The primary difference in our capacity fade model versus a model that does not consider sorbent degradation is the relationship between the cumulative amount of CO2 captured (NCO2) and time. If a sorbent maintains a constant capacity, it will capture a consistent amount of CO2 each cycle. However, when a sorbent degrades, the amount of CO2 captured varies from cycle to cycle, leading to a nonlinear NCO2 with respect to time. Tracking the captured CO2 each cycle for tens of thousands of cycles would be computationally expensive, so we instead employ integration to determine the cumulative amount of CO2 captured at specific time points based on the relationship between working capacity and time.