# A Review of Experimental and Numerical Studies of Lithium Ion Battery Fires
## 6 Modeling of LIBs
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Duration (s)** & \(\mathbf{D_{12}}\) & \(\mathbf{D_{23}}\) & \(\mathbf{D_{34}}\) & \(\mathbf{D_{45}}\) & \(\mathbf{D_{56}}\) \\ \hline Experiment & 245 & 163 & 186 & 164 & 159 \\ Model & 236 & 158 & 179 & 189 & 170 \\ \hline Temperature (\({}^{\circ}\)C) & \(\Delta T_{\text{p,1,2}}\) & \(\Delta T_{\text{p,2,3}}\) & \(\Delta T_{\text{p,3,4}}\) & \(\Delta T_{\text{p,4,5}}\) & \(\Delta T_{\text{p,5,6}}\) \\ \hline Experiment & 144 & 121 & 183 & 146 & 146 \\ Model & 141 & 174 & 168 & 165 & 168 \\ \hline \hline \end{tabular}
\end{table} 
Table 18: Comparison of the duration of TR propagation from one battery to the next, defined as \(D_{i,i+1}\), and comparison of the temperature differences through the negative and positive poles of adjacent batteries, defined as \(\Delta T_{\text{p,i,i+1}}\)[146]. * TR propagation can be prevented by adding additional thermal layers between adjacent batteries (validated by experiment). [PERSON] et al. [147] used two classical models to simulate the critical condition of LIB and predict self-accelerating decomposition temperature (SADT) of TR for LIB and TR propagation. The study suggested that there could be potential of TR propagation over neighboring cells when the critical condition based on SADT was reached. There were some discrepancies in actual measured temperatures and predicted SADT temperatures. Between two classical models there also were differences. [PERSON] et al. [147] attributed the difference to the underlying model assumptions and difficulty in measuring temperatures inside the LIBs. To improve further, [PERSON] et al. [148] took the critical parameters of overall reaction as a weighted average of four exothermic reactions and revised the critical criteria by the consumption of reactants. Revised models resulted in an accuracy of within 5 \({}^{\circ}\)C when the result of an LCO/graphite cell was compared. Through these revised models, they predicted the critical ambient temperature of the 18650 NCM/LTO battery and analyzed the influences of convective heat transfer coefficient, cell size, and shape to critical condition. To date, a comprehensive simulation of the fires produced by the flammable gases and other battery materials venting from LIB has not been conducted. Accurate quantification of ejection velocity and temperature of these materials are a challenging subject. So far, most studies aimed to analyze the combustion chemistry of the organic solvents used in LIB [149] or the mixture of the vented gases at TR [150,151]. [PERSON] et al. [151] modelled the laminar burning velocities of the ejecting gases from the LIB premixed with air. It was reported that the burning of vented gases is comparable to propane and methane, presenting a serious hazard of explosion and fires in enclosures, and laminar burning velocities of the gases are similar or slightly higher than that of methane. In another study, [PERSON] et al. [150] used a detailed reaction mechanism of flammable gases and DMC to calculate the combustion parameters of the battery venting gases, such as laminar flame velocities, adiabatic flame temperature, and HRR. To date, most of the LIB combustion modeling is limited to the analyses of combustion chemistry in simplified conditions such as premixed or counter flow diffusion flames of the electrolyte carbonated solvents and the venting flammable gases, and simulations of the gas-venting dynamics and their combustion processes are yet to be conducted. The complex nature of the structure of different LIB cells provides difficulties in ascertaining the required fire property variables such as thermal conductivity, density, specific heat, and Arrhenius parameters. To obtain reliable and accurate modeling results, precise thermal properties are required. Boundary conditions and fire properties are fundamental to computational simulations and inaccurate boundary conditions/fire properties may lead to the unrealistic results which were apparent at the time of and during TR in the study by [PERSON] et al.