Academic Journal of Science and Technology 
ISSN: 2771-3032 | Vol. 7, No. 3, 2023 

 

305 

Modelica	Modeling	of	Thermodynamic	Properties	of	
LiBr‐H2O	Solutions	
Kunfeng Sun* 

School of Energy and Environment, Zhongyuan University of Technology, Zhengzhou, China 
*Corresponding author: Kunfeng Sun (Email: skf0558@sina.com) 

 

Abstract: Absorption refrigeration system is one of the basic refrigeration systems, with LiBr-H2O solution being the most 
common working fluid. In order to perform thermodynamic design and analysis on the absorption refrigeration cycle, it is 
essential to develop a program to calculate the thermodynamic properties of the solution. Modelica is the most promising digital 
twin modeling language and has been widely used in heat flow system modeling. In this study, a new interface library for 
calculating the thermophysical properties of LiBr-H2O solution is introduced. This library can calculate the vapor pressure, 
solution temperature, enthalpy, entropy, mass concentration, etc., as well as dynamic viscosity, thermal conductivity, surface 
tension coefficient, and other heat transfer or thermodynamics characteristic parameters. It enables researchers to easily modeling 
and analyze complex LiBr-H2O absorption refrigeration cycles in Modelica within specific temperature and concentration ranges. 

Keywords: Thermodynamic properties, LiBr-H2O, Solutions, Modelica. 
 

1. Introduction 
With the development of the world economy, human beings 

are facing increasingly severe energy shortages and    
resources crises. Therefore, research on the utilization of 
renewable energy such as solar energy, geothermal energy, 
and low-grade energy such as industrial waste heat is 
receiving increasing attention. The unique advantage of 
absorption refrigeration, which can directly use low-grade 
heat sources to drive and does not use working fluids such as 
CFCs that damage the ozone layer, has been widely 
recognized [1]. 

Absorption refrigeration system is one of the fundamental 
refrigeration systems, in which LiBr-H2O Solutions being the 
most common working fluid. In order to perform 
thermodynamic calculations and analysis on the absorption 
refrigeration cycle, it is essential to develop a program to 
calculate the thermodynamic properties of the solution. 
Modelica language is currently the most promising digital 
twin development language. When modeling thermal-fluid 
systems, the Modelica standard library provides many 
medium models, but they may not be sufficient for many 
applications.  

Absorption refrigeration system is one of the fundamental 
refrigeration systems. Currently, LiBr-H2O and NH3-H2O are 
widely used as working fluids in absorption refrigeration. 
Among them, NH3-H2O is limited in many applications due 
to its strong odor and toxicity, which compromises its safety.  

On the other hand, LiBr-H2O primarily uses water as the 
refrigerant and can be used as long as the evaporation 
temperature is not lower than 5℃ . In order to perform 
thermodynamic calculations and analysis on the absorption 
refrigeration cycle, it is essential to develop a program to 
calculate the thermodynamic properties of the solution. Many 
researchers have conducted data fitting on the experimental 
data of lithium bromide-water solution's thermophysical 
properties and obtained equations for major property 
parameters [2]. ASHRAE has also provided equilibrium 
equations for lithium bromide-water solution [3].  

Some scholars have developed software for calculating 
thermophysical properties using computer languages such as 
C, VB, Python, and Fortran etc. [4-6]]. These software 
packages generally include relationships between enthalpy, 
temperature, and concentration as the main parameters. 
However, developing refrigeration models in these languages 
is challenging, especially for complex models. 

The release of Modelica is a significant event in the history 
of digital modeling technology development, marking the 
transition of these techniques from component-level to 
system-level in multiple disciplines and fields. After more 
than 20 years of development, Modelica has been widely 
applied in various industries such as aerospace, vehicles, 
energy, education, etc. Modelica combines the advantages of 
multiple modeling languages. Modelica is a high-level 
declarative language for describing mathematical behavior. It 
can easily describe the working characteristics of different 
engineering components, and at the same time, it can form 
complex systems of components [7, 8]。 

Modelica provides broad technical support for various 
modeling forms, including object-oriented and noncausal 
declarative modeling. Importantly, Modelica has an open 
language standard design, and its language specification is 
freely available. Additionally, there is an open-source IDE 
called OpenModelica. With its comprehensive features, 
Modelica has become the most promising digital twin 
development language and has the potential to become the de 
facto international standard for system simulation in the 
future. 

Due to various advantages mentioned above, Modelica has 
been increasingly applied in the field of heat flow system 
modeling. When modeling a thermal fluid system, a 
fundamental question is whether a Modelica model can be 
obtained for calculating the properties of the working fluid. 
The Modelica standard library provides many medium 
models, but it is not sufficient in many specific applications, 
such as obtaining the thermodynamic properties of the 
working fluid solution for thermal calculation and analysis of 
absorption refrigeration cycles, which is essential and 



 

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challenging. To address this issue, the author of this article 
developed the Lithium Bromide solution thermodynamic 
property library for calculating the thermophysical properties 
of lithium bromide aqueous solutions. This library allows 
researchers to easily and conveniently model, calculate, and 
analyze complex absorption refrigeration cycles in Modelica 
within specific temperature and concentration ranges. 

2. Framework of Library 
The thermophysical property library consists of five main 

parts: LiBr , Saturation , Transports, tools and Example. 

The framework of the thermophysical properties 
calculation library for LiBr-H2O solution is shown in Figure 
1. 

 
Figure 1. LiBr-H2O solution library framework 

3. Thermal Properties 

3.1. Enthalpy of LiBr-H2O Solution 
The main calculations in absorption refrigeration models 

are the enthalpy difference, temperature difference, pressure 
difference, and concentration difference of each component. 
The enthalpy equation for the LiBr-H2O solution can be 
found in many different studies. In this work, ASHRAE 
handbook’s enthalpy equation was used to develop the code. 
According to the ASHRAE handbook, enthalpy equation is 
expressed as following [3]: 
ℎ ∑ 𝐴 100𝑥 𝑇∑ 𝐵 100𝑥 𝑇 ∑ 𝐶 100𝑥    (1) 
(15℃<T<165℃，0.4<x<0.7)  
Where, h is enthalpy in kJ/kg, x is mass concentration and t is 
the solution temperature in °C, A(n), B(n) and C(n) are 
constants respectively. 

Based on this code, a diagram of the relationship between 
solution concentration, solution temperature, and enthalpy 
can be generated, as shown in Figure 2. 

3.2. Entropy of LiBr-H2O Solution 
Just like calculating enthalpy, there are many equations for 

calculating the entropy of LiBr-H2O solution. Here, the 
equation in reference [9]. 

𝑆 ∑ ∑ 𝐵 100𝑥 𝑇           (2) 
(40℃<T<210℃，0.4<x<0.65) 

Where S is solution entropy in kJ/(kg.K). B are constants. 
 

 
Figure 2. The LiBr-H2O solution enthalpy-concentration-

temperature diagram 

 

Other parameter calculations can refer to the functions in 
Table 1 and be calculated based on the corresponding 
functions. 

 
Table 1. The Thermal Properties Functions 

Number Name Function Scope 

1 

H_tx Determine 
enthalpy given 

temperature and 
concentration 

15℃<T<165℃， 
0.40<x<0.70 

2 

H_tp Determine 
enthalpy given 

temperature and 
pressure 

15℃<T<165℃， 
0.25<P<200 

3 

S_tx Determine 
entropy given 

temperature and 
pressure 

40℃<T<210℃， 
0.40<x<0.65 

4 

T_xp Determine 
temperature given 
concentration and 

pressure 

0.25<P<200, 
0.45<x<0.75 

5 

P_xt Determine 
pressure given 

temperature and 
concentration  

15℃<T<165℃， 
0.40<x<0.70 

6 

X_tp Determine 
concentration 

given temperature 
and pressure 

15℃<T<165℃， 
0.25<P<200 

7 

T_hx Determine 
temperature given 

enthalpy and 
concentration 

0.40<x<0.70 

8 
Hcn_h Enthalpy 

conversion 
function 

 

9 

Tcry_x Determine 
crystallization 

temperature given 
concentration 

0.55<x<0.65 

4. Other Parameters 

4.1. Transport Parameters 
When calculating the heat exchanger model, the transport 

parameters are used, including specific heat capacity at 
constant-pressure, dynamic viscosity, thermal conductivity, 
and surface tension coefficient. Several references [5,9] have 
conducted fittings on these heat transfer parameters of lithium 
bromide-water solution, resulting in different fitting 



 

307 

equations. The computational accuracy of these equations is 
similar, with only slight variations in their applicable ranges. 
In this article, the following formula is selected. 

Thermal conductivity： 
 

    𝑘 ∑ 𝐴 𝑇 ∑ 𝐵 𝑥             (3) 
 

Dynamic viscosity： 
 

𝜂 ∑ 𝐴 𝑥 𝑇∑ 𝐵 𝑥 𝑇 ∑ 𝐶 𝑥      (4) 
 

Surface tension coefficient： 
 

𝜎 ∑ 𝐴 𝑇 ∑ 𝐵 𝑥              (5) 
 

Where , k is thermal conductivity W/(m.K) ; 
η is Dynamic viscosity Pa.s ; 
σ is surface tension coefficient N/m; 
A, B is constants. 
Figure 3 illustrates the relationship curve between thermal 

conductivity and solution concentration at 40 ℃. 
 

 
Figure 3. conductivity-x diagram at 40℃ 

 

Transport parameters calculations can refer to the functions 
in Table 2 and be calculated based on the corresponding 
functions. 

 
Table 2. Transport Properties Functions 

Number Name Function Scope 

1 
Density_tx Determine density given temperature and 

concentration 
 

0℃<T<200℃， 
0.40<X<0.70 

2 
Cp_tx Determine specific heat capacity given 

temperature and concentration 
 

20℃<T<190℃， 
0.30<X<0.65 

3 
Visc_tx Determine Dynamic viscosity given 

temperature and concentration 
 

0℃<T<200℃， 
0.45<X<0.65 

4 
Cond_tx Determine thermal conductivity given 

temperature and concentration 
 

20℃<T<200℃， 
0.30<X<0.65 

5 
Sigma_tx Determine Surface tension coefficient 

given temperature and concentration 
 

20℃<T<130℃， 
0.40<X<0.70 

 

4.2. Saturation Parameters 
The calculation of saturation parameters requires the use of 

some physical properties of water vapor. There are two 
methods that can be used here. One is to directly call the water 
vapor physical properties package in the Modelica Media 
library, which has high calculation accuracy. The second 

method is to separately use some empirical formulas in the 
range of 0-200 ℃ for calculation. This calculation library 
uses several simple formulas provided in reference[10], 
which are simple, fast, and can ensure accuracy, I won't list 
them all here anymore。Please refer to Table 3 for specific 
calculation functions. 

 
Table 3. Saturation Parameters Functions 

Number Name Function Scope 

1 
Tsat_DtX Determine Saturation temperature given dew 

temperature and concentration 
0℃<T<200℃， 

X<0.70 

2 Tsat_Dpx Determine Saturation temperature given dew 
pressure and concentration 

 

3 Xsat_Pdt Determine Saturation concentration given 
dew pressure and solution temperature 

 

4 Xsat_Dtt Determine Saturation concentration given 
dew temperature and solution temperature 

 

5 hsat_tx Determine Saturation enthalpy given solution 
temperature and concentration 

 

 

4.3. Derived Parameter  
There is not a direct equation for concentration in 

ASHRAE handbook. For example, given the pressure and 

concentration, there is no equation that can directly calculate 
the solution temperature. in order to calculate the solution 
temperature, it is necessary to solve a nonlinear equation. 

In this study, the nonlinear equation solving function 



 

308 

provided by Modelica is called, which uses the brent method 
to solve the nonlinear equation. 

The sample code is as follows： 
function X_tp  
  extends Modelica.Icons.Function; 
  input Real T; 
  input Real p; 
  output Real x; 
protected  
  Real x1 = 0.4; 
  Real x2 = 0.7; 
  Real tolerance = 100 * Modelica.Constants.eps; 
algorithm   

x:=Modelica.Math.Nonlinear.solveOneNonlinearEquation 
 ( function AqueousLiBr.tools.fun(T = T, p = p),  
    x1,  
    x2,  
    tolerance); 
end X_tp; 
Figure 4 is the pressure-concentration-enthalpy diagram 

calculated by solving the nonlinear equations. 
 

 
Figure 4. The enthalpy-concentration-pressure diagram 

5. Conclusion  
A thermophysical model library for LiBr-H2O solution was 

established using Modelica., Several parameters were 
explained in detail, and the calculation formulas for transport 
parameters and saturation parameter calculation functions 

were provided. The tables explain the usage methods and 
limitations of LiBr-H2O solution. This library can 
conveniently calculate the thermophysical parameters of 
absorption refrigeration system cycles, meet the accuracy 
requirements of engineering calculations, and it can 
intuitively and conveniently draw parameter lines in the 
modelica. 

References 
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Properties Parameter of LiBr-H2O”,J. ZhanJiang Ocean 
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[2] Pátek J, Klomfar J. “A computationally effective formulation 
of the thermodynamic properties of LiBr–H2O solutions from 
273 to 500”. Int. J.  Refrigeration, vol.29,no.4, pp.566-
578,2006. 

[3] LA. M. “Thermodynamic properties of aqueous solutions of 
lithium bromide”. ASHRAE Trans.,vol 85, pp.413-434, 1979. 

[4] Wang Lei, LU Zhen, “Visualized Program about Properties of 
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40,Chn,2001. 

[5] YunChen ,Guozhen Xie,“Simulation of the Property of 
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2004. 

[6] Wang Lin, “Principle and Application of Small Absorption 
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[7] Fritzson P., “Introduction to Modeling and Simulation of 
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[8] Association M., Modelica - A Unified Object-Oriented 
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Version 3.7-dev. 2023. 

[9] Kaita Y, “Thermodynamic properties of lithium bromide–
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[10] Shen Yuhao,Ding Lixing,”The Thermodynamic Properties of 
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