1 · Core Model Equation

2 · Productivity Scenarios (k calibration)

The calibration constant k translates OD₆₈₀ into volumetric biomass productivity (P = k × OD). The three scenarios bracket the performance range documented in the Carbelim study report and peer-reviewed pilot 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 = 1.833 (50% C assumption) is consistent with the Carbelim study report and the de facto standard in microalgae life-cycle assessment literature.^{[8, 9, 11]}

O₂ Release Stoichiometry

Photosynthesis releases O₂ stoichiometrically with CO₂ fixation. The Carbelim study report uses this ratio to compute annual O₂ output alongside CO₂ capture.^[11]

4 · Operating Envelope & Constraints

• OD₆₈₀ 0–4: 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 ≈ 4. 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 the model.^{[5, 7]}
• System efficiency η: The default 100% represents the report's raw-productivity baseline. 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 Equivalence Metrics

CO₂ capture is expressed via two equivalence benchmarks:

A mature oak tree absorbs approximately 22.44 kg CO₂/year. This figure is adopted from the Carbelim study report (Kumar 2026).^[11]

The factor 0.166 kg CO₂ km⁻¹ (= 166 g CO₂ km⁻¹) is derived from the IEA Global Fuel Economy Initiative 2021 report, documenting a global average of 167 g km⁻¹ for new light-duty vehicles.^[10]

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 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.
• k calibration uncertainty: The default k = 0.6 is calibrated to the Carbelim PRO15 reference system. Different strains, reactor geometries, and growth conditions may require k recalibration (±20–30%).
• 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.
• Energy & cost: The study report includes energy (kWh) and cost (₹) per product model; these are product-specific values that do not scale with volume and are not computed by this calculator.