Mathematical Modeling of an Absorption Chiller System Energized by a Hybrid Thermal System: Model Validation


 Energy Procedia   34  ( 2013 )  159 – 172 

1876-6102 © 2013 The Authors. Published by Elsevier B.V.
Selection and peer-review under responsibility of COE of Sustainalble Energy System, Rajamangala University of Technology 
Thanyaburi (RMUTT)
doi: 10.1016/j.egypro.2013.06.744 

10th Eco-Energy and Materials Science and Engineering  

(EMSES2012)  
Mathematical Modeling of an Absorption Chiller System 

Energized by a Hybrid Thermal System: Model Validation 
Boonrit Prasartkaew* 

Department of Mechanical Engineering, Faculty of Engineering, Rajamangala University of Technology,  
39 Moo 1, Klong 6, Thanyaburi, Pathumthani, 12110, Thailand 

Abstract 

Nowadays, global warming and energy crisis problems become serious issues which affect on all 
creatures on our earth. One of the best ways to simultaneously address or mitigate these problems is more 
utilizing the renewable energy sources instead of the fossil fuel. A solar-biomass hybrid cooling system is 
one of the technologies for the climate change and green-house-gas mitigation. The mathematical model 
of this system was developed and used in the theoretical prediction of its performance and system design.  
To assess the accuracy of the developed mathematical model, the obtained experimental data is then 
compared with the simulation results, with the same operating parameters and weather conditions. This 
paper presents the validation of the developed model. The validation results show that the simulation 
results are in good agreement with the experimental results from both qualitative and quantitative points 
of view.  
 
© 2013 The Authors. Published by Elsevier B.V.  
Selection and/or peer-review under responsibility of COE of Sustainable Energy System, Rajamangala 
University of Technology Thanyaburi (RMUTT) 
Keywords: Solar-biomass hybrid; Cooling system; Simulation model; Validation 

1. Introduction 

Nowadays, the global warming and energy crisis problems become the most serious issues. These 
problems, mainly attributed to the combustion of fossil fuel [1], substantially affect on all life on the 
earth. To address these problems, the renewable energy based should be encouraged. Among the energy 
utilization systems, cooling applications demand higher energy for their functioning [2]. Solar cooling 
technology is environmentally friendly and contributes to a significant decrease of the CO2 emissions 
which cause the green house effect [3]. From this point of view, solar powered cooling systems as a green 

 

* Corresponding author. Tel.: +662-549-3430; fax: +662-549-3422 
E-mail address: prasartkaew@yahoo.com 

Available online at www.sciencedirect.com

© 2013 The Authors. Published by Elsevier B.V.
Selection and peer-review under responsibility of COE of Sustainalble Energy System, Rajamangala University of Technology 
Thanyaburi (RMUTT)

Open access under CC BY-NC-ND license.

Open access under CC BY-NC-ND license.



160   Boonrit Prasartkaew  /  Energy Procedia   34  ( 2013 )  159 – 172 

cold production technology are the best alternative [4]. As a green energy technology for the climate
change and green-house-gas mitigation, a solar-biomass hybrid cooling system was proposed by [5].

Nomenclature

A area (m2)

Cp specific heat capacity, (kJ/kg.K)

FR heat removal factor

solar insolation on tilted surface (kW/m2)

h specific enthalpy (kJ/kg)

M mass (kg)

mass flow rate (kg/s)

energy rate (kW)

T temperature (K)

U heat transfer coefficient (W/m2 K)

UL overall heat transfer coefficient (W/m
2 K)

volumetric flow rate (m3/s)

v specific volume (m3/kg)

x mass concentration (%)

efficiency

transmittance

absorptance

tank load control function

temperature differential control function

boiler load control function

heat exchanger effectiveness

density (kg/m3)

0 initial condition

a ambient

ab absorber

aux auxiliary

b boiler



 Boonrit Prasartkaew  /  Energy Procedia   34  ( 2013 )  159 – 172 161

BM biomass 

bl boiler to load 

c  collector 

co  condenser 

cg combustion gas 

ev  evaporator 

f  liquid state 

fg liquid-vapor mixture 

g  vapor state 

ge  generator 

gw  gas to water 

hi  high 

i inlet 

lo  low 

o outlet 

PG producer gas 

set set point value 

st storage tank 

tl tank to load 

u  solar useful energy 

w  water 

we  water to environment 

 
Regarding the use of biomass, which is a CO2 neutral energy source and fruitfully available in all 

argricultural crountries, gasification of biomass offers advantages over other sources. Using solar and 
biomass can significantly contribute to the reduction of CO2 emission. A theoretical study on the 
performance of a solar-biomass hybrid air conditioning (SBAC) system has been done by [5]. Their 
results show that the proposed SBAC system for tropical locations is feasible, and can replace 
conventional vapor compression systems, thus reducing the need for fossil fuel based energy systems for 
cooling purposes. Subsequently, [6] reported the experimental study on the performance of the SBAC 
system. 

The main advantage of theoretical study via mathematical model is that the model can be used to 
predict all output parameters at any conditions. Compared to the experimental study, the simulation 
results can be obtained with very low expense and less study time. The accuracy of the simulation results, 
however, depends on the reliability of the model. To know the reliability of developed model, the results 
of observed experimental results should be compared with the predicted results from the simulation with 
the same input parameters.  



162   Boonrit Prasartkaew  /  Energy Procedia   34  ( 2013 )  159 – 172 

It should be noted that the mathematical model proposed by [5] had already been validated only for
some of system components using the experimental results available from a literature (no available SBAC
system at that time)   and the proposed model has been used for the system design. The complete SBAC
system was subsequently constructed and test as presented in [6]. Hence, this study aims at presents the
model validation, comparison results, between the simulation results predicted from the developed model
[5] and the experimental results obtained from the fabricated experimental system [6]. Section 2 describes
the proposed system relevant to the mathematical model and experimental setup. Section 3 presents the
uncertainty of measurement analysis. The statistical tool for experiment and model comparison is defined
in Section 4. Section 5 reports the validation results using the comparison between the experimental and
experimental results. The conclusion of study is presented in section 6.

2. System Description

Developed Mathematical Model and Input Data

Figure 1 shows the schematic of the proposed SBAC system relevent to the developed model. The
first part (in the left) is a solar water heating (SWH) system, which consists of a field of flat plate solar 
collectors, a hot water storage tank and a circulating pump. The second part (in the middle) is a biomass
gasifier-boiler (BGB) which consists of an automatic up-draft gasifier and a gas-fired sensible-heat boiler. 
The part on the right hand side is an absorption chiller (ABC) which consists of an absorption chiller 
equiped with a fan coil unit, a cooling tower and three aqua-pumps: hot, chilled and cooling water pumps.
Where the details of assumptions used in the model development was presented in [5].

Solar 
collector

P1

Hot
water 

storage
tank

Controller 1

P4

Controller 2

Biomass

Gasifier-
b il

MM
P2

10
Evaporator

Condenser

Solution heat
exchanger

1

2

43

5
6

7

8

9

Absorber

P3

ABC system

Generator

Fan
coil
unit

Cooling 
tower

SWH system

Fig. 1. Schematic diagram of the solar-biomass hybrid absorption cooling system

The model was developed using the following assumptions:

1) The model considered the energy and mass balances at each component, and of the overall
system.

2) The system is considered to be at steady state
3) The specific heat and density of the working fluids are constant.
4) The loss of the water vapor and moisture (at the hot water storage tank and solar collector 

vents) is not taken into account.



 Boonrit Prasartkaew  /  Energy Procedia   34  ( 2013 )  159 – 172 163

5) There is no pressure loss and no heat loss/gain in the lines (pipes) connecting the system 
components.

6) The fluid temperatures increasing due to the friction in plumbing and valves, blowers and
pumps are negligible. 

7) The energy considered are solar and biomass energy, while the power consumed by other 
equipment (e.g. pumps, blower, fans and controllers) is excluded.

Solar Water Heating System

The expression (Eq. (1)) for collector efficiency given by the Hottel-Whillier Bliss equation was used:

(1)

where,

(2)

(3)

(4)

The temperature distribution in the hot water storage tank is obtained from the energy balance
expressed as:

(5)

where, the extracted heat and control functions used for the collector and load energy terms, are
defined as:

(6)

(7)

(8)

Whenever the temperature of hot water supplied to the chiller machine is lower than SPT, the
auxiliary heat ( aux) is needed and this required heat will be supplied by the biomass gasifier-boiler. This
required heat can be determined as follows:

(9)

      



164   Boonrit Prasartkaew  /  Energy Procedia   34  ( 2013 )  159 – 172 

Biomass Gasifier-rr Boiler-

The gas-fired boiler is modeled as a heat exchanger, where heat is transferred between combustion
products and water. The transient temperature of water inside the boiler can be determined by:

(10)

where, the added heat into the water heater boiler and its effectiveness relations for the heat 
exchangers between combustion gases to water can be calculated from:

(11)

(12)

(13)

where,

(14)

(15)

Heat losses from flue gas and from boiler surface to ambient surrounding have been considered in the
overall energy supplied by the gasifier, and is given by

(16)

where, the extracted heat from the boiler to meet the load can be calculated from:

(17)

The consumption rate of biomass feed stock is obtained from:

                (18)

Absorption Chiller

The thermodynamic model of absorption chiller was used to simulate its performance with the
assumptions presented in [5]. The effectiveness of generator can be calculated as:

(19)

At the generator, knowing the hot water inlet temperature and generator heat flow, the generator 
temperature can be determined by the following equations:

(20)

             

                         



 Boonrit Prasartkaew  /  Energy Procedia   34  ( 2013 )  159 – 172 165

(21)

where,

(22)

(23)

For a defined solution mass fraction (range of 45<X<70%LiBr) and calculated generator temperature,
the saturation pressure, and can be calculated from.

(24)

(25)

(26)

(27)

where, all of above cofactors can be calculated as shown in [5].
At point 7, the refrigerant is in superheated state and its enthalpy, can be determined from 

(28)

where,

(29)

(30)

0.1193 P+2689 (31)

The mass flow rate of dilute solution in the generator can be determined using the energy and mass
balances on the generator, as:

(32)

The energy balance on the generator is given by,

(33)

P8 = P4, T8TT can be calculated from Eq. (25) and can then be obtained by , where
and are given by the curve fit equations. The enthalpy at point 9 can be calculated by considering 

the throttling process, as h9 = h8. 

(34)



166   Boonrit Prasartkaew  /  Energy Procedia   34  ( 2013 )  159 – 172 

(35)

The heat rejected at condenser, where , can be determined by writing the heat balance at 
condenser as:

(36)

At the evaporator, and can be calculated from the curve fit of Eqs. (37) and (34).

(37)

From the energy balance at the evaporator, the cooling capacity at the evaporator can be
calculated from:

(38)

The enthalpy at point 1 can be calculated by Eq. (27) with absorber temperature (calculated by Eqs.
(25) and (26)) at the same pressure as the evaporator.

The solution pump is modeled as an isenthalpic process, then . At the heat exchanger, the
enthalpyy can then be calculated as:

(39)

At the throttling process, . The enthalpy can be determined at the solution heat exchanger, 
and the absorber heat rejection can be calculated as:

(40)

The minimum pump power can be determined by

(41)

(42)
where,

(43)

All four heat quantities must be satisfy the chiller energy balance equation, expressed as

(44)



 Boonrit Prasartkaew  /  Energy Procedia   34  ( 2013 )  159 – 172 167

Experimental Setup 

Figure 2 shows the experimental setup of SBAC system relevent to the model used in [6]. The 
collector field set for the experimental study had 26 collectors with total area about 49 m2 (The 
specification of solar collector is given in [5]) connected in series and parallel (as shown in Figure 3). 

 

  
 

Fig. 2. Fabricated experimental setup of the solar-biomass hybrid absorption cooling system [6] 
 

 
Fig. 3. Schematic diagram of the collector field set for the experimental study [6] 

Collector pump 

Storage tank 
BGB system 

Absorption chiller 

Cooling tower 

Fan coil unit 

Controller unit 

Data logger 

Solar collector 



168   Boonrit Prasartkaew  /  Energy Procedia   34  ( 2013 )  159 – 172 

3. Uncertainty of Measurement

The errors or uncertainties of the measurement are determined and used for assessing the reliability of 
the experiments. Generally, it has two terms: relative uncertainty (REU) and absolute uncertainty (ABU).
For the direct measurement values, the accuracy of devices used for the measurement can be adopted asff
the uncertainty of measurement. For the quantities which cannot be measured directly, their uncertainties
have to be calculated based on the measured parameters [7].

Uncertainties of heat rate

The uncertainties of all heat rates, e.g.: heat removal rate, depend on the uncertainties of the water
flow rate, and the water temperatures at the inlet and outlet of each component. The water flow rates and
temperatures are measured using flow cells and thermocouples with the same accuracy of ±0.1 m3/hr (or 
0.028 kg/s) and ±0.8 C, respectively. The relative uncertainties of heat rate at all components should be
about the same level which can be calculated from Eq. (45):

(45)

Uncertainties of COP

The COP can be calculated as [2,3]. Therefore, the REU of this output variable is then be calculated as
Eq. (46):

(46)

Uncertainties of COPsysP

The REU of the COPsys can be calculated from Eq. (47):

(47)

4. Statistical Parameters

The statistical indicators are used for the comparison between the values obtained from model and
experiments results. Two indicators: root mean square error (RMSE) and mean bias difference (MBD) are
used in the validation. If the values of MBD and RMSE are close or lower than its uncertainties, it shown 
that the model and experimental results are in good agreement with each other. RMSE is defined as Eq.
(48):

(48)



 Boonrit Prasartkaew  /  Energy Procedia   34  ( 2013 )  159 – 172 169

MBD is defined as Eq. (49):

(49)

where CiC corresponds to the model simulation values,

MiMM corresponds to the measurements values

NN is the number of data values.

5. Validation Results

All parameters of the experimental system were used as input parameters of the model as shown in 
Table 1. The measured solar insolation and ambient temperature of this day were also used as weather 
data input. The between experimental and simulation results were compared. The comparison results of 
each component are compared as demonstrated in Figure 4 to 7.

The temperature profile of water at collector inlet and outlet, and the useful energy rate at the SWH
from both the experimental observations and model predictions are illustrated in Figure 4. The
comparison results show that the RMSE of collector inlet/outlet temperatures and useful energy were 0.6,
0.73 and 1.76, respectively. With the same trend, the MBD of these values were -0.18, 0.4 and 1.14, 
respectively. This indicates the predicted values by the model are in agreement with the experimental
results.

Table 1. The input parameters used in the validation



170   Boonrit Prasartkaew  /  Energy Procedia   34  ( 2013 )  159 – 172 

0

5

10

15

20

25

30

35

40

45

50

0

10

20

30

40

50

60

70

80

90

100

8 9 10 11 12 13 14 15 16 17 18

En
er

gy
 r

at
e 

[k
W

]

Te
m

pe
ra

tu
re

 [C
]

Time [hr]

Tci Tci,ex Tco Tco,ex Qu Qu,ex
 

Fig. 4. Measured and predicted parameters of SWH system 
 
Figure 5 shows the measured and predicted boiler temperature and its energy rate supplied to the chiller 

generator. The 17-data of each parameter during the steady state condition were compared. The 
comparison results show that the RMSE of boiler temperature and energy rate supplied from boiler to 
load were 0.71 and 1.12, respectively. The MBD of these values was 0.59 and 0.81, respectively. This 
indicates the close prediction of developed model with the experimental results provides reliable results. 

 

0

5

10

15

20

25

30

35

40

45

50

0

20

40

60

80

100

8 9 10 11 12 13 14 15 16 17 18

En
er

gy
 r

at
e 

[k
W

]

Te
m

pe
ra

tu
re

 [C
]

Time [hr]

Tb Tb,ex Qbl Qbl,ex
 

Fig. 5. Measured and predicted parameters of BGB system 



 Boonrit Prasartkaew  /  Energy Procedia   34  ( 2013 )  159 – 172 171

 

0

5

10

15

20

8 9 10 11 12 13 14 15 16 17 18

En
er

gy
 r

at
e 

[k
W

]

Time [hr]

Qgen Qgen,ex Qev Qev,ex
 

Fig. 6. Measured and predicted parameters of ABC system 
 
The heat power supplied to its generator and absorbed at evaporator during the steady state condition 

were compared and shown in Figure 6. The comparison results show that the RMSE of generator and 
evaporator heat rates were 0.3 and 0.41, respectively. The MBD of these values was 0.57 and -0.39, 
respectively. This also indicates that the predicted values by the model are in good agreement with the 
experimental results 

0.00

0.20

0.40

0.60

0.80

1.00

6 7 8 9 10 11 12 13 14 15 16 17 18

CO
P

Time [hr]

COP COP-exp. COPsys COPsys-exp.
 

Fig. 7. Measured and predicted COP and COPsys 



172   Boonrit Prasartkaew  /  Energy Procedia   34  ( 2013 )  159 – 172 

Finally, the measured and predicted values of COP and COPsys were compared as presented in Figure 
7. The comparison result shows that the RMSE of COP and COPsys were 0.05 and 0.08, respectively. The 
MBD of these values was -0.04 and -0.02, respectively. This indicates the close prediction of developed 
model with the experimental results. 
 

 
6. Conclusion 

 
To know the reliability of developed model, the results of observed experimental results were 

compared with the predicted results from the simulation with the same input parameters. The calculated 
statistical parameters, RMSE and MBD, of all temperature are very close to the uncertainty of the 
temperature measurements. The average value of RMSE for temperature, energy rate and COP are 0.96, 
0.9 and 0.07, respectively. The average value of MBD for these parameters are 0.25, 0.53 and -0.03, 
respectively. The validation results show that the simulation results predicted by the developed model are 
in good agreement with the experimental results from both qualitative and quantitative points of view. 

 
Acknowledgment 

The author wishes to thank Rajamangala University of Technology Thunyaburi (RMUTT) for 
providing financial support for his research. 

 
References 

[1] Saidura, R.; Abdelaziza, E.A.; Demirbasb, A.; Hossaina, M.S.; and Mekhilef, S. 2011. A review on biomass as a fuel for 
boilers, Renewable and Sustainable Energy Reviews 15: 2262 2289. 

[2] Ramana, A.S.; Chidambaram, L.; Kamaraj, G.; and Velraj, R. 2012. Evaluation of renewable energy options for cooling 
applications, International Journal of Energy Sector Management 6: 65-74. 

[3] Zhaia, X.Q.; Qub, M.; Li, Y.; and Wang, R.Z.  2011. A review for research and new design options of solar absorption 
cooling systems, Renewable and Sustainable Energy Reviews 15: 4416  23. 

[4] Hassan, H.Z.; and Mohamad, A.A. 2012. A review on solar cold production through absorption technology, Renewable and 
Sustainable Energy Reviews 16: 5331 48. 

[5] Prasartkaew, B.; and Kumar, S. 2010. A low carbon cooling syste using renewable energy resources and technologies, 
Energy and Buildings 42: 1453 1462. 

[6] Prasartkaew, B., and Kumar, S. 2011.  The Quasi-steady State Performance of a Solar-Biomass Hybrid Cooling System, In 
Proceedings of the Second TSME International Conference on Mechanical Engineering (The 2nd TSME-ICoME 2011), Krabi, 
Thailand, 19-21 October. 

[7] Taylor, J. R. 1997. An Introduction to Error Analysis (2nd Ed.), Sausalito: University Science Books.