In modern energy storage systems, the lithium ion battery stands as a cornerstone technology due to its high energy density and long cycle life. However, safety concerns, particularly thermal runaway triggered by abuse conditions such as mechanical, electrical, or thermal stress, pose significant challenges. During thermal runaway, a lithium ion battery undergoes exothermic reactions that generate substantial gases, leading to complex gas-liquid two-phase flows within the cell. Traditional solid-liquid two-phase models fail to capture these dynamics accurately, limiting our understanding of thermal runaway mechanisms. This article aims to address this gap by developing an electrochemical-thermal coupling model for a gas-liquid two-phase lithium ion battery pack, specifically focusing on 18650 cells. We investigate the influence of thermal runaway gases on internal stress, temperature distribution, and electrolyte concentration, and propose correction methods to refine theoretical predictions. Validation is performed using COMSOL Multiphysics 5.5 software, with comparisons between simulation results and corrected theoretical models. The findings highlight the positive feedback effects of gases on battery behavior, offering insights for enhancing safety in lithium ion battery applications.
The thermal runaway process in a lithium ion battery involves a series of exothermic reactions that release both heat and gases. Key reactions include the decomposition of the solid electrolyte interphase (SEI), reactions between electrode materials and electrolytes, and electrolyte decomposition. For instance, the SEI breakdown can produce gases like ethylene (C2H4), while cathode material decomposition releases oxygen, which further reacts with electrolytes to form carbon dioxide and water. Additionally, electrolyte salts such as LiPF6 decompose to generate hydrogen fluoride (HF) and hydrogen (H2). These gases accumulate, increasing internal pressure and potentially leading to venting or explosion. Understanding these mechanisms is crucial for modeling the gas-liquid two-phase behavior in a lithium ion battery during thermal runaway.
To model the gas-liquid two-phase lithium ion battery, we establish an electrochemical-thermal coupling framework. This model integrates electrochemical processes with heat transfer, accounting for gas generation and its effects. The coupling relationship is depicted where electrochemical reactions produce heat and gases, which in turn alter mechanical stress, temperature, and electrolyte concentration, feeding back into the electrochemical model. This approach allows for a comprehensive analysis of thermal runaway in a lithium ion battery.
The electrochemical model is based on charge and mass conservation laws. For charge conservation in the solid electrode and electrolyte, we use Ohm’s law-derived equations. The current densities in the solid phase (is) and electrolyte phase (ie) satisfy:
$$ \nabla i_s + \nabla i_e = 0 $$
with:
$$ i_s = – \sigma_s \nabla \Phi_s $$
$$ i_e = – \sigma_e \nabla \Phi_e + \frac{2RT\sigma_e}{F}(1 – t^+) \nabla(\ln c_e) $$
where σs and σe are conductivities, Φs and Φe are potentials, R is the gas constant, T is temperature, F is Faraday’s constant, t+ is the lithium ion transference number, and ce is electrolyte concentration. These equations govern the electrical behavior of the lithium ion battery.
Mass conservation for lithium ions in solid particles follows Fick’s second law:
$$ \frac{\partial c_s}{\partial t} = D_s \frac{\partial^2 c_s}{\partial x^2} $$
where cs is solid-phase concentration, Ds is diffusion coefficient, and x is spatial coordinate. For the electrolyte, considering gas-liquid two-phase flow, the concentration change accounts for gas mixing. The mixed concentration cmix of the gas-liquid phase is given by:
$$ c_{\text{mix}} = \frac{124.9 c_e p + 2.7 \varepsilon c_g p}{198.7 p + \varepsilon T Z} $$
where ε is gas volume fraction, cg is gas concentration, p is pressure, and Z is compressibility factor. This formulation captures the dilution effect of gases on electrolyte in a lithium ion battery.
Electrode kinetics are described by the Butler-Volmer equation:
$$ I = I_0 \left[ \exp\left( \frac{\alpha_a F}{RT} \eta \right) – \exp\left( \frac{\alpha_c F}{RT} \eta \right) \right] $$
where I0 is exchange current, αa and αc are transfer coefficients, and η is overpotential. This governs the reaction rates in the lithium ion battery.
The thermal model incorporates heat generation and transfer via Fourier’s law and energy conservation:
$$ \rho c_p \frac{\partial T}{\partial t} = \nabla (\lambda \nabla T) + q $$
where ρ is density, cp is specific heat, λ is thermal conductivity, and q is heat source. The heat source q includes reaction heat (qre), activation heat (qact), and ohmic heat (qohm). Boundary conditions use Newton’s cooling law:
$$ J_e = -\lambda \left( \frac{\partial}{\partial x} + \frac{\partial}{\partial y} + \frac{\partial}{\partial z} \right) T = h(T – T_1) $$
with h as heat transfer coefficient and T1 as ambient temperature. This model simulates temperature rise in the lithium ion battery during thermal runaway.
Given the complex interactions, theoretical models require correction for accuracy. We propose corrections for pressure, temperature, and electrolyte concentration based on simulation data and empirical adjustments. For pressure, during the reaction phase, corrected pressure P1 accounts for thermal expansion:
$$ P_1 = \frac{P[(1 + \beta) V_l + V_g]}{V_l + V_g} $$
where β is volume expansion coefficient, Vl is liquid volume, and Vg is gas volume. In the diffusion phase, corrected pressure P2 includes gas release impact:
$$ P_2 = \frac{dm}{dt} \frac{RT}{A_v} + P $$
with dm/dt as gas release rate and Av as vent area. These corrections refine stress predictions in the lithium ion battery.
Temperature correction considers gas combustion heat. The corrected temperature T1 is:
$$ T_1 = \frac{Q}{m \times c_p} + T_0 (1 – \eta) $$
where Q is heat of combustion, m is gas mass, cp is specific heat, T0 is initial temperature, and η is combustion efficiency. This addresses hotspot formation in the lithium ion battery.
Electrolyte concentration correction accounts for temperature and pressure effects:
$$ c_{\text{mix1}} = c_{\text{mix}} – kP \frac{P}{P – P_0} \times T \times \exp\left( \frac{\Delta H}{R} \left( \frac{1}{T} – \frac{1}{T_0} \right) \right) $$
where k is Henry’s constant, ΔH is enthalpy change, and P0 and T0 are reference values. This improves concentration estimates in the gas-liquid two-phase lithium ion battery.
For validation, we construct a 3D model of an 18650 lithium ion battery pack using COMSOL. The geometry includes positive electrode, negative electrode, separator, and electrolyte. Key parameters for the electrochemical and thermal models are summarized in tables below. These parameters ensure realistic simulation of the lithium ion battery behavior.
| Parameter | Value |
|---|---|
| Time t (s) | 1000 |
| Initial Temperature T0 (°C) | 25 |
| Initial Stress σ0 (MPa) | 0.103 |
| Activation Energy Ea (J/mol) | 8 × 104 |
| Battery Capacity Q (Ah) | 3.6 × 104 |
| Battery Volume V (m3) | 3.6 × 10-5 |
| Thermal Conductivity λ (W/(m·K)) | 30 |
| Convective Heat Transfer Coefficient h (W/(m2·K)) | 30 |
| Initial State of Charge (SOC) | 1 |
| Component | Density (kg/m3) | Concentration (mol/m3) | Specific Heat cp (J/(kg·K)) | Thermal Conductivity λ (W/(m·K)) | Thickness (μm) |
|---|---|---|---|---|---|
| Positive Electrode | 2791.0 | 398.6 | 0.77 | 71.5 | 71.5 |
| Separator | 1122.5 | 885.5 | 0.41 | 16.0 | 16.0 |
| Negative Electrode | 1647.6 | 668.2 | 0.60 | 75.0 | 75.0 |
| Electrolyte | – | 1200 | 1400 | 0.20 | – |
Simulation results reveal the impact of thermal runaway gases on the lithium ion battery. Internal stress analysis shows that gas generation causes significant pressure fluctuations. In the reaction phase (0–530 s), stress remains relatively stable due to electrolyte absorption, but in the diffusion phase (530–585 s), rapid gas release leads to a peak stress. The corrected theoretical pressure aligns closely with simulation values, with an error of only 0.04 MPa, improving accuracy by 80%. This demonstrates the effectiveness of our correction method for the lithium ion battery model.
Temperature distribution is critically affected by gases. The lithium ion battery experiences thermal runaway around 60°C, with gases igniting near 160°C. At 640 s, the simulation peak temperature reaches 177°C, while the corrected temperature is 172°C. Hotspots form due to gas combustion, causing uneven temperature gradients. This underscores the role of gases in exacerbating thermal effects in a lithium ion battery.
Electrolyte concentration declines throughout the thermal runaway process. Initially at 1200 mol/m3, concentration drops to approximately 837 mol/m3 in both simulation and corrected theory. This reduction stems from gas-liquid two-phase formation, where gases dilute the electrolyte, and from decomposition reactions. The consistency between models validates our approach for the lithium ion battery.
In conclusion, this study develops a gas-liquid two-phase electrochemical-thermal coupling model for lithium ion battery packs under thermal runaway. The model incorporates corrections for pressure, temperature, and electrolyte concentration, enhancing prediction accuracy. Results show that thermal runaway gases exert positive feedback on internal stress, temperature, and concentration, leading to hazardous conditions. The corrected models reduce errors and provide reliable insights for safety design. Future work could explore real-time monitoring and mitigation strategies for gas effects in lithium ion battery systems. Overall, understanding these dynamics is vital for advancing the safety and performance of lithium ion battery technologies in applications like electric vehicles and energy storage.
The integration of gas-phase considerations into traditional models marks a significant step forward. By repeatedly emphasizing the lithium ion battery context, we highlight its centrality in modern energy solutions. The use of tables and formulas, as shown, facilitates clear communication of complex parameters and relationships. This research contributes to a deeper comprehension of thermal runaway mechanisms, paving the way for safer lithium ion battery designs that can withstand abuse conditions without catastrophic failure.