where 𝑚 𝑆 is the sorbent mass (kg), 𝑞 𝛿 is the working capacity (mol/kg) at time t, 𝑞 𝛿,0 is the initial working capacity (mol/kg), 𝑚 𝑟 ̇ is the sorbent replacement rate (kg/cycle), and k is the degradation rate (cycle -1 ). To consider other forms of degradation, such as linear or piecewise exponential, we simply modify the reaction term in the differential equation (Eq. S19, S24).