It seems like a lot of water. 56k square miles is bigger than Lake Superior and Lake Huron combined.

yes but how deep is it?

I don't think it has to be very deep to be a problem. If you're talking about flooding an area the size of the state of Iowa to a depth of several inches, and then replacing the huge amount of water that evaporates every day, you're talking about water use on a scale that is mind boggling. We're already having trouble getting enough fresh water to irrigate the crops we already grow.

Profitable algae to biofuels has not been accomplished. It is like solar photovoltaic cells and making electricity. It can be done but is not practical or profitable on a large scale compared to more competitive power generation. Cellulosic ethanol is so far from profitable it might bankrupt any nation attempting to convert to it.

One idea I saw took advantage of the fact that algae only needs around 1/10th of the amount of sunlight to grow, the rest causing the algae to need agitating to bring the algae which has not been exposed to the surface up and submerge the stuff on the top that has had its dose of sunlight.

That takes energy, and makes the process expensive.

the idea is simply to pipe the sunlight in with optic cables in the right amount, so you would have a building with several levels, each with tanks of algae, and each would get the correct amount of sunlight and would simply need skimming to harvest, and then drying.

Doing things indoors would also reduce evaporation.