DOI: 10.3303/CET25117112 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Paper Received: 8 December 2024; Revised: 18 February 2025; Accepted: 15 May 2025 
Please cite this article as: Tulabi M., Bubbico R., 2025, Impact of Battery Degradation on Thermal Runaway Risks in Lithium-ion Batteries: a 
Statistical and Modelling Approach, Chemical Engineering Transactions, 117, 667-672  DOI:10.3303/CET25117112 
  

 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 117, 2025 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.cetjournal.it 

Guest Editors: Fabrizio Bezzo, Flavio Manenti, Gabriele Pannocchia, Almerinda di Benedetto 

Copyright © 2025, AIDIC Servizi S.r.l. 

ISBN 979-12-81206-17-5; ISSN 2283-9216 

Impact of Battery Degradation on Thermal Runaway Risks in 

Lithium-Ion Batteries: a Statistical and Modelling Approach 

Milad Tulabi*, Roberto Bubbico 

Department of Chemical Material and Environmental Engineering, “Sapienza” Rome University, Via Eudossiana 18, 00184, 

Rome, Italy  

milad.tulabi@uniroma1.it 

Li-ion batteries are commonly used in an increasing number of applications, but they are characterized by 

different safety problems connected with their operating temperature. In fact, depending on the balance between 

the heat internally produced during operation and that dissipated towards the external environment, a thermal 

runaway can occur beyond certain values of the internal temperature, with possible dangerous events, such as 

fires and explosions. While most existing research investigates TR in new or minimally cycled batteries, real-

world TR incidents predominantly occur in aged batteries, underscoring the need for a targeted investigation 

into the aging effects. This study will examine the effect of battery degradation on the likelihood of thermal 

runaway (TR) events, with a focus on the main degradation parameters that impact thermal behavior in lithium-

ion batteries (LIBs), such as internal resistance, the charge/discharge current, and the cell capacity. A 

mathematical model was developed and validated against established literature, allowing for a detailed 

statistical analysis of each parameter's influence on TR. Preliminary results indicate that charge/discharge 

current is the most significant contributor, showing the lowest p-value with confident level of 95% in relation to 

temperature increases at a state of charge (SOC) of 50%. The findings of this study will enhance understanding 

of TR risks in aged LIBs and provide a foundation for improved battery management strategies to mitigate safety 

hazards in degraded batteries.  

1. Introduction 

Energy production, particularly from fossil fuels, is the primary source of global greenhouse gas emissions and 

air pollution (Wang and Azam, 2024), contributing to millions of deaths each year. The current reliance on fossil 

fuels is increasingly problematic due to rising demand, depletion of resources, and geopolitical instability. To 

address climate change and cut CO₂ emissions, a transition to low-carbon energy sources like wind and solar 

power is crucial. Effective energy storage solutions, such as batteries and supercapacitors, are needed to 

manage the variability of renewable energy and maintain a consistent power supply. Additionally, adopting 

electric and hybrid vehicles can play a significant role in reducing emissions in the transportation sector. Lithium-

ion batteries are a type of secondary battery that is usually used for portable electronic devices and electric 

cars, and every day they are getting more popular for use in various industries. 

The safety of lithium-ion batteries is heavily influenced by the failure of individual components, or the integrity 

of the battery system. These vulnerabilities become pronounced under various abusive conditions, including but 

not limited to overcharging, which can lead to Thermal Runaway (TR) and subsequent catastrophic failure, 

dendritic lithium growth within the cell, causing internal short circuits, dissolution of current collectors 

compromising electrical conductivity, and the evolution of gas, potentially leading to pressure build-up and 

rupture (Bubbico et al., 2018). These factors collectively contribute to the intricate safety challenges inherent in 

lithium-ion battery technology (Wen et al., 2012). Thermal runaway involves a chain reaction mechanism 

triggered by abnormal temperature increases in Li-ion cells under abusive conditions. This process is fueled by 

the Heat-Temperature-Reaction (HTR) loop. Initially, abnormal heat generation raises the cell's temperature, 

initiating side reactions like the decomposition of the solid electrolyte interface (SEI). These reactions release 

additional heat, perpetuating the HTR loop until the cell undergoes Thermal Runaway (Feng et al. 2018). 

667



Reactions leading to thermal runaway can be categorized based on the area where they happen: anode 

reactions, cathode reactions and electrolyte decompositions. 

Battery models developed over the years. Doyle and Newman (Doyle et al., 1993, Doyle et al., 1996) studied 

modeling of Li-ion batteries and their work is the basis of many afterward studies. Doyle et al. (1996) compares 

modeling predictions with experimental data from plastic lithium-ion cells, focusing on discharge curves, 

resistance profiles, and parameter optimizations. They discuss the impact of electrode thickness, film resistance, 

and diffusion limitations on battery performance and highlight the importance of accurate parameter values and 

design optimization for enhancing specific energy and power capabilities in lithium-ion batteries. These models 

typically function in a one-dimensional manner across the battery cell layers, adding an additional dimension to 

represent solid lithium diffusion within the electrode particles. This is known as a "pseudo-2D" (P2D) approach. 

However, setting up such a model generally requires around 40 parameters, making it impractical for 

engineering applications where detailed knowledge of the internal battery chemistry might be limited. For low to 

moderate currents, and to improve computational efficiency without sacrificing accuracy, the Newman model 

can be simplified using a single-particle (SP) approach. The SP model simplifies the process by ignoring the 

detailed distribution of local concentration and potential in the solution phase, instead using a lumped solution 

resistance term. Additionally, it assumes that local reaction currents across the porous electrode are constant, 

treating the porous electrode as a collection of single particles all under the same conditions. These assumptions 

are valid for low applied current densities, thin electrodes, and highly conductive electrodes, where overpotential 

is primarily influenced by solid-state diffusion. At high current densities, concentration gradients in the electrolyte 

become significant. The SP model does not account for these concentration gradients and is therefore limited 

to low to moderate current densities (Guo et al, 2012). 

Modeling thermal runaway in lithium-ion batteries is a critical area of research aimed at understanding and 

mitigating safety risks associated with battery operation (Cianciullo et al., 2022). Another significant aspect is 

the incorporation of thermal abuse models, which simulate extreme conditions such as overcharging or external 

heating to predict how these conditions can trigger thermal runaway. In the wake of a previous study (Menale 

et al., 2019), the present analysis is focused on the main influential factors on temperature of a cell in an aged 

cell. 

2. Methodology 

The main aim of this study is to develop an electrochemical-thermal model which predict the behavior of an 

aged cell. In the following section, the energy and mass balances governing this model are discussed. 

2.1 Energy Balance 

The following is the energy balance equation used in the system: 

𝜕(𝜌𝑐𝑝𝑇)

𝜕𝑡
=  −∇(𝑘∇𝑇) + 𝑆 

(1) 

When Temperature is increasing, side reactions will happen. Four side reactions are: the SEI decomposition 

reaction (SEID), negative electrode-electrolyte reaction (NE), two positive electrode-electrolyte reactions (PE) 

(Kim et al., 2007). Heat source terms related to the above reactions are shown in Eq (2), where SSEI is the heat 

source for SEI decomposition, Sne is the heat source for NE, Spe is the heat source for PE: 

𝑆 = 𝑆𝑆𝐸𝐼 + 𝑆𝑛𝑒 + 𝑆𝑝𝑒 
(2) 

For simplicity, a 2D geometry with axial symmetry feature will be investigated. The Li-ion battery in this study is 

modeled after a commercial 18650 NCM/graphite battery which has a length of 65 mm, a radius of 9 mm, a 

container thickness of 0.25 mm, and a mandrel thickness of 2 mm. 

For solving the energy balance, these assumptions were made: at t=0 (beginning of the study), the battery and 

surrounding area are at steady state and the temperature equals 298.15 K; at r=R (the maximum point with 

respect to radius), at z=0, and z=L, heat transfers to ambient, meaning heat conducted will be released to 

ambient with natural convection with a heat transfer coefficient of 10 W/m2K. 

Due to differences in active material with respect to battery parts and lumped assumption of the battery itself, 

thermal properties of global active material should be calculated. This formulation is shown in Eq (3) and Eq (4): 

𝑘𝑇,𝑟 =
∑ 𝐿𝑖

∑ 𝐿𝑖
𝑘𝑇,𝑖

⁄
 

(3) 

668



𝑘𝑇,𝑎𝑛𝑔 =
∑ 𝐿𝑖𝑘𝑇,𝑖

∑ 𝐿𝑖
 

(4) 

For other thermal properties, the same equations can be used. As mentioned before, when the temperature is 

rising, exothermic side reactions will happen: 

𝑅𝑖 = 𝐴𝑖𝑒𝑥𝑝 (−
𝐸𝑎,𝑖

𝑅𝑇
) 𝑐𝑖

𝑛𝑖,1(1 − 𝑐𝑖)𝑛𝑖,2 

(5) 

S𝑖 = 𝐻𝑖𝑊𝑖𝑅𝑖 
(6) 

𝑑𝑐𝑖

𝑑𝑡
= {

𝑅𝑖 ,             𝑓𝑜𝑟 𝑃𝐸
−𝑅𝑖 ,    𝑓𝑜𝑟 𝑜𝑡ℎ𝑒𝑟𝑠

 

(7) 

 

The parameters for solving the energy balance and for calculating the heat generated by these reactions are 

extracted from reference study of Guo et al. (2023). 

2.2 Mass Balance and Electrochemical Reactions 

To simplify and expedite the thermal management calculations for Li-ion batteries, the assumption of a lumped 

battery model will be used. In the Single-Particle (SP) model, electrodes are represented by spherical 

intercalation particles of uniform size, assuming a uniform current distribution across the thickness of the porous 

electrode. Also, at high current densities, concentration gradients in the electrolyte become significant. This 

model does not account for these concentration gradients; thus, it is suitable only for low to moderate current 

densities (Guo et al., 2010). Mass balance is presented in Eq (8) with initial conditions of Eq (9).  

𝜕𝑐𝑎,𝑗

𝜕𝑡
+

15𝐷1,𝑗

𝑅𝑗
2 (𝑐𝑠,𝑗 − 𝑐1̅,𝑗) = 0 

15𝐷1,𝑗

𝑅𝑗
(𝑐1̅,𝑗 − 𝑐𝑠,𝑗)  +  

𝐽𝑗

𝐴𝑗𝐹
= 0 

(8) 

𝑐𝑠,𝑗|
𝑡=0

= 𝑐1,𝑗,0 
(9) 

The battery cell voltage Ecell is defined as in Eq (10) (Ekström et al., 2018) 

E𝑐𝑒𝑙𝑙 = E𝑂𝐶𝑉(𝑆𝑂𝐶𝑎𝑣𝑒𝑟𝑎𝑔𝑒) + 𝜂𝐼𝑅 + 𝜂𝑎𝑐𝑡 + 𝜂𝑐𝑜𝑛𝑐 
(10) 

Fickian diffusion of a dimensionless SOC variable is solved for in a 1D pseudo extra dimension corresponding 

to the particle dimension of length 1 with X as the dimensionless spatial variable, using spherical symmetry (for 

spherical particles), according to Eq (11): 

τ
𝜕𝑆𝑂𝐶

𝜕𝑡
=  −∇. (−∇𝑆𝑂𝐶) 

(11) 

The interval represents an average particle of the electrode governing the battery, where X = 0 and X = 1 

represent the center and surface of the particle, respectively. The boundary conditions are as follows: 

∇SOC = 0|𝑋 = 0 

∇SOC =
𝜏𝐼𝑐𝑒𝑙𝑙

𝑁𝑠ℎ𝑎𝑝𝑒𝑄𝑐𝑒𝑙𝑙,0
|

𝑋=1

 

(12) 

Where Nshape is 3 for spherical particles. The surface state-of-charge, SOCsurface, is defined at the surface of the 

particle (X = 1). The average state-of-charge, SOCaverage, is defined by integrating over the volume of the particle, 

appropriately considering spherical coordinates, and defined by Eq (13): 

SOC𝑎𝑣𝑒𝑟𝑎𝑔𝑒 =
∫ 𝑆𝑂𝐶4𝜋𝑋2𝑑𝑋

1

0

∫ 4𝜋𝑋2𝑑𝑋
1

0

=  3 ∫ 𝑆𝑂𝐶𝑋2𝑑𝑋

1

0

 

(13) 

I1C, the current at 1C rate can be calculated by Eq (14): 

669



I1𝐶 =
𝑄𝑐𝑒𝑙𝑙,0

3600
 

(14) 

Rohm (ohmic resistance) is a specific type of resistance that obeys Ohm’s Law and excludes any reactive 

components. It is generally constant across frequencies and provides a purely resistive behavior. The lumped 

voltage loss associated with ohmic process in the electrolyte and electrodes is given by Eq (15): 

𝜂𝐼𝑅 = 𝜂𝐼𝑅,1𝑐

𝐼𝑐𝑒𝑙𝑙

𝐼1𝐶
=  𝑅𝑜ℎ𝑚𝐼𝑐𝑒𝑙𝑙 

(15) 

The dimensionless charge exchange current J0 is used to define the lumped voltage loss associated with the 

charge transfer reactions (activation overpotential) on both the positive and negative electrode surfaces: 

𝜂𝑎𝑐𝑡 =
2𝑅𝑇

𝐹
sinh−1(

𝐼𝑐𝑒𝑙𝑙

2𝐽0𝐼1𝑐
) 

(16) 

and the lumped voltage loss associated with concentration overpotential is defined as 

𝜂𝑐𝑜𝑛𝑐 = 𝐸𝑂𝐶𝑉(𝑆𝑂𝐶𝑠𝑢𝑟𝑓𝑎𝑐𝑒) − 𝐸𝑂𝐶𝑉(𝑆𝑂𝐶𝑎𝑣𝑒𝑟𝑎𝑔𝑒) 
(17) 

According to literature (Vetter et al., 2005), after undergoing many charge-discharge cycles, batteries 

experience degradation, which manifests itself as a decrease in capacity and an increase in internal resistance. 

From Eq (14) and Eq (15), Eq (18) can be derived 

𝜂𝐼𝑅,1𝑐 = 𝑅𝑜ℎ𝑚

𝑄𝑐𝑒𝑙𝑙,0

3600
 

(18) 

For investigation of degradation leading to increment of impedance, Rohm can be used. Therefore, for this study, 

response surface methodology with three 2-level factors and one central point on capacity, ohmic resistance 

and charging rate will be tested. Charging rates included a base rate of 1C and a high rate of 8C, with capacities 

of 3 Ah and 0.5 Ah, respectively. Additionally, resistances of 30 micro-ohms and 5 micro-ohms were selected. 

For assessing the behavior of the cell, the mean temperature of the cell in a 50% charged battery is selected. 

The results from this design of experiments investigate the influence of the independent parameters using p-

score. The model is simulated in Comsol Multiphysics and statistical analysis in Python. 

3. Results and discussions 

The proposed model has been first tested against experimental data from the literature (Dong et al., 2018) 

providing values of the temperature under different charging/discharging rates. In the experiments the 

temperature monitoring point is set at the center of the cell cathode outer surface and in the simulation, outer 

surface temperature at the center is recorded. Figure 1 presents a comparison between simulated and 

experimental cell temperatures during the 1C and 8C charging processes with initial SOC of nearly zero (0.01): 

at a given SOC, the temperature of the cell with higher charging rate is higher and increasing the charge rate 

results in a greater rise in cell temperature, indicating a greater variation in temperature over time. The data 

indicates a strong correlation between the simulation results and the experimental measurements, 

demonstrating good alignment between the two.  

Figure 2 shows the results of the first simulation. As discussed, the initial charge of the cell was near zero and 

it was charged using a 4.5 C current to fully charged state, as can be seen in Figure 2a. As the cell is charging, 

its temperature increases due to electrochemical reactions. Therefore, due to low capacity and impedance, 

temperature difference is also low. There is a small difference in the temperature trend in Figure 2b, that can be 

related to heat dissipation of the cell to the ambient conditions and thermal characteristics of the cell. Also, as 

can be seen in Figure 2c, the temperature at the center of the cell's core is higher, which is influenced by the 

geometry of the system. 

To find the most influential parameters on temperature and temperature deviation over time, a linear regression 

method was applied. After feature selection using p-value test with 5% confident range, presented in Table 1, 

five parameters were identified as the effective factors affecting temperature at 50% SOC: capacity, current, 

ohmic resistance and two two-way interactions of capacity with current and ohmic resistance. R-squared of the 

fitted model is 96.55% which shows a very good agreement between predicted and measured values. Based 

on the reported p-values, a relationship between temperature and parameters such as capacity, current, and 

ohmic resistance can be established. These factors directly influence the cell's temperature, with higher values 

of these parameters leading to increased cell temperature.  

 

670



 

Figure 1: Temperature vs SOC in Charging test for 1C and 8C simulation vs experiment (Dong et al., 2018)  

a) b) 

  
c)  

 

Figure 2 – Simulation of the cell number 1 – 0.5 Ah, 4.5C and 5 µΩ – a) state-of-charge vs time, b) mean 

temperature deviation of cell vs time and c) Temperature distribution in the cell at 800s 

Table 1: P-values for mean temperature at 50 % charge 

Source DF P-Value 

Model 5 0.000 

Capacity 1 0.000 

Current 1 0.000 

Impedance 1 0.010 

Capacity*Current 1 0.001 

Capacity*Impedance 1 0.027 

Error 7  

Total 12  

4. Conclusions 

One of the major safety issues in Li-ion cells usage is the thermal runaway which is a catastrophic heat release, 

with possible ignition and explosion. Most of the studies devoted to understanding the behavior of the cell during 

a thermal runaway are focused on a fresh and uncycled battery, which has a much better resilience to thermal 

stress; as already reported in the literature, the capacity and internal resistance of a cycled cell is different from 

those of a new one. In this study, the influence of these factors was investigated, with specific reference to 

Ohmic resistance and capacity of the cell and to charging current. The statistical analysis of the results shows 

a very good agreement between the fitted and measured values, showing a strong relationship between these 

factors and the temperature of the cell. As can be concluded from the results of the simulation, a faded capacity 

battery is less prone to go beyond the designed temperature. However, in real-world scenario, an aged cell with 

faded capacity has a lower life span and battery performance. Furthermore, as battery degrades, the internal 

resistance will increase, leading to more significant effect on the temperature. Under the same conditions, a cell 

20

25

30

35

40

45

50

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Te
m

p
er

at
u

re
 (
ºC

)

State-of-Charge

1C Simulation

1C Experiment

8C Simulation

8C Experiment

671



with higher ohmic resistance tends to reach a higher temperature due to increased heat generation. As 

discussed, these two factors can cancel each other out and the objective of the study was set to understand the 

predominant factor. The statistical analysis showed that the capacity is a more influencing factor. The study 

insights could guide predictive maintenance schedules, enabling timely interventions and informing actionable 

strategies to enhance the safety and reliability of energy storage systems in real-world applications. 

Nomenclature

𝜌 – density, kg/m3 

𝑐𝑝 – specific heat capacity, J/kg*K 

𝑇 – temperature, K or ⁰C 

k – Thermal conductivity, W/m*K 

t – time, s 

Si – heat generated by ith side reaction, W/m3 

Li – thickness of ith part, m 

ci - dimensionless concentration  

Ri - reaction rate for the ith side reaction, s-1 

Wi - specific active substance content of the ith 

side reaction, kg/m3 

Ai – rate coefficient of ith side reaction, s−1  

Hi - the reaction heat for the ith side reaction, J/kg  

Ea,i – activation energy of ith side reaction, J/mol  

τ - the diffusion time constant, s 

I – current, A 

Q – cell capacity, Ah 

J - dimensionless charge exchange current  

Rohm - ohmic resistance, mΩ 

SOC – state-of-charge of the cell 

F – Faraday constant 

η - Overpotential, V 

D – Diffusivity coefficient, m/s 

Ecell – Voltage of the cell, V 

Acknowledgments 

The results of this work have been obtained with the financial support of the National Recovery and Resilience 

Plan (PNRR), Mission 4 Component 2 Investment 1.3, funded by the European Union - NextGenerationEU, 

Spoke 6 "Energy Storage" of the Extended Partnership (PE2) NEST - Network 4 Energy Sustainable Transition. 

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	Impact of Battery Degradation on Thermal Runaway Risks in Lithium-Ion Batteries: a Statistical and Modelling Approach