This models a fixed bed of a solid CO₂ sorbent (e.g. amine-functionalized silica) split into 24 slices along the flow direction. Each slice tracks a gas-phase CO₂ concentration C and a solid loading q.
Equilibrium (Langmuir): q* = q_max · b(T) · C / (1 + b(T) · C)
Van't Hoff: b(T) = b0 · exp(−ΔH/R · (1/T − 1/T0))
Kinetics (LDF): dq/dt = k · (q* − q)
Column mass balance: dC/dt = −v·(C_i − C_i−1)/Δz − ρ_bed/ε · dq/dt
Because ΔH < 0 (adsorption is exothermic), b(T) — and hence the equilibrium capacity q* — falls sharply as temperature rises. That single fact drives the whole cycle:
- Adsorb — bed held near 300 K, flue gas (with your chosen CO₂%) flows in at the bottom. High b(T) means high q*, so each slice loads up and a "breakthrough front" of loaded sorbent (orange) advances up the column while clean gas (green) exits the top.
- Regenerate — the bed is heated to your chosen temperature. b(T) collapses, q* drops far below the current loading, and the LDF term drives CO₂ back out of the solid into the gas phase — releasing it as a concentrated stream you can capture and compress.
- Velocity sets how fast gas convects through the bed (residence time); a faster flow reaches breakthrough sooner but gives each slice less time to equilibrate.
- CO₂ captured integrates the mass actually retained by the solid phase over time — the real output of a TSA carbon-capture plant.
Real plants (e.g. Climeworks-style direct-air-capture units) run exactly this adsorb/heat/desorb cycle, swapping temperature instead of pressure (as pressure-swing plants do) to regenerate the sorbent.