I know most growers would not advise growing citrus by seed but I have rooted several varieties of citrus seeds in peat with the baggie method (tangerines, blood oranges, regular oranges, limes, lemons, pumellos, kumquots, etc). The seeds need to be peeled first. In answer to your question, however, the following link gives some tips on hydroponic citrus growing:
http://forums.gardenweb.com/forums/load/hydro/msg1102465920401.html

Hi Baci,

Thanks!

Here is a picture of my moro orange:
{{gwi:1009217}}

Thanks for the reference link. Its a bit short on specifics, since I don't know the keywords. Based on my reading, it says:

1. Hydroponics works for citus.
2. The best media appears to be one that is fairly coarse and free draining, which is irrigated with nutrient solution fairly regularly.
3. The hydroponic citrus trees seem to prefer the hydroponic nutrient to soil.
4. Pumice, expanded clay, coconut fiber, and fine gravel, would work.

Mark

Your tree looks very healthy - the blood oranges have the best taste. There is not much concrete information online regarding hydroponic citrus growing. Those pictures that I found were of young trees  not fruit bearing ones. It was unclear to me as to whether the young trees were being raised hydroponically and being later placed in soil during the fruiting stage. Some of my neighbors grow dwarf citrus varieties in pots, however, & have had good success although limited quantities of fruit.

It is difficult to find concrete growing information on hydroponics online because of all the sales material. You might consider looking at soil based information and adapt that to hydroponics. Some of the state and federal universities have good information on growing - Texas A & M has some information on growing citrus for your state.

If I find more information I will post it.

>>>At the present, I'm thinking about using modified platic trash barrels with perlite/gravel for medium. I suspect I could use a 'Dutch Pot' scheme, but may misunderstand the concept.Check out http://www.alabamahydroponics.com/GH/plans/hydropots.htm

The man who runs this site also sells some of the parts to make the hydropots if you can't find them locally. He also sells very inexpensive hydro fertilizer ($6 for 100 gallons). His main focus is on Do-It-Yourself which I appreciate. Most hydro stuff is over priced considering the materials that go into them.