Decaffeination Extraction Front: scCO2 Diffusion Kinetics

Process Conditions

Pressure 300 bar

Temperature 60 °C

Bean particle radius 4.0 mm

scCO2 flow rate 1.0×

Below CO2's critical pressure (73.8 bar) — the fluid is a subcritical gas/liquid, solvating power collapses and extraction stalls.

Extraction State

Batch time elapsed

0.0 h

Caffeine removed (bed avg.)

0.0 %

Extraction front depth

0 %

How it works

Caffeine leaves a bean by Fickian diffusion through the solid matrix to the surface, then partitions into the flowing supercritical CO2. For a spherical particle the exact PDE is Fick's second law in spherical coordinates, but its well-known linear-driving-force (LDF) approximation (Glueckauf, 1955) tracks only the bean's average loading q:

∂C/∂t = D_e/r² · ∂/∂r(r² ∂C/∂r)   (exact, per particle)

dq/dt = −k_LDF·(q − K·C_f),   k_LDF = 15·D_e / R_p²   (LDF approx.)

D_e (effective intraparticle diffusivity) follows an Arrhenius law in temperature; K, the solid/fluid partition coefficient, only turns on once the CO2 is truly supercritical (P > 73.8 bar) — below that it is ≈0 and nothing extracts. Fresh CO2 enters the bed caffeine-free and is treated as flowing in quasi-steady plug flow through 14 stacked bins: each bin strips caffeine from its beans into the passing fluid, so the fluid arriving at the next bin upward is already partly loaded. That progressively weakens the driving force (q − K·C_f) further up the column, producing a moving extraction front — beans near the inlet deplete first while beans near the outlet stay near-saturated until the front reaches them.

Pressure — sets K (solvating power); zero below the critical point, rising with CO2 density above it.
Temperature — sets D_e via an Arrhenius factor; hotter CO2 diffuses caffeine out faster.
Bean radius — k_LDF ∝ 1/R_p², so smaller particles (crushed beans) extract far faster than whole beans.
Flow rate — more fresh solvent per unit time dilutes the fluid phase, keeping C_f low and sustaining a steep front longer.

This is the mechanism behind industrial scCO2 decaffeination (e.g. the Kraft/UCC and Coca-Cola Hag processes): moistened beans are packed into a pressure vessel and supercritical CO2 is circulated until the diffusion front has swept the whole bed, selectively pulling out caffeine while leaving flavor compounds largely behind.

Caffeine-laden bean Decaffeinated bean Caffeine-laden scCO2

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