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It's a column similar to a packed column used in process engineering. Some books of chemical engineering processes can give you all you need for your question.
The question is kind of open ended. It would be easier to answer if you could mention if you are trying to work on metals, anions, organics or bulk parameter like BOD,COD.
If you are trying to work on natural soil be sure to quantify Hydraulic conductivity, bulk density and fraction of organic component of the natural soil and let the porosity of the material be not altered while packing in.
A antigravity/upward flow reactor might be desirable