CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 76, 2019 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Petar S. Varbanov, Timothy G. Walmsley, Jiří J. Klemeš, Panos Seferlis 
Copyright © 2019, AIDIC Servizi S.r.l. 

ISBN 978-88-95608-73-0; ISSN 2283-9216 

Systematic Assessment of Model Robustness in Simulation of 

Absorption Refrigeration Processes 

Dimitris Gkouletsosa, Athanasios I. Papadopoulosa,*, Panos Seferlisb,a, Ibrahim 

Hassanc 

aChemical Process and Energy Resources Institute, Centre for Research and Technology Hellas, 57001, Thessaloniki, 

 Greece 
bDepartment of Mechanical Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece 
cMechanical Engineering Department, Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar 

 spapadopoulos@cperi.certh.gr 

A systematic sensitivity analysis approach is proposed to assess the robustness of thermodynamic model 

predictions employed in ABR processes. A sensitivity matrix is developed which incorporates the derivatives of 

multiple ABR performance indicators (e.g. coefficient of performance, generated cooling, mass flowrate of 

working fluid etc.) with respect to multiple thermodynamic property parameters propagated through different 

thermodynamic prediction models. The dominant eigenvector direction of the sensitivity matrix is identified and 

used to explore the ABR process behaviour as indicated by the change of ABR performance indicators under 

simultaneous, multiple and finite thermodynamic parameter variations. This enables the robust mapping of ABR 

performance toward the direction of maximum variability in the multiparametric space and hence the 

identification of a thermodynamic model which supports robust predictions regardless of variability. The 

approach is illustrated in a single effect ABR process system using the NH3/H2O mixture. Among various 

thermodynamic models we find that the Schwartzentruber-Renon with eNRTL are the most robust combination 

to parameter variability.  

1. Introduction 

Absorption Refrigeration (ABR) is a widely investigated process for transformation of renewable or waste heat 

into cooling (Kale et al., 2018). A detailed review of the absorption refrigeration technologies can be found in 

Papadopoulos et al. (2019). Performance evaluation of different ABR working fluids and process configurations 

is largely approached in published literature through process models (Wu et al., 2017). The latter are based on 

equations of state (EoS) and activity coefficient models to support the prediction of the equilibrium mixture 

properties necessary for process simulation. The thermodynamic models currently reported vary significantly 

from Peng-Robinson (Han et al., 2016) and soft-SAFT (Crespo et al., 2017) to NRTL and UNIFAC (Chaudhari 

et al., 2008). All these options result in significant prediction differences even for exactly the same ABR working 

fluid and process (Zehioua et al., 2010). As such, the validation of ABR models based on experimental data or 

available model-based results, and the assessment of ABR performance, include significant uncertainty. The 

latter reduces confidence in the obtained model predictions, as results may differ from the actual process 

operation. 

In current literature, parameter estimation studies for the development of thermodynamic models used in ABR 

processes consider the difference of the predicted results from validated reference data (e.g. experimental) 

(Han et al., 2016), while ABR process model predictions are also compared with reference data (e.g. Adewusi 

and Zubair, 2004). However, this does not constitute a systematic treatment of uncertainty. Different sets of 

reference data used as input in a thermodynamic model affect the predictions provided for a desired property. 

Different thermodynamic models also result in divergent predictions for the same desired property. ABR process 

simulations require predictions of multiple properties over wide ranges of different temperatures, pressures and 

concentrations. Reference data are often only available for specific conditions and process parameters, 

 
 
 
 
 
 
 
 
 
 
                                                                                                                                                                 DOI: 10.3303/CET1976121 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper Received: 02/04/2019; Revised: 06/05/2019; Accepted: 06/05/2019 
Please cite this article as: Gkouletsos D., Papadopoulos A.I., Seferlis P., Hassan I., 2019, Systematic Assessment of Model Robustness in 
Simulation of Absorption Refrigeration Processes, Chemical Engineering Transactions, 76, 721-726  DOI:10.3303/CET1976121 
  

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prohibiting validation within wider ranges for all the desired parameters. The latter is very important because 

multi-parametric variations can occur on thermodynamic models causing the onset of nonlinear effects (e.g., 

non-smooth behaviour due to sharp changes in parameter profiles) which may result in unexpectedly detrimental 

process performance. It is therefore necessary to be able to quantify uncertainty and to select thermodynamic 

models which exhibit low sensitivity to multi-parametric variability, regardless of the availability of reference data.  

2. Sensitivity analysis method 

The above challenges are addressed through a systematic sensitivity analysis approach which accounts for the 

propagation of multi-parametric variability through multiple different thermodynamic models used in ABR 

processes. The purpose of the proposed approach is a) to identify the thermodynamic parameters that have the 

highest influence on the ABR performance and b) to select the thermodynamic models which exhibit the lowest 

sensitivity when such parameters are varied simultaneously toward a systematically identified direction of the 

highest variability. A model identified through such an approach would provide robust and reliable predictions 

even in cases of intense variability in the parameters used as input. The proposed method has been previously 

implemented in a single thermodynamic model to assess organic Rankine cycle working fluids (Papadopoulos 

et al., 2013). It is implemented here for the first time in ABR processes and considers for the first time multiple 

different thermodynamic models.  

We start by considering a set 𝐷 of thermodynamic models, an 𝑁𝑝-dimensional vector 𝜺 representing the 

parameters which will be subjected to variability as inputs in the thermodynamic models of 𝐷 and an 𝑁𝐹-

dimensional vector 𝑭 of performance indicators. Let a vector 𝜺𝑛𝑜𝑚 representing the nominal values for the model 

parameters of the ABR process. For every thermodynamic model 𝑑 𝜖 𝐷, we identify the model parameters which 

are the most sensitive with respect to the performance indicators 𝑭 by generating a local sensitivity matrix 𝑷 

around the nominal model parameter vector 𝜺𝑛𝑜𝑚 as follows, 

𝑷 =

[
 
 
 
 
 
𝜕𝑙𝑛𝐹1
𝜕𝑙𝑛𝜀1

 ⋯
𝜕𝑙𝑛𝐹1
𝜕𝑙𝑛𝜀𝛮𝑝

⋮ ⋱ ⋮
𝜕𝑙𝑛𝐹𝑁𝐹
𝜕𝑙𝑛𝜀1

⋯
𝜕𝑙𝑛𝐹𝑁𝐹
𝜕𝑙𝑛𝜀𝛮𝑝 ]

 
 
 
 
 

𝜺𝑛𝑜𝑚

. (1) 

The logarithmic functions represent locally scaled transformations for the performance indicators and the model 

parameters, whereas matrix 𝑷 constitutes a measure of variation of the process model under the influence of 

infinitesimal changes imposed on model parameters. 

The major directions of variability are identified by calculating the eigenvectors 𝜣𝑖 (𝑖 = 1, … , 𝑁𝑝) of the matrix 

𝑷𝑇𝑷 for every model 𝐷. The dominant direction of variability is represented as the combination of parameters 𝜺 

which are causing the largest change in the performance indicators in a least square sense. The eigenvector 

𝜣1, with the largest in magnitude eigenvalue of 𝑷𝑇𝑷, is related to the largest change in the performance indices 

𝑭. The identification of major variability direction indicates that is not necessary to investigate other directions. 

Following the determination of the sensitivity matrix, a sensitivity index 𝛺 is defined, which accounts for the 

behavior of the performance indicators 𝑭 within a wide variation range, explored through a magnitude parameter 

variation 𝜁 along the dominant direction of variability. As a result, for every thermodynamic model 𝑑 𝜖 𝐷 , the 

sensitivity metric is obtained for finite parameter variations, as follows 

𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒
𝑑 𝜖 𝐷

 𝛺(𝜁, 𝑑) = 100 ∙ ∑ |
𝐹𝑖(𝒙, 𝑑, 𝜺(𝜁)) − 𝐹𝑖(𝒙, 𝑑, 𝜺

𝑛𝑜𝑚))

𝐹𝑖(𝒙, 𝑑, 𝜺
𝑛𝑜𝑚)

 |

𝑁𝐹

𝑖=1

   

𝑠. 𝑡.      ℎ𝑖(𝒙, 𝑑, 𝜺) = 0             ,     𝑖 = 1, … , 𝑁ℎ 

𝑔𝑖(𝒙, 𝑑, 𝜺) ≤ 0             ,     𝑖 = 1, … , 𝑁𝑔 

  𝑥𝑖
𝐿 ≤ 𝑥𝑖 ≤ 𝑥𝑖

𝑈          ,     𝑖 = 1, … , 𝑁𝑥 

𝜀𝑖(𝜁) − 𝜀𝑖
𝑛𝑜𝑚

𝜀𝑖
𝑛𝑜𝑚 = 𝜁 ∙ 𝜃𝑖

1     ,     𝑖 = 1, … , 𝑁𝑝 

                                     𝜁 ∈ [𝜁𝐿, 𝜁𝑈]   
 

(2) 

with 𝑁𝑥-dimensional vector 𝒙 representing the state variables, with 𝑥
𝐿 and 𝑥𝑈 being lower and upper bounds, 

𝑁ℎ-dimensional vector 𝒉 and 𝑁𝑔-dimensional vector 𝒈 representing the equalities and inequalities of the ABR 

process. The 𝛺 is calculated under the assumption that the eigenstructure of the local sensitivity matrix does 

not change considerably with the variation of parameters. The sensitivity index 𝛺 represents the sum of the 

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relative change of performance indicators 𝑭 from the nominal values, as a function of 𝜁, which is the parameter 

variation magnitude coordinate indicating the range of imposed change in the direction of 𝜣1. The maximum 

change along this direction is addressed through the lower and upper bound, 𝜁𝐿 and 𝜁𝑈.  Indices 𝛺 resulting 

from different models are rank-ordered identifying the model with the lowest sensitivity to model parameter 

changes. The emphasis is therefore concentrated on the sensitivity of the process performance rather than on 

the actual value of the performance indicators. In this way, the model that ensures a predicted performance 

near the nominal design point can be determined. 

3. Implementation 

3.1 Absorption refrigeration process 

Figure 1 illustrates the single stage, single effect ABR process. NH3 is used as the refrigerant and H2O as the 

absorbent. The latter has strong affinity for NH3 and they are soluble with each other in a wide range of operating 

conditions. The main system components are the absorber, condenser, evaporator, and generator. Some other 

auxiliary components are solution (SHX) and condenser-evaporator (CEHX) heat exchangers, expansion 

valves, pump and rectifier. Low pressure conditions are indicated with blue color, whereas high pressure with 

red color.  

 

 

Figure 1:Single-stage, single-effect NH3/H2O ABR configuration. 

3.2 Investigated thermodynamic models and reference data 

The proposed sensitivity analysis method is addressed through the consideration of different EoS, based on the 

available options in AspenPlus Version 9 Software (www.aspentech.com). The Redlich-Kwong, the 

Schwartzentruber-Renon, the Cubic-Plus-Association and the Peng-Robinson (with Boston-Mathias 

modification) EoS are selected in order to describe the vapor-phase properties of NH3/H2O mixture. The liquid-

phase non-ideality of NH3/H2O mixture is modelled using the Electrolyte NRTL (ELECNRTL) model. The 

package used for the calculation of thermodynamic properties was mainly ASPENPCD, followed by AQUEOUS, 

ELECPURE, PURE20, ENRTL-RK and EOS-LIT databanks. Our results are validated against data obtained 

from simulations performed by Adewusi and Zubair (2004). This source is selected mainly for two reasons. 

Firstly, it includes detailed stream data for a single effect cycle hence facilitating both the modeling and 

comparison of results obtained from the simulation of the cycle. Secondly, it employs correlations developed 

directly from NH3/H2O experimental mixture data by Ibrahim and Klein (1993). These correlations have been 

validated by Thorin et al. (1998), showing that for temperature and pressure conditions similar to those in our 

work the predicted mixture properties match experimental data closely. 

3.3 Process operating assumptions 

AspenPlus Version 9 Software has been used for ABR process design and simulation. The majority of the 

components has been considered as “Heater Blocks”, pump and valves as adiabatic “Pump Block” and “Valve 

Blocks”, respectively and the generator-rectifier system as distillation column. The simulation assumptions have 

been selected to be similar with the operating conditions in Adewusi and Zubair (2004). Low and high pressure 

are considered as the vapour pressures of NH3/H2O mixture and NH3 at 40 oC, respectively. Their values are 

equal to 244.85 kPa and 1,555.76 kPa. The strong-solution mixture mass flow is 1 kg/sec with 0.3709 NH3 mass 

fraction. The SHX and CEHX effectiveness are 1 and 0.95, respectively, while on evaporator’s exit, the 

requirement is 0.998 vapor fraction. The generator’s heat flow input is equal to 267.9 kW. However, for the 

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generator-rectifier’s distillate-to-feed ratio and number of stages, there is no information in Adewusi and Zubair 

(2004). Therefore, the distillate-to-feed value was determined equal to 0.13224 kg/kg so that the temperature in 

the rectifier refrigerant vapour stream matches the corresponding steam in the literature source. The number of 

stages was determined equal to 5 so that the purity of NH3 in the rectifier refrigerant vapour stream matches 

that of the literature source. 

3.4 Technical details and constraints 

Table 1 summarizes the parameters varied during the sensitivity analysis (vector 𝜺) and the performance 

indicators of vector 𝑭. Uncertainty is introduced in selected critical parameters and NH3 vapor pressure 

(corresponding to the high pressure of the cycle), using experimentally obtained values as nominal points. These 

parameters are selected as they affect both the operational conditions of the ABR process, and the employed 

EoS. Note that coefficient of performance is defined as the ratio of evaporator heat flow to generator’s heat flow 

input. 

Table 1: Varying parameters and performance indicators 

Varied parameters of vector 𝜀  Symbol Performance indicators of vector 𝐹 Symbol 

Critical temperature of H2O 𝑇𝑐
𝐻2𝑂 Absorber heat flow 𝑄𝑎𝑏𝑠 

Critical temperature of NH3 𝑇𝑐
𝑁𝐻3 Condenser heat flow 𝑄𝑐𝑜𝑛𝑑 

Critical pressure of H2O 𝑃𝑐
𝐻2𝑂 Evaporator heat flow 𝑄𝑒𝑣𝑎𝑝 

Critical pressure of NH3 𝑃𝑐
𝑁𝐻3 Coefficient of performance 𝐶𝑂𝑃 

High pressure of cycle 𝑃𝐻𝑖𝑔ℎ
    

 

The process operability is ensured by avoiding cavitation in the pump’s entrance. Consequently, a saturated (or 

subcooled) liquid mixture is required, as parameter variability may lead to vapor-liquid phase conditions, by 

altering the mixture’s vapor pressure in pump inlet. For this reason, AspenPlus Software introduces the 

constraint that the vapor fraction in the pump entrance should be less than 0.1 %. 

4. Results and discussion 

4.1 Influence of model parameters on absorption refrigeration process under variability 

Table 2 summarizes the contribution of varied parameters to the dominant direction of variability for every 

thermodynamic model. Parameters on the left side of the table have a higher impact on the eigenvector 𝜣1 and, 

subsequently, on the performance indices compared to the right-aligned table parameters. For every 

thermodynamic model, the parameter with the highest influence is 𝑇𝑐
𝑁𝐻3, as it is a major input parameter on the 

applied EoS. For the same reason, 𝑃𝑐
𝑁𝐻3 contributes significantly to the process variability. It is obvious that 

variability introduced to the critical properties of NH3 influences significantly performance indexes due to use of 

NH3 on every stream of the working cycle either as vapour-refrigerant or as liquid-component of binary mixture. 

Moreover, 𝑃𝐻𝑖𝑔ℎ
  has a high variability contribution as it affects all the high pressure streams and components of 

the system. 𝑇𝑐
𝐻2𝑂 and 𝑃𝑐

𝐻2𝑂 have the lowest impact on the ABR working cycle, with 𝑃𝑐
𝐻2𝑂 having zero contribution 

to Schwartzentruber-Renon EoS. Note that this is reasonable considering that H2O participates mainly only to 

the liquid binary mixture. 

Table 2: Ordering of most influential parameters from left to right for each model on ABR process. Most dominant 

parameter is marked with bold. Sign in brackets indicate negative values and opposite directions of change 

compared to positive values; zero in brackets indicate no influence of the parameter on the process. 

Model  Parameters ordered based on contribution to eigenvalue direction 

ELECNRTL – Redlich-Kwong 𝑻𝒄
𝑵𝑯𝟑 , 𝑃𝑐

𝑁𝐻3 (−) , 𝑃𝐻𝑖𝑔ℎ , 𝑇𝑐
𝐻2𝑂 , 𝑃𝑐

𝐻2𝑂(−) 

ELECNRTL – Schwartzentruber-Renon 𝑻𝒄
𝑵𝑯𝟑 , 𝑃𝐻𝑖𝑔ℎ (−) , 𝑇𝑐

𝐻2𝑂 ,  𝑃𝑐
𝑁𝐻3 (−),  𝑃𝑐

𝐻2𝑂(0) 

ELECNRTL – Peng-Robinson 𝑻𝒄
𝑵𝑯𝟑 , 𝑃𝑐

𝑁𝐻3 (−) , 𝑃𝐻𝑖𝑔ℎ , 𝑇𝑐
𝐻2𝑂, 𝑃𝑐

𝐻2𝑂(−) 

ELECNRTL – CPA 𝑻𝒄
𝑵𝑯𝟑 , 𝑃𝐻𝑖𝑔ℎ (−) ,  𝑃𝑐

𝑁𝐻3 (−),  𝑇𝑐
𝐻2𝑂,  𝑃𝑐

𝐻2𝑂(−) 

4.2 Evaluation of sensitivity index 𝜴 and performance indicators 

This section presents the proposed sensitivity analysis method implementation. Figure 2 illustrates the 

sensitivity index 𝛺 with respect to the magnitude parameter 𝜁. Thermodynamic models with steep profile close 

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to region 𝜁 = 0 exhibit significantly different performance compared to their nominal point, implying that they are 

very sensitive to variability. A small change in the model parameters will lead to a large variation on the 

performance indicators. On the other hand, thermodynamic models with a flat profile close to region 𝜁 = 0 

absorb efficiently model disturbances. As a result, their performance is more robust to model variations and 

does not vary significantly compared to the nominal operation. Models with Redlich-Kwong and Peng-Robinson 

Eos exhibit a steeper profile, whereas models with Schwartzentruber-Renon and CPA EoS exhibit a profile with 

a lower slope. Furthermore, nonlinear thermodynamic model behaviour is observed in regions with small 𝜁 

positive values. After a critical 𝜁 positive value, the model’s behaviour could be approached as linear. In addition, 

note that upper bound 𝜁𝑈 ≈ 0.05 corresponds to 5 % increment of the most influential parameter of Table 2 from 

its AspenPlus Software nominal value. Negative 𝜁 values are bounded by the cavitation phenomenon on pump’s 

inlet. 

 

Figure 2: Index 𝛺 with respect to variation of coordinate magnitude 𝜁 

Figures 3a and 3b illustrate the nominal values of condenser heat flow 𝑄𝑐𝑜𝑛𝑑 and process coefficient of 

performance 𝐶𝑂𝑃 for every thermodynamic model compared to reference values from Adewusi and Zubair 

(2004). Variability on these elements is introduced through black errorbars with right-direction corresponding to 

increase of positive 𝜁 values. Nominal and reference values of 𝑄𝑐𝑜𝑛𝑑 are very close to each other. However, the 

sensitivity of this performance indicator to parameter variation is high, hence moving towards the positive 𝜁-

direction increases 𝑄𝑐𝑜𝑛𝑑 values so that it deviates significantly from nominal and reference point. For every 

thermodynamic model 𝐶𝑂𝑃 nominal value deviates slightly from the reference value, while exhibits, 

simultaneously, a low range of variability. As a result, the process performance remains unaffected to model 

uncertainties introduced in the parameter vector 𝜺. 

 

 
 

(a) (b) 

Figure 3: (a) nominal 𝑄𝑐𝑜𝑛𝑑 and (b) 𝐶𝑂𝑃 values under variability (black errorbars) compared to reference 

values (Adewusi and Zubair, 2004) on ABR single-effect process. 

 

 

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5. Conclusions 

Current work presents a nonlinear sensitivity analysis of the NH3/H2O single-effect absorption refrigeration 

process under model parameter variability using different thermodynamic models. Firstly, the most influential 

parameters on ABR process performance are identified, by calculating the dominant direction of variability.  

Then, sensitivity index 𝛺 is introduced, representing the sum of the relative change of performance indicators 

from their nominal values. Thermodynamic models with different EoS have been considered, while literature 

studies are introduced for validation and comparison purposes. In terms of variability, a few parameters 

contribute to the ABR process variation with 𝑇𝑐
𝑁𝐻3 being the most crucial. Observing the sensitivity index 𝛺 

curves towards the dominant direction of variability, the deviations among the models are considered small. The 

Schwartzentruber-Renon EoS appears as the least sensitive to the parameter uncertainty. The decomposition 

of sensitivity index to its performance indicators reveals that variability is more intense to the condenser, 

whereas system’s efficiency is not significantly affected as 𝐶𝑂𝑃 still remains close to the reference values.  

Acknowledgements 

This paper was made possible by an NPRP award [#NPRP10-1215-160030] from the Qatar National Research 

Fund (a member of The Qatar Foundation). The statements made herein are solely the responsibility of the 

authors. 

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