1 · Core Model Equation

2 · Capture-Factor Scenarios

F is derived from reported areal and volumetric productivities for flat-panel PBRs, converted to OD-normalised units using typical path-lengths (2–5 cm) and published dry-weight/OD calibration data.^{[2, 3, 5]} The three scenarios bracket the performance range documented in peer-reviewed pilot and industrial studies:

3 · CO₂ Fixation Stoichiometry

Microalgal dry biomass contains approximately 48–52% carbon by mass across commonly cultivated genera — Chlorella, Scenedesmus, Nannochloropsis, and Spirulina.^{[1, 8]} The representative empirical formula CH₁.₈O₀.₅N₀.₂ implies a carbon mass fraction of 48.8%, yielding τ ≈ 1.79–1.83 kg CO₂/kg.^[9] The value τ = 1.83 (50% C assumption) is the de facto standard adopted in microalgae life-cycle assessment and techno-economic literature.^{[8, 9]}

4 · Operating Envelope & Constraints

• OD₆₈₀ 0–10: Chlorophyll a absorbs maximally near 680 nm; the Beer–Lambert linear relationship between OD and biomass concentration holds in well-stirred suspensions up to OD₆₈₀ ≈ 10. Beyond this threshold, mutual shading limits productive culture depth and the linear model overestimates CO₂ fixation.^[4]
• PAR ≥ 200 µmol photons m⁻² s⁻¹: Light saturation for photoautotrophic growth typically falls in the range 150–350 µmol m⁻² s⁻¹ depending on species and acclimation state. Below this threshold, photosynthetic rate and CO₂ fixation drop non-linearly (photolimitation regime).^{[5, 6]}
• Flat-panel geometry: Flat-panel PBRs offer surface-to-volume ratios of 80–300 m² m⁻³, outperforming tubular reactors (30–80 m² m⁻³) and open raceways (<10 m² m⁻³), enabling the higher volumetric productivities underpinning F.^{[5, 7]}
• Geometry correction ±10–20%: Switching to tubular or open-raceway systems typically reduces volumetric productivity by 10–30% due to longer light-path lengths and lower illuminated volume fraction.^{[6, 7]}
• System efficiency η: The default 95% represents an idealised controlled indoor system. Outdoor systems under variable irradiance typically achieve η ≈ 60–80%; factoring in seasonal variation and non-productive periods (cleaning, harvest, maintenance) brings realistic annual η to 70–90%.^{[2, 3]}

5 · CO₂ Emission Equivalence Factor

Captured CO₂ is expressed as an equivalent passenger-car driving distance offset using:

The factor 0.166 kg CO₂ km⁻¹ (= 166 g CO₂ km⁻¹) is derived from the IEA Global Fuel Economy Initiative 2021 report, which documents a global average rated CO₂ intensity of 167 g km⁻¹ for new light-duty vehicle registrations in 2019 (petrol, diesel, and hybrid combined).^[10] This figure is illustrative: regional averages vary significantly — EU 2022 fleet average ≈ 120 g km⁻¹; US 2022 ≈ 215 g km⁻¹.

6 · Model Scope & Limitations

• OD as biomass proxy: OD₆₈₀ is sensitive to cell size, pigmentation, and suspended debris. A strain-specific OD-to-dry-weight calibration curve is required for quantitative pilot validation.
• Linear volume scaling: The model assumes constant CO₂ uptake per unit OD per unit volume. Real systems experience light attenuation at high volume with fixed illumination area — estimates for V > 2,000 L with fixed lighting should be treated as upper bounds without proportional illumination scaling.
• F calibration uncertainty: Published F values carry ±20–30% inter-study variability due to differences in strain, reactor geometry, and local climate. Pilot-scale experimental determination of F for the specific strain–reactor combination is recommended before commercial sizing.
• Steady-state assumption: The model assumes continuous or semi-continuous operation at constant OD. Batch or fed-batch systems will yield lower effective annual capture due to lag and stationary phases.