and generator can be expressed as function of the evaporator load substituting Eq 5 in Eq 3 as follows:
where:
[Eq 7]
[Eq 6]
2 – REVIEW OF THE CHARACTERISTIC EQUATION METHOD
8J. C. Bruno – 1st Workshop on Development and Progress in Sorption Technologies – Berlin, 2012
2.2 – First approach of the Characteristic Equation Method
In this first approach to the characteristic equation method two different ways of solving the set of equations, depending on the available information, were used:
Hellman et al. (1999) determined the average values of the characteristicparameters B, s, �, ��tmin and G’ required in the model using design data: UA-values, weak solution flow rate and the external heat carrier flow rates for a H2O/LiBr absorption chiller.
The Solac Computer Design Tool (Albers, 2002) uses the same definition for ��t (Eq. 3) but proposes an equation for each main heat exchanger:
where the subindex u corresponds to the different heat exchanger units(Evaporator, Generator, Absorber and Condenser).
[Eq 8]
2 – REVIEW OF THE CHARACTERISTIC EQUATION METHOD
9J. C. Bruno – 1st Workshop on Development and Progress in Sorption Technologies – Berlin, 2012
2.2 – First approach of the Characteristic Equation MethodThe external outlet temperatures and heat loads of the heat exchangers can be calculated as:
[Eq 9]
Combining Eq 9 into Eq 8 the following linear equation system is derived:
To calculate the value of su and ��Tminu, for each heat exchanger only two points of operational data are needed.
[Eq 10]
2 – REVIEW OF THE CHARACTERISTIC EQUATION METHOD
10J. C. Bruno – 1st Workshop on Development and Progress in Sorption Technologies – Berlin, 2012
2.2 – First approach of the Characteristic Equation MethodIt has been proposed to reduce the deviation from real behaviuor assuming that the characteristic parameters are not constant but linear funtions of the �tACE:
�tACE = TAC - TE [Eq 11]
To find the values suI, suII, ruI, ruII to determine the characteristic parameters (su
and ��tminu), four operation points must be used instead of two.
[Eq 12]
2 – REVIEW OF THE CHARACTERISTIC EQUATION METHOD
11J. C. Bruno – 1st Workshop on Development and Progress in Sorption Technologies – Berlin, 2012
2.3 – Second approach of the Characteristic Equation Method
In this approach, described by Kühn and Ziegler (2005), a numerical fit was carried out to improve the results of the characteristic equation method using anarbitrary characteristic temperature function:
And the linear characteristic equation was defined as :
The use of the ��t’ definition in the characteristic equation yields:
[Eq 13]
[Eq 14]
[Eq 15]
3 – COMPARISON OF THE DIFFERENT APPROACHES
12J. C. Bruno – 1st Workshop on Development and Progress in Sorption Technologies – Berlin, 2012
These two approaches have been compared using the data for a solar poweredwater/LiBr absorption chiller reported by Gommed and Grossman (1990). Thesame data used in Hellmann et al (1999).
Using the first approach
3 – COMPARISON OF THE DIFFERENT APPROACHES
13J. C. Bruno – 1st Workshop on Development and Progress in Sorption Technologies – Berlin, 2012
First approach considering su and ��tminu as constants
Two groups of points were arbitrarily chosen to study how selection of the experimental data influences the results.
3 – COMPARISON OF THE DIFFERENT APPROACHES
14J. C. Bruno – 1st Workshop on Development and Progress in Sorption Technologies – Berlin, 2012
First approach considering suand ��tminu as linear functions of �tACE
Two groups of points were arbitrarily chosen to study how selection of the experimental data influences the results.
3 – COMPARISON OF THE DIFFERENT APPROACHES
15J. C. Bruno – 1st Workshop on Development and Progress in Sorption Technologies – Berlin, 2012
With this second approach no point selection is needed. A multiregression fitwas carried out with Microsoft Excel to calculate the value of the fourparameters: s’, a’, e’ and r’ in Eq. 15. The multiple linear regression algorithmchooses regression coefficients to minimise the residual sum of squares.
[Eq 16]
4 – MODIFICATION OF THE SECOND APPROACH
16J. C. Bruno – 1st Workshop on Development and Progress in Sorption Technologies – Berlin, 2012
To characterise the part-load behaviour of an absorption chiller instead of the external arithmetic mean temperature of the external flows of the absorption chiller (TG, TAC, TE) the usual information available is TinG, ToE and TinAC.
Albers and Ziegler (2008) suggested that if a linear part load behaviour is found for ��t, a linear behaviour should also be expected for modified characteristic temperature difference (��t*):
Thus another characteristic equation is proposed ��t”:
[Eq 17]
[Eq 18]
4 – MODIFICATION OF THE SECOND APPROACH
17J. C. Bruno – 1st Workshop on Development and Progress in Sorption Technologies – Berlin, 2012
Single effect hot-water-fired H2O/LiBr 4.5 kW absorption chiller (Rotartica, 2006)
Results using the second approach
Results using the second approachmodified
5 – EXAMPLES OF APPLICATIONS AT THE CREVER-URV PROJECTS
18J. C. Bruno – 1st Workshop on Development and Progress in Sorption Technologies – Berlin, 2012
Use of the characteristic equation method to calculate the hourly coolingproduction of an absorption chiller integrated in a solar cooling plant
Case study of Puig-Arnavat et al (2010)
0
5
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30
10.00 12.00 14.00 16.00 18.00 20.00Hours
Hea
t Flo
w (k
W)
Qe real Qg real Qe TRNSYS Qg TRNSYS
0
5
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25
30
10.00 12.00 14.00 16.00 18.00 20.00
Hours
Hea
t Flo
w (k
W)
Qe real Qg real Qe TRNSYS Qg TRNSYS
Cooling and driving heat capacity for experimental data (Safarik, 2007) and simulated data using ��t’ approach.
Cooling and driving heat capacity for experimental data (Safarik, 2007) and simulated data using ��t’ a constant COP of 0.7.
5 – EXAMPLES OF APPLICATIONS AT THE CREVER-URV PROJECTS
19J. C. Bruno – 1st Workshop on Development and Progress in Sorption Technologies – Berlin, 2012
Comparative evaluation of five different modeling methods for predicting the absorption chiller performance (Pink Absorption chiller)
Jerko Labus, Modelling of Small Capacity Absorption Chillers driven by Solar Thermal Energy or Waste Heat, PhD Thesis, URV, 2011.
*iii yy ���
iy Estimated value
*iy Observed value
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5 – EXAMPLES OF APPLICATIONS AT THE CREVER-URV PROJECTS
20J. C. Bruno – 1st Workshop on Development and Progress in Sorption Technologies – Berlin, 2012
Modelling of absorption and adsorption chillers for the solar air conditionig plant of the European POLYCITY project in Cerdanyola del Vallès (Barcelona)
and the Festo AG office building (Germany)
Solar collector area required to produce 700 MWh per year of cooling in Cerdanyola
del Vallès.
Mycom water/silicagel Adsorption chiller of 350 kW.
J. López, Integración de sistemas de refrigeración solar en redes de distrito de frío y de calor, PhD Thesis, URV, 2010.
5 – EXAMPLES OF APPLICATIONS AT THE CREVER-URV PROJECTS
21J. C. Bruno – 1st Workshop on Development and Progress in Sorption Technologies – Berlin, 2012
Integration into a biomass gasification trigeneration plant
M. Puig-Arnavat, Performance modelling and validation of biomass gasifiers for trigeneration plants, PhD Thesis, URV, 2011.
5 – EXAMPLES OF APPLICATIONS AT THE CREVER-URV PROJECTS
22J. C. Bruno – 1st Workshop on Development and Progress in Sorption Technologies – Berlin, 2012
Developmentof a userfriendlysoftware basedon GAMS.
J. Ortiga, Modelling environment for the design and optimisation of energy polygeneration systems, PhD Thesis, URV, 2011.
6 – CONCLUSIONS AND PERSPECTIVES
23J. C. Bruno – 1st Workshop on Development and Progress in Sorption Technologies – Berlin, 2012
After comparing the results obtained using experimental data, it was concluded that the second approach is the simplest and that provides similar or better accuracy than the first approach.
Instead of using the external arithmetic mean temperature of the external flows of the absorption chiller (TG, TAC, TE), is interesting to use the temperatures usually given to characterise the part-load behaviour (TinG, ToE and TinAC).
Coupling of the Characteristic Equation Method to a general procedure ofdata treatment for absorption chillers covering: steady-state detection, degrees of freedom analysis and simultaneous Data reconciliation and gross-error detection.
Possibility to integrate the method in dynamic models for absorption chillers.
ACKNOWLEDGEMENTS
24
The authors acknowledge the financial support given by the Ministerio de Economía y Competitividad of Spain through the
project ref. ENE2009-14182
J. C. Bruno – 1st Workshop on Development and Progress in Sorption Technologies – Berlin, 2012
1
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Deduction and Application of an improved Characteristic Equation Method
Dipl.-Ing. Jan Albers
1. Established characteristic equation method 2. Type of heat exchanger construction 3. Variable loss parameter 4. Consideration of bypass heat flows 5. Application of improved method 6. Discussion
2
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Rated cooling capacity:
Temperatures (inlet):
850 kW 10 kW
110° / 25° / 12°C 75° / 27° / 18°C
Reichstagsbuilding Solar Cooling
90° / 30° / 21°C
160 kW
New Development
Image source: EnEff-Project Foto: Sonnenklima AG Image source: York International / Johnson Control
RTG FA2AC160
Desorber: pool boiling falling film falling film
Single stage absorption chiller
3
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
0 10 20 30 40 50 0
5
10
15
20
25
�����
� ��� ����
Motivation
Comparison between established method and measurements
Foto: Sonnenklima AG
��t / K
Measurements (open symbols) by Annett Kühn et al.
4
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Motivation
0 10 20 30 40 50 0
5
10
15
20
25
�����
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Comparison between improved method and measurements Is there really a single characteristic (straight) line? How to determine the constant(?) slope and intersect?
��t / K
Measurements (open symbols) by Annett Kühn et al.
5
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Eq. 1 Property of working fluid
Eq. 2 Combining external and internal energy balance, using enthalpy coefficients KX temperature coefficients zX
Eq. 3 Inserting eq.1 into eq. 2 and using an ‘abbreviation’
Eq. 4 Leads to a linear equation if sE and ��tmin are constant � �����
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Characteristic equation method – established
��t characteristic temperature difference sE and ��tmin,E characteristic parameters KX characteristic coefficients
6
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Characteristic equation method – established
Evaporator capacity
Slope- parameter
Loss- parameter
Characteristic temperature difference
KX enthalpie difference ratios � 1 zX temperature difference ratios � 1
Emin,EE ttsQ ΔΔΔΔ ����
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7
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Eq. 5 Using enthalpy coefficient KD
Eq. 6 leads to
Eq. 7 Inserting and
Eq. 8 Finally
Desorber capacity – established method
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8
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Determination of characteristic parameters
With given UA-values from measurements we calculate
KX enthalpie difference ratios � 1 zX temperature difference ratios � 1
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A
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��tmin,E from rated capacity or at ��t0 = (tD,0 – tA,0) – B·(tC,0 – tE,0) ��
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9
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Determination of characteristic parameters
� �����
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KX enthalpie difference ratios � 1 zX temperature difference ratios � 1
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��tmin,E from rated capacity or at ��t0 = (tD,0 – tA,0) – B·(tC,0 – tE,0) ��
or from their ratio:
���
With given UA-values from measurements we calculate
10
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
0 10 20 30 40 50 0
5
10
15
20
25
�����
� ��� ����
Result of established method
Established method: - KX = 1 - zX = 1 - UAX from measurements
��t / K
Measurements (open symbols) by Annett Kühn et al.
11
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Steps of improvement
Step 1a: Accounting for variable external flow rates by heat permeability ratios �X
Step 1b: Calculation of temperature difference ratio zX without internal temperatures
Step 2: Revision of heat transfer calculation
Step 3: Application of dimensionless temperature glides
Step 4: Consideration of bypass heat flows
Step 5: Dissociation from load dependent heat permeabilities YX = Y(QX) = Y(T)
12
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Results of step 1a and 1b
� � � � � ����������� � � � �������
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Heat permeability ratio
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Temperature difference
ratio Effective heat permeability
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~
Heat permeability
Step 1a: Accounting for variable external flow rates by heat permeability ratios �X
Step 1b: Calculation of temperature difference ratio zX without internal temperatures
13
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Results of step 1a and 1b
X
Xlog,X ΔT
ΔTz �
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XX
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�
Step 1a: Accounting for variable external flow rates by heat permeability ratios �X
Step 1b: Calculation of temperature difference ratio zX without internal temperatures
Heat capacity flow rate ratio
Temperature difference ratio
Dimensionless heat permeability
14
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Steps of improvement
Step 1a: Accounting for variable external flow rates by heat permeability ratios �X
Step 1b: Calculation of temperature difference ratio zX without internal temperatures
Step 2: Revision of heat transfer calculation
Step 3: Application of dimensionless temperature glides
Step 4: Consideration of bypass heat flows
Step 5: Dissociation from load dependent heat permeabilitys YX = Y(QX) = Y(Q(TX))
15
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Pseudo specific
heat capacity
Application of dimensionless
temperature glides
��
Eq. 1 Property of working fluid
Eq. 2 Combining external and internal energy balance, using coefficients KXNx
� �����
� � � � ����
����� ��
Characteristic equation method – extended
����
���
�
��
���
���
���
�
����
���
��� ~~ �����
Revision of heat transfer calculation Consideration of bypass heat flows
16
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Eq. 1 Property of working fluid
Eq. 2 Combining external and internal energy balance, using coefficients KXNx
� �����
� � � � ����
����� ��
Characteristic equation method – extended
����
���
�
��
���
���
���
�
����
���
��� ~~ �����
Revision of heat transfer calculation
- Heat flow ratios KX2 instead of enthalpy coefficients KX
- Description as function of inlet temperatures tXi
- Consideration of heat exchanger construction type - Internal losses as explicit function of external temperatures
(e.g. external lift �tLi = tCi – tEi ) and coefficients KXNx
17
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Eq. 1 Property of working fluid
Eq. 2 Combining external and internal energy balance, using coefficients KXNx
� �����
� � � � ����
����� ��
Characteristic equation method – extended
����
���
�
��
���
���
���
�
����
���
��� ~~ �����
Eq. 3 Inserting eq.1 into eq. 2 and using an ‘abbreviation’
Eq. 4 Leads to two explicit equations for cooling capacity and driving heat � ������
� � � ������
� ������
18
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Step 2: Revision of heat transfer calculation a) type of heat exchanger construction b) variable loss parameter
19
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
� � � � logDmDD ΔTUAΔTUAQ �����
Revision of heat transfer calculation
Boiling point of solution
Dew
poi
nt
of re
frige
rant
TDe
TSor
SQ�
irrD,Q�
� � � ���� ���� ��
��� ��� ��
��
��ED
DevapourRefRef
irrD,
SorDerD
QKQ
hhmhhmQ�
������
load dependent loss � const.
ED QK ��
Driving heat
DQ�
20
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Revision of heat transfer calculation
Boiling point of solution
Dew
poi
nt
of re
frige
rant
TDe
TSor
SQ�
TDs
D1Q� D2Q�
� � � ���� ���� ��
��� ��� ��
��
��ED
DevapourRefRef
irrD,
SorDerD
QKQ
hhmhhmQ�
������
load dependent loss � const.
� � � � logDmDD ΔTUAΔTUAQ �����
� � � ���� ���� ��
���� ���� ��
�
��D2
DsDeD2p,r
D1
SorDsrp,r
TTcmTTcm �������� ~
phase change sub-cooling - heat of evaporation (load) - heat of solution (loss) - sensible heat (loss)
(loss)
Driving heat
DQ�
21
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Integral apperant specific heat capacity
D2Q�
T(pC) TD2
TDs TDe
Boiling point of solution
Dew
poi
nt
of re
frige
rant
pc~
Short: Pseudo heat capacity
KkgkJ525
TTQc
DsDe
D2D2p, �
���
��~
Inte
gral
app
eran
t spe
cific
hea
t cap
acity
� � �������
�� ~
Scharfe, Ziegler, Radermacher, 1986: Differential heat of desorption
i.e. ±20%
setting we get
Enthalpy balance in domain D2
defines an internal heat capacity flow rate
22
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Heat transfer calculation for mode A and B
desorbed refrigerant poor solution (in equilibrium)
desorbed refrigerant
rich solution (sub-cooled)
Falling film desorber Flooded desorber
rich solution (sub-cooled)
23
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Heat transfer calculation for mode A
rich solution (sub-cooled)
DsT
DeT
SorT
D1Q��
� D2Q�
Refm�
DiTadiabatic absorption of refrigerant
D1Ref,m� Mode A
�� ��
poor solution (in equilibrium)
desorbed refrigerant
TD1 TD2
TSor TDs TDe TDi
Boiling point of solution
Dew
poi
nt
of re
frige
rant
D1Ref,m�
T(pC)
pxrx
24
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Heat transfer calculation for mode A
DsT
DeT
SorT
D1Q��
� D2Q�
Refm�
DiTadiabatic absorption of refrigerant
D1Ref,m� Mode A
�� ��
Boiling point of solution
Dew
poi
nt
of re
frige
rant
� � � � � ���������� ~~ ����
D2Q�D1Q�
� ����� ~�
�
rich solution (sub-cooled)
TD1 TD2
TSor TDs TDe TDi
T(pC)
D1Ref,m�
pxrx
25
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Heat transfer calculation for mode A
Boiling point of solution
Dew
poi
nt
of re
frige
rant
� � � � � ���������� ~~ ����
D2Q�D1Q�
� ����� ~�
�
TD1 TD2
TSor TDs TDe TDi
DTDΔT Dt
DitDotT(pC)
Heat transfer equation:
� � � ������ ��
� ����� ~��Internal balance:
pxrx
26
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Heat transfer calculation for mode A
TD1 TD2
TSor TDs TDe TDi
Dmax,ΔT
DitDotT(pC)
� ����� ~��
Heat transfer equation:
� �DiDiDDD2D1 TtPWQQ ����� ���
Dühring's rule:
� � BTTTT ECA2D2 ����Dp,r
D2D2De cm2
QTT ~����
�
�
Inserting and solving for TD2:
D2p,r
D2
D1p,r
D1
DD
DDiD2 cm2
Qcm
QPW
QtT ~~ ���
��
���
�
�
�
��
With adiabatic absorption:
Dp,r
D1
Dp,r
D2D2Di cm
Qcm2
QTT ~~ ��
����
�
�
�
�
Internal balance:
ED2D2 QKQ �� ��LD1rD1sED1 ΔtKKQQ ���� ��
Determination of and D1Q� D2Q�
pxrx
27
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Heat transfer calculation for mode A and B
DsT
DeT
SorT
D1Q��
� D2Q�
Refm�
DiTadiabatic absorption of refrigerant
D1Ref,m� Mode A
�� ��Refm�
rich solution (sub-cooled)
SorT
D1Q��� D2Q�
DeT
DsT
Mode B
�� ��
rich solution (sub-cooled) desorbed refrigerant
poor solution (in equilibrium)
desorbed refrigerant
28
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Heat transfer calculation for mode A and B
Boiling point of solution
Dew
poi
nt
of re
frige
rant
TD1 TD2
TDs TDe
BD,max,ΔT
DitDot
Mode A Mode B
BD,max,AD,max, ΔTΔT �
TD1 TD2
TSor TDs TDe TDi
AD,max,ΔT
DitDotT(pC)
TSor
T(pC)
� ?
pxrxpxrx
29
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
� � � ��������� ~���
Heat transfer calculation for mode B
Heat transfer equation:
Internal balance:
� �
� � ���
���
���
�
�
Driving temperature difference correction factor for temperature dependent heat capacity flow rates:
����
����
��� ���
TD1 TD2
TDs TDe
BD,max,ΔT
DitDotTSor
T(pC)
Everything is load dependent �
� �DiDiDDD TtPWQ ���� ��
rx px
30
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
� � � ��������� ~���
Heat transfer calculation for mode B
Heat transfer equation (in domain D2):
� �DsDiD2DD2 TtPWQ ���� ��
Internal balance:
TD2
TDs TDe
D2max,ΔT
DitDotT(pC)
Dühring's rule:
� � BTTTT ECA2D2 ����
� �
� � ���
���
���
�
~���
���
�
�
�
�Inserting and solving for TD2:
~����
�
�Let us assume we would know nD2, and:
D2Q�
ED2D2 QKQ �� ��
Determination of nD2 and
� ���
pxrx
31
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Mode A Mode B
ED2D2 QKQ �� ��LD1rD1sED1 ΔtKKQQ ���� ��
Determination of and D1Q� D2Q�
� �����
~���
���
�
�
�
�
D2p,r
D2
D1p,r
D1
DD
DDiD2 cm2
Qcm
QPW
QtT ~~ ���
��
���
�
�
�
��
ED2D2 QKQ �� ��
Determination of nD2 and D2Q�
� ���
A2p,r
A2
A3p,r
A3
AA
AAiA2 cm2
Qcm
QPW
QtT ~~ ���
��
���
�
�
�
��
� � � ������
~���
���
�
�
�
�
~���
���
�
�
�
�
32
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Comparison of case A and B (for FA2 and RTG)
0 10 20 30 40 50 0
10
20
30
40
�����
� �����
�������� ����������
FA2
X YX/(kW/K) mX/(kg/s)
D 1.5 0.33
E 3.5 0.81
C 4.0 0.72
A 2.0 0.72
S 1.0 0.09
.
~���
���
�
�
�
�
Case B (flooded desorber)
Case A (falling film desorber)
Dp,r
D2
Dp,r
D1
DD
D2D1DiD2 cm2
Qcm
QPWQQtT ~~ ��
��
���
���
�
�
���
��t / K
BAX,Q�
1st letter: calculation case for Desorber
2nd letter: calculation case for Absorber
�
�
�
�
33
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Comparison of case A and B (for FA2 and RTG)
0 10 20 30 40 50 0
10
20
30
40
�����
� �����
�������� ����������
0 10 20 30 40 50 0
10
20
30
40
�����
� �����
�������� ����������
FA2 RTG
0 10 20 30 40 50 0
10
20
30
40
�����
� �����
�������� ��������������������
RTG’ COP·50
X YX/(kW/K) mX/(kg/s)
D 1.5 0.33
E 3.5 0.81
C 4.0 0.72
A 2.0 0.72
S 1.0 0.09
X YX/(kW/K) mX/(kg/s)
D 7.5 0.19
E 14.0 0.81
C 12.0 1.08
A 8.0 1.08
S 1.2 0.38
. .
��t / K ��t / K
�
�
�
�
�
�
�
�
34
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Mode A Mode B
ED2D2 QKQ �� ��LD1rED1sD1 ΔtKQKQ ���� ��
Determination of and D1Q� D2Q�
� �����
~���
���
�
�
�
�
D2p,r
D2
D1p,r
D1
DD
DDiD2 cm2
Qcm
QPW
QtT ~~ ���
��
���
�
�
�
��
ED2D2 QKQ �� ��
Determination of nD2 and D2Q�
� ���
A2p,r
A2
A3p,r
A3
AA
AAiA2 cm2
Qcm
QPW
QtT ~~ ���
��
���
�
�
�
��
� � � ������
~���
���
�
�
�
�
~���
���
�
�
�
�
How to go on ?
35
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Characteristic coefficients KXNx in Desorber
ED2EDV
D2 QKQμ1
Q rlr
��� ����
��
throttle loss � 0.03 - 0.05
constant property data: Kw � 1.1
� � � � � � LSrp,rD2p,rS
D2
EC
C
p,A2r
A2
D2p,r
D2Srp,rED1 ΔtBP1cm
cmP1K
Y1
YKB
cm2K
cm2KP1cmQQ �������
�
�������
����
��
����
�
�
���
�������� �
������ ~~~~~
KD1s and KD1r from geometry of solution field with: - constant property data - effective heat permeabilities - given solution flow rate
D1Q� D2Q�
ED2 QK ��
D1rLD1sED1 KΔtKQQ ���� ��
36
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Deduction of QD1 = f(YX, mr) . .
Established method: QD,irr = mr · (hDe - hSor) Extended method: QD1 = mr · (hDs - hSor) = mr · cp,r · (TDs -TSor)
TSiede
TTau
rm�
TAe
rx
TDe
px
TC pC
TE
pE maxS,ΔT
YS oder S
TDs TSor
QD1
. QD2
.
.
. . .
.
Dimensionless temperature glide of Solution Heat Exchanger (rich solution side)
(a)
(b)
37
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Deduction of QD1 = f(YX, mr) . .
TAe
T(pC) TD2
TA2
2GA2
2GD2
A2D2 TT �
TDe
T(pE)
�TS,max
From Diagram we derive:
Inserting into the Eq. (a) and (b) leads to …
(a)
(b)
38
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Deduction of QD1 = f(YX, mr)
Inserting the specific heat flows
without internal Temperatures, but load dependant (due to QE and �tL)
.
For absorber in similar way:
. .
LD1rED1sD1 ΔtKQKQ ���� ��
� � � � ED2p,rS
D2
EC
C
A2p,r
A2
D2p,r
D2Srp,rD1 Q
cmP1K
Y1
YKB
cm2K
cm2KP1cmQ �
����� �
���
�������
����
��
���
���
�
���
������� ~~~~~
� � LSrp,r ΔtBP1cm ������ �
LA3rEA3sA3 ΔtKQKQ ���� ��
DVE
D2D2 μ1Q
Q rlr
���
�
�
�K
DVE
A2A2 μ1Q
Q rlr
���
�
�
�K
DVE
CC μ1Q
Q�
��1
�
�K
39
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Slope parameter for Desorber
ED2D2 QKQ �� ��
LD1rD1sED1 ΔtKKQQ ���� ��D2D1D QQQ ��� ��
LD1rED1sED2D ΔtKQKQKQ ������ ���
� � � � �������
��
��
����
����
������
���
40
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Characteristic equation method – improved
� � � � � � � �
1
EECC
C
AA
A
DD
DE zUA
1zUA
K'BzUA
KzUA
Ks�
��
��
����
����
��
��
���
��
�
� � � � ��
��
��
���
��AA
irrA,DD
irrD,Emin, zUA1Q
zUA1QΔΔt ��
Evaporator capacity
Slope- parameter
Loss- parameter
Characteristic temperature difference
� ��
���
���
����
����
�
��
��
�����
����
�
���
��
���
���
� ������� ~~
� � ����
���
����
����
�
���
����
��
����
�
���
��� ~~ ����
�
old
new
old
new
� � � � XEmin,XEE VttVsQ ��� ΔΔΔΔ ���
41
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
0 10 20 30 40 50 0
5
10
15
20
25
�����
� ��� ����
Result – established method
Established method: - KX = 1 - zX = 1 - UAX,0 from measurements
Measurements (open symbols) by Annett Kühn et al.
��t / K
42
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Results – improved method
0 10 20 30 40 50 0
5
10
15
20
25
�����
� �����
����� ���� ��� ��� ��� ��� �
Measurements (open symbols) by Annett Kühn et al.
Improved method: - KX = 1 KXNx - zX = f(NTUX, RX) - UAX,0 from measurements
Characteristic coefficients KXNx calculated from: - UA-values, - solution flow rate mr - constant property data.
��t / K
.
43
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Step 4 Consideration of bypass heat flows
44
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Bypass heat flows
E
C
A
D
���
���
������
45
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Bypass heat flows – multi stream heat exchanger
DCQ�
Dint,Q�Cint,Q�
Aint,Q�
CEQ� DAQ�
AEQ�
Eint,Q�
Internal flow
External flow
DCDADint,Dext, QQQQ ���� ����
� ���
Approximation procedure for dimensionless temperature glides PX
����
���
�
��
���
���
���
�
����
���
��� ~~ �����
46
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Bypass heat flows – multi stream heat exchanger
DCQ�
Dint,Q�Cint,Q�
Aint,Q�
CEQ� DAQ�
AEQ�
Eint,Q�
DCDADint,Dext, QQQQ ���� ����
����
���
�
��
���
���
���
�
����
���
��� ~~ �����
� � �����
� ��
� � �����
� ��
Dimensionless temperature glides P’X , Pbyp,X according to Butkevich1987 with changes by Albers2012
47
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Characteristic equation method – improved
Evaporator capacity
Slope- parameter
Loss- parameter
Characteristic temperature difference
� ��
���
���
����
����
�
��
��
�����
����
�
���
��
���
���
� ������� ~~
� � ����
���
����
����
�
���
����
��
����
�
���
��� ~~ ����
�
� � � � XEmin,XEE VttVsQ ��� ΔΔΔΔ ���
� ���
48
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Explanation of Kühn&Ziegler2005 approach
� � � ������
� ����
� � � � ����������
� �����
49
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Explanation of Kühn&Ziegler2005 approach
���
���
����
����
������
�
����
������
�
����
������
�
����
����� !!!!�
����������
� ������
� � � ������
� ����
��������
Compare with: Kühn&Ziegler, OTTI-Symposium 2005
50
J. Albers • Deduction and Application of an improved Characteristic Equation Method
Technische Universität Berlin • Department of Energy Engineering
Conclusions 1) Slope parameters sX
� not only size dependent (UA-values) � load dependent losses included � ratio sD / sE > KD is now clear
2) Loss parameter ��tmin is not constant but a function of external temperature lift �tL (or �tLi)
3) Characteristic coefficients KXNx � derived from UA-values and rich solution mass flow rate only, � are equal for all characteristic equations of QE, QA+C, QD
4) The method of characteristic equations has been extended: � off-rated and variable flow rates included, � heat exchanger construction type considered, � bypass heat flows included, � higher accuracy obtained, � deeper understanding accomplished.
. . .
1st Workshop Development and Progress in Sorption Technologies
Characteristic Equation Method (ChEM)
Application of the Characteristic Equation Method to Double-Effect Absorption Chillers
Andrés Montero, Joan Carles Bruno, Alberto Coronas
2012.02.27-28 / Berlin
Group of Applied Thermal Engineering – CREVER Universitat Rovira i Virgili
1
Application of the characteristic equation method to double-effect absorption chillers
Outline • Objective • Introduction • Methodology • Application
• Double-effect absorption chiller / Parallel flow • Conclusions
Berlin: 2012.02.27-28 / 2
Application of the characteristic equation method to double-effect absorption chillers
Objective Characterize the performance of a double-effect absorption chiller by means of the characteristic equation method in order to use it in energy system simulation packages.
Berlin: 2012.02.27-28 / 3
Application of the characteristic equation method to double-effect absorption chillers
Introduction To model any physical phenomenon in order to include it in a simulation environment, it is necessary to take into account: - Does the model have a nonlinear structure? - Does the user need to understand all the principles that rule that specific phenomenon? What happens if an absorption cycle needs to be included in a energy system simulation tool? Berlin: 2012.02.27-28 / 4
Application of the characteristic equation method to double-effect absorption chillers
Introduction The application of the characteristic equation method can help us to include an absorption chiller model into a simulation tool due to: - Simplicity of the model (algebraic equations). - User does not need to be an experienced expert to simulate absorption cycles. PLUS: WE CAN OBTAIN A GOOD REPRESENTATION OF THE ACTUAL PART-LOAD BEHAVIOUR OF THE CHILLER Berlin: 2012.02.27-28 / 5
Application of the characteristic equation method to double-effect absorption chillers
Methodology 1. To select a generic absorption cycle (double-effect) based on the working fluid H2O/LiBr and to solve the thermodynamic model
Berlin: 2012.02.27-28 / 6 Source: Engineering Equation Solver Source: Engineering Equation Solver
1
2
43
5
6
7
8
9
10
11
12
13 14
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16
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2122
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� �� oi mm ��
ooii xmxm ���� � ��
� � � � ����� iiooX xmhmWQ ���
XXX TLMUAQ ����
Application of the characteristic equation method to double-effect absorption chillers
Methodology 2. Several ratios of internal specific enthalpy differences related to the specific enthalpy differences at the evaporator and high condenser-low desorber are calculated.
Berlin: 2012.02.27-28 / 7
1
2
43
5
6
7
8
9
10
11
12
13 14
15
16
17
18
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� �81010 hhQm E �� �� � � � �810510 hhhhA ���
� � � �81087 hhhhC ��� � � � �18171870 hhhhK ���
� � � �18171417 hhhhD ���
� �181717 hhQm K �� ��
� � � �810471 hhhhK ���
� � � �18171472 hhhhK ���
Application of the characteristic equation method to double-effect absorption chillers
Methodology 3. Each component is expressed in terms of ratios of internal specific enthalpy differences, cooling capacity and solution heat exchanger losses.
Berlin: 2012.02.27-28 / 8
1
2
43
5
6
7
8
9
10
11
12
13 14
15
16
17
18
19
2122
2423
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1LOSSEA QQAQ ��� ��
� � � � � �22121 11 KQQKQKQ LOSSLOSSEK ��� ����
2LOSSKD QQDQ ��� ��
KEC QKQCQ ��� ���� 0
Application of the characteristic equation method to double-effect absorption chillers
Methodology 4. By means of Dühring’s rule, applied to the dissolution of aqueous lithium bromide, the internal temperatures of the heat exchangers can be combined in a single expression, as
Berlin: 2012.02.27-28 / 9
P
T
HC D
LD
C
E A
ΔT
� �� �TTT
TTBTTTTBTT
LDHC
ECALD
EHCAD
�����������
� � � � TBTBBTBTBT ECAD �������� 221
Application of the characteristic equation method to double-effect absorption chillers
Berlin: 2012.02.27-28 / 10
� � � �� � � � TB
UAQBB
UAQB
UAQB
UAQ
tBBtBtBtt
E
E
C
C
A
A
D
D
ECAD
������
������������ 22
22
1
1
Methodology 5. Internal temperatures can be replaced by heat transfer equation in each heat exchanger, where ΔTLMX can be treated as equivalent to the difference of arithmetic mean temperatures1 ( ≈ ). The characteristic equation of a double-effect absorption cycle is:
tT_____
�
1Ziegler (1998)
Application of the characteristic equation method to double-effect absorption chillers
Methodology 6. Combining previous equations, the equation that describes the part-load behavior of absorption chiller is:
Berlin: 2012.02.27-28 / 11
� �TBwwtsQ EEEE ��������� 21�
� � � �1
2
2
101
2
2
1 11
111
�
�
�
�
��
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���
����
����
�
�����
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E UABB
KKKC
UAB
UAAB
KK
UADs
Application of the characteristic equation method to double-effect absorption chillers
Methodology 6. Combining previous equations, the equation that describes part-load behavior of absorption chiller is:
Berlin: 2012.02.27-28 / 12
E
LOSSEE s
Qw 111
����
� � ��
���
��
���
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2
0
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1111
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KBUAKUA
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EE�
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Qw 222
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Application of the characteristic equation method to double-effect absorption chillers
Methodology 7. The rest of the components (Absorber, Condenser and Desorber) will maintain the same structure but different coefficients.
Berlin: 2012.02.27-28 / 13
� �TBwwtsQ XXXX ��������� 21�
The case here described is useful when the chiller has a cooling circuit in parallel. If it is applied to a chiller with a cooling circuit in series the only equation to modified is that on slide Number 10.
Application of the characteristic equation method to double-effect absorption chillers
Application In order to apply this method to a double-effect absorption cycle, a chiller has been selected from the bibliography 2. The cycle represents a parallel flow double-effect water/lithium bromide chiller with cooling circuit in parallel.
Berlin: 2012.02.27-28 / 14 1Gommed and Grossman (1990)
Application of the characteristic equation method to double-effect absorption chillers
Application
Berlin: 2012.02.27-28 / 15
Variable Value Temperature, t [ °C ] Pressurized hot water (t31) 126.7 Cooling water inlet (t33, t35) 29.4 Chilled water outlet (t38) 7.2 Mass flow rate, m [ kg·s-1 ] Pressurized hot water (m31) 3.1 Cooling water- absorber (m33) 3.7 Cooling water - condenser (m35) 3.0 Chilled water (m37) 2.3 Weal solution (m1) 0.45
Component UA [ kW·K-1 ] Evaporator (E) 11.9 Absorber (A) 6.1 Condenser (C) 17.9 Desorber (G) 8.5 High condenser – Low desorber (GB) 5.8 Solution heat exchanger (ICS) 2.0
QE = 42 kW COP=1.22
Application of the characteristic equation method to double-effect absorption chillers
Application The cycle was analyzed for 66 different conditions where the pressurized hot water was varied from 100 to 150°C while the rest of the temperatures were kept constant at a selected temperature.
Berlin: 2012.02.27-28 / 16
Pressurized hot water, t31: 100 / 110 / 120 / 130 / 140 / 150°C Cooling water, t33 t35: 26 / 29.4 / 35°C Chilled water, t37: 9 / 12 / 15 / 18°C External flow rates were kept constant at nominal conditions
The parameter B was kept constant during all the analysis (B=1.15) The ΔT was fitted to a linear equation in terms of the total temperature difference ΔΔt since it varies according to the external conditions.
Application of the characteristic equation method to double-effect absorption chillers
Application - The first assumption was to keep all the characteristic parameters invariable3 (sX, wX1 and wX2). Those parameters were calculated under rated conditions.
Berlin: 2012.02.27-28 / 17 3Ziegler et al. (1999)
0
20
40
60
80
100
0 20 40 60 80 100
Cool
ing
capa
city
, QE
[ kW
]
Fitted cooling capacity, QEec [ kW ]
Exact simulation ±10% Deviation
Present model
0%
20%
40%
60%
80%
100%
120%
0
5
10
15
20
25
30
0 5 10 15 20 higherFr
eque
ncy
Range
Relative error (Evaporator)
Frequency % cumulative
Application of the characteristic equation method to double-effect absorption chillers
Application - The second assumption was to maintain sX constant and equal to the average for all the conditions. In case of wX1 and wX2, these two variables were fitted as function of ΔΔt.
Berlin: 2012.02.27-28 / 18
0
20
40
60
80
100
0 20 40 60 80 100
Cool
ing
capa
city
, QE
[ kW
]
Fitted cooling capacity, QEec [ kW ]
Exact simulation ±10% deviation
Present model
0%
20%
40%
60%
80%
100%
120%
0
10
20
30
40
50
0 5 10 15 20 higher
Freq
uenc
y
Range
Relative error (Evaporator)
Frequency % cumulative
Application of the characteristic equation method to double-effect absorption chillers
Application - In the third assumption the characteristic parameters (sX, wX1 and wX2) were fitted as function of ΔΔt for all the range of conditions.
Berlin: 2012.02.27-28 / 19
0
20
40
60
80
100
0 20 40 60 80 100
Cool
ing
capa
city
, QE
[ kW
]
Fitted cooling capacity, QEec [ kW ]
Exact simulation ±10% deviation
Present model
0%20%40%60%80%100%120%
0
10
20
30
40
50
0 5 10 15 20 higher
Freq
uenc
y
Range
Relative error (Evaporator)
Frequency % cumulative
Application of the characteristic equation method to double-effect absorption chillers
Application
Berlin: 2012.02.27-28 / 20
0
10
20
30
40
50
60
70
80
90
0 10 20 30 40 50 60 70 80 90
Cool
ing
capa
city
, QE
[ kW
]
Total temperature difference, ΔΔt [ K ]
Thermodynamic modelChEM
Application of the characteristic equation method to double-effect absorption chillers
Application The Characteristic Equation Method (ChEM) can be included into simulation packages, e.g. TRNSYS in order to simulate ab/ad sorption cycles. The model of the absorption chiller previously described has been implemented in TRNSYS.
Berlin: 2012.02.27-28 / 21
Type 813
Application of the characteristic equation method to double-effect absorption chillers
Conclusions • A set of equations were obtained in order to simulate each of the components of an absorption chiller from physical information (UA values, internal flow rates, etc) . • The characteristic equation method allowed to simulate the behavior of a double effect absorption chiller under different conditions. A deviation of ±10% was obtained for the cooling capacity. • This method, due to its characteristics, can be used in energy system simulation packages.
Berlin: 2012.02.27-28 / 22
Application of the characteristic equation method to double-effect absorption chillers
Berlin: 2012.02.27-28 / 23
The authors acknowledge the financial support given by the Ministerio de Economía y Competitividad of Spain through the
project SOLEF (ref. ENE2009-14177)
Application of the characteristic equation method to double-effect absorption chillers
THANK YOU FOR YOUR ATTENTION!!!
Berlin: 2012.02.27-28 / 24
1
F. Cudok • Application of the Characteristic Equation Method to Heat Transformers
Technische Universität Berlin • Department of Energy Engineering
Application of the Characteristic Equation Method to Heat Transformers
Falk Cudok
1. Motivation for using the Characteristic Equation Method
2. Deduction3. Calculated and fitted characteristic equation4. Expanding with the z-factor5. Summary and Outlook
2
F. Cudok • Application of the Characteristic Equation Method to Heat Transformers
Technische Universität Berlin • Department of Energy Engineering
Motivation for using the Characteristic Equation Method
• Simulation algorithmic with low usage of computing performance
• Optimize the operation in part load• More detailed understanding of the heat transformer
process• Design tool
3
F. Cudok • Application of the Characteristic Equation Method to Heat Transformers
Technische Universität Berlin • Department of Energy Engineering
Deduction - Process scheme
Assumptions• Adiabatic• Steady state••
Indices• X - A (Absorber), E (Evaporator), D (Desorber), C (Condenser) • r – rich solution• p – poor solution• R – Refrigerant • S - Solution
.constmp ��.)( constUA X �
4
F. Cudok • Application of the Characteristic Equation Method to Heat Transformers
Technische Universität Berlin • Department of Energy Engineering
HeatTransfer (1)
Enthalpybalance (2)
For condenser and evaporator
(3)
Example: Condenser
(4)
with
Deduction
5
F. Cudok • Application of the Characteristic Equation Method to Heat Transformers
Technische Universität Berlin • Department of Energy Engineering
Deduction
legend:
absorption chiller
6
F. Cudok • Application of the Characteristic Equation Method to Heat Transformers
Technische Universität Berlin • Department of Energy Engineering
Dühring’s rule (9)
(10)
(5-8) and (10) into (9)
(11)
with
Deduction
Refer to Albers, J., Kühn, A., Peterson, St., Ziegler, F.: Control of Absorption Chiller by insight: The Characteristic Equation
7
F. Cudok • Application of the Characteristic Equation Method to Heat Transformers
Technische Universität Berlin • Department of Energy Engineering
Calculated slope- and loss-parameter
• For 20 different measured working points (Peter Riesch, 1986) • B = 1.15• Enthalpy (pressure, concentration) • Poor Solution mass flow (density, volume flow)
� �KkW /103165.0 3��
� �K4.056.0 �
8
F. Cudok • Application of the Characteristic Equation Method to Heat Transformers
Technische Universität Berlin • Department of Energy Engineering
Calculated and fitted characteristic equation
Calculated for every working point : ))4.056.0(()103165.0( 3 ������ � tQA
�
• With B = 1.15 • 20 different working points
Linear regression :
)7.2(2292.0 ���� tQA�
Measurement results: Riesch, P.: Aufbau und Betrieb eines Absorptionswärmetransformators. Diplomarbeit. Technische Universität München, 1986, pp. 53-54
9
F. Cudok • Application of the Characteristic Equation Method to Heat Transformers
Technische Universität Berlin • Department of Energy Engineering
HeatTransfer (12)
(13)
with
Expanding with the z-factor
z-factor: refer to the presentation of Jan Albers
]/[10*6.1228.0 3 KkW��
][9.026.1 K�
• z-factor depends on the external mass flows
10
F. Cudok • Application of the Characteristic Equation Method to Heat Transformers
Technische Universität Berlin • Department of Energy Engineering
Calculated and fitted characteristic equation with z-factor
Calculated for every working point : ))9.026.1(()10*6.1228.0( 3
, ������ � tQ zA�
• With B = 1.15 • 20 different working points
Linear regression :
)7.2(2292.0 ���� tQA�
Measurement results: Riesch, P.: Aufbau und Betrieb eines Absorptionswärmetransformators. Diplomarbeit. Technische Universität München, 1986, pp. 53-54
z-factor: refer to the presentation of Jan Albers
11
F. Cudok • Application of the Characteristic Equation Method to Heat Transformers
Technische Universität Berlin • Department of Energy Engineering
summary
• Development of a simple characteristic equation• Linear correlation between power output and ��t was
shown for measurement results• Large deviation between the calculated and fitted
equation• By using the z-factor the smaller deviation between the
calculated and fitted equation
12
F. Cudok • Application of the Characteristic Equation Method to Heat Transformers
Technische Universität Berlin • Department of Energy Engineering
outlook
• Analyse the deviation resulting of the assumptions• Compare my result with other published equations for
heat transformer and absorption chillers• Compare the results of the equation with measurement
and simulation results• Develop a detailed simulation model for the heat
transformer
13
F. Cudok • Application of the Characteristic Equation Method to Heat Transformers
Technische Universität Berlin • Department of Energy Engineering
Thank you for your attention.
Falk CudokFalk.cudok@tu-berlin.de
(030) 314-28483
Department of Energy Engineering, Prof. Dr.-Ing. Felix ZieglerMarchstrasse 18, 10587 Berlin. Tel.: (+49) 030 314 - 22387 Fax: - 22253
14
F. Cudok • Application of the Characteristic Equation Method to Heat Transformers
Technische Universität Berlin • Department of Energy Engineering
Comparison of the capacities
• With B = 1.15 • 20 different working points• linear regression• balance error: about 1 kW
)70.2(23.0 ���� tQA�
)61.1(23.0 ���� tQC�
)41.1(22.0 ��� tQD�
)42.2(23.0 ��� tQE�
Measurement results: Riesch, P.: Aufbau und Betrieb eines Absorptionswärmetransformators. Diplomarbeit. Technische Universität München, 1986, pp. 53-54
15
F. Cudok • Application of the Characteristic Equation Method to Heat Transformers
Technische Universität Berlin • Department of Energy Engineering
Calculated slope- and loss-parameter
Measurement results: Riesch, P.: Aufbau und Betrieb eines Absorptionswärmetransformators. Diplomarbeit. Technische Universität München, 1986, pp. 53-54
As : X
mint�� : +
16
F. Cudok • Application of the Characteristic Equation Method to Heat Transformers
Technische Universität Berlin • Department of Energy Engineering
Calculated slope- and loss-parameter with z-factor
Measurement results: Riesch, P.: Aufbau und Betrieb eines Absorptionswärmetransformators. Diplomarbeit. Technische Universität München, 1986, pp. 53-54
As : X
mint�� : +
z-factor: refer to the presentation of Jan Albers
1st Workshop Development and Progress in Sorption Technologies
Characteristic Equation Method
February 27-28, 2012 Berlin (Germany)
Performance analysis of Absorption Heat Transformers
using Ionic Liquids with 2,2,2-Trifluoroethanol as
working fluid pairs
Dereje S. Ayou, Joan Carles Bruno and Alberto Coronas
CREVER, Dep. Mechanical Engineering, Universitat Rovira i Virgili, Tarragona (Spain)
1st Workshop Development and Progress in Sorption Technologies
Outline 1. Introduction
2. AHT cycle configurations
3. Cycle description and modelling
4. Results and discussion
5. Conclusions
Simulation of heat transformers with new working fluids - Berlin (Germany), 2012
1st Workshop Development and Progress in Sorption Technologies
1. In
trod
uctio
n
1 Simulation of heat transformers with new working fluids - Berlin (Germany), 2012
Enormous energy is dissipated as low temperature waste heat in the industry. Absorption heat pumps (AHPs) can recover low temperature waste heat from various industrial processes and upgrade it to deliver useful heat for heating and hot water supplies. Unlike electrical driven heat pumps, AHPs can also work as heat transformers.
The purpose of an Absorption Heat Transformer (AHT) cycle is to use heat at an intermediate temperature level and to upgrade a portion of it to a higher temperature and transfer this heat as a useful output.
AHTs are driven by recovery waste heat
The most used working fluid for AHTs has been water + lithium bromide (H2O + LiBr) due to its excellent properties (no toxicity, high latent of water as a refrigerant, no need for rectification to separate the mixture, etc).
But, has some drawbacks such as corrosion, crystallization and very low system pressure.
2
1. I
ntro
duct
ion
1st Workshop Development and Progress in Sorption Technologies
The objective of this work is to study the performance of AHTs using two working fluid pairs composed of ILs:
2,2,2-trifluoroethanol (TFE) +
1-ethyl-3-methylimidazolium tetrafluoroborate ([emim][BF4]) and
2,2,2-trifluoroethanol (TFE)+ 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4])
Alternative working fluid pairs: � The use of organic solvents was proposed in the literature as an
alternative to the conventional H2O + LiBr mixture mainly because of low corrosion, complete miscibility with refrigerants and thermal stability at relatively high temperatures.
� Ionic Liquids (ILs) have been proposed as new absorbents to overcome the problems of high volatility and low system performance that the organic absorbents show in absorption systems.
Simulation of heat transformers with new working fluids - Berlin (Germany), 2012
3
2. A
HT
cycl
e co
nfig
urat
ions
Simulation of heat transformers with new working fluids - Berlin (Germany), 2012
1st Workshop Development and Progress in Sorption Technologies
Cycle schematic for SEAHT (Herold et al, 1996) Cycle schematic for Modified SEAHT (Esteve, 1996)
Two-stage absorption heat transformer (TSAHT)
Cycle schematic for TSAHT (Best et al, 1997)
Single-effect absorption heat transformers (SEAHTs)
4
2. A
HT
cycl
e co
nfig
urat
ions
Simulation of heat transformers with new working fluids - Berlin (Germany), 2012
1st Workshop Development and Progress in Sorption Technologies
Double-absorption heat transformers, (type-1, type-2 and type-3)
Double-effect absorption heat transformer (DEAHT)
Cycle schematic for DEAHT (Gomri, 2010)
type-1 cycle configuration, (Zhao et al, 2003)
type-2 cycle configuration (Zhao et al, 2003)
type-3 cycle configuration (Zhao et al, 2003)
5
3. C
ycle
des
crip
tion
and
mod
ellin
g
Simulation of heat transformers with new working fluids - Berlin (Germany), 2012
1st Workshop Development and Progress in Sorption Technologies
Vapour-liquid equilibria and liquid enthalpies have been modelled for the mixtures (TFE+[emim][BF4] and TFE+[bmim][BF4]) with NRTL equation from experimental data (Wang et al 2010, Curras et al 2010, Chaudhari et al 1995, Kim et al 2004 and Herraiz 2001)
Selected AHT cycle configurations for modelling:
1. For high energy performance (high COP) 2. For high Gross Temperature Lift (GTL)
g gy p ( g
Schematic diagram of modified SEAHT
g p (
Schematic diagram of double-AHT (type-3)
6
3. C
ycle
des
crip
tion
and
mod
ellin
g
Simulation of heat transformers with new working fluids - Berlin (Germany), 2012
1st Workshop Development and Progress in Sorption Technologies
A model for the steady-state operation of AHTs have been developed.
Model inputs: � tgen and tevap
� tcond
� tabs (useful output heat temperature)
(for Double-AHT)
� Mass fraction difference between the strong and weak solution, ∆X
(for modified SEAHT)
� ɛSHE = 95% and ɛRHE = 95%
� 1kg/s of refrigerant flow through the evaporator
(basis for calculation)
� Ambient temperature, to= 25 oC
7
3. C
ycle
des
crip
tion
and
mod
ellin
g
Simulation of heat transformers with new working fluids - Berlin (Germany), 2012
1st Workshop Development and Progress in Sorption Technologies
Model outputs:
� Performance parameters:
COP - Coefficient of performance
ECOP - Exergy efficiency
f - Solution circulation ratio
GTL- Internal gross temperature lift
� Heat load in heat exchanging components
� Stream characteristics (t, P, X, h, )
8
4.
Res
ults
and
dis
cuss
ion
Simulation of heat transformers with new working fluids - Berlin (Germany), 2012
1st Workshop Development and Progress in Sorption Technologies
4.1 Modified single-effect AHT: Baseline input values: tevap = tgen = 70 oC, tcond = 35 oC, ∆X = 8%
4.1.1 – Operating condition for TFE + [emim][BF4]:
1 16.5 35.0 0.00 1 54.12 86.1 35.04 0.00 1 54.162a 86.1 53.4 0.00 1 85.63 86.1 70.0 0.00 1 495.94 86.1 107.2 55.16 7.9 192.95 86.1 76.0 55.16 7.9 145.66 16.5 76.0 55.16 7.9 145.67 16.5 70.0 63.16 6.9 134.98 86.1 70.04 63.16 6.9 134.99 86.1 105.4 63.16 6.9 189.110 16.5 70.0 0.00 1 500.4
10a 16.5 36.8 0.00 1 469.0
Enthalpy (kJ/kg)
Stream Pressure (kPa)
Temperature ( o C)
IL Mass (%)
mass flow rate (kg/s)
Parameter Value Parameter Value Parameter ValueCOP 0.40 Q abs , (kW) 276.6 Q SHE , (kW) 373.1ECOP 0.66 Q cond , (kW) 414.9 Q RHE , (kW) 31.4GTL (°C) 37.2 Q evap , (kW) 410.4 W pump1, (kW) 0.06f (kg/kg) 6.9 Q gen , (kW) 280.6 W pump2, (kW) 0.44
9
4. R
esul
ts a
nd d
iscu
ssio
n
Simulation of heat transformers with new working fluids - Berlin (Germany), 2012
1st Workshop Development and Progress in Sorption Technologies
4.1.2 – Operating condition for TFE + [bmim][BF4]:
1 16.5 35.0 0.00 1 54.12 86.1 35.04 0.00 1 54.162a 86.1 53.4 0.00 1 85.63 86.1 70.0 0.00 1 495.94 86.1 108.0 52.04 7.5 197.25 86.1 76.2 52.04 7.5 148.26 16.5 76.2 52.04 7.5 148.27 16.5 70.0 60.04 6.5 137.78 86.1 70.04 60.04 6.5 137.79 86.1 106.1 60.04 6.5 194.310 16.5 70.0 0.00 1 500.4
10a 16.5 36.8 0.00 1 469.0
Stream Pressure (kPa)
Temperature ( o C)
IL Mass (%)
mass flow rate (kg/s)
Enthalpy (kJ/kg)
Parameter Value Parameter Value Parameter ValueCOP 0.40 Q abs , (kW) 279.8 Q SHE , (kW) 368.0ECOP 0.66 Q cond , (kW) 414.9 Q RHE , (kW) 31.4GTL (°C) 38.0 Q evap , (kW) 410.4 W pump1, (kW) 0.06f (kg/kg) 6.5 Q gen , (kW) 283.8 W pump2, (kW) 0.44
10
4. R
esul
ts a
nd d
iscu
ssio
n
Simulation of heat transformers with new working fluids - Berlin (Germany), 2012
1st Workshop Development and Progress in Sorption Technologies
4.1.3 – Performance parameters for the new and conventional working fluid
pairs at the baseline input conditions:
� The RHE is not considered for cycle with H2O + LiBr working fluid pair.
� The RHE improves the cycle COP and ECOP by 4-5%.
TFE + [emim][BF4] TFE + [bmim][BF4] TFE + TEGDME H2O + LiBr COP 0.40 0.40 0.36 0.49ECOP 0.66 0.67 0.68 0.71GTL, (°C ) 37.0 38.0 52.3 24.6Q abs, (kW) 276.6 279.8 236.2 2419f, (kg/kg) 6.9 6.5 6.6 5.9
Working fluid pair Parameter
11
4. R
esul
ts a
nd d
iscu
ssio
n
Simulation of heat transformers with new working fluids - Berlin (Germany), 2012
1st Workshop Development and Progress in Sorption Technologies
4.1.4 – Effect of ∆X on COP and Qabs at the baseline condition
12
4. R
esul
ts a
nd d
iscu
ssio
n
Simulation of heat transformers with new working fluids - Berlin (Germany), 2012
1st Workshop Development and Progress in Sorption Technologies
4.1.5 – Effect of tevap = tgen on COP at the baseline condition
13
4. R
esul
ts a
nd d
iscu
ssio
n
Simulation of heat transformers with new working fluids - Berlin (Germany), 2012
1st Workshop Development and Progress in Sorption Technologies
4. 2 Double-AHT, type 3:
4. 2.1 – Performance parameters for TFE + [emim][BF4], TFE + [bmim][BF4]
TFE + TEGDME and H2O + LiBr working pairs at the operating conditions:
tevap = tgen = 70 oC, tcond = 30 oC, ɛSHE1, 2 = 95%, GTL = 60 oC
TFE + [emim][BF4] TFE + [bmim][BF4] TFE + TEGDME H2O + LiBr COP 0.20 0.21 0.21 0.32ECOP 0.38 0.38 0.39 0.61Q abs, (kW) 212.2 215.2 238.8 2403
Working fluid pair Parameter
14
4. R
esul
ts a
nd d
iscu
ssio
n
Simulation of heat transformers with new working fluids - Berlin (Germany), 2012
1st Workshop Development and Progress in Sorption Technologies
4. 2. 2 – Effect of tabs (or GTL) on COP for TFE + [emim][BF4],
TFE + [bmim][BF4] and H2O + LiBr.
15
4. R
esul
ts a
nd d
iscu
ssio
n
Simulation of heat transformers with new working fluids - Berlin (Germany), 2012
1st Workshop Development and Progress in Sorption Technologies
4. 2. 3 – Effect of tabs (or GTL) on ECOP for TFE + [emim][BF4],
TFE + [bmim][BF4] and H2O + LiBr.
16
4. R
esul
ts a
nd d
iscu
ssio
n
Simulation of heat transformers with new working fluids - Berlin (Germany), 2012
1st Workshop Development and Progress in Sorption Technologies
4. 2. 4 – Effect of tabs (or GTL) on Qabs for TFE + [emim][BF4]
and TFE + [bmim][BF4].
17
5
. Con
clus
ions
Simulation of heat transformers with new working fluids - Berlin (Germany), 2012
1st Workshop Development and Progress in Sorption Technologies
The performance of [emim][BF4] and [bmim][BF4] as absorbent for TFE in a modified single-effect AHT and Double-AHT were analysed for different operating conditions and the simulation results compared with those of the conventional and organic absorbents in AHTs (LiBr and TEGDME respectively).
For the considered operating conditions similar performance was observed for [emim][BF4] and [bmim][BF4] absorbents. Therefore, the transport properties are also important factors for selecting the better absorbent.
In a modified single-effect AHT [emim][BF4] and [bmim][BF4] perform better than TEGDME.
For Double-AHT at operating condition of tevap = tgen = 70 oC, ɛSHE1, 2 = 95%, and GTL = 60 oC, the transport properties (such as viscosity and surface tension) are the main key factors for comparing the absorbents.
18 Simulation of heat transformers with new working fluids - Berlin (Germany), 2012
1st Workshop Development and Progress in Sorption Technologies
Thank you for your attention
T. Zegenhagen • Application of the characteristic equation method to vapor jet-ejector cycles
Application of the characteristic equation method to vapor jet-ejector cycles
Prof. Dr.-Ing. Felix ZieglerDipl.-Ing. Tobias Zegenhagen
1Technische Universität Berlin • Department of Energy Engineering
• Motivation
• Jet-ejector cycle and jet-compression
• Application of the characteristic equation method
• Conclusion and outlook
T. Zegenhagen • Application of the characteristic equation method to vapor jet-ejector cycles
Characteristic equation method:
• device with at least two heat exchangers
2Technische Universität Berlin • Department of Energy Engineering
• phase change dominated heat transfer
• a closed or open thermodynamic cycle
T. Zegenhagen • Application of the characteristic equation method to vapor jet-ejector cycles
Jet-ejector cycle• Cycle and its parameters
3Technische Universität Berlin • Department of Energy Engineering
• Operating map jet-compression
T. Zegenhagen • Application of the characteristic equation method to vapor jet-ejector cycles
4Technische Universität Berlin • Department of Energy Engineering
Sorption process:
• process with two working media
• definition of a thermodynamic state by means of the solution field, i.e. temperature, pressure and concentration
� coupling by Dühring’s rule
Jet-ejector process:
• process with a single working medium
• definition of the thermodynamic state by means of the vapor pressure curve, i.e. temperature and pressure
� coupling by the Clausius-Clapeyronequation
T. Zegenhagen • Application of the characteristic equation method to vapor jet-ejector cycles
5Technische Universität Berlin • Department of Energy Engineering
(4)� (5): isentropic pumping
(4)�(1): isenthalpic expansion
(1)�(2), (5)�(6)/ (3)�(4): isobaric heat supply/ rejection
(2), (6)�(3): jet compression
T. Zegenhagen • Application of the characteristic equation method to vapor jet-ejector cycles
6Technische Universität Berlin • Department of Energy Engineering
(2,s)�(2,a): isentropic expansion of driving flow in supersonic nozzle
(2,a)�(2,x): overexpansion into mixing zone due to nozzle shape
(0,s)�(0,x): isentropic expansion of suction flow in dynamic Venturi nozzle
(2,x)+(0,x)�(M): isobaric mixing
(M)�(M,n): non-isentropic shock
(M,n)�(1,s): isentropic compression in subsonic diffuser
T. Zegenhagen • Application of the characteristic equation method to vapor jet-ejector cycles
N h k d d i i fl
7Technische Universität Berlin • Department of Energy Engineering
� choked mass flow dependent on stagnation pressure p2,s and temperature T2,s only
Choked driving mass flow:
Non-choked driving mass flow:
T. Zegenhagen • Application of the characteristic equation method to vapor jet-ejector cycles
8Technische Universität Berlin • Department of Energy Engineering
Critical ejector operation:
• dependent on stagnation pressures p2,s, p1,s , p0,s and temperatures T2,s, T1,s , T0,s only
• driving and suction mass flow at maximum �limit=�0,max/�2,max
Choked driving and
suction mass flow:
T. Zegenhagen • Application of the characteristic equation method to vapor jet-ejector cycles
Increase in evaporator pressure p0,s� at
constant p2,s and p1,s:
• �0,2� and �0,1� and
• higher entrainment ratio �=�0/�2�(�2=const./ �0=const.)
Jet-ejector operating regimes:
9Technische Universität Berlin • Department of Energy Engineering
1. normal supersonic (Ma2,a>1, Ma0,x<1)
2. saturated supersonic (Ma2,a>1, Ma0,x=1)
� critical-pressure curve: separates
saturated and normal supersonic regimes
� limiting entrainment ratio �limit: thermodynamic optimum
T. Zegenhagen • Application of the characteristic equation method to vapor jet-ejector cycles
Application of the characteristic equation method• Heat exchange and enthalpy balances
10Technische Universität Berlin • Department of Energy Engineering
• Process inherent restrictions for mass flows
• Functional relation between pressure and temperature
T. Zegenhagen • Application of the characteristic equation method to vapor jet-ejector cycles
Heat exchange and enthalpy balances…
for evaporator (V), condenser (C) and heater (H)…
11Technische Universität Berlin • Department of Energy Engineering
T. Zegenhagen • Application of the characteristic equation method to vapor jet-ejector cycles
Lead with the mass balance…
And the introduction of…
To the set of 3 coupled equations with 5 unknowns:
12Technische Universität Berlin • Department of Energy Engineering
To the set of 3 coupled equations with 5 unknowns:
If K, G as well as U0·A0, U1·A1 and U2·A2 are assumed
constant.
T. Zegenhagen • Application of the characteristic equation method to vapor jet-ejector cycles
Process inherent restrictions: maximum flow density at critical velocity
13Technische Universität Berlin • Department of Energy Engineering
Definition of the limiting entrainment ratio on critical pressure curve (geometrical relation)…
� one additional equation with no new unknowns except �0,2 (A0,x=f(A2,x)=f(AM,min,�0,2))
� no information about the achievable condenser pressure
T. Zegenhagen • Application of the characteristic equation method to vapor jet-ejector cycles
Process inherent restriction: jet compression by means of momentum exchange
14Technische Universität Berlin • Department of Energy Engineering
Momentum balance of ejector mixing section with mixing at constant area, i.e. AM,min=A2,x+A0,x
(energetical relation)…
With the assumption of isobaric mixing, i.e. pM=p2,x=p0,x…
T. Zegenhagen • Application of the characteristic equation method to vapor jet-ejector cycles
15Technische Universität Berlin • Department of Energy Engineering
With the energy equation for the single isentropic flows (w2,s=w0,s=w1,s=0)…
T. Zegenhagen • Application of the characteristic equation method to vapor jet-ejector cycles
Assumption of isentropic expansion/ compression and ideal gas…
16Technische Universität Berlin • Department of Energy Engineering
Assumption of working at critical back pressure:
� one additional equation with no new unknowns except �0,1
T. Zegenhagen • Application of the characteristic equation method to vapor jet-ejector cycles
Approximation for the functional relation between pressure and temperature:
17Technische Universität Berlin • Department of Energy Engineering
In analogy:
T. Zegenhagen • Application of the characteristic equation method to vapor jet-ejector cycles
Alternative approximation:
18Technische Universität Berlin • Department of Energy Engineering
T. Zegenhagen • Application of the characteristic equation method to vapor jet-ejector cycles
System of coupled equations:
19Technische Universität Berlin • Department of Energy Engineering
T. Zegenhagen • Application of the characteristic equation method to vapor jet-ejector cycles
Assessment of assumptions, conclusion and outlook
20Technische Universität Berlin • Department of Energy Engineering
T. Zegenhagen • Application of the characteristic equation method to vapor jet-ejector cycles
Assessment of model assumptions:
• negligible inlet and outlet velocities, i.e. w2,s=w0,s=w1,s=0
• isentropic expansion of the propellant and suction stream until mixing
• application of the ideal gas law
• mixing at constant area, i.e. AM min=A2 x+A0 x
21Technische Universität Berlin • Department of Energy Engineering
mixing at constant area, i.e. AM,min A2,x A0,x
• isobaric mixing, i.e. pM=p2,x=p0,x
• isentropic compression
• no consideration of superheating, i.e. stagnation temperatures Tscorrespond to stagnation pressures ps
T. Zegenhagen • Application of the characteristic equation method to vapor jet-ejector cycles
Conclusion:• feasible derivation of a simple set of algebraic equations for the jet-
ejector cycle
• mathematical complication due to physical differences in process description
• questionable analytical or numerical solution
22Technische Universität Berlin • Department of Energy Engineering
Outlook:• attempt of analytical or numerical solution
• sensitivity check of critical assumptions
• comparison to experimental results
T. Zegenhagen • Application of the characteristic equation method to vapor jet-ejector cycles
2
2.5
3m
ent r
atio
μ limit
T2,s �
23Technische Universität Berlin • Department of Energy Engineering
1.5 2 2.5 3 3.5 4 4.5 5 5.50.5
1
1.5
limiti
ng e
ntra
in
ratio of expansion to compression enhtalpy difference Δ h2,exp/ Δ hcomp
T2,s �
T. Zegenhagen • Application of the characteristic equation method to vapor jet-ejector cycles
5
6
7
8
9
10
nmen
t rat
io μ lim
it
24Technische Universität Berlin • Department of Energy Engineering
0 2 4 6 8 10 12 14 160
1
2
3
4
5
limiti
ng e
ntra
in
ratio of expansion to compression enhtalpy difference Δ h2,exp/ Δ hcomp
David Martínez-MaradiagaCREVER – Research Group on Applied Thermal Engineering
Mechanical Engineering Department. Universitat Rovira i VirgiliTel. 977 55 96 60 / Fax: 977 55 96 91
E-mail: davidestefano.martinez@urv.cat
Integration of the characteristic equation in complete data treatment and modeling approaches
of absorption chillers
1st Workshop: Development and Progress in Sorption
Technologies: Characteristic Equation MethodBerlin (Germany) – 27-28th February 2012
1. Modelling Approaches
2. Data Treatment
3. Examples
Outline
4. Conclusions
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012 1
Thermodynamic Models
Empirical/Semi-Empirical Models
• Characteristic Equation
Modelling Approaches
• Artificial Neural Networks
• Multivariable Polynomial Regressions
• Gordon-Ng
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012 2
Data Treatment
Problems with Data
Random Error
Systematic Errors
Redundancy
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012 3
Berlin, February 2012Data Treatment
Steady-State Identification
Gross ErrorsIdentified?
Yes
No
Model Raw Data
Reconciled Data
SSI
DoF
DR
GED
Eliminate Measurements
with GE
Degrees of Freedom Analysis
Data Reconciliation
Gross Error Detection
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012 4
Data Treatment: Steady-State Detection
Moving Data Window SS Detector (Kim et al, 2008)
Window Size
Key Variables
Standard Deviation
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012 5
Berlin, February 2012Data Treatment: Degrees of Freedom Analysis
Systematic Methodology for Determining Degrees of Freedom
Unit/Element Streams
Absorber�(A) 5C+17 C+8 4C+9
Condenser�(C) 2C+11 C+3 C+2
Evaporator�(E) 4C+15 2C+8 2C+7
Generator�(G) 3C+13 C+9 2C+4
Solution�Heat�Exchanger��������(SHX) 4C+9 2C+4 2C+5
Solution�pump�(SP) 2C+5 C+2 C+3
Expansion�valve�(EV) 3C+6 2C+3 C+3
Units and elements catalogue for components of absorption cycles (Sendeku et al., 2011)
uvN u
rN udN
Wp
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012 6
Data Treatment: Data Reconciliation
Two Stage Data Reconciliation
2*2
*
min ���
����
� ��
��
����
� �
uy
uuyyJ��
0),,( uyxf
Data Reconciliation stage
Simulation stage
Matlab(fmincon)
EESModel
u
y, x
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012 7
Data Treatment: Gross Error Detection
Modified Iterative Test
� ** , uuyye ��
i
ii
ez
�
Calculation of residuals, e
Calculation of statistical, z
Comparison with zc ci zz �
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012 8
Example 1: Single Effect NH3/H2O
Chilled Water
AE
CGR
SHX
1
2
3
4
5
6
8
7
9
10
Cooling WaterHot Water
SP SEVREV
11 12
13
14
15
16 17Single-effect ammonia-water absorption chiller
Nominal cooling capacity of 12kW Chillii® PSC12 Simplified diagram of the absorption chiller
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012 9
Number of tests with measurements containing gross errors after the 1st DR(a) and the 2nd DR (b).
Example 1: Single Effect NH3/H2O
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012 10
Value of the objective function before and after DR.
Example 1: Single Effect NH3/H2O
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012 11
Qe and COP calculation using raw and reconciled
measurements.
Example 1: Single Effect NH3/H2O
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012 12
Heat Balances Before and After DR.
Example 1: Single Effect NH3/H2O
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012 13
Example 2: Double Effect H2O/LiBr
CVS Graphs
HT Generator
Exhaust gas
23
Recirculation pump Absorbent
pump Solution spray nozzle
Refrigerant spray nozzle
Solution splitter
14
13
11
10
26
9
1
7
27
19
8
18
LP Condenser
22
20
21
24
25Refrigerant combiner
Cooling water
28 2931
Chilled water
32
17
16
124
30
29
Absorber
LP Condenser
Evaporator
HP Condenser
LT Generator
LT Solution heat exchanger
HT Solution heat exchanger
Heat from HP Condenser
Heat to LT Generator
Diluted absorbent Intermediate absorbent Strong absorbent Refrigerant
2
3
15
5
Solution mixer
6
Drain Heat exchanger
Temperature
Pres
sure
Solution spray nozzle
Refrigerant spray nozzle
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012 14
Example 2: Double Effect H2O/LiBr
0
1
2
3
4
5
6
1 2 3 4 5 6 7 8 9 10
z
t12 t20 x 12
zc
Value of z for the measurements flagged as Gross Errors after the 1st DR for the 10 Steady-State periods.
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012 15
Example 2: Double Effect H2O/LiBr
Value of the objective function after the 1st and 2nd DR for the 10 Steady-State periods.
0
10
20
30
40
50
60
70
80
1 2 3 4 5 6 7 8 9 10
Valor
final
de la
func
ión ob
jetivo
(J) RD1
RD2
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012 16
Example 2: Double Effect H2O/LiBr
Heat Flows and Heat Balances calculated from unreconciled (a) and reconciled (b) data for the 10 Steady-State periods.
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
1 2 3 4 5 6 7 8 9 10
Fluj
o de
cal
or (k
W)
Calor Rechazado Calor Absorbido Diferencia
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
1 2 3 4 5 6 7 8 9 10
Fluj
o de
cal
or (k
W)
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012 17
Example 3: Single-Effect H2O/LiBr
SPREV SEV
C
E
SHX
Fixed Data
mSP = 1 (kg/s)UAA, UAG, UAC, UAE, �SHX
“Measured” Data
48 operating conditions
mcw, mhw mch
tcw,in, tcw,int , tcw,out , thw,in , thw,out , tch,in, tch,out
t1, t3, t4, t8phigh, plow
1
2
3 4
5
6
7
8
9
10
G
A
30 samples/operating condition
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012 18
Example 3: Single-Effect H2O/LiBr
Inputs
mcw
mhw
mch
tcw,in
thw,in
tch,out
Random NoiseEES
Model
Outputs
(rand-0.5)*3�x+
tcw,int
tcw,out
thw,out
tch,in
t1t3t4T8
plow
phigh
Random Noise
(rand-0.5)*3�x+
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012 19
Example 3: H2O/LiBr
15
30
45
Tem
pera
ture
(ºC
)
29
30
31
Mas
s flo
w ra
te (k
g/s)
tcw,in
tcw,int
tcw,out
mcw
0
5
10
15
20
Tem
pera
ture
(ºC
)
8
9
10
Mas
s flo
w ra
te (k
g/s)
thw,in
thw,out
mhw
70
80
90
100
Tem
pera
ture
(ºC
)
11
12
13
Mas
s flo
w ra
te (k
g/s)
tch,in
tch,out
mch
-15
-10
-5
0
5
10
15
Ener
gy B
alan
ce (k
W)
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012 20
Example 3: H2O/LiBr
A 1.2633Arec 1.2485
E 0.2446Erec 0.2475
R 31.8732Rrec 28.9250
S 3.1972Srec 3.2349
Characteristic equation coefficients
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012 21
Example 3: H2O/LiBr
R2
1- 0,9970
2- 0,9968
3- 0,9993
4- 0,9995
1 2 3 40
0.25
0.5
0.75
1
Coe
ffici
ent o
f var
iatio
n
1- raw data vs raw calc
2- raw data vs rec calc
3- rec data vs raw calc
4- rec data vs rec calc
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012 22
Conclusions
This methodology is demonstrated analysing the operational data of a small-capacity single effect ammonia/water absorption chiller tested in a testbench and a double effect water/lithium bromide absorption chiller workingin a polygeneration plant.
This presented methodology includes a steady-state detection step, asystematic degrees of freedom analysis, and DR including GED. Thismethodology allows a reliable calculation of important parameters, such asCOP and cooling capacity and at the same time the identification ofmeasurements with systematic errors
Empirical modelling approaches, such as the Characteristic EquationMethod, benefit from the DR since the data used for their construction haslower noise and is consistent with the laws of conservation.
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012 23
ACKNOWLEDMENT
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012
The author acknowledges the financial support given by the Ministerio de Economía y Competitividad of Spain through the
project ref. ENE2009-14182
24
Thanks for your attention
D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012
Example 1: NH3/H2O
Steady State Detection
E-1D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012
Example 1: NH3/H2O
Measurement Standard Deviation
Original Value
Reconciled Value Residual z
t1 (ºC) 0.08 29.59 29.59 2.90E-04 0.00t4 (ºC) 0.12 70.54 70.54 3.13E-04 0.00t7 (ºC) 0.13 64.12 65.01 8.86E-01 6.81t8 (ºC) 0.09 32.69 32.69 1.33E-04 0.00t9 (ºC) 1.00 1.90 1.86 3.55E-02 0.04t11 (ºC) 0.19 84.97 85.11 1.48E-01 0.78t12 (ºC) 0.13 78.97 78.88 9.21E-02 0.71t13 (ºC) 0.08 27.00 27.08 7.22E-02 0.90t14 (ºC) 0.09 29.50 29.50 8.28E-04 0.01t15 (ºC) 0.09 31.53 31.44 9.39E-02 1.04t16 (ºC) 0.13 9.24 9.35 1.09E-01 0.84t17 (ºC) 0.09 6.98 6.94 4.14E-02 0.46
Ph (bar) 0.50 12.50 12.54 4.23E-02 0.08Pl (bar) 0.50 4.60 4.57 3.29E-02 0.07
G11 (m3/h) 0.01 2.20 2.20 2.43E-03 0.24G13 (m3/h) 0.01 4.79 4.79 1.18E-03 0.12G16 (m3/h) 0.01 3.37 3.37 1.26E-03 0.13
Raw and reconciled measurements for hot water inlet temperature (t11) at 85 ºC, cooling water inlet temperature (t13) at 27, and chilled water outlet temperature (t17) at 7 ºC
E-2D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012
Example 1: NH3/H2O
Parameters calculated during the three DR steps (at the same conditions of Table 7)
Parameter Without DR After After After Qe (kW) 7.98 8.55 8.69 8.52Qa (kW) 13.85 13.50 13.42 13.45Qc (kW) 11.26 10.64 10.91 10.73Qg (kW) 17.01 15.49 15.53 15.55Wp (kW) 0.12 0.10 0.10 0.12
COP 0.47 0.55 0.56 0.54�shx 0.82 0.83 0.84 0.86
UAe (kW/K) 0.34 0.43 0.43 0.37UAa (kW/K) 0.84 0.80 0.81 0.87UAc (kW/K) 0.21 0.20 0.21 0.20UAg (kW/K) 0.26 0.23 0.23 0.24
E-3D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012
Example 2: H2O/LiBr
E-4D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012
Example 2: H2O/LiBr
VariableDesviaciónEstándar
Valor MedidoValor
ReconciliadoResiduo z
t9 0.66 113.38 113.69 0.31 0.47t12 0.34 66.66 63.79 2.87 8.37t13 0.87 40.07 40.08 0.01 0.01t16 0.46 73.13 73.04 0.08 0.18t20 0.22 26.96 26.96 0.00 0.01t26 0.41 364.53 364.52 0.00 0.01t27 0.94 136.75 136.78 0.03 0.04t28 0.23 23.78 23.64 0.14 0.62t30 0.20 26.45 26.65 0.20 0.98t31 0.11 7.21 7.20 0.01 0.06t32 0.08 5.15 5.15 0.00 0.02m26 0.60 7.32 7.16 0.16 0.26G31 1.43 659.28 659.28 0.00 0.00x12 0.12 57.62 57.60 0.01 0.11G28 3.74 980.28 980.37 0.09 0.02
Mediciones reconciliadas y no reconciliadas para uno de los períodos estacionarios analizados en el caso de estudio
E-5D.Martinez-Madariaga 1st Workshop Development and Progress in Sorption Technologies, Berlin 2012
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