Modeling of Thermal Runaway Propagation in a Pouch Cell Stack

Abstract

Characterizing propagation of a thermal runaway hazard in cell arrays and modules is critical to understanding fire hazards in energy storage systems. In this paper, the thermal runaway propagation of a pouch cell array has been examined by developing a 1D finite difference model. The results are compared with experimental data. First, the thermal runaway reactions found in the literature are reviewed. Using the insight of the literature review and premixed flame propagation theory, a global first order Arrhenius type reaction is characterized. While applying the multiple kinetic reactions, an “onset temperature” of the combustion reactions has been determined by performing an induction time analysis on ethylene. The propagation speeds are predicted with a 1D finite difference model by using both multi-reaction kinetics and one step reduced-order kinetics. These results are in a good agreement with experiments for both 10 Ah and 5 Ah cell arrays.

Appendix: Ignition Time Discussion

There are various hydrocarbons that may present when oxygen is available in the cell. The main fuel source is the electrolyte. Since DMC and DEC have high vapor pressures at low temperatures (low boiling tempearture), a significant amount of them might be vented before the presence of oxygen. Therefore, we assumed that when oxygen appears at around 240°C, the available fuel is rich for EC and its related Lithium-Electrolyte reaction (labeled as A3 or AnE in the text) product, ethylene (C₂H₄). Varatharajan and Williams [33] examined the ignition and detonation characteristics of ethylene extensively. At low temperatures, the ignition consist of a chain-branching stage and a constant concentration stage. In the chain-branching stage, the ethylene and oxygen starts forming radicals such as HO₂ and H₂O₂. In the study [33], it is shown that the time of this chain-branching stage can be determined by the concentration of the HO₂ radical. Thus, a reduced order chemical model is applied for the chain-branching stage and the time evolution for HO₂ concentration has been modeled. [33] The evolution of the radical HO₂ is given as

$$\frac{{d\left[ {HO_{2} } \right]}}{dt} = \left[ {4 - q - s\left( {2 - q} \right)} \right]\alpha_{16} \left[ {C_{2} H_{4} } \right] + \left[ {7 - 6s - 3q\left( {1 - s} \right)} \right]\alpha_{20} \left[ {HO_{2} } \right] - k_{10} \left[ {HO_{2} } \right]^{2}$$

(29)

Chain-branching stage will end when the concentration of HO₂ will reach the following

$$\left[ {HO_{2} } \right] = \frac{{\left[ {7 - 6s - 3q\left( {1 - s} \right)} \right]\alpha_{20} }}{{k_{10} }}$$

(30)

$k$ and $\alpha$ are the reaction rates such as

$$k_{i} = A_{i} T^{{n_{i} }} \exp \left( { - \frac{{E_{i} }}{RT}} \right)$$

(31)

$$\alpha_{16} = k_{16} \left[ {O_{2} } \right]$$

(32)

$$\alpha_{20} = k_{20} \left[ {C_{2} H_{4} } \right]$$

(33)

q and s are also related with reaction rates such as

$$q = \frac{{\alpha_{18} }}{{\alpha_{18} + \alpha_{19} }}$$

(34)

$$s = \frac{{\alpha_{25} }}{{\alpha_{25} + \alpha_{26} }}$$

(35)

where the subscript numbers are associated with the number of reactions defined in Varatharajan and Williams [33]. This means, for any initial C₂H₄, O₂ concentration and temperature, the ignition time can be estimated as follows: starting with zero HO₂ concentration, Eq. 29 can be integrated, and the ignition happens when HO₂ concentration reaches the value determined by Eq. 30. This is often called numerical estimation. Varatharajan and Williams [33] also developed an analytical formula to estimate the chain-branching time as

$$\tau_{cb} = \frac{1}{{\left[ {7 - 6s - 3q\left( {1 - s} \right)} \right]\alpha_{20} }}\ln \left( {1 + \frac{{\alpha_{20}^{2} \left[ {7 - 6s - 3q\left( {1 - s} \right)} \right]^{2} }}{{\alpha_{16} \left[ {C_{2} H_{4} } \right]k_{10} \left[ {4 - q - s\left( {2 - q} \right)} \right]}}} \right)$$

(36)

Therefore, the ignition time can either be evaluated by using the analytical formula in Eq. 36, or numerically. Further details can be found in Varatharajan and Williams [33].

Concisely, the ignition time can be written as a function of temperature and initial fuel and oxygen concentrations as

$$\tau_{ign} = f\left( {T,C_{{C_{2} H_{4} }} ,C_{{O_{2} }} } \right)$$

(37)

Fuel and oxygen concentrations are determined by using a mixture concentration and an equivalence ratio. Using the equation of state, the concentration of the mixture can be evaulated as

$$C_{mix} = \frac{P}{RT}$$

(38)

In Eq. 38, P is the total pressure of the gas mixture and R is the specific gas constant. The concentration of the mixture can be distributed to the fuel and oxygen based on the equivalence ratio ($\phi$) as follows

$$C_{{C_{2} H_{4} }} = C_{mix} \frac{\phi }{3 + \phi }$$

(39)

$$C_{{O_{2} }} = C_{mix} \frac{3}{3 + \phi }$$

(40)

Since the experiment was performed in a nitrogen environment, the oxygen that caused combustion must be provided by LCO decomposition. Many researchers observed the oxygen after 240°C or associated exothermic reactions to oxidation of electrolyte after 200°C. At this temperature, there can be flammable hydrocarbons in the cell due to Anode–Electrolyte reaction or electrolyte evaporation. As long as there is oxygen and fuel in the cell, combustion might occur, providing a sufficient time for auto-ignition. At low temperatures, the ignition times can be high due to long chain branching stages. For stoichiometric ethylene–oxygen mixture at 1 bar, the ignition times are predicted using the aforementioned analytical and numerical models and compared with the values in the literature in Fig. 10. The data provided by Varatharajan are evaluated by using detailed chemical mechanisms. Please note that for temperatures lower than 1000 K, Varatharajan does not provide ignition time data. Therefore, as a sanity check, we presented the ignition times of propane and butane in this low temperature (500 K to 1000 K) range [34]. The results are in a reasonable agreement.

Fig. 10

Ignition time prediction for stoichiometric ethylene–oxygen mixture at 1 bar

At the lower temperatures for which the oxygen–hydrocarbon mixture may present in the cell, (after 240°C), assuming that the oxygen starts to be present after 240°C, it is possible to estimate the onset temperature of thermal runaway by evaluating the ignition time after oxygen is generated. Ignition is assumed to happen when the ignition time is achieved

$$t_{runaway} = t_{240^\circ C} + \tau_{ign}$$

(41)

A representative temperature profile is compared with the ignition times that are evaluated by the numerical model in Fig. 11. At the left-hand side of the dashed dot and solid curve intersection, the cell temperature is low and corresponding required ignition time is so high that the necessary conditions for ignition could not be achieved. When temperature is increased and intersected with the ignition time prediction, a sufficient time has been passed after the presence of oxygen and fuel, which makes the ignition possible. For the ignition time prediction, the pressure is set to 1.2 bar, which is measured by the load cell in the experiment.

Fig. 11

Time history of the battery temperature after runaway in comparison with the ignition time prediction