Biochar carbon is not one substance — pyrolysis produces a mixture of thermally-altered organic matter that mineralizes (returns to CO₂) at wildly different rates. The standard way to model this is a three-pool first-order decay (Zimmerman 2010; Wang et al. 2016 meta-analysis of biochar incubation studies):
C(t)/C0 = f_L e^(-k_L t) + f_I e^(-k_I t) + f_R e^(-k_R t)
f_L + f_I + f_R = 1
Labile (L): half-life ~ 2 years (k_L ≈ 0.35 /yr)
Intermediate (I): half-life ~ 35 years (k_I ≈ 0.02 /yr)
Recalcitrant (R): half-life ~ 460 years (k_R ≈ 0.0015 /yr)
Pyrolysis temperature sets the pool split. Higher temperature drives off volatiles and increases aromatic ring condensation (a falling H:C_org ratio), so more carbon ends up locked in the recalcitrant pool: f_R rises from ~15% at 300 °C to ~70% at 700 °C, while the labile fraction shrinks accordingly.
Soil temperature scales every pool's decay rate through a Q10 relationship — a common empirical model for how microbial decomposition responds to warming:
k(T) = k(15°C) · Q10^((T − 15)/10), Q10 = 2
The weighted mean residence time of the whole batch is MRT = f_L/k_L + f_I/k_I + f_R/k_R. In the 3D view, each instanced chunk is one of ~2,400 sampled parcels of applied biochar carbon; every parcel is pre-assigned an individual random decay age (drawn from its pool's exponential distribution) and shrinks away exactly when that age is reached — so the population-level curve above emerges from thousands of independent, physically-motivated events rather than being animated directly.
Real-world relevance: this multi-pool framework is exactly what IPCC-aligned soil carbon accounting and biochar carbon-credit protocols use to estimate how many tonnes of CO₂-equivalent stay locked in soil decades to centuries after application — the recalcitrant fraction is what makes biochar a genuine long-duration carbon removal method rather than just a fertilizer amendment.