Cradle-to-grave energy efficiency is a metric for "cradle-to-gate and use" and "cradle-to-grave" life cycle assessments of energy storage technologies. Cradle-to-grave energy efficiency is equal to the total energy extracted from the battery during its life (a.k.a. lifetime energy throughput) divided by the total energy that went into the battery. The latter includes the energy spent while mining the raw materials for the battery, cell and battery manufacturing, and recycling, minus the energy that would be required to mine and prepare the raw materials if they weren't recovered during recycling.
For recyclable batteries, I think that a metric like cradle-to-grave energy efficiency would be more convenient than Energy stored on energy invested (ESOI) as Cradle-to-grave energy efficiency ****could be directly used in downstream calculations such as assessing energy efficiency of renewable or nuclear power installations with accompanying energy storage for daily power balancing and manoeuvring, as well as in lifecycle greenhouse gas emission comparisons between internal combustion, hybrid, and fully electric vehicles for different carbon intensities of the grids in different countries.
It takes 50 times more energy to produce a battery pack than its capacity. The energy needed to recycle most of cell materials is higher/lower? (TOFO), like Redwood Materials promises to do.
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Cradle-to-grave energy efficiency is one of the System needs for a vehicle battery.