Kerogen (the solid organic precursor in oil shale) decomposes thermally by a single dominant first-order reaction over the retorting range. The unconverted-kerogen fraction C obeys
dC/dt = −k(T)·C
k(T) = A·exp(−Ea / (R·T))
with R = 8.314 J/(mol·K), T in kelvin, A the pre-exponential (frequency) factor and Ea the activation energy — both real Arrhenius parameters for kerogen pyrolysis (Ea typically 180–260 kJ/mol depending on shale grade/maturity, A in the 10¹⁰–10¹⁶ s⁻¹ range for the dominant decomposition step). The retort temperature ramps linearly, T(t) = T₀ + β·t, exactly like a real programmed-heating assay. The equation is integrated at a fixed sub-step so the conversion curve stays accurate regardless of on-screen frame rate.
Conversion X = 1 − C traces the characteristic S-shaped pyrolysis curve: slow at low T (k is exponentially small), a steep rise through the "kerogen breakdown window" once k·(heating timescale) ≈ 1, then flattening as C is exhausted. Each unit of converted kerogen splits into shale oil, gas and char by the fixed product-split slider; oil yield is reported in litres per tonne of shale (a standard Fischer-assay-style unit), scaled from the conversion fraction.
- Left pane — retort cross-section: shale bed color shifts from raw (dark brown) to converted/char (grey) as X grows, with rising oil droplets and gas bubbles proportional to instantaneous rate dX/dt.
- Right pane — conversion X vs. temperature T, the live S-curve, with the current state marked.
- Raising Eₐ (lower-grade/more mature shale) shifts the S-curve to higher temperature and steepens it less; raising heating rate β shifts the curve to higher temperature too (classic non-isothermal kinetics behavior — faster heating outruns the reaction, so more of it happens at higher T).