Helium barely adsorbs on carbon-based adsorbents, while CH₄, N₂ and CO₂ do — that gap is what pressure-swing adsorption (PSA) exploits. This is a lumped (single well-mixed stage) model of one adsorber bed: a competitive Langmuir isotherm sets the equilibrium loading, linear-driving-force (LDF) kinetics set how fast the solid actually gets there, and a real-gas mass balance ties the void-gas impurity pressure to both the feed/product flow and the adsorption rate:
q_eq(p) = q_max·b·p / (1 + b·p) (Langmuir)
dq/dt = k_LDF·(q_eq(p) − q) (uptake kinetics)
dp/dt = (p/P)·(dP/dt)
+ (RT/V_void)·[F·y_f − F·(p/P) − m_ads·dq/dt]
During the feed/adsorption step the bed holds at P_high while feed flows through continuously; impurity partial pressure p climbs as the bed loads, so product purity (1 − p/P_high) declines over the step — a real breakthrough trend, not decoration. During regeneration the vessel blows down toward P_low; the isotherm's equilibrium loading drops with pressure, so the bed desorbs and resets before the next cycle. A rushed regeneration step (short t_reg) leaves residual loading behind and the cycle settles to a slightly lower steady-state purity — verified by running the model for many cycles back to back.
Carbon molecular sieve (CMS) has a higher capacity and selectivity (larger q_max, b) but slower kinetics (smaller k_LDF) than plain activated carbon — a genuine, literature-consistent contrast, not just a relabelled slider.