Abstract Introduction

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2018-01-0437 Published 03 Apr 2018

A Computational Study on the Critical Ignition Energy and Chemical Kinetic Feature for Li-Ion Battery Thermal Runaway Liwen Zhang, Meng Xu, Peng Zhao, and Xia Wang Oakland University Citation: Zhang, L., Xu, M., Zhao, P., and Wang, X., “A Computational Study on the Critical Ignition Energy and Chemical Kinetic Feature for Li-Ion Battery Thermal Runaway,” SAE Technical Paper 2018-01-0437, 2018, doi:10.4271/2018-01-0437.

Abstract

L

ithium-ion (Li-ion) batteries and issues related to their thermal management and safety have been attracting extensive research interests. In this work, based on a recent thermal chemistry model, the phenomena of thermal runaway induced by a transient internal heat source are computationally investigated using a three-dimensional (3D) model built in COMSOL Multiphysics 5.3. Incorporating the anisotropic heat conductivity and typical thermal chemical parameters available from literature, temperature evolution subject to both heat transfer from an internal source and the activated internal chemical reactions is simulated in detail.

Introduction

A

s one major category of advanced energy storage medium, Li-ion batteries have attracted extensive research interests due to the advantages of high power density, long life cycle and little memorizing effect, and are widely used to power the battery electric vehicles (BEV) and hybrid electric vehicles (HEV) [1, 2, 3]. However, safety concerns have been raised on potential thermal runaway of Li-ion batteries induced by an external heat source, internal short circuit, collision, and penetration. It is expected that with a significant amount of electrical and chemical energy stored in a battery, the thermal runaway and explosion could lead to severe danger to both passengers and the vehicle. The very high temperature rise rate during thermal runaway also imposes extreme difficulty to the battery thermal management system (BTMS) to control and maintain the optimum operation temperature of the battery pack. As such, many studies on the thermal modeling of the Li-ion batteries have been performed to understand the thermal runaway behavior under limiting conditions. Hatchard et al. [4] conducted oven exposure tests for cylindrical and prismatic Li-ion batteries, and presented a model based on expressions for the exotherms of the electrodes materials with electrolyte exposed to high temperature obtained by accelerating rate calorimetry (ARC) and differential scanning calorimetry (DSC) studies to calculate the reaction kinetics for thermal abuse. Spotnitz and Franklin [5] extended this method, and considered a few possible exothermic © 2018 SAE International. All Rights Reserved.

This paper focuses on the critical runaway behavior with a delay time around 10s. Parametric studies are conducted to identify the effects of the heat source intensity, duration, geometry, as well as their critical values required to trigger thermal runaway. The characteristics of different concentrations and heat release from each chemical reaction in the scenario of thermal runaway are discussed. Based on the current kinetic model, the simulation results further suggest that the concentration of negative-electrolyte is closely related to the occurrence of thermal runaway. This study provides useful guidance on the simulation and control of thermal runaway of battery systems.

reactions assuming Arrhenius expressions to simulate a variety of abuse tests (oven, short-circuit, overcharge, nail penetration, crush). Tanaka and Bessler [6] presented a thermo-electrochemical model for the Li-ion cell at an elevated temperature. Their model only considered the Solid Electrolyte Interface (SEI) formation and decomposition as exothermic reaction and they determined that the SEI decomposition reaction plays a relatively unimportant role in thermal runaway but it may trigger additional exothermic reactions. Spotnitz et al. [7] built a lumped thermal runaway propagation model using empirical equations for a battery pack with eight 18650 cells to evaluate the abuse tolerance of packs. Their simulation results showed that the thermal abuse tolerance of a pack is extremely sensitive to the exothermic behavior of the cell, and even a small amount of heat generation from the chemical reactions could induce thermal runaway propagation. All of the above models are one-dimensional (1D), as such they cannot capture the localized heat release and the propagation of the chemical reaction inside a cell. To overcome this effect, Kim et al. [8] extended the 1D model from Hatchard [1] to 3D so that the geometrical features of the battery could be further considered, together with the spatial distributions of thermal conductivity and temperature. Guo et al. [9] used finite element method to develop a 3D electrochemicalthermal coupled model for evaluating the temperature distribution in large capacity and high power Li-ion batteries under thermal abuse conditions. Then the model was compared to the oven test results with good agreement. Recently, Xu et al.

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FIGURE 2 Schematic of mesh used in the simulation.

Model Description

Governing Equations

Configuration A 3D heat transfer model is developed for a typical prismatic battery cell with a cylindrical region representing internal heat source. As shown in Figure 1, the geometrical dimensions of the battery are 180 mm (height) * 130 mm (width) * 50 mm (depth). A 1.5 mm (radius) * 40 mm (length) cylinder is placed perpendicular to the left side surface of the battery. The mesh near the interface of the cylindrical area and its adjacent region is highly refined as shown in Figure 2, given the fact that it is the most probable region for thermal runaway to occur.

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[10] utilized a 3D thermal chemical model to computationally investigate the effects of the external cooling system on the prevention of thermal runaway. This study focuses on the thermal runaway behavior of a Li-ion battery and its kinetic feature under limiting conditions. A 3D computational thermal runaway model of a typical Li-ion battery with LiCoO2 (LCO)/graphite chemistry has been established in the commercial software COMSOL Multiphysics 5.3, incorporating reaction kinetics described by ordinary differential equations (ODE) with a 3D transient heat transfer model. A spatial region with given uniform heat release rate has been selected to represent the effect of internal heat generation in the scenario of internal short circuit or nail penetration. We are particularly interested in the threshold values of the critical parameters, such as heat source intensity and duration, which could trigger the runaway in a short initial period, say around 10 s. This study could provide useful insights on the fundamental understanding and prevention of thermal runaway behavior, induced by the realistic local hot spot effects from short circuit, collision and nail penetration.

Energy Conservation Equation We consider the simplest scenario with two dominant physical-chemical processes during thermal runaway: heat transfer from a cylindrical region with an artificially assigned heat source with uniform intensity and a certain duration, and the chemical kinetics involving the electrodes and electrolyte that contribute to heat generation within the bulk of battery. The energy conservation equation of the computational domain is shown in the following: ¶ ( r c pT )

¶t

ïì Ssei + Sne + S pe + Se S=í ïîQ

FIGURE 1 Schematic of the model geometry and the

= Ñ × ( kÑT ) + S (1)

cylinder location.

( cell region ) ( cylindrical region )

(2)

where ρ is the density, c p is the heat capacity, k is the thermal conductivity. Due to the multi-layered structure of the Li-ion battery, the anisotropic thermal conductivity of the battery (through-plane and in-plane) is considered. The values of thermal properties are taken from a recent study [10] and listed in Table 1. S represents the heat source term from the chemical reactions and the artificially assigned heat source. More details about the heat source are shown in the next section.


TABLE 1 Material properties of the battery [4].

Parameter

Battery

Cylinder

k (W/(m K))

3.4 (through-plane) / 34 (in-plane)

44.5

cp (J/(kg K))

830

475

ρ (kg/m3)

1700

7850 © 2018 SAE International. All Rights Reserved.


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A Computational Study on the Critical Ignition Energy and Chemical Kinetic Feature

The Simulated Heat Source Term The cylindrical region is provided a uniform constant heat source (Q) within a certain duration (dt), such that a high temperature region could be created in the center. Heat transfer occurs across the interface and gradually activates the chemical reactions in the bulk and eventually triggers thermal runaway. By individually varying the magnitude of the heat source term and its duration time, as well as the radius of the cylindrical region, the subsequent effect on the heat generation from different chemical reactions and potential thermal runaway event are separately studied. Heat Source Terms from Chemical Reaction Four reactions are considered in the thermal abuse model utilized in the current work, and all of them are exothermic, including the solid electrolyte interface decomposition reaction, the negative-electrolyte reaction, the positiveelectrolyte reaction and the electrolyte decomposition. The quantitative characteristics of these reactions depend on the battery material properties, thermal chemical parameters, and the battery temperature. The reaction model, frequency factor, and activation energy that describe the kinetics between the electrolyte and electrode materials have been previously obtained by fitting the experimental measurements from accelerating rate calorimetry (ARC) and differential scanning calorimetry (DSC) tests. A mathematical model that describes the heat production from chemical reactions within a Li-ion cell is readily available from the literature [4]. Solid Electrolyte Interface Decomposition Reaction Solid electrolyte interface (SEI) is formed during the first cycle in Li-ion batteries. It plays a vital role in preventing the side reaction between the active material and electrolyte. This layer is metastable and can decompose exothermically [8]. The corresponding reaction can be expressed in the following equations [4, 8]:

é E ù msei (3) Ssei (T ,c sei ) = H seiWc Asei exp ê - a , sei ú c sei ë RT û

dc sei é E ù msei (4) = - Asei exp ê - a , sei ú c sei dt ë RT û

where Ssei(T, c sei) is the heat release rate from the SEI decomposition. It depends on the dimensionless amount of lithium-containing meta-stable species (csei) in the SEI, the temperature of the battery (T) and the material properties of the battery. Negative-Electrolyte Reaction At further elevated temperatures, the SEI layer has been decomposed and cannot protect the negative electrode from contact with the electrolyte such that the exothermic reaction between the intercalated lithium and electrolyte can occur [4, 8]: é E ù mne ,n Sne (T ,c ne ,t sei ) = H neWc Ane exp é - t sei ù c ne exp ê - a ,nne ú (5) ê t ú ë RT û ë sei 0 û © 2018 SAE International. All Rights Reserved.

3

dc ne é t ù mne ,n é E ù exp ê - a ,ne ú (6) = - Ane exp ê - sei ú c ne dt ë RT û ë t sei 0 û

dt sei é t ù mne ,n é E ù exp ê - a ,ne ú (7) = Ane exp ê - sei ú c ne dt ë RT û ë t sei 0 û

where Sne(T, cne, tsei) is the heat release rate from the negative-electrolyte reaction. It depends on the dimensionless amount of lithium intercalated within the carbon (cne), the dimensionless measure of SEI layer thickness (tsei), the temperature of the battery (T) and the material properties of the battery. Positive-Electrolyte Reaction Positive active materials can disproportionate at elevated temperatures. In the oxidized state, the positive material reacts directly with the electrolyte. The chemical reduction of the positive active material with the electrolyte is highly exothermic [4, 8]: S pe (T ,a ) = H peW p A pea m pe , p1 (1 - a )m pe , p 2 exp é - Ea , pe ù (8) ê RT ú ë û

da m pe , p 2 é E ù m exp ê - a , pe ú (9) = A pea pe , p1 (1 - a ) dt ë RT û

where Spe(T, α) is the heat release rate from the positiveelectrolyte reaction. It depends on the degree of conversion (α), the temperature of the battery (T) and the material properties of the battery. Electrolyte Decomposition Reaction The electrolyte can also decompose exothermically at elevated temperatures [4, 8]:

é E ù Se (T ,c e ) = H eWe Ae exp ê - a , pe ú c eme (10) ë RT û

dc e é E ù = - Ae exp ê - a , pe ú c eme (11) dt ë RT û

where Se(T, ce) is the heat release rate from the electrolyte decomposition. It depends on the dimensionless concentration of electrolyte (ce), the temperature of the battery (T), and the materials properties of the battery. The thermal chemical parameters involved in these four reactions are included in Table 2 with their reference values listed.

Initial and Boundary Conditions The initial temperature of the system is set as 293.15 K. Since we are interested in very fast runaway process (with delay time around 10 s or less), during which the convection heat transfer on the battery surface and the coolant could be highly ineffective, the boundary conditions of the battery are intentionally set as adiabatic. These adiabatic boundary conditions can

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TABLE 2 Physical and kinetic parameters and initial values used for thermal abuse model with LiCoO2/graphite chemistry [4, 8].

Physical description

1.667E15 (1/s)

SEI-decomposition frequency factor

Ane

2.5E13 (1/s)

Negative-electrolyte frequency factor

Ape

6.667E13 (1/s)

Positive- electrolyte frequency factor

Ae

5.14E25 (1/s)

Electrolyte decomposition frequency factor

Ea, sei

1.3508E5 (J/mol) SEI-decomposition activation energy

Ea, ne

1.3508E5 (J/mol) Negative- electrolyte activation energy

Ea, pe

1.396E5 (J/mol)

Positive- electrolyte activation energy

Ea, e

2.74E5 (J/mol)

Electrolyte decomposition activation energy

csei0

0.15

Initial value of csei

cne0

0.75

Initial value of cne

α0

0.04

Initial value of α

ce0

1

Initial value of ce

msei

1

Reaction order for csei

mne, n

1

Reaction order for cne

mpe, p1

1

Reaction order for α

mpe, p2

1

Reaction order for (1 − α)

me

1

Reaction order for ce

tsei0

0.033

Initial value of tsei

Hsei

2.57E5 (J/kg)

SEI-decomposition heat release

Hne

1.174E6 (J/kg)

Negative- electrolyte heat release

Hpe

3.14E5 (J/kg)

Positive- electrolyte heat release

He

1.55E5 (J/kg)

Electrolyte decomposition heat release

Wc

6.104E2 (kg/m3)

Specific carbon content in jellyroll

Wp

1.221E3 (kg/m )

Specific positive active content in jellyroll

We

4.069E2 (kg/m3) Specific electrolyte content in jellyroll

R

8.314(J/mol/K)

3

Universal gas constant

also help to rule out the ambiguity on the threshold ignition energy to be evaluated from the calculation, from heat transfer across the boundary.

Numerical Methods The energy equations including heat transfer and chemical reactions in this model are solved by commercial software Comsol Multiphysics 5.3. A domain ODE model is used to account for the heat generation from thermal runaway process due to the chemical reactions. The fastness of the chemical reactions could place substantial difficulty on the usage of explicit CFD solvers and requires tiny integration time step, which is frequently referred as the chemical stiffness [11]. In order to solve the stiff chemical reaction term, we choose the


Value

Asei

and cylinder: (a). Extremely fine (b). Extra fine (c). Fine.


Symbol

FIGURE 3 The grid detail on the interface of the battery

backward differentiation formula (BDF) method to set as the time stepping method, which is the one of the implicit timedependent solver in Comsol Multiphysics 5.3, with the maximum BDF order of 5 and minimum BDF order of 2. The relative tolerance and absolute tolerance are set as 1e-6 and 1e-8 respectively. Global constraints have been added in the system to ensure that the variables representing dimensionless concentration remain none negative, such that the exothermic nature of the corresponding reaction is not affected by any random numerical error during integration. Grid independence study has been conducted by using the three different specifications of the mesh, as shown in Figure 3a-c, varying from dense to sparse. The amount of computation substantially increases as the grid becomes more dense. The results obtained by using each these meshes to compute the reaction kinetics for thermal abuse under the same condition are shown in Figure 4. The maximum temperature profile and runaway behavior only exhibit slight difference, and hence the mesh shown in Figure 3c is sufficient for © 2018 SAE International. All Rights Reserved.



dt increased to 14 s (but not both). No runaway phenomenon has been observed for these three cases. For these cases, the maximum temperature quickly decreases when the heat source disappears. However, if we further increase the Q to be 1.18E9 W/m3 and meanwhile increase the duration time dt to be 14 s, obvious thermal runaway with very large temperature rise rate has been captured. If we start from the case with thermal runaway, by either reducing the heat source intensity Q or the duration time dt, thermal runaway cannot be triggered, showing sensitive dependence on the testing conditions. As such, the critical condition for thermal runaway has been identified. To confirm such phenomena and the intrinsic role of chemical kinetics in the process of thermal runaway, the evolution of maximum temperature with and without the consideration of chemical reaction source terms are compared, for both cases with and without thermal runaway. It is seen in Figure 6 that all the curves overlap with each other before t = 8 s, indicating the negligible role of chemistry within the initial period. After that, for both dt = 13 s and 14 s cases, the maximum temperature for the reactive case deviates from that of the non-reactive case, and the difference gradually increases. For dt = 14 s, such a difference becomes so large that thermal runaway occurs at about t = 13.7 s, within the duration time of the heat source. It should be noted that even for the non-runaway case with dt = 13 s, pre-ignition chemistry is still substantial, causing a temperature difference around 80 K between the reactive and non-reactive cases. The chemical effect continues during the following heat transfer process after the heat source stops. To further investigate the kinetic feature during thermal runaway, a point very close to the interface is randomly selected to show the evolution of the five dimensionless chemical parameters involved in the aforementioned reactions, for both with and without thermal runaway. It can be observed in Figure 7 that the solid electrolyte interface decomposition reaction occurs first, followed by the mild reaction between the negative electrode and the electrolyte. However, given the information is shown in Figure 6, these two reactions have negligible thermal effects during this stage. What drive the system and cause thermal feedback are

FIGURE 4 The evolution of the maximum temperature with


different meshes.

the following computations, where the minimum element size is 3.6E-5 m and the maximum element size is 3.6E-3 m.

Results and Discussion In order to capture the critical condition that is able to trigger thermal runaway in the delay time of interest, different combinations for heat source intensity (Q) and duration time (dt) in the cylindrical region have been applied. Figure 5 compares the maximum temperatures for four different combinations of heat source intensities and durations. As expected, all the four cases show increasing maximum temperature within the heat source duration time. For the base case Q = 1.17E9 W/ m3 and duration time dt = 13 s, the maximum temperature starts to decrease as soon as the heat source disappears at 13 s. The sole effect of the heat source is, therefore, to increase the bulk temperature by a certain degree when thermal equilibrium is approached. The same observations are obtained for the other two cases, either with Q increased to 1.18E9 W/m3 or with

FIGURE 6 The evolution of maximum temperature for

FIGURE 5 The evolution of maximum temperature for heat

Q = 1.18E9 W/m3 with and without chemistry.



sources with different intensities and durations.

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5



FIGURE 7 The evolution of the dimensionless concentrations of different reactions for a randomly selected point close to the interface.

FIGURE 8 The heat generation rate from each chemical

the reactions between the positive electrode and the electrolyte as well as the electrolyte decomposition reaction. For the case without runaway (dt =12 s), the dimensionless concentration cne and tsei reach constant values (See Eqs. (6) and (7)), the dimensionless concentration csei and ce become close to zero (See Eqs. (4) and (11)) and the degree of conversion α become close to unity (See Eq. (9)). Therefore, all the other reaction rates diminish, such that the reaction between the negative electrode and the electrolyte becomes the single most important reaction that contributes to heat release in the final stage (i.e., after t = 12 s). In addition, the only difference between the two cases is also on the dimensional concentration of cne and tsei, which keep decreasing as temperature further increases, therefore generating more heat and thermal feedback to the system and leading to thermal runaway. For the non-runaway case, cne and tsei stay as constants in the last stage and therefore do not have any contribution to the thermal runaway. For the runaway case, the dimensionless concentration cne and tsei keep decreasing and therefore sharp increase of temperature is observed when thermal runaway occurs around 13.7 s. The same results have been observed for other sampling points close to the interface. The results here provide important and useful guidance on the understanding of the thermal abuse mechanism and thermal runaway, and demonstrate that the reaction between the negative electrode and the electrolyte plays a controlling role in the thermal runaway of a Li-ion battery. The heat generation rates induced by each reaction for the two different cases are sampled and compared for the randomly selected point very close to the cylindrical interface, as shown in Figure 8a, b. By comparing the two cases with different duration time, we can see that the only difference is the reaction source term of the negative-electrolyte reaction, which leads to the different heat generation profile in the later stage (i.e., after t = 12 s) approaching thermal runaway. This result further confirms with the observations from Figure 7. It should also be noted that the heat release rate profile has a



reaction for (a) the runaway case with Q = 1.18E9 W/m3 and dt = 14 s and (b) a non-runaway case with Q = 1.18E9 W/m3 and dt = 12 s.

double peak behavior, with the first one induced by the solid electrolyte interface decomposition reaction, and the second one mainly by the positive-electrolyte reaction. From Figure 6, it is found that the thermal chemistry also occurs in the case without thermal runaway. The heat release rate and dimensionless concentration from each chemical reaction are further investigated for the non-runaway case with Q = 1.17E9 W/m3 and duration time dt = 14 s. In Figure 9a, the double peak phenomena on the total heat release rate profile is again observed, consistent with the previous simulation performed [8]. The first peak is again induced by the solid electrolyte interface decomposition reaction, while the second peak instead of being controlled by the positive-electrolyte reaction, is contributed mostly by the negative-electrolyte reaction. As shown in Figure 9b, the dimensionless concentration of the electrolyte almost stays constant, demonstrating the negligible role of the heat release from the electrolyte decomposition reaction. In order to capture the critical conditions that can trigger thermal runaway in the range of delay time of interest, critical heat source intensity (Q) needed for thermal runaway is seeked for various duration time (dt) with fixed radius of the © 2018 SAE International. All Rights Reserved.



cylindrical heat source. As shown in Figure 10, with shorter duration time, the critical intensity of the heat source needed for thermal runaway increases. A power law fitting has shown that a relationship between the critical heat source and duration time can be expressed as Q = 2E9dt−0.225. The required heat source intensity, therefore, becomes less and less sensitive to increasing duration time.

7

To further understand the geometric effect of the heat source, simulations have been conducted for different heat source radius with fixed heat source intensity (Q = 1.18E9 W/ m3) and duration (dt = 14 s). As seen in Figure 11, with small enough radius of the heat source, thermal runaway does not occur at all. The larger the radius, the earlier thermal runaway occurs. The results suggest that the interface of the heat source plays a crucial role in heat transfer and creates broader high temperature regions for the chemical reactions to occur. With fixed duration time 14 s, the relationship between critical heat source intensity and radius of the heat source is demonstrated in Figure 12. With increasing radius of the cylindrical region, the heat source intensity required to trigger thermal runaway gradually decreases, following a scaling law of Q ∝ r−1.32, instead of being inversely proportional to the radius. The required heat source intensity, therefore, also becomes less and less sensitive to increasing radius of the cylindrical region.

FIGURE 9 (a). The heat generation rate from each chemical

reaction; (b). The dimensionless chemical parameters for a non-runaway case with Q = 1.17E9 W/m3 and dt = 14 s


FIGURE 10 The relation between heat source intensities and durations under the same radius condition.

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FIGURE 12 The relation between heat source intensities and radius at the same duration.



FIGURE 11 The evolution of maximum temperature for the heat source with same intensities and durations but different radius.



Conclusion In this work, a 3D thermal-chemical model has been established in COMSOL Multiphysics 5.3 to study the critical ignition energy and chemical kinetic feature of the thermal runaway model of a typical Li-ion battery. The critical condition for thermal runaway has been identified for the current configuration, starting from which any condition with lower heat resource intensity, shorter duration time or smaller radius of the heat source cannot trigger the thermal runaway. The role of each chemical reaction in the process of thermal runaway is also investigated in details. It is seen that the preignition heat release is mainly induced by the heat generation from positive-electrolyte reaction and the electrolyte decomposition reactions, while the solid electrolyte interface decomposition reaction and reaction between the negative electrode and the electrolyte is not of significance. It is also shown that the negative-electrolyte reaction plays a very important role towards the final stage approaching ignition and is critical to trigger the occurrence of thermal runaway. By seeking the critical heat source intensity with varying duration time or heat source radius, it is found that the critical intensity of heat source needed to trigger thermal runaway decreases with increasing duration time and increasing radius of the heat source. Analytical power-law scaling rules have been obtained to describe such dependence.

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Contact Information Peng Zhao, Ph.D. Assistant Professor Department of Mechanical Engineering Oakland University, Rochester, MI Office: Tel: 248-370-2214; Fax: 248-370-4416 [email protected]

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