Long transparent tubes floating on the ocean surface circulate seawater seeded with microalgae. Sunlight drives photosynthesis, CO2 is bubbled in as carbon feedstock, and dissolved nutrients (nitrogen, phosphorus) support growth — governed by Monod-style kinetics limited by whichever resource is scarcest.
μ = μmax · min( I/(I+Ki), [CO2]/([CO2]+Kc), [N]/([N]+Kn] )
dX/dt = μ·X − harvest_rate·X (logistic-limited by tube capacity)
- Sunlight intensity — main energy input for photosynthesis; growth saturates at high light (photoinhibition ignored here for simplicity).
- CO₂ feed rate — carbon supply; becomes limiting if light and nutrients are abundant but CO2 is scarce.
- Nutrient dosing — nitrogen/phosphorus supply rate; often the true bottleneck in offshore cultivation.
- Harvest rate — fraction of the culture removed per day for biofuel/biomass processing, which also caps how dense the tubes can get.
Real-world: offshore photobioreactor arrays are being explored to grow algae for biodiesel, animal feed, and carbon capture without competing with farmland or freshwater, using ambient seawater and open ocean space.