Batch-adsorber (equilibrium) construction for the 4-step
temperature–vacuum swing direct-air-capture cycle (CO₂/H₂O/N₂) —
the graphical companion to the dynamic DAC simulator. Water is solved first (its GAB
isotherm never sees CO₂), then CO₂ rides on the water state through the
modified-Toth coupling and takes what is left of the vacuum-pressure budget. Every KPI
— purity, working capacity, thermal and electrical energy — is a closed-form
path integral, so the energy landscape can be painted directly onto the isostere plane
the cycle is drawn on.
Sorbent — Toth (CO₂) + GAB (H₂O), Stampi-Bombelli coupling
qs0 mol/kg
b₀ 1/Pa
−ΔH kJ/mol
t₀ –
α –
T₀ K
CO₂
Cm mol/kg
CG –
K –
−ΔHw kJ/mol
ψ kg/mol
β kg/mol
H₂O
Ambient air & design point
Drag on either map to move the design
point (TH, Pvac) and watch every panel follow.
Energy accounting
Batch idealization: the bed is spatially uniform and always at
equilibrium; the pump withdraws gas at the instantaneous composition. Water is
one-way coupled (GAB never sees CO₂) — the shared-denominator competitive
option of the dynamic DAC app is deliberately out of scope here. Equilibrium water
overstates the water swing, so the water heat and pumping penalties are conservative;
fw < 1 brackets slow water kinetics. Numbers are
screening-grade — rank sorbents and spot regimes, then verify with the dynamic
DAC app.
Cycle schematic
Conjugate construction — q–T plane
(left) and q–p plane (right), welded through the shared loading axis