Thermal runaway in battery packs is a major safety concern with potentially
catastrophic outcomes, such as battery pack fires. This phenomenon occurs in
batteries due to exothermic degradation reactions when a battery is subjected to
abuse conditions, such as physical damage, internal short circuits, overcharging, or
overheating. These conditions, along with the associated decomposition of battery
components, for example, anode, cathode, and separator, lead to significant heat
release and an uncontrollable rise in temperature. When a single cell enters these
thermally unstable conditions, the heat release can cause adjacent cells to heat up
and enter thermal runaway, eventually propagating through and consuming the entire
battery pack. Additionally, the decomposition reactions generate flammable gases
that can ignite, causing fires to spread through the battery pack.
SimLab battery solutions for thermal runaway provide a
virtual experimental platform to test pack designs for thermal safety, including the
assessment of propagation characteristics and heat shield effectiveness. Three
models are available to simulate thermal runaway:
- NREL model
- Arc reaction heat model
- Heat rate model
The first two models are chemical kinetic models based on the Arrhenius equation. The
NREL model takes a mechanistic approach to model the kinetics and heat release of
individual cell components, while the arc reaction heat model adopts a more
phenomenological approach, deriving the kinetics directly from ARC data. The heat
rate model also uses ARC data but directly reads this data to determine the
volumetric heat source.
All of the mathematical models for thermal runaway add an additional heat source (
) to the energy equation.
The form of the heat source (aggregated or direct calculation) depends on the model.
A brief description of these models and the heat source term is given in the
following sections.
NREL Thermal Runaway Model Formulation
The mathematical model for thermal abuse involves heat generation resulting from
series of exothermic decomposition reactions of various battery components. The heat
generation from these individual reactions are aggregated and incorporated into the
energy equation as a combined source term.
The decomposition reactions within the battery are characterized using Arrhenius
equations, accounting for: 1) Solid electrolyte interface (SEI) decomposition at the
anode-electrolyte interface (
); 2) Anode decomposition (intercalated lithium
reacting with electrolyte, facilitated by SEI decomposition); 3) Cathode conversion
(active material decomposition releasing oxygen), which is highly exothermic; and 4)
Electrolyte decomposition at very high temperatures. The final source term from the
above is written:
, representing the heat release from the exothermic
decomposition reactions of the SEI, anode, cathode, and electrolyte,
respectively.
The governing equations for these reactions and each exothermic heat source
contributing to the energy equation are summarized below.
SEI decomposition reaction rate:
Where
is the fraction of lithium in the
anode,
the frequency factor for anode
decomposition,
the activation energy
for anode decomposition,
the
temperature, and
the Boltzmann
constant.
SEI decomposition exothermic heat:
Anode decomposition reaction rate:
Where
is the fraction of lithium in the anode,
the frequency factor for anode decomposition,
the activation energy for anode decomposition. As
part of anode decomposition, the tunneling effect is considered due to the reduction
in thickness of the SEI, where
represents the relative SEI
thickness:
Anode decomposition exothermic heat:
Where
is the negative solvent enthalpy,
is the specific carbon content in
the jelly roll.
Cathode conversion reaction rate:
Cathode conversion exothermic heat:
Where
is the positive solvent enthalpy,
is the specific cathode active
material content in the jelly roll.
Electrolyte decomposition exothermic heat:
Finally, short circuit events can also be included, for example, separator melting
leading to direct connection between the anode and cathode. The short circuit leads
to charge depletion and is given as a function of state of charge
(SOC):
In which
becomes active when temperature
is above a pre-defined internal short circuit temperature.
ARC Reaction Model Formulation
The ARC reaction model is a staged Arrhenius-based kinetic model that can be directly
fitted to Accelerating Rate Calorimetry (ARC) data. This enables fitting N number of
stages to the data based on the desired level of accuracy. Up to five ODEs (i = 1-5)
are employed to represent the data, each with distinct parameters for activation and
decay, characterizing a specific stage. The summation of these heat sources
represents the ARC heat rate data. The general form of the equation is as
follows:
Where
is the frequency factor for a specific stage (1/s),
is the activation energy (J),
is the Boltzmann constant,
the cell temperature (K), n and m are related to the
form of the solid reaction model. Depending on the value of m this reaction can be
nth order (when m=0) or an auto-catalytic type, that is, the reaction increases as
the product is generated (m>0).
The above equation is a more phenomenological modeling approach compared to the NREL
model; however, it can still be motivated from a physical perspective providing the
stages are divided into bands that represent an approximate physical reaction
process occurring, for example, anode decomposition.
The total exothermic heat generation for this model is given by,
Where
is the enthalpy of the component defined
by,
The heat contribution for each stage combines to form the heat source,
, in the energy equation.
Direct Reading of ARC Data Formulation
A direct reading of thermal runaway ARC data provides a source term directly in the
energy equation derived from the heat rate-temperature data. To calculate this heat
source using ARC data the following equation is utilized:
Where
is the effective density of the
cell,
is the effective specific heat of
the cell and
is the heat rate data
directly read from the ARC test.