If you do a couple of searches it will yeald some good info.
Now to the question, A plenium is a water void under the sand bed. It is created by placing eggcrate (used with florescent lighing) and a screen over it to keep sand from filling the space. It covers the tank bottom less an inch or so around the edges. The sand it 4 inches thick and the space 1 inch.
The grain size of the sand is recommended to be 1-4 MM ranging more toward the bigger particles. The reason for this is better water movement.
The water movement comes form the differences in the ORP (Oxygen Redox Potential) levels. Sory I don't know my chemistry to properly explain it but is is basically measuring oxygen. (Don't flame me for the answer I know it isn't right just type in the correct answer if you care.) Tank water has a + number and the Oxygen depleted sand bed has a - number. So the water moves from + to -. The purpose of the plenium is that the plenium still has a - value but less then the sand above it thus not making a "nutrient sink". A "nutrient sink" is when it only captures waste and builds it up which will eventually release back into the tank.
The people for it say it is suposed to be a more efficient form of nitrate reduction as compared to a DSB. This is where the debate starts and where I will leave it.
How does a DSB differ you may ask? A DSB is 4 inches thick but has a smaller grain size. Depending on who you ask it should be .2-1 MM. A DSB also has life in it keeping it clean. A plenium will also have some life but a DSB place an emphasis on it as benificial and a plenium says it can be harmful.
The differences in the process of a plenium and DSB are as such. The people for a plenium believe that there are 3 levels of bacteria. High O2, Reduces O2, and finally no O2. A plenium will allow for reduced O2 areas and DSB will not. The debate is wheather the O2 is good or not. More to the debte but my fingers are getting tired so do the search
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I was giong to use a plenium but decided not to because of the ratio of DSB to Plenium tanks. More DSB tanks and they are really sucessful. Both systems reduce nitrates and both systems seam to work. There are some scientific questions that were raise about the plenium that have not been answered well enough for me. So until they are it is a DSB for me.
I really hope this answered you question. If not ask me to clarify.