Implementation of the characteristic equation method in quasi-dynamic.pdf

Energy Conversion and Management: X 13 (2022) 100165
Available online 16 December 2021
2590-1745/© 2021 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Implementation of the characteristic equation method in quasi-dynamic
simulation of absorption chillers: Modeling, validation and first results
S.C.S. Alcântara a,b
, A.A.S. Lima a,c
, A.A.V. Ochoa a,d
, G. de N. P. Leite a,d
, J.Â.P. da Costa a,d
, C.A.
C. dos Santos c
, E.J.C. Cavalcanti e
, P.S.A. Michima a
a
PPGEM, Federal University of Pernambuco, Recife, Brazil
b
Federal University of Piaui, Teresina, Brazil
c
DEM, Federal University of Paraiba, João Pessoa, Brazil
d
DACI/IFPE Federal Institute of Technology of Pernambuco, Recife, Brazil
e
DEM, Federal University of Rio Grande do Norte, Natal, Brazil
A R T I C L E I N F O
Keywords:
Absorption chiller
Transient analysis
Ammonia/Lithium Nitrate
COP
A B S T R A C T
This work presents a quasi-dynamic approach to an absorption refrigeration system that uses NH3/LiNO3 as the
working fluid. The goal is linked to the development and validation of a mathematical model, based on the
characteristic equation method, to simulate the quasi-dynamic behavior of absorption chillers. The mathematical
model was developed using the first law of thermodynamics through the conservation of mass and energy and the
integration of the characteristic equation method, considering external parameters such as temperatures and
flow rates of hot, cold, and chilled water circuits as the global heat transfer coefficients. The computational
model was built using the F-Chart EES® software, the initial part, to facilitate the resolution of the equations
(characteristic equation method). Finally, MATLAB software was used to perform the simulation with the
characteristic equation and the transient model. The comparison between the experimental results found in the
literature and those obtained by the developed model showed good agreement with relative errors lower than 5%
within the values found in the measurement uncertainties. A sensitivity analysis was performed to verify the
dynamic behavior of the absorption chiller, considering the activation, cooling, and thermal load temperatures
and the products of the global heat transfer coefficients, checking the temperature, pressure, profiles, heat fluxes,
and the COP of the chiller. The results showed a coherent behavior when the system was disturbed by varying
activation, cooling, and chilled water temperature.
1. Introduction
The energy demand for space cooling has more than tripled since
1990. In some regions of the world, the average cooling consumption
accounts for approximately 15% of the peak electricity demand, and
during extremely hot days this figure can reach 50% or more of the peak
residential demand [1]. This shows the importance of discussing and
studying cooling systems in general, especially to improve the energy
efficiency standards of these systems. The idea is to study more
improved systems, which allow greater integration of renewable en
ergies and also a greater utilization of the energy used.
In this context, the use of absorption refrigeration systems has
increased over the years, thanks to its economic and environmental
advantages arising mainly from the possibility that these systems have to
use renewable energy for their activation [2–5]. Moreover, the appli
cation of this equipment is closely linked to the application of more
efficient systems, such as polygeneration energy systems [6–9], where
the energy demand to operate them is reduced, and also for applications
with low-temperature heat sources [10,11].
The analysis of these systems, whether operating in the steady-state
or transient regime is not so simple, since this type of simulation requires
various information, such as internal temperatures, global heat co
efficients, mass flows, and other parameters that are usually not easy to
find and/or estimate. A widely used method to facilitate the simulation
of these types of systems is the characteristic equation method, which
allows the thermal loads of the components to be calculated using simple
linear functions [10,12–16]. Ochoa et al. [14] compared the results of
theoretical modeling of an absorption cooling chiller with the results
obtained from the characteristic equation, finding errors of less than 4%
for most of the operating conditions examined. Fischer et al. [15]
developed a new approach based on previous studies to find the pa
rameters of the characteristic equation to improve the results obtained
by the characteristic equation method. Their approach performed
satisfactorily with a deviation of less than 10% between the results of the
method and the manufacturer’s data. Meyer and Ziegler [16] adapted
the characteristic equation method to analyze the chiller behavior based
on mass transfer and concluded that this approach also provides good
Contents lists available at ScienceDirect
Energy Conversion and Management: X
journal homepage: www.sciencedirect.com/journal/energy-conversion-and-management-x
https://doi.org/10.1016/j.ecmx.2021.100165
Received 21 October 2021; Received in revised form 29 November 2021; Accepted 13 December 2021

2
predictability of the equipment part-load behavior. Recently, by
combining the a single-effect H2O/LiBr absorption chillers with a simple
dry-cooler model, Albers [17] presented an improved control strategy by
using the characteristic equations method to predict the part load
behavior of both equipment’s aiming the find a cut-in and a cut-off
condition for the solar heat operation and absorption chiller cooling
assembly taking into account the specific electricity demand and cooling
technology applied.
In recent decades, besides the intense research and development of
new methods to evaluate these systems, due to the importance that
refrigeration systems have gained, many researchers have sought
promising alternatives that could improve their performance, especially
regarding the low performance coefficient and the need for purification,
and the crystallization problem that the fluid pairs most commonly used
in these systems present [18]. One of the alternatives found was the use
of alternative working fluids (different from the conventional fluids
LiBr/H2O and NH3/H2O), such as lithium nitrate/ammonia (LiNO3/
NH3), which would allow the chiller operation at lower temperatures
besides avoiding problems such as corrosion, high pressures, and crys
tallization of the binary solution [18]–[20].
Several works on simulations of chillers that use the LiNO3/NH3 pair
have been published, proving their good performance. Zamora [21]
developed two physical models of a pre-industrial prototype NH3/LiNO3
chiller, one water-cooled and one air-cooled. The results show that even
at a high ambient temperature, 41 ◦
C, the chillers were capable of
delivering 64% of their rated capacity. The pre-industrial water-cooled
prototypes of the ammonia-lithium nitrate absorption refrigeration
cycle were also characterized in the part-load operating mode, which
showed the sensitive effect of heat on the sorption elements [19,22].
Lima et al. [23] performed a study of the same prototype NH3/LiNO3
chiller proposed by [24], using mass and energy balance and the char
acteristic equation method. The results showed good agreement with the
experimental data, with maximum relative errors around 5% for most of
the system operating conditions. Altamirano et al. [25] also analyzed the
behavior of a 10 kW absorption chiller, based on the patent developed
by Zamora [26] using four different methods that use the external
temperatures of the fluid to map the operating conditions of the ma
chine, including the characteristic equation method, this being the most
recommended method when the number of experimental results is
limited but the design data of the machine components is available.
Several studies of simulation and analysis of absorption chillers in
steady-state have been done over the years using the 1st and 2nd Laws of
Thermodynamics, aiming at the energetic and exergetic performance
[6,23,27], financial feasibility, and the optimization of systems
[7,28,29]. In the case of transient regimes, several studies and analyses,
several ways of modeling have been presented, such as global analysis
by the 1st Law [30–32], using the entropy generation [33], as well as
different numerical methods for solving the equations, aiming at the
dynamic behavior [31,34], either when turning the equipment on or off,
or during the introduction of any load variation, as well as the verifi
cation of a control strategy that can expand the operating range of these
systems, without harming their operation [35,36]. Even so, the dynamic
modeling of those types of equipment is not easy, in the sense of the
number of parameters necessary for its simulation, type of fluid, inputs,
and outputs, among others, as well as the complexity [17,37,38]. Thus,
the proposal of a simplified modeling with the precision that allows
evaluating these systems with a minimum number of parameters has not
yet been proposed. Hence, this work presents a new proposal that
combines the characteristic equation method and a global energy bal
ance to simplify the simulation of absorption refrigeration systems,
aiming the dynamics performance at the external and internal temper
atures, and considering the NH3/LiNO3 as the working fluid. This type of
proposal can be used for other types of absorption chillers, aiming at
different control applications, and optimization of the operating range
from this simplified energetic approach.
Based on the above, this study presents a dynamic approach to the
absorption chiller with NH3/LiNO3 as a working fluid pair. The objective
is to develop and validate a mathematical model, based on the charac
teristic equation method, to simulate the quasi-dynamic behavior of
absorption chillers.
2. Absorption prototype description - NH3/LiNO3
The prototype of the absorption refrigeration system [39] that was
dimensioned, constructed, and tested at the Universitat Rovira and Virgili
[19,22,24] consists of 6 main components (generator, absorber,
Nomenclature
Q̇ Heat Flow [kW]
ṁ Mass flow rate [kg s− 1
]
Δt Temperature difference [K]
ΔTlm Logarithmic mean temperature difference [◦
C]
A Area [m2
]
cp Heat capacity [kJ kg-1
K− 1
]
d diameter
h Enthalpy [kJ kg− 1
.K− 1
]
LiNO3 Lithium nitrate
M Mass [kg]
NH3 Ammonia [-]
P Pressure [kPa]
V Volume [m3
]
X Concentration of the solution [%]
Z Level of the solution [m]
COP Coefficient of Performance, dimensionless
T arithmetic mean internal temperature [◦
C]
UA Heat transmission [kW K− 1
]
t arithmetic mean external temperature [◦
C]
Greek Symbols
η Efficiency [-]
ρ Density [kg m− 3
]
Subscripts
ach Absorption chiller
equi equivalent
exp, sim Experimental and simulate results
g, c, e, a, Generator, condenser, evaporator, absorber
gen, eva, ac Generator, evaporator, and absorber-condenser
h, c, ch Hot, cold, and chilled water
h, hot, cold, c, chilled, ch Hot, cold, and chilled water
l, r, v, sol Liquid, refrigerant, vapor, solution
Low, high Low and High pressure
og, oc Orifice of generator and condenser tanks.
pump pump
sat Saturation state
shell Material components - Walls
T Tank
total total
W Water, solution, refrigerant
x, y Components
i,in,o,out Inlet and outlet stream
p,r Poor and rich solution
she,rhe Solution heat exchanger and refrigerant heat exchanger
S.C.S. Alcântara et al.

3
condenser, evaporator, solution, and refrigerant) and auxiliary compo
nents such as pumps, expansion valves, and storage tanks, Fig. 1. The
operation of the prototype is similar to the circuit of commercial systems
such as Yazaki and Robur, but using the NH3/LiNO3 solution as an
alternative working fluid.
Initially, in the operation of the prototype chiller, the NH3/LiNO3
solution is in the storage tank of the absorber and condenser and the
separator of the generator. The drive of the system starts from turning on
the circulation pump of the solution to circulate it through the thermal
compressor (generator - solution exchanger - absorber). Next, the power
supply (heat from hot water) starts heating the solution. During the
heating, only the thermal compressor operates to heat its walls and so
lution. It is important to note that during this heating, the pumps of the
chilled and cold-water circuits only do not operate. Only the hot water
circuit pump, which is the activation source of the chiller, is on.
The refrigeration system (condenser, refrigerant heat exchanger, and
evaporator) is coupled to the thermal compressor when the temperature
of the solution inside the generator (Tg) reaches the ammonia saturation,
where NH3 refrigerant vapor is produced.
3. Thermodynamic modeling of the absorption chiller
The modeling of the single-effect absorption refrigeration system,
Fig. 1, was based on the equation of the 1st Law of Thermodynamics,
using the dynamic behavior through mass balance, concentrations, and
energy balances. The rate of vapor formation governs this dynamic
behavior in the generator, and the heat flows are exchanged by the
thermal compressor components (generator - exchanger - absorber). The
analysis of this chiller shows the study of the external and internal cir
cuits of each heat exchanger, taking into account the average tempera
tures of those circuits.
The dynamic modeling of the prototype single-effect absorption
chiller was adapted to be simulated. The following changes were
applied:
• The generator consists of the plate heat exchanger and the separator
of vapor - solution as a single component;
• The condenser is comprised of the plate heat exchanger and the
condensed refrigerant storage tank as a single component;
• The absorber comprises the plate heat exchanger and the NH3/LiNO3
solution storage tank as a single component.
In the model, the heat exchangers are considered thermal compo
nents that dissipate heat among the external circuits (hot, cold, and
chilled water) and the internal circuit (refrigerant NH3 and the NH3/
LiNO3 solution).
Simplifying hypotheses were included to develop the mass and en
ergy balances of the process:
Fig. 1. Simplified scheme of the absorption prototype chiller NH3/LiNO3.

4
a. Temperature, pressure, and concentration are homogeneous within
each component [30,40]
b. There are only two levels of pressure: high (generator - condenser)
and low (absorber - evaporator)[41];
c. The NH3/LiNO3 solution leaving the generator and absorber is
saturated, and the vapor leaving the generator has the equilibrium
temperature of the strong solution at generator pressure [42];
The heat transfer equation q = UAΔTlm is determined as a function of
the heat exchange area, the global heat transfer coefficient, and the log
mean temperature difference, which is used to study the performance of
heat exchangers. As a simplifying part of the model, the logarithmic
mean temperature difference (ΔTlm), Eq. 4, is a function of the average
temperatures of each fluid (hot and cold), respectively. This has been
done by other authors in the literature about absorption chiller dynamic
simulation [31,33,43] and, according to the literature consulted for
analysis of heat exchangers [36,36,40], can be used in absorption
refrigeration systems. Hence, each component is expressed as:
ΔTlm =
(
Tx,i − Ty,o
)
−
(
Tx,o − Ty,i
)
ln
(
Tx,i− Ty,o
Tx,o− Ty,i
) ≈
(
Tx − Ty
)
(4)
Tx =
Tx,i + Tx,o
2
(5)
Ty =
Ty,i + Ty,o
2
(6)
3.1. Lithium nitrate/ammonia as working fluid
The use of this mixture as a working fluid in absorption refrigeration
systems is based on common problems found in commercial type ab
sorption chillers that use LiBr/H2O and NH3/H2O mixtures for operation
[10,18,23,44,45]. The LiBr/H2O mixture has corrosion problems, vac
uum operation, toxicity problems, and solution crystallization, limiting
operation under certain conditions [10]. In the case of the NH3/H2O
mixture, despite operating in a positive pressure regime, there is a need
for purification of the mixture due to ammonia, which makes the
equipment operationally more complex, in addition to the high energy
loss and high pumping consumption [10]. In this way, the LiNO3/ NH3
mixture allows elimination and/or minimization of these problems. In
addition, due to the thermodynamic properties, the activation energy
tends to be lower, which leads to the use of solar energy as a primary
source for single effect systems, being a viable solution for small air
conditioning processes, such as residential, among others. Therefore,
this mixture is ideal for absorption processes in the sense of simulation,
as the pressures involved are positive, the thermodynamic properties
well established, and they have low activation temperature. Therefore,
solar energy as a primary activation source combined with relatively
lower viscosity compared to commercial pairs, and mainly, the decrease
in the amount of mixture within the internal circuit of the absorption
chiller, allow the use of compact heat exchangers, in this case plates,
with ease of analysis and numerical and experimental simulation (size,
cost, production, among others).
3.2. Thermodynamic properties
The working fluids used in the model were pure water (external
circuits - hot, chilled, and cold water) and the NH3/LiNO3 solution. The
properties of the solution (NH3/LiNO3) were determined from numerical
correlations made and validated, found in the literature [45,46]. In pure
ammonia (NH3), the properties were determined from adjusted corre
lations using data from literature [47]. Finally, the thermodynamic
properties of pure water were determined from the numerical correla
tions developed in [48] and applied in [30,31], from the vapor tables
[49].
3.3. Products (UA) - global heat transfer coefficients
The UA products of each heat exchanger of the prototype were those
used in the system design, from plate changers through SWEP SSP G7
software [50] to the evaporator, condenser, and exchanger of the solu
tion. The development was carried out in the work presented in [24],
and those values are nominal from the prototype. For the generator and
absorber, the UA products were calculated from the nominal thermal
powers using the heat transfer equation of the components and the
nominal temperatures [51]. The characteristic parameters of the pro
totype chiller were extracted from literature [19,22,24], and Table 1
shows the initial conditions of the simulation.
3.4. Implementation of the characteristic equation method
The characteristic equation method applied to absorption refrigera
tion systems allows analyzing the operational behavior of equipment
such as absorption chillers, heat pumps, and others through algebraic
equations, which represent their refrigerating capacity and the COP as a
function of the so-called characteristic temperature difference
[16,52,53]. This methodology is based on the information found in the
literature, as shown in [42] and the work by [40]. This method aimed at
thermodynamic fundamentals and nominal characteristics of the chiller,
to determine the absorption chiller behavior considering the average
temperatures of cold, hot, and chilled water (external circuits) and
specific characteristics of the chiller as; overall heat transfer coefficients
and flow rates [14,17,54]. The implementation takes into account the
Duhring rule, which allows relating the internal average temperatures of
each heat exchanger of the chiller, the rich and poor concentrations
(Xsol) of the system and the solution saturation temperatures (Tsat,sol)
from a linear equation with slope B and intersection Z.
The four main heat exchangers (absorber, evaporator, condenser,
and generator) and the heat flow (Q̇i), as a function of the product (UAy),
and the average logarithmic difference were modeled (ΔTlmy) as:
Q̇y = UAyΔTlmy (1)
where:
ΔTlmy =
(
θy,in − Ty,in
)
−
(
θy,out − Ty,out
)
Ln
{
(θy,in− Ty,in)
(θy,out− Ty,out)
} (2)
The subscript y identifies the chiller components (absorber, evapo
rator, condenser, and generator). The temperatures of the external water
circuit are represented by the letter (t), and the temperatures of the
internal circuit of the chiller are represented by (T). For this method, the
simplification of the term (ΔTlm) of the characteristic equation, was
added as the mean temperature difference between the hot and cold
fluids (ΔTlmX ≈ |tX − TX|) [33,36,36,40],
Q̇E = UAE(tE − TE) (3)
Q̇A = UAA(TA − tA) (4)
Table 1
Thermal compressor equations of the characteristic method.
Q̇A = ṁref h10 + ṁstrongh6 − ṁweakh1
˙
ṁstrongh6 = ṁstrongh4 − Q̇she
Q̇G = ṁref h7 + ṁstrongh4 − ṁweakh1 − Q̇she Q̇max = ṁweak(h4 − h1)
A =
(h10 − h4)
(h10 − h8)
G =
(h7 − h4)
(h10 − h8)
Q̇loss = Q̇max − Q̇she
Q̇A = A • Q̇E + Q̇max − Q̇she Q̇G = G • Q̇E + Q̇loss

5
Q̇G = UAG(tG − TG) (5)
Q̇C = UAC(TC − tC) (6)
Respectively, Q̇E, Q̇A, Q̇G, Q̇C represent the evaporator, absorber,
generator, and condenser heat flows. In Tables 1 and 2, the subscripts
max, loss, ref, she, rhe, strong and weak represent maximum, heat loss,
refrigerant fluid, solution, and refrigerant heat exchanger. The letter (h)
expressed the specific enthalpy of each point of the cycle, the (ṁi) mass
flow and the letter (A, G, C, E) represent the enthalpies ratios of the
absorber, generator, condenser, and evaporator, respectively.
The equations that model based on the characteristic method were
divided into two sections: thermal compressor (Generator - solution heat
exchanger - Absorber) at Table 1.
And the refrigeration systems (Evaporator – Refrigerant heat
Exchanger – Condenser) are shown in Table 2.
Combining equations 3–6 of the heat exchangers and the equations
from Tables 1 and 2, it is possible to structure a system of equations on
the cooling capacity of the chiller and the temperature difference be
tween the external and internal circuits, as follows:
Q̇E = UAE(tE − TE) (7)
C • ˙
QE = UAC(TC − tc) (8)
A • Q̇E + Q̇loss = UAA(TA − tA) (9)
G • Q̇E + Q̇loss = UAG(θG − TG) (10)
Applying the Duhring rule for two temperature levels (high and low),
two equations depending on the concentration and the refrigeration
systems are obtained:
TG = B(Xsol) • TC + Z • (Xsol) (11)
TA = B(Xsol) • TE + Z • (Xsol) (12)
Finally, operating (11) - (12) leads to equation 13:
TG − TA = B(Xsol) • (TC − TE) (13)
It is important to define that the term B in equation 13 is the slope in
the Duhring diagram [10,40,55]. To find the total temperature differ
ence (ΔΔt), equations 7 to 10 have to be combined considering the
Duhring equations, the enthalpies fractions (G, A, and C) and the UA
product, expressed as:
Finally, the member on the left is the total temperature difference
(ΔΔt):
ΔΔt = tG − tA − B • (tC − tE) (15)
Equation 15 could be divided into two portions: the difference be
tween the temperature thrust (Δtthrust) and temperature lift (Δtlift):
ΔΔt = Δtthrust − B • Δtlift (16)
Where:
Δtthrust = (tG − tA) (17)
Δtlift = (tC − tE) (18)
The total temperature difference can also be defined in terms of the
design parameters, as follows:
ΔΔt = Q̇E •
(
G
UAG
+
A
UAA
)
+ Q̇loss •
(
1
UAG
+
1
UAA
)
+ B • Q̇E
•
(
C
UAC
+
1
UAE
)
(19)
ΔΔt =
Q̇E +
Q̇loss•
(
1
UAG
+ 1
UAA
)
[
G
UAG
+ A
UAA
+B•
(
C
UAC
+ 1
UAE
)]
1
[
G
UAG
+ A
UAA
+B•
(
C
UAC
+ 1
UAE
)]
(20)
Making (SE) the proportion of the global coefficient of each compo
nent of the chiller (evaporator, condenser, absorber, and generator);
SE =
1
[
G
UAG
+ A
UAA
+ B •
(
C
UAC
+ 1
UAE
) ] (21)
and (αE) the distribution of the overall heat transfer coefficients in
side the equipment,
αE =
(
1
UAG
+ 1
UAA
)
[
G
UAG
+ A
UAA
+ B •
(
C
UAC
+ 1
UAE
) ] (22)
Then, the total temperature difference can be simplified to the
function of two parameters;
ΔΔt =
Q̇E + αE • Q̇loss
SE
(23)
The minimum total temperature difference (ΔΔtminE) represents the
relationship between the parameters (SE, αE and Q̇loss):
ΔΔtminE =
αE • Q̇loss
SE
(24)
The total temperature difference then is defined as:
ΔΔt =
Q̇E
SE
+ ΔΔtminE (25)
Hence, the thermal power activation (generator) and cooling ca
pacity (evaporator) of the absorption chiller can be expressed as:
Q̇E = SE • (ΔΔt − ΔΔtminE) (26)
Table 2
Refrigeration system equations of the characteristic method.
Q̇E = ṁref • (h20 − h19) Q̇rhe = ṁref • (h10 − h20)
Q̇C = ṁref • (h7 − h8) Q̇rhe = ṁref • (h8 − h19)
Q̇rhe = R • Q̇E→R =
(h10 − h20)
(h20 − h19)
Q̇C = C’
• Q̇rhe→C’
=
(h7 − h8)
(h8 − h19)
Q̇C = C • Q̇E→C = C’
• R
tG − tA − B • (tC − tE) = Q̇E •
(
G
UAG
+
A
UAA
)
+ Q̇loss •
(
1
UAG
+
1
UAA
)
+ B • Q̇E •
(
C
UAC
+
1
UAE
)
(14)

6
Q̇G = G • [SE • (ΔΔt − ΔΔtminE) ] +
SE
αE
• ΔΔtminE (27)
For the condenser and absorber, the heat flow rates are:
Q̇C = C • [SE • (ΔΔt − ΔΔtminE) ] (28)
Q̇A = A • [SE • (ΔΔt − ΔΔtminE) ] + Q̇loss (29)
3.5. On and off transients of the prototype absorption chiller – An
approach
As the flow rates of the hot and cold water were off, the characteristic
equations of the generator, condenser, and absorber could identify the
variation of the chiller since there is no thermal capacity (Thermal
Inertia) imposed by the sudden drop or increase of the dynamic process,
in this case, the turning off and on of the hot and cold-water circulation
pumps. Therefore, it is necessary to introduce the equivalent thermal
capacity of the generator and the absorber-condenser to the transient
process to predict the chiller behavior.
The model includes the equivalent thermal capacity in the compo
nents of the prototype chiller, represented by Eq. 30.
Cequi = Mequi • cpequi (30)
The equivalent thermal mass considers the mass of the solution (Msol)
and mass due to the component walls (Mshell), as:
Mequi = Msol + Mshell (31)
The equivalent specific heat considers the specific heats of the so
lution and the material of the walls of the components, as:
cpequi =
cpsol • Msol + cpshel • Mshell
Msol + Mshell
(32)
3.5.1. Generator approach
In this simplification, the thermal capacity inside the generator tends
to enter into thermodynamic equilibrium over time with the external hot
water circuit, as a response to the inertia exerted by the volume of so
lution and the walls of the internal component and the volume of water
contained inside the generator at the external circuit.
(Mcp)g
∂Tg
∂t
= (Mcp)hot,water •
(
Th,w,i − Th,w,o
)
(33)
Mg = Msol,g + Mshell,g (34)
3.5.2. Absorber – Condenser approach
In the case of the dissipation system, also, the thermal capacity inside
the absorber and condenser tends to enter into thermodynamic equi
librium over time with the external cold-water circuit as a response to
the inertia exerted by the volume of solution/refrigeration and the in
ternal walls of both components and the volume of cold water contained
inside the dissipation system at the external circuit.
(Mcp)ac
∂Tg
∂t
= (Mcp)cold,water •
(
Tc,w,o − Tc,w,i
)
(35)
Mac = Msol,ac + Mshell,ac (36)
3.6. Internal parameters modeling of the absorption prototype chiller
Applying this methodology, we determine the mean temperatures of
the main components, such as absorber (TA), generator (TG), condenser
(TC) and evaporator (TE), also the high (Phigh) and low (Phigh) pressures of
the chiller, and even the solution concentrations of the thermal
compressor (Xstrong and Xweak).
3.6.1. Mean temperatures of the thermal compressor and refrigeration
circuit
The mean temperatures are modeled as the overall mean tempera
ture of the main components, such as:
TG = θw,h − UAG (37)
TE = θw,ch − UAE (38)
TA = θw,c,A + UAA (39)
TC = θw,c,C + UAC (40)
3.6.2. Prototype chiller solution concentrations
There are two solution concentrations at the thermal compressor:
rich (high in ammonia) and poor (low ammonia) ones.
Xrich = f(TA, Plow) (41)
Xpoor = f
(
TG, Phigh
)
(42)
3.6.3. Prototype chiller pressures
Two pressures are considered: high pressure (generator - condenser)
and line of low pressure (absorber - evaporator).
Phigh = PG = PC = Psat@(TC) (43)
Plow = PA = PE = Psat@(TE) (44)
3.7. Coefficient of performance of the chiller (COP)
The COP of the chiller is the ratio of the energy removed in the
evaporator to the energy supplied by the hot water in the generator
[10,23,30,31], expressed as:
3.8. Methodology implementation of the quasi-transient model
The implementation of the methodology to develop the quasi-dy
namic model of the absorption chiller through the characteristic equa
tion and thermal inertia method was performed according to the steps
shown in the flowchart, Fig. 2, where the use of permanent and transient
regimes of the equipment was necessary.
Initially, the nominal data of the absorption chiller were needed,
such as UA products of the heat exchangers, temperatures (T), and flow
rates (m) of the cold, hot, and chilled water circuits. By analyzing the
first law of thermodynamics and the model of the characteristic equation
method (section 3.3), the absorption chiller in steady-state was simu
lated, and the parameters of the characteristic equation of the absorp
tion chiller were found. Then, it was necessary to use experimental data
COP =
Q̇E
Q̇G
=
SE • (ΔΔt − ΔΔtminE)
G • [SE • (ΔΔt − ΔΔtminE) ] + Q̇loss
=
ΔΔt − ΔΔtminE
G • ΔΔt •
(
SE •
(
1
αE
− G
) )
+ ΔΔtminE
(45)

7
to validate the method and define the equations that energetically
govern the absorption chiller. In the work presented previously in Ochoa
et al., 2019, the entire procedure of the thermodynamic model and the
implementation of the characteristic equation method are described, as
well as the validation of the characteristic equation method. In the
second part of the methodology, it was necessary to integrate the
characteristic equations of the absorption chiller and the thermal inertia
model (situation of the system on and off, hot and cold water). In this
part, the integrated model was calibrated and validated using dynamic
data from the chiller under study. Subsequently, a parametric analysis,
selecting some simulation parameters, such as thermal load (chilled
water temperature) and drive energy (hot water temperature), among
others, to verify the chiller’s behavior in a partial load situation in a
transient regime was conducted. Finally, a critical analysis of the results
presented by the model developed for the absorption chiller was
performed.
4. Validation of the thermodynamic quasi-transient model of
prototype NH3/LiNO3 chiller
The validation of the model was carried out from the experimental
data in [56], using at 100% (Full load) and 75% (partial load) at the
load, considering the water-cooled dissipation prototype chiller. The
experimental tests were carried out by Zamora [56] to verify the oper
ation of the absorption refrigeration prototype at full (100%) and partial
load (less than 100%), considering disturbances during the partial
operation of the equipment. (Switching off the drive load and heat
dissipation). In the case of full operating capacity, the tests were carried
Fig. 2. Flowchart of the methodology implemented for the development of the quasi-dynamic model of the NH3/LiNO3 absorption chiller.
Fig. 3. Scheme of the experimental tests performed by Zamora. Adapted from [56,22].

8
out by regulating the thermal load by fixing the chilled water
temperature.
In the case of the partial load tests (75% of full load), the PID control
was configured, maintaining a dissipation cold water temperature dif
ference of approximately 3 K, as shown in the adapted scheme (Fig. 3) of
the works by Zamora [56] and Zamora et al. [22]. The disturbances were
placed through the disconnection of the pumps of the external hot water
drive and cold-water heat dissipation circuits. These pumps only work
during the chilled water production semi-cycles when the absorption
process is taking place. A more detailed and complete description of the
experiments performed on the refrigeration prototype is found in the
literature [56,22].
The idea of this comparison is to verify the precision of the model
proposed to simulate the energetic performance of the absorption pro
totype chiller. The inlet temperatures of the water circuit were used as
input of the modeling and the outlet temperatures were selected as the
variable target to compare the precision with the real values. The vali
dation of the numerical model was conducted by comparing the outflow
temperatures of the cold, chilled and hot water systems. They were
obtained from the numerical model developed, and the values of the
outflow temperatures of these circuits collected experimentally in the
laboratory. Since the experimental data collected from Zamora [24] was
not obtained dynamically, the temperature, pressure and concentration
inside the prototype chiller, were compared with the values taken solely
through the external water circuits. This validation methodology has
been applied by many authors before using LiBr/H2O [30,31,36,43] and
NH3/H2O in the literature [57], and also considering steady regime
using NH3/LiNO3 by the same authors [23,25].
Table 3 shows the nominal conditions of the absorption chiller from
the literature [19,22,26,56].
Table 4 shows the coefficients of the parameters in the characteristic
equations of the absorption chiller found in Lima et al. [58].
4.2.1. Transient comparison of the values at 100% load
At first, the values obtained by the dynamical modeling were
compared with the experimental values from the absorption chiller at
100% of the load. Those values were taken from the literature [56,22].
In this test, the absorption chiller was working until it stabilizing in a
permanent regime. After this point, the temperatures of the hot, cold,
and chilled values were taken. The test lasted around 20 min. The
comparison was conducted with the chilled temperature (Tch) values
shown for the inlet (in) and outlet stream (out).
As the results show in Fig. 3, it is possible to see the accuracy of the
model since the deviation between the simulated (sim) and experi
mental (exp) values was slight (Fig. 3a), with a lower and more
considerable difference of 0.1 and 0.8, respectively (Fig. 3b). This rep
resented a maximum relative error of 5%, which is within the un
certainties shown in [19,56,22]. Fig. 3b also shows that the values do
not present a systematic pattern, demonstrating the efficiency of the
model developed [59].
4.2.2. Transient comparison of the values at 75% load
Finally, a second comparison was made with the experimental values
with the absorption chiller operated at partial load (75%). This test was
conducted by introducing a perturbance to the system. The equipment is
started up and allowed to operate autonomously. The pumps of the
external circuits (hot, cold, and chilled water) started to operate. After
achieving the permanent regime, the hot and cold-water pumps are only
activated during the refrigeration production intermediary cycles, when
the absorption process is on. The comparison was conducted with the
hot (Thw), cold (Tcc), and chilled (Tch) temperatures values. Figs. 4, 5,
and 6 show the comparison of the simulated values from the modeled
development and the experimental values from [19,56,22], considering
the operation of the absorption chiller at partial load (75%).
In the same context, as discussed in comparing the absorption chiller
at 100% load, the same behavior was achieved in this case, shown in
Figs. 4 to 6. The accuracy is also reasonable considering the partial load
with the experimental values from the hot, cold, and chilled water
temperatures.
The maximum relative errors found in comparing the hot, cold, and
chilled water temperatures were 6%, 8%, and 7%, with minimum errors
of 0.5%, 0.4%, and 0.2%, respectively. It is important to highlight that
almost all the relative errors were within the uncertainties presented in
[19,56,22]. The maximum differences between simulated and experi
mental values were 5 ◦
C, 3 ◦
C, and 1.3 ◦
C, respectively, and those values
were commonly found when the pumps were disconnected. Only a few
values were more significant than the uncertainties but inside 10% of
the values. This can be attributed to the data collected from the litera
ture used [19,56,22], and effects related to the control of the system,
which were not taken into account in the modeling. Therefore, and it is
seen from the results obtained, it can be considered that the model
adequately represents the dynamic behavior of the absorption chiller.
5. Discussion and results
This section presents the sensibility analysis of the transient ab
sorption chiller considering the variation of the activation energy and
the thermal load by varying the hot and chilled inlet temperature of the
water.
5.1. Sensibility analysis of the absorption chiller
Four cases were tested to show the accuracy of the developed model
for the absorption chiller. The first two cases aimed to increase and
decrease the hot water temperature, activation energy (considering
ramps of 80–90 ◦
C and 90–80 ◦
C) to see the behavior of the internal
parameters of the system. The last two cases aimed to increase and
decrease the chilled water temperature, thermal load, (considering
ramps of ramps 15–18 ◦
C and 18–15 ◦
C), also to see the behavior of the
internal parameters of the system. The inlet cold water temperature was
kept constant along with the simulation, at 31 ◦
C, 35 ◦
C, and 38 ◦
C for
the cases analyzed. The thermal load was introduced with the duration
of 200 s, considering constant cold-water temperatures. This value
(perturbation of 10 K and 3 K) was considered because the activation
source is the input of operation of the absorption chiller and the input
thermal load to overcome to produce chilled water to any climatization
processes. Such consideration was made and discussed in many studies
over the years by many authors with optimal results
Table 3
Initial conditions of the Simulation and Nominal UA products of the Absorption
Chiller.
Mass flows (kg s− 1
) Temperatures (◦
C)
Hot water 0.833 Inlet Hot water 90.0
Cold Water 0.800 Inlet Cold water - Absorber 35.0
Chilled Water 0.7986 Inlet Cold water - Condenser 35.0
Rich Solution (NH3/LiNO3) 0.100 Outlet Chilled Water 15.0
UA Product (kW K− 1
)
Generator 3.69 Evaporator 1.56
Condenser 2.43 SHE 1.06
Absorber 3.00 RHE 0.05
Pump Efficiency (%) 100
Table 4
Coefficients of the thermal power equations transferred in the generator and
evaporator.
SE[kW/K] αE[kW/K] G ΔΔtminE[K] B
0.52 0.290 1.27 2.751 1.18

9
[30,31,33,36,43,60,61]. The flow values of the hot, chilled, and cold
water were kept constant throughout the simulation.
5.1.1. Case I. Increase in the temperature of the hot water (80–90 ◦
C)
The first case introduced a ramp of (10 K) at the activation power
(Inlet hot water) to see the behavior of the refrigeration prototype
before, during, and after the perturbation. Figs. 7, 8, and 9 show the
temperatures, pressures, concentrations, and heat flow rate profiles.
Fig. 7a and 7b show the temperature profiles of the generator (Tg)
and condenser (Tc) when subjected to a thermal disturbance imposed by
the hot water temperature entering the generator (Th;in). Since the hot
water temperature at the inlet behaves as the driving source for the
prototype, raising it leads the chiller to another energy step, altering all
the temperatures inside the generator as a function of the energy being
added, such as inlet (Th;in), outlet (Th;out) and mean (Tm;h) hot water
temperatures and (Fig. 7a).
The changes in the activation power, Fig. 7a, caused changes to the
system as well since the last tries to adapt to the ramp variation. Since
more energy is sent to the chiller generator, more vapor is produced,
increasing the cooling capacity inside of the prototype. This leads the
condenser, Fig. 7b, to dissipate more heat to the environment through
the cold water. The positive ramp introduced also had a positive effect
on the evaporator temperature (Te). Since more energy produces more
vapor, the evaporator has more capacity to absorb the thermal load from
Fig. 4. Chilled Water at 100% Load. a) Comparison of the outlet temperatures of the simulated and experimental. b) Distribution of the residuals between the
experimental and simulated values.
Fig. 5. Hot Water at 75% load. a) Comparison of the outlet temperatures of the simulated and experimental. b) Distribution of the residuals between the experi
mental and simulated values.
Fig. 6. Cold Water at 75% load. a) Comparison of the outlet temperatures of the simulated and experimental. b) Distribution of the residuals between the exper
imental and simulated values.

10
Fig. 7. Chilled Water at 75% load. a) Comparison of the outlet temperatures of the simulated and experimental. b) Distribution of the residuals between the
experimental and simulated values.
Fig. 8. Temperature profiles to a ramp variation in the driving source. a) Generator (Tg). b) Condenser (Tc).
Fig. 9. Temperature profiles to a ramp variation in the driving source. a) Absorber (Ta). b) Evaporator (Te).
Fig. 10. Profiles to a ramp variation in the driving source a) Pressures (Phigh, Plow) and Concentration (Xpoor, Xrich). b) Heat Flow (Qg, Qe, Qc, Qa).

11
the chilled water, Fig. 8b. This effect in the evaporator has to be
compensated at the absorber component to balance the heat in the
chiller. The absorber temperature (Ta) increases because more water
vapor is supplied to be condensed and absorbed through the mass
transfer in it, Fig. 8a, with the ammonia poor solution coming from the
generator (Fig. 7a).
It is important to emphasize that this process of increasing the acti
vation energy in the generator also induces a change in the chiller
pressure levels, Fig. 9a, hence, the high pressure (Phigh) increases with
the rise of the condensing temperature, and the low pressure (Plow)
decreases as the evaporator temperature (Te) decreases, since these
parameters are directly proportional. Therefore, they tend to be similar.
On the other hand, the concentration effect of the weak and rich solution
(Xpoor and Xrich) follows the same tendency, that is, with more energy to
produce ammonia vapor, the poor concentration solution decreases, and
the rich solution decrease as well (Fig. 9a), following the balance of the
species of the mixture components, in this case, HN3 and LiNO3. This
phenomenon had been shown and explained by several authors in the
literature ([30,31,33,36]) with a different solution working fluids.
Finally, the flow heat rate profiles show that the ramp introduction
increases the dissipated heat flow at the condenser (Qc) and absorber
(Qa). The cooling capacity increases, Fig. 9b, as discussed in Figs. 7 to 9.
The transient performance of the absorption chiller is shown with the
thermal COP, as seen in Fig. 9b, where the increase in the activation
energy (Qg) and cooling capacity (Qe) of the evaporator tend to elevate
the COP after the positive ramp (10 K). The entire behavior of the en
ergetic parameters studied show agreement, qualitatively, with several
studies conducted before with other absorption chillers
[30,33,36,61,62].
5.1.2. Case II. Decrease in the temperature of the hot water (90–80 ◦
C)
In the second case, a negative ramp of (-10 K) was introduced at the
activation power (Inlet hot water) to see the behavior of the refrigera
tion prototype before, during, and after the perturbation. Figs. 10, 11,
and 12 show the temperatures, pressures, concentrations, and heat flow
rate profiles.
the decreasing of the hot water temperature entering the generator. The
behavior of the second case had opposed the behavior of the first case
analyzed due to the reduction of the activation water, decreasing the
heat to produce ammonia vapor, less refrigerant going through the ab
sorption chiller (Fig. 10a). In the same context, the temperature of the
condenser (Tc) tended to a small value since there was no need to
dissipate more heat (Qc and Qa), as the vapor production is less than in
the first case. (Fig. 10b).
The change on the activation power to a lower value of temperature
(-10 K), changed the system as well as the last tries to back off to the
actual values of the thermal load imposed with the negative ramp. The
temperatures of the evaporator (Te) increase, Fig. 11b, since there is not
enough refrigerant vapor (NH3) to lower the temperature and, also
because of this, the temperature of the absorber (Ta) decreases along the
negative ramp, Fig. 11a. As it was mentioned at the beginning, the
response to the negative ramp in the (Th;in) hot water temperature (-10
K), is to reduce the high pressure (Phigh) and increase the low pressure
(Plow) and the poor and rich solution concentration (Xpoor and Xrich), as
seen in the Fig. 11a, 11b, and 12a.
It is important to emphasize that this process of decreasing the
activation energy in the generator also produces a change in the chiller
pressure levels as well, Fig. 11a, hence, the high pressure (Phigh) de
creases with the reduction of the condensing temperature (Tc), and the
low pressure (Plow) increases with as the evaporator temperature
increases.
On the other hand, the concentration effect of the poor and rich
solution (Xpoor and Xrich), follows the same tendency, i.e., the system had
less energy to produce ammonia vapor; hence, the poor concentration
solution (Xpoor), increases and the rich solution (Xrich), increases as well
(Fig. 11a), to complete the species balances of the mixture components.
Several authors had also explained this phenomenon in the literature
([30,31,33,36]).
Finally, the heat flow rate profiles (Qg, Qe, Qc and Qa), show that the
ramp introduction decreases the dissipated heat flow at the condenser
and absorber (Qc and Qa), and the cooling capacity is reduced since the
evaporator temperature (Te) and low pressures (Plow) increase simulta
neously, Fig. 11b and 12a, as discussed through the Figs. 10 to 12. The
transient performance of the absorption chiller is shown with the ther
mal COP in Fig. 12b, where the decrease of the activation energy also
makes the COP lower than in the first case. When compared to the first
case, the behavior of the energetic parameters studied in the second case
show agreement, qualitatively, with several studies conducted before
with other absorption chillers [30,33,36,61,62].
For cases III and IV, the thermal load was varied by introducing a
positive and negative ramp (3 K) to verify the behavior of the absorption
chiller, as previously presented with the hot water temperature.
5.1.3. Case III. Decrease in the temperature of the chilled water (18–15 ◦
C)
Case III was conducted by reducing the chilled water temperature
(Tch;in), which implies adding more energy (thermal load) to the sys
tem. In this situation, the absorption chiller must continue working to
reduce the evaporator temperature (Te) to achieve the demand imposed
by the returning chilled water. Figs. 13, 14, and 15 show the tempera
tures, pressures, concentrations, and rate heat flow profiles.
the temperature of the chilled water entering the evaporator (thermal
load). Since the chiller water temperature (Tch) is lower than before, the
system may stabilize the process by searching for the production of the
ammonia vapor by adding more activation energy. Due to the higher
energy demand, the absorption chiller tries to return to the new steady
regime by balancing the energy flows across the control volumes; hence,

12
the hot water temperature (Th) raises, Fig. 13a, and the condenser
temperature (Tc) decreases to match the exact heat to be dissipated to
stabilize the demand needed for the absorption chiller at the water
circuit (Fig. 15b).
The absorber temperature (Ta) decreases (Fig. 13a) slightly, induced
by the input of the new thermal load, to achieve the energy balance of
the dissipate heat (Qc and Qa) to return to the new steady regime.
Regarding the pressures and the concentrations behaviors, the new
thermal load (-3K) made the high (Phigh) and low (Plow) pressures
decrease lightly to achieve the steady regime after the perturbation

13
caused by the added load. As more ammonia vapor had to be produced
to achieve the thermal load, the rich and poor concentration solutions
(Xpoor and Xrich), Fig. 15a, decrease to satisfy the mass balance through
the absorption process at the absorber component. Finally, the behavior
of the heat flow and the COP are presented in Fig. 15b. It is possible to
observe that the negative ramp imposed at the absorption chiller caused
the values of the energy to change in and out of it to match the mass and
energy balance to the whole process.
The COP, Fig. 15b, tends to decrease while the ramp was introduced
to the chiller; as explained in cases I and II. The heat rate in the evap
orator is more significant than the heat rate supplied to the generator,
causing the absorption chiller to have a poorer performance, with lower
COP in the new steady regime (Fig. 15b). The phenomenal description in
case III has been described by several studies, as shown in the literature
[10,23,33,36,61,62]
5.1.4. Case IV. Increase in the temperature of the chilled water (15–18 ◦
C)
In this case IV, the thermal load was reduced by increasing the
chilled water inlet temperature (Tch:in) in the evaporator, positive ramp
(3 K), Fig. 17b. The energetic behavior in case IV was the opposite to the
one presented in the third case because the increase in the chilled water
temperature (Tch) causes more ammonia vapor to be left over to achieve
the demand, Fig. 17b, and hence, more activation energy at the gener
ator is left, Fig. 16a, making the absorption chiller more efficient
through the COP value. The COP value raises to achieve the mass and
energy balance to the new steady regime. In this case, specific demand is
produced with the same amount of the activation heat for case III,
making the absorption chiller present better energetic behavior.
Dissipated heat from the condenser and absorber (Qc and Qa) was
higher in the same context (Fig. 18b). The condenser and absorber
temperature (Tc and Ta) tended to increase to achieve this thermody
namic state.Fig. 19.
Regarding the pressures (Phigh and Plow) and concentration solution
(Xpoor and Xrich) profiles, Fig. 18a showed that pressures increase lightly
after the thermal load is introduced, due to the condenser (Tc) and
evaporator (Te) temperatures and rise as well, to achieve the new steady
regime of the absorption chiller. In the same context, the concentration
solutions increase with the thermal load imposed. On the other hand, the

14
heat flows of the heat exchangers of the absorption chiller presented a
behavior opposed the case III due to the increase of the generator (Tg)
and evaporator (Te) temperatures. The condenser (Tc) and absorber (Ta)
(dissipate systems) lead to raising the values of the heat around the
chiller, as shown in Fig. 18b. Finally, the COP behavior corresponding to
an absorption chiller where the rate of output product (cooling capacity)
was more significant than the rate of the activation heat (hot water);
hence, the COP value was higher after the thermal load was introduced.
The inlet chilled water temperature (Tch:in) was higher than before,
putting the system in a condition where the effort to produce cold water
at this temperature was less than at lower temperatures, as mentioned in
case III.
6.2. Final remarks of the parametric analysis on the prototype absorption
chiller
As a result of the proposed approach of an initial approach of the
transient study of a prototype chiller, the energy behavior parameters
and the COP of it were verified and analyzed considering the variation of
the activation energy and thermal load. The chiller was operating in
steady-state conditions when it received a variation of the activation
energy through a ramp (positive and negative) at the hot water inlet
temperature (10 K) and the chilled water inlet temperature (3 K),
causing the modification within the absorption chiller to achieve the
new steady regime.
At first, when the positive ramp was introduced by the hot water
temperature, causing an increase in the temperature of the solution in
the generator (Tg), Fig. 7a. At the same time, there is an increase in
ammonia refrigerant vapor production, increasing the possibility to
produce a higher cooling effect due to the lower temperature in the
evaporator (Te), Fig. 8b, and thus a lower temperature of the chilled
water (Tch), Fig. 7b. This addition of activation energy to the system will
lead to the need to transfer more heat to the environment due to the heat
exchange capacity to remove the thermal load imposed on the system
and thus maintain the energy balance of the prototype chiller (Figs. 7, 8
and 9).
Furthermore, the addition of energy to the generator and greater
production of refrigerant vapor will cause the need for greater vapor
absorption in the absorber (mass and heat transfer process), leading to
the use of higher dissipation energy due to the increase in the temper
ature of the condenser (Tc) (Fig. 7b) and absorber (Te) (Fig. 8a), and
thereby significantly increase the cooling water temperature (Fig. 7b).
This shows the importance of the direct influence of the chilled water
temperature in the absorption and desorption of vapor in the final per
formance of the chiller.
Regarding the pressures of the system (Phigh;Plow), all the energy
introduced and the increase in the production of refrigerant vapor first
led to the rise of the high pressure due to the adequacy of mass and
energy balances in the generator and condenser. In the evaporator and
absorber section, the opposite occurs since the low pressure undergoes a
reduction in its value to increase the capacity to withdraw heat and
thermal load (Fig. 9a). This is also necessary for the vapor to have a
lower temperature and pressure and be absorbed by the lithium nitrate-
rich solution (Xrich) in the absorber (Fig. 9a).
As the thermodynamic equilibrium must be reached again for the
imposed conditions due to the additional activation energy introduced,
the masses and concentrations must also reach new equilibrium levels.
The components of the chiller can reach the total balance of mass and
energy.
Finally, all this process is reflected in the performance of the proto
type chiller visualized in the COP, from the initial conditions of the
permanent regime, through the transition and/or thermal disturbance in
hot water (Th) until the thermodynamic equilibrium of the system is
reached again (Fig. 9). The increase of the COP in the chiller’s final stage
was because the activation energy rate was lower than the rate of
evaporation of the evaporator, leading to the increasing of the COP. The
COP values varied around 0.45 to 0.515 (±0.5) by using this approach to
combine the characteristic equation method and the thermal inertia,
values similar to those obtained experimentally in Zamora [21].
When the hot water temperatures were kept constant and the chiller
water varied, with the ramp at the chilled water (3 K), the behavior of
the chiller was coherent with the thermal load imposed. As the chilled
water increases, it is less thermal load getting into the system. With the
same amount of hot water, there was a slightly positive change in the
COP since less energy was demanding in the evaporator (Qe), and the
generator heat (Qg)was higher.
In the end, the quasi-dynamic development modeling for the ab
sorption chiller using the characteristic equation method and the ther
mal capacity brought excellent results when the hot and chilled water
temperatures were varied by positive and negative ramp (simulating the
activation source and the thermal load), even when the results were
compared, qualitatively, with the data found in the literature for several
authors and different solution working fluid, as LiBr/Water
[31,33,36,43,61] and also with ammonia/water [57,63,64].
7. Conclusions
A quasi-dynamic modeling to simulate an NH3/LiNO3 absorption
refrigeration system integrating two methodologies such as character
istic equation and the First Law of thermodynamic was built, giving
excellent results since the numerical and experimental results were de
viation lower than 8%. Even when the results were compared, qualita
tively, with the data found in the literature for several authors and
different solutions working fluid, such as LiBr/Water and ammonia/
water. Among the most significant results of the study are:
• The results provided by the dynamic model developed for the chiller
prototype were good, since the maximum relative errors found in
comparing the hot, cold, and chilled water temperatures were 6%,
8%, and 7%, with minimum errors of 0.5%, 0.4%, and 0.2%,
respectively;
Fig. 19. Profiles to a ramp variation in the driven source a) Pressures (Phigh, Plow) and Concentration (Xpoor, Xrich). b) Heat Flow (Qg, Qe, Qc, Qa).

15
• When the hot water temperatures were kept constant and the chiller
water varied, with the ramp at the chilled water (3 K), the behavior
of the chiller was coherent with the thermal load imposed;
• Regarding the input of the positive ramp by the hot water temper
ature caused an increase in the temperature of the solution in the
generator and also increased the ammonia refrigerant vapor pro
duction, raising the possibility to produce a higher cooling effect due
to the lower temperature in the evaporator, and thus a lower tem
perature of the chilled water;
• As the chilled water increases, it is less thermal load getting into the
system. With the same amount of hot water, there was a slightly
positive change in the COP since less energy was demanding in the
evaporator, and the generator heat was higher;
• At the chiller’s final stage, the COP tended to rise since the activation
energy rate was lower than the rate of evaporation of the evaporator,
leading to the increasing of the COP. The COP values varied around
0.45 to 0.515 (±0.5) by using this approach to combine the char
acteristic equation method and the thermal inertia, values similar to
those obtained experimentally in the literature;
CRediT authorship contribution statement
S.C.S. Alcântara: Conceptualization, Methodology, Formal analysis,
Writing – original draft. A.A.S. Lima: Conceptualization, Methodology,
Formal analysis, Writing – original draft. A.A.V. Ochoa: Methodology,
Formal analysis, Writing – review & editing, Supervision, Funding
acquisition. G. de N. P. Leite: Conceptualization, Methodology, Writing
– original draft. J.Â.P. da Costa: Formal analysis, Visualization, Inves
tigation, Writing – review & editing. C.A.C. dos Santos: Conceptuali
zation, Writing – original draft. E.J.C. Cavalcanti: Writing – review &
editing, Supervision. P.S.A. Michima: Writing – review & editing,
Supervision.
Declaration of Competing Interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
Acknowledgment
The first and second authors thank the CAPES for the support in the
Doctorate’s degree. The third author thanks the program Science
Without Borders – CNPq/Brazil, for the scholarship of the post-doctoral
study (PDE:203489/2014-4), and also thanks Professor Alberto Coronas
for his support during the post-doctoral research at the Rovira and
Virgili University and also the Staff from the same university, especially
the CREVER group. The second author also thanks to the CNPq for the
Productivity scholarship of Productivity n◦
309154/2019-7 and the IFPE
for its financial support throughout the Call 10/2019/Propesq. The au
thors thank FACEPE/CNPq for financial support for research project
APQ-0151-3.05/14 and the CNPq for the research project - Universal
402323/2016-5.
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