1st workshop development and progress in sorption · pdf filedevelopment and progress in...

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

[email protected]

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



The Japanese start: Takada, Furukawa, Sonoda

3



4



Enthalpy balance across each main component:

)( 67 ��

)( 65 ��

��

��

7

6

5

4

3

2

1

Rm�

sSm ,�

wSm ,�

5



�� ,��

Variable

��

Constant (almost)

��

�

��

�

�� ,

6



)( ��

�

�

�� (�Heat transfer across each main component:

��

�

��

�

��

��

�

��

�

��

��

��

��

��

��

1(exp1

1(exp1

Constant (almost)

Variable

With heat capacity flow

7



��

��

�

��

�

��

��

�

��

�

��

��

��

��

��

��

1(exp1

1(exp1and

yields

��

�

��

�

��

��

�

��

�

��

��

��

��

��

��

1(exp1

1(exp1

8



��

�

��

�

��

��

�

��

�

��

��

��

��

��

��

1(exp1

1(exp1

��

Constant (almost)

Variable

4 times!

9



��

Connect temperatures: �� )()(�� )()(

)( ��

From this you can derive all heat flows

��

is fitted as linearly dependent on � �

��

10



11



12



Variable Constant (almost)

Enthalpy balance across each main component:

? „Solution heat exchanger loss“

�� ,��

The Munich-Berlin adaptation: Alefeld, Kern, Riesch, Scharfe, Ziegler et al….

13



Heat transfer across each main component:

Mean temperatures

�� (�

14



�� ,( ��

��

��

�� ,( ��

��

�

��

�

��

��

�

��

�

��

��

��

��

��

��

1(exp1

1(exp1Furukawa:

15



��

Connect temperatures:

�� )()(

�� )()(

��

��

��

0)()( ��

�� )()(

��

�� ,��

Boiling point elevation Dühring relation

External temperatures:

16



02468

101214161820

0 5 10 15 20 25 30 35 40 45

Characteristic temperature function � � t [K]

Co

olin

g c

ap

acit

y [k

W]

2.12.2 ��

17



0

2

4

6

8

10

12

14

16

18

20

0 5 10 15 20 25 30 35 40 45Adapted characteristic temperature function ��t' [K]

Coo

ling

capa

city

[kW

] ��

18



.

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



Or: for each mass flow rate an additional restriction for temperatures or mass flow is necessary

�

Absorption chiller: Dühring ��

1��

Compression chiller:

��

� �� 2

��

with August-equation: 21ln ��

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 [email protected]

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


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.



2.1 – 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]



2.1 – 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]



2.1 – 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.



2.1 – 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]



2.2 – 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]



2.2 – 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]



2.2 – 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]



2.3 – 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


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



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.



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.



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


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


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


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

10

15

20

25

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

10

15

20

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.



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

��

�N

iiN

RMSE1

21 �

%100�y

RMSECV



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.



Integration into a biomass gasification trigeneration plant

M. Puig-Arnavat, Performance modelling and validation of biomass gasifiers for trigeneration plants, PhD Thesis, URV, 2011.



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


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


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



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



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



Motivation

0 10 20 30 40 50 0

5

10

15

20

25

��

� ��

��

Comparison between improved method and measurements Is there really a single characteristic (straight) line? How to determine the constant(?) slope and intersect?

��t / K


5



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 � ��

� � � ��

� ��

� � � � ��

��

��

Characteristic equation method – established

��t characteristic temperature difference sE and ��tmin,E characteristic parameters KX characteristic coefficients

6



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 ��

� � � � ��

��

��

��

��AA

irrA,DD

irrD,Emin, zUA1Q

zUA1QΔΔt ��

QX,irr load independent (thermodynamic) losses � const. � ��tmin,E and sE � const. � linear equation

� � � � � � � �

1

EECC

C

AA

A

DD

DE zUA

1zUA

KBzUA

KzUA

Ks�

��

��

��

��

��

��

��

��

�

7



Eq. 5 Using enthalpy coefficient KD

Eq. 6 leads to

Eq. 7 Inserting and

Eq. 8 Finally

Desorber capacity – established method

��

��

� �

1�

�

��

��

8



Determination of characteristic parameters

With given UA-values from measurements we calculate


��

� � � � � � � �

1

EECC

C

AA

A

DD

DE zUA

1zUA

KBzUA

KzUA

Ks�

��

��

��

��

��

��

��

��

�

��tmin,E from rated capacity or at ��t0 = (tD,0 – tA,0) – B·(tC,0 – tE,0) ��

� ��

9



Determination of characteristic parameters

� ��

��

�

��

��


� � � � � � � �

1

EECC

C

AA

A

DD

DE zUA

1zUA

KBzUA

KzUA

Ks�

��

��

��

��

��

��

��

��

�

��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



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


11



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



Results of step 1a and 1b

� � � � � ��

��

�

�

�

Heat permeability ratio

��

Temperature difference

ratio Effective heat permeability

� ��~�

~

Heat permeability



13



Results of step 1a and 1b

X

Xlog,X ΔT

ΔTz �

� �� 1eR1NTU

1e2XX

XX

R1NTUXX

R1NTU

��

� ��

��

� ��

�

�

��

�

��

� ��

�



Heat capacity flow rate ratio

Temperature difference ratio

Dimensionless heat permeability

14



Steps of improvement



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



Pseudo specific

heat capacity

Application of dimensionless

temperature glides

��


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





� ��

� � � � ��

��


��

��

�

��

��

��

��

�

��

��

�� ~~ ��

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





� ��

� � � � ��

��


��

��

�

��

��

��

��

�

��

��

�� ~~ ��

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



Step 2: Revision of heat transfer calculation a) type of heat exchanger construction b) variable loss parameter

19



� � � � logDmDD ΔTUAΔTUAQ ��


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





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

QQ

TTcmTTcm �� ~

phase change sub-cooling - heat of evaporation (load) - heat of solution (loss) - sensible heat (loss)

(loss)

Driving heat

DQ�

21



Integral apperant specific heat capacity

D2Q�

T(pC) TD2

TDs TDe


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



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


23



Heat transfer calculation for mode A


DsT

DeT

SorT

D1Q��

� D2Q�

Refm�

DiTadiabatic absorption of refrigerant

D1Ref,m� Mode A

��

poor solution (in equilibrium)


TD1 TD2

TSor TDs TDe TDi


Dew

poi

nt

of re

frige

rant

D1Ref,m�

T(pC)

pxrx

24




DsT

DeT

SorT

D1Q��

� D2Q�

Refm�


D1Ref,m� Mode A

��


Dew

poi

nt

of re

frige

rant

� � � � � �� ~~ ��

D2Q�D1Q�

� �� ~�

�


TD1 TD2

TSor TDs TDe TDi

T(pC)

D1Ref,m�

pxrx

25





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




TD1 TD2

TSor TDs TDe TDi

Dmax,ΔT

DitDotT(pC)

� �� ~��


� �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




DsT

DeT

SorT

D1Q��

� D2Q�

Refm�


D1Ref,m� Mode A

�� Refm�


SorT

D1Q�� D2Q�

DeT

DsT

Mode B

��

rich solution (sub-cooled) desorbed refrigerant

poor solution (in equilibrium)


28





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



� � � �� ~��

Heat transfer calculation for mode B


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



� � � �� ~��

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



Mode A Mode B

ED2D2 QKQ �� LD1rD1sED1 ΔtKKQQ ��


� ��

~��

��

�

�

�

�

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



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



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


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


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



Mode A Mode B

ED2D2 QKQ �� LD1rED1sD1 ΔtKQKQ ��


� ��

~��

��

�

�

�

�

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



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



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



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



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



Slope parameter for Desorber

ED2D2 QKQ ��

LD1rD1sED1 ΔtKKQQ �� D2D1D QQQ ��

LD1rED1sED2D ΔtKQKQKQ ��

� � � � ��

��

��

��

��

��

��

40



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


� ��

��

��

��

��

�

��

��

��

��

�

��

��

��

��

� �� ~~

� � ��

��

��

��

�

��

��

��

��

�

��

�� ~~ ��

�

old

new

old

new

� � � � XEmin,XEE VttVsQ �� ΔΔΔΔ ��

41



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


��t / K

42



Results – improved method

0 10 20 30 40 50 0

5

10

15

20

25

��

� ��

��


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



Step 4 Consideration of bypass heat flows

44



Bypass heat flows

E

C

A

D

��

��

��

45



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



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



Characteristic equation method – improved

Evaporator capacity

Slope- parameter

Loss- parameter


� ��

��

��

��

��

�

��

��

��

��

�

��

��

��

��

� �� ~~

� � ��

��

��

��

�

��

��

��

��

�

��

�� ~~ ��

�

� � � � XEmin,XEE VttVsQ �� ΔΔΔΔ ��

� ��

48



Explanation of Kühn&Ziegler2005 approach

� � � ��

� ��

� � � � ��

� ��

49



Explanation of Kühn&Ziegler2005 approach

��

��

��

��

��

�

��

��

�

��

��

�

��

�� !!!!�

��

� ��

� � � ��

� ��

��

Compare with: Kühn&Ziegler, OTTI-Symposium 2005

50



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


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


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


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


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

15

16

17

18

19

2122

2423

2526

28 27

� �� oi mm ��

ooii xmxm ��

� � � � �� iiooX xmhmWQ ��

XXX TLMUAQ ��


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

19

2122

2423

2526

28 27

� �81010 hhQm E �� 810510 hhhhA ��

� � � �81087 hhhhC �� 18171870 hhhhK ��

� � � �18171417 hhhhD ��

� �181717 hhQm K ��

� � � �810471 hhhhK ��

� � � �18171472 hhhhK ��


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

2526

28 27

1LOSSEA QQAQ ��

� � � � � �22121 11 KQQKQKQ LOSSLOSSEK ��

2LOSSKD QQDQ ��

KEC QKQCQ �� 0


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


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)


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

�

�

�

�

��

��

��

��

��

�

��

��ECAD

E UABB

KKKC

UAB

UAAB

KK

UADs


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

��

� � ��

��

��

��

�� 2

2

0

21 1

1111

1 BKUA

KBUAKUA

DsCAD

EE�

��

��

��

��

�

��

�

�� 2

2

0

22 1

11

11 BKUA

KK

DUA

sCD

EE�

E

LOSSEE s

Qw 222

��


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 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

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 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 - 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 - 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

]


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




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

]


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




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 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


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


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)


THANK YOU FOR YOUR ATTENTION!!!

Berlin: 2012.02.27-28 / 24

1

F. Cudok • Application of the Characteristic Equation Method to Heat Transformers


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



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



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



HeatTransfer (1)

Enthalpybalance (2)

For condenser and evaporator

(3)

Example: Condenser

(4)

with

Deduction

5



Deduction

legend:

absorption chiller

6



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



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



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



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



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�



11



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



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



Thank you for your attention.

Falk [email protected]

(030) 314-28483

Department of Energy Engineering, Prof. Dr.-Ing. Felix ZieglerMarchstrasse 18, 10587 Berlin. Tel.: (+49) 030 314 - 22387 Fax: - 22253

14



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�


15



Calculated slope- and loss-parameter


As : X

mint�� : +

16



Calculated slope- and loss-parameter with z-factor


As : X

mint�� : +



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)


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


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


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.


3

2. A

HT

cycl

e co

nfig

urat

ions



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



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



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



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



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



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



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



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



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



4.1.5 – Effect of tevap = tgen on COP at the baseline condition

13

4. R

esul

ts a

nd d

iscu

ssio

n



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



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



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



4. 2. 4 – Effect of tabs (or GTL) on Qabs for TFE + [emim][BF4]

and TFE + [bmim][BF4].

17

5

. Con

clus

ions



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


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


Characteristic equation method:

• device with at least two heat exchangers


• phase change dominated heat transfer

• a closed or open thermodynamic cycle


Jet-ejector cycle• Cycle and its parameters


• Operating map jet-compression



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



(4)� (5): isentropic pumping

(4)�(1): isenthalpic expansion

(1)�(2), (5)�(6)/ (3)�(4): isobaric heat supply/ rejection

(2), (6)�(3): jet compression



(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


N h k d d i i fl


� choked mass flow dependent on stagnation pressure p2,s and temperature T2,s only

Choked driving mass flow:

Non-choked driving mass flow:



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:


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:


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


Application of the characteristic equation method• Heat exchange and enthalpy balances


• Process inherent restrictions for mass flows

• Functional relation between pressure and temperature


Heat exchange and enthalpy balances…

for evaporator (V), condenser (C) and heater (H)…



Lead with the mass balance…

And the introduction of…

To the set of 3 coupled equations with 5 unknowns:


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.


Process inherent restrictions: maximum flow density at critical velocity


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


Process inherent restriction: jet compression by means of momentum exchange


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…



With the energy equation for the single isentropic flows (w2,s=w0,s=w1,s=0)…


Assumption of isentropic expansion/ compression and ideal gas…


Assumption of working at critical back pressure:

� one additional equation with no new unknowns except �0,1


Approximation for the functional relation between pressure and temperature:


In analogy:


Alternative approximation:



System of coupled equations:



Assessment of assumptions, conclusion and outlook



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


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


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


Outlook:• attempt of analytical or numerical solution

• sensitivity check of critical assumptions

• comparison to experimental results


2

2.5

3m

ent r

atio

μ limit

T2,s �


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 �


5

6

7

8

9

10

nmen

t rat

io μ lim

it


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: [email protected]

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


Data Treatment

Problems with Data

Random Error

Systematic Errors

Redundancy


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


Data Treatment: Steady-State Detection

Moving Data Window SS Detector (Kim et al, 2008)

Window Size

Key Variables

Standard Deviation


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


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


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 �


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


Number of tests with measurements containing gross errors after the 1st DR(a) and the 2nd DR (b).



Value of the objective function before and after DR.



Qe and COP calculation using raw and reconciled

measurements.



Heat Balances Before and After DR.



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



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.



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



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)


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


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+


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)


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


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


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.


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


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


Example 2: H2O/LiBr


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


1st workshop development and progress in sorption · pdf filedevelopment and progress in...

Documents