Modeling of the Thermal Runaway Phenomenon of Cylindrical 18650 Li-Ion Cells

Abstract

The thermal runaway (TR) is the main safety concern of lithium-ion batteries (LIBs). Methods for predicting and preventing TR are critical to achieve greater battery safety. Many researchers have studied the reactions that take place inside the cell and that because of their exothermicity trigger the TR. In this work the coupled electrochemical-thermal model for a lithium-ion cell was extended with contributions from exothermic reactions based on an Arrhenius law to model mechanisms of abuse, which could lead to a thermal runaway. Firstly, differential scanning calorimetry (DSC) tests were conducted on the individual components of the cell to characterize the reactions of the TR process in terms of onset temperature, thermal and kinetic parameters. The kinetic parameters of each reaction were identified by the Kissinger method. Then the thermal and kinetics parameters of the reactions occurring during the thermal runaway together with the phenomena involving the electrolyte (i.e., evaporation, boiling and venting) were included in the Battery and Fuel Cell Module of COMSOL Multiphysics simulator, to simulate the behaviour of a cylindrical 18650 cell under thermal abuse conditions. In particular, the results of the model appear to agree with the experimental data, concerning to a NCA 18650 cell subjected to radiative heat flux in a cone calorimeter.

1 Introduction

Lithium-ion batteries (LIBs) are widely used for their high energy density, power density, relatively high cell voltage and low weight-to-volume ratio compared to other types of batteries. The advantages of LIBs are well known, but the criticalities associated with this type of cell cannot be underestimated. In fact, in recent years, several incidents have been reported in which LIBs have been the source of fires and/or explosions. The instability of these device is due both to the high energy density and to the presence inside the cell of toxic and highly flammable substances, which increase the hazard in case of malfunction, breakdown or abuse. In conditions of normal use, the Li-ions dissolved in the electrolytic solution, migrate from the anode to the cathode passing through the polymeric membrane. If a failure accidentally occurs, the heat generated can become greater than the heat that the cell is able to dissipate through the safety systems, such as the relief valve in the case of cylindrical cells. This triggers a mechanism characterized by a series of spontaneous exothermic chain reactions that cause an uncontrollable increase in pressure and temperature which can ultimately lead to the catastrophic rupture of the cell and the consequent expulsion of parts of the electrodes and toxic and flammable gases. The mechanism is called thermal runaway (TR).

The characteristics of thermal instability of a cell are determined by the interaction of three distinct thermal processes: (a) generation of heat inside the cell due to the exothermic decomposition reactions of the constituents of the cell, (b) conduction of heat inside the cell and (c) heat dissipation from the cell surface to the environment. The difference between the heat generated inside the cell and the heat transferred to the environment determines the thermal state of the cell and whether or not runaway occurs.

The prediction of the TR through a mathematical model is fundamental for optimizing the safe design of the cells, both during the phase of normal use (charge and discharge cycles) and in the case of abuse (electrical, mechanical or thermal). For normal use, the aim is to develop a mathematical model that relates the thermal behaviour, such as thermal energy and temperature distribution inside the cell, to the operating conditions. Using the model, it is therefore possible to evaluate the trend of temperature inside the battery and define the optimal temperature range. It appears, from literature studies, that the temperature distribution in the battery is considerably greater during the discharge phase than in the charge one, when the same current is applied [1]. The other condition to study is the abuse, in order to predict the temperature profile that is established during the TR [2]. The most critical step of modelling is to identify, and then characterize, the fundamental reactions that occur inside the cell that cause the production of heat. Due to the complex chemical reactions that take place inside a battery under conditions of abuse the problem associated with the TR is still difficult to predict and solve.

Several studies have focused on the thermal runaway of commercial 18650 batteries, but controversies have been observed regarding the maximum temperature and maximum self-heating rate [3,4,5,6,7]. The results obtained with modelling differ to each other and do not coincide with the results studied by calorimetry. The conflicts between the various temperature values derive from the imprecise chemical kinetics of the battery, used in the prediction model for the study of the TR. Existing kinetics studies of cell components have mainly focused on one or two specific exothermic reactions, while battery kinetic models should account for all exothermic reactions. In fact, large deviations in temperature values do not allow the validation of a model for the design of a LIB with better performances.

It is therefore important to find models to predict and prevent the thermal runaway to ensure greater safety and better battery performance. To this end the behaviour of a 18650 Li-ion cell was analysed using the COMSOL Multiphysics modelling software. COMSOL contains the Batteries & Fuel Cells module which models and simulates the fundamental processes in the electrodes and electrolytes of batteries and fuel cells [8]. These simulations cover the transport of charged and neutral species, current conduction, fluid flow, heat transfer and electrochemical reactions in porous electrodes. This model then allows to examine the performance of batteries and fuel cells under different operating conditions for different configurations of electrodes, separators, collectors, different materials and chemistry. The Batteries & Fuel Cells module for a lithium-ion cell was then extended with contributions from exothermic reactions based on the Arrhenius law to model the reactions that occur during the abuse, which could lead to a thermal runaway.

Both the thermal phenomena that arise during the normal operation of the cell in a charge and discharge cycle, and the behaviour of the cell when exposed to a condition of thermal abuse were analysed. The thermal abuse was simulated by applying a radiant heat flux from an external source, to reproduce the conditions that arise during the evolution of a fire in which the cell may be involved. Therefore, both the temperature trend and the time that lead to the thermal runaway were observed. The results of the model were analysed and validated by comparing them with the experimental data obtained from tests on lithium cobalt nickel aluminium oxide (LiCoNiAlO2, NCA) 18650 cells carried out using a cone calorimeter, with an applied external radiative heat flux from 25 to 50 kW/m².

2 Material and Methods

2.1 Material

Panasonic NCR18650B lithium-ion cells, shown in Fig. 1, were used in the experiments. Lithium cobalt nickel aluminium oxide (LiCoNiAlO₂, NCA) and graphite are the active materials for cathode and anode respectively, while the separator is made of polyolefins, such as polyethylene and polypropylene. The electrodes are immersed in an electrolyte solution made of ethylene carbonate (C₃H₄O₃) (EC), diethyl carbonate (C₅H₁₀O₃) (DEC) and dimethyl carbonate (C₃H₆O₃) (DMC) as solvents, and lithium hexafluorophosphate (LiPF₆) as salt. Technical specifications of the cell are reported in Fig. 2.

Fig. 1

Panasonic NCR 18650B

Fig. 2

Technical specifications of Panasonic NCR18650B

2.2 DSC

Before the tests, cells were carefully dismantled in an argon-filled glovebox and the main cell components identified. Then the two electrodes and the separator were carefully stored in separate sealed containers until the DSC tests. The electrodes were tested including the current collector with the purpose to study the real system “current collector/active material” and not completely modify the electrode system.

To perform the tests, high pressure resistant pans (up to 24 atm) purchased by Perkin Elmer and hermetically sealed were used, to prevent the escape of the gases formed during the test and to avoid the danger of a catastrophic rupture of the capsule and the consequent loss of the content material. Approximately 10–20 mg of the electrodes were loaded. The high-pressure capsules were crimped using a special sealing tool provided by the PerkinElmer, with fixed torque.

DSC measurements were performed using a Perkin Elmer DSC equipment (model 8500) in nitrogen flow (20 mL/min), in the temperature range of 298–623 K and at a heating rate of 5 K/min. Experimental data were carefully analyzed by Pyris software provided by the PerkinElmer.

2.3 Cone Calorimeter

Tests were performed in a cone calorimeter (GA01, noselab ats) on single cell by varying the state of charge (SOC) of the cells (i.e., 0, 50 and 100% SOC) and the radiative heat flux of the conical heater (i.e., 25, 35 and 50 kW/m²) as reported previously [7]. Each specimen was weighed before and after test to determine the total mass loss. The temperature of the cell surface was monitored and the tests were also recorded by a video camera.

HRR of cell was calculated following the calculation method proposed by ISO 5660-1:2015. The error of HRR values was calculated to be about 20%.

The gas venting time was defined by a clearly audible sound, immediately followed by the appearance of aerosol jets from the safety vent ports. The thermal runaway time was defined as the time at which the thermal runaway is triggered as observed by the rapid increase in temperature which is accompanied by the catastrophic rupture of the cell.

3 Mathematical Models

3.1 The Electrochemical Model

The mathematical model is formulated using the Arrhenius equations for the different reactions (Eqs. 1–10) to consider the concentration of the different components of the cell during the thermal runaway [8,9,10,11].

• Decomposition of the anode (neg):

$$ \frac{dc_{neg}}{\textrm{dt}}=-{R}_{neg} \vspace*{-1pc} $$

(1)

$$ {R}_{ne g}\left(T,{c}_{el},{c}_{ne g},{t}_{sei}\right)={A}_{ne}{e}^{-\frac{t_{sei}}{t_{sei, ref}}}{c}_{ne g}^{m_{ne,n}}{e}^{-\frac{E_{a, neg}}{RT}} $$

(2)

• Decomposition of the cathode (pos):

$$ \frac{\textrm{d}\upalpha}{\textrm{d}\textrm{t}}={R}_{pos} \vspace*{-4pt}$$

(3)

$$ {R}_{pos}={A}_{pos}{\alpha}^{m_{p\textrm{o}s}}{\left(1-\alpha \right)}^{m_{pos}}{e}^{-\frac{E_{a, pos}}{RT}} $$

(4)

• Decomposition of the Solid Electrolyte Interface (SEI):

$$ \frac{dc_{SEI}}{\textrm{dt}}=-{R}_{SEI} $$

(5)

$$ {R}_{SEI}\left(T,{c}_{SEI}\right)={A}_{SEI}{e}^{-\frac{E_{a, SEI}}{RT}}{c}_{SEI}^{m_{SEI}} $$

(6)

• Reaction of the electrolytic solution (el):

$$ \frac{dc_{el}}{\textrm{dt}}=-{R}_{el} $$

(7)

$$ {R}_{el}\left(T,{c}_{el}\right)={A}_{el}{e}^{-\frac{E_{a, el}}{RT}}{c}_{el}^{m_{el}} $$

(8)

• Degradation of the binder (PVDF):

$$ \frac{dc_{PVDF}}{\textrm{dt}}=-{R}_{PVDF} $$

(9)

$$ {k}_{PVDF}\left(T,{c}_{PVDF}\right)={A}_{PVDF}{c}_{PVDF}^{m_{PVDF}}{e}^{-\frac{E_{a, PVDF}}{RT}} $$

(10)

The model parameters are reported in the Table 1.

Table 1 Model parameters

3.2 Thermal Model

To simulate the temperature distribution inside the cell, thermal model is built, through heat balances. The thermal model is given by a generic thermal diffusion equation with an internal heat source:

$$ \frac{\partial \left({\rho c}_pT\right)}{{\partial t}}=-\nabla \left(\textrm{k}\nabla \textrm{T}\right)+S $$

(11)

where ρ (g/cm³) is the density, cp (J/(g*K)) the heat capacity, T (K) the temperature, t (s) the time, k (W/(cm*K)) the thermal conductivity and S (W/cm³) represents the heat source.

Reliable prediction of the temperature profiles of individual cells and the whole battery system requires a quantitative assessment of the total heat generation rate. The heat source term (S) is defined as the sum of all sources:

$$ S={S}_{SEI}+{S}_{el}+{S}_{neg}+{S}_{pos}+{S}_{PVDF} $$

(12)

3.3 Venting and Boiling Model

The heat generated inside the cell is determined by the reaction of the decomposition of the anode, the cathode and the SEI layer, the reaction of the electrolytic solution and the degradation of the PVDF binder. Furthermore, during the thermal runaway, the electrolyte is involved in a complex phenomenon that includes evaporation, boiling and venting, which is accompanied by the possible explosion of the cell.

To model venting, the electrolyte is assumed to behave as an ideal gas flowing isoentropically through an orifice that opens and remains open when the pressure inside has reached a critical value, P_crit = 3448 kPa [12]. The pressure and the temperature during the venting are defined in Eqs. 13 and 14:

$$ {P}_{vent}=\frac{P}{{\left(1+\frac{\gamma -1}{2}{M}^2\right)}^{\frac{\gamma }{k-1}}} $$

(13)

$$ {T}_{vent}=\frac{T}{\left(1+\frac{\gamma -1}{2}{M}^2\right)} $$

(14)

Where P is the total local static pressure, in Pa, γ is the fraction of the electrolyte passed through the vent and M is the Mach number, which is conditioned by the type of flow (subsonic or choked).

Therefore, to consider the venting in the thermal model, the thermal contribution given by the heat dissipated during the venting of the electrolyte is given by:

$$ {Q}_{vent}=-{m}_{el}{h}_{vap}\frac{dy}{dt}-{m}_{el}{cp}_{el}T\frac{dy}{dt} $$

(15)

where h_vap is the enthalpy of vaporization of the electrolyte, in J/kg, cp_el is the specific heat of the electrolyte in the vapor phase, in J/kg*K.

During the decomposition of the electrolyte, the system undergoes an endothermic boiling process where the heat is stored as latent heat and therefore reduces the temperature, which exhibits a further sharp drop during venting. Moreover, the pressure inside the cell will drop significantly, reaching the ambient conditions [12]. The heat absorbed during the boiling is given by:

$$ {Q}_{boil}={m}_{el}{h}_{vap}\frac{d{\theta}_{el}}{dt}-{V}_h\frac{dP}{dt} $$

(16)

A significant amount of the electrolyte and parts of the jelly roll are vented outside the cell when the valve is opened, and it is therefore important to determine its contribution. The heat contribution due to venting of the ejecta is given by:

$$ {Q}_{ej}=-{m}_{ej}{c}_{pel, jr}T\frac{dy}{dt} $$

(17)

The value of parameters in Eqs. 15, 16 and 17 are reported in Table 2.

Table 2 Values parameters for Eqs. (15), (16) and (17)

4 Modelling Procedures

The 3D geometry has been created using the Finite Element tool – COMSOL Multiphysics v.5.5. The simulations involved modelling the thermal runaway phenomenon of an NCA cylindrical 18650 Li-ion cell.

The materials that make up the cell were first defined from the software database: the active material for the cathode is lithium-nickel-aluminium-cobalt oxide (NCA), while for the anode it is graphite. The binder is in polyvinylidene fluoride (PVDF) while the electrolyte is composed of lithium hexafluorophosphate, diethyl carbonate and ethyl carbonate solvents (1:1). The internal structure of a cell consists of five very thin repeating layers: (i) anode, (ii) copper anode current collector, (iii) separator, (iv) cathode and (v) aluminium cathode current collector (Fig. 3).

Fig. 3

Internal structure of NCR18650B cell

For this reason, due to the difficulty of bringing this layered structure with each thickness, the cylindrical cell was modelled with a 1D model coupled to a 3D model composed of a single layer of active material that describes all the layers of the cell. A 1D model is used to generate an electrochemical heat source in the active material of the 3D cylindrical cell, as shown in Fig. 4.

Fig. 4

Internal cylindrical model

Once obtained the geometric model, the mesh has been created using elements of triangular shape that generates prisms in 3D as shown in Fig. 5.

Fig. 5

Mesh of the NCR18650B cell

4.1 Charge-Discharge Cycle

The behaviour of the cell under nominal operating conditions during a charge and discharge cycle was simulated, evaluating the temperature profile in the cell. The initial conditions of the cell were set as follows: E_min = 2.55 V and Q_cell = 3.18 Ah. The correct activation of the cell chemistry and the correct formation of the SEI are allowed through several cycles of charge and discharge with CC.

At a constant charge/discharge current of 1.6 A, each charge and discharge cycle lasts about 1500s. In a charge and discharge cycle the variation of temperature is low, of about 1 K in 1500s. From this data, it can be deduced that in the normal use conditions the cell maintains its initial temperature with small variations.

4.2 Thermal Abuse

During thermal abuse, heat is generated in the cell by the following exothermic reactions: SEI decomposition, reaction between the Li-ions intercalated in the anode and the electrolyte, reaction between cathode and electrolyte, decomposition reaction of the electrolyte and reaction of PVDF. Therefore, to predict the critical conditions, in terms of temperature and time at which the thermal runaway is triggered, the kinetic parameters of the exothermic reactions that occur during the TR are required. The thermal parameters were obtained by DSC tests on the main cell components and the kinetic parameters were evaluated by the Kissinger method as reported in Table 3.

Table 3 Kinetic parameters

To simulate the conditions of a thermal abuse, a radiative heat flux has been applied on the surface of the cell. The radiative heat flux was varied between 25 and 50 kW/m² (Fig. 6). The T inside the cell and of the surface was evaluated through the model (Fig. 7).

Fig. 6

Modelling of the cylindrical cell and of the radiative heat source

Fig. 7

Temperature profile of the cylindrical cell

To validate the model, the results of the simulations were compared with the experimental data obtained through tests carried out in a cone calorimeter on NCA cells at different state of charge (100%, 50%, and 0% SOC) by varying the radiative heat flux of the conical heater (Table 4).

Table 4 Comparison between the experimental data (exp.) and those obtained through simulation (sim.)

5 Discussion

The results of the simulations and those of cone calorimeter tests, varying the SOC and the radiative heat flux, are compared in Table 4. The comparison in reported in terms of time at which the thermal runaway is triggered as observed by the rapid increase in temperature which is accompanied by the catastrophic rupture of the cell in the experiments.

For a full charged cell, at radiative heat flux of 25 kW/m², it is observed at 385 s that the simulated temperature rise becomes uncontrollable (the trend assumes a vertical line: there is a significant increase in temperature in 0.01 s). This time can be considered as the moment when the thermal runaway is triggered. By increasing the radiative heat flux to 35 kW/m² the time at which the thermal runaway is triggered is reduced to 318 s, while for the value of 50 kW/m² the time is equal to 230 s. Similar behaviour was observed at SoC = 50%.

6 Conclusions

In the present work a model has been developed and validated to predict the thermal runaway conditions when a 18650 Li-ion cell is subjected to thermal abuse. The 3D geometry study was re-created by combining a 1D model and a 3D model together. The coupled electrochemical-thermal model for a lithium-ion cell included in the Battery and Fuel Cell Module of COMSOL Multiphysics simulator was extended with contributions of exothermic reactions based on the Arrhenius law to model mechanisms of abuse, which could lead to a thermal runaway. The thermal and kinetics parameters of these reactions were obtained by DSC tests on the single components of the cell. Furthermore, the phenomena involving the electrolyte (i.e., evaporation, boiling and venting) were included in the model.

The results of the model were compared with the experimental data obtained on the same type of cell in a cone calorimeter. The results of the model appear to be in good agreement with the experimental data. This demonstrates that the model can well reproduce the cell’s thermal runaway mechanism and be reliable to safely predict battery performance without assembling a real battery. The model constitutes a starting point for evaluating other conditions of abuse and improving the performance of the cells considered.