What would a Seaweed farm Need?
Why are oceans currently mostly deserts?
One of the things that make oceans so appealing source of negative carbon is the fact that it is UNDERUTILIZED right now. Why is that? The answer is that life needs a variety of raw materials (nutrients) and if any are in short supply life simply does not happen. The good news is that the ocean (along with the atmosphere) supply many of these raw materials. The first two are 'obvious'
Water - living things tend to be about 90% water.
Carbon - Carbon is in almost every component of living things
The ocean has plenty of water, and the atmosphere has plenty of carbon, so those are not limiting resources. After that the elements that living things needs most abundantly are
Nitrogen - present in every protein which make up most tissues.
We even know how much we need of these nutrients we need. The ratio of carbon to nitrogen to phosphorus (called the Redfield ratio) is 106:16:1. Thus for every 106+16+1=123 tons of DRY seaweed/algae, we need 16 tons of nitrogen and 1 ton of phosphorous to produce it.
There are other elements that life needs in small amounts including
Potassium, Sulfur, Calcium, Magnesium
which are already present in seawater in relative abundance and thus are never a limiting factor. The next set of elements
Iron, Molybdenum, Boron, Copper, Sodium, Zinc Fluorine
are needed in only very small quantities, and so typically are present in seawater abundantly enough to not be a limiting factor (the exception sometimes is iron, which is why iron fertilization is an area of research).
(Ignoring Oxygen and Hydrogen)
Thus Nitrogen, Phosphorus are the Limiting Resources
Helpfully, nitrogen is present in the atmosphere, and just like on land, there are microbes in the sea that can pull the nitrogen it needs from the atmosphere. However fixing atmospheric nitrogen requires significant energy, so nitrogen fixing organisms are relatively rare in nature. Thus it will take some engineering to create an ecosystem that can get the nitrogen it needs from the air, but at least the raw material is readily available.
Phosphorus is the Key Nutrient
So that leaves only phosphorus as the nutrient needed in the largest quantity that is 'missing' in the open ocean. In nature this element comes from either dust blowing off the land, or from sediment from the bottom (churned up by ocean currents or carried into the oceans by rivers). Missing phosphorus is the key reason why most of the ocean is not already teaming with photosynthesis. It is also the primary 'cost' of large scale ocean farming because phosphorus is the primary nutrient that isn't already present 'on site' in the open ocean.
Seaweed Farm Logistics
Large seaweed farms have the potential to be low cost.
The open ocean already has MOST of the raw materials needed either in the seawater or in the atmosphere (the primary exception being phosphorus), and the needed energy comes from 'free' sunlight.
If the goal is to sequester carbon, doing that is as 'easy' as simply allowing some of the seaweed to sink to the bottom, where it will be sequestered. Thus there is no transport costs associated with 'harvesting' or sequestering.
In the limit, the main cost is transporting the phosphorus fertilizer. Like with all fertilizers you get a good 'bang for your buck' as 1 ton of phosphorus yields 106 tons of negative carbon (by the way since seaweed is about 90% water, that one ton of phosphorus yields over 1000 tons of seaweed, and we NEVER had to haul that weight anywhere. This is an important reason why this kind of carbon sequestration is inexpensive.
Where do we get the Phosphorus?
Getting Phosphorus fertilizer for a seaweed farm is pretty much the same as getting it for land-based farming. There are four main possibilities.
Grinding up phosphorus-bearing rock - this is how we get it for the fertilizer you have probably bought at the hardware store. This is a finite resource (but we are not in danger of it running out any time soon), and is moderately expensive.
Solids from sewage treatment plants - The food humans eat are living things and thus contain phosphorus (and nitrogen), and that ends up as 'bio-solids' that are sometimes used to fertilize land crops. It could just as easily be used to fertilize seaweed.
From ocean sediment - When living things die in the ocean, they sink to the bottom and the resulting sediment contains phosphorus. Dredging and transporting sediment would work.
From deeper in the ocean - When plankton dies, a small fraction of it is not recycled by life near the surface and VERY SLOWLY sinks to the bottom. Thus as you descend in the ocean, nutrient levels actually go up. By pumping this water up, you an bring these nutrients where they can be used.
The good news is that we have options on where to get it.