I believe that you will need more area for your collector..
Quote..
Home Air Conditioning
"However, if your air conditioning needs are for more than a few hours at a time, this approach will soon lose its effect. Gradually, the soil underneath the basement floor will warm up. Since it is a finite volume of soil (basically the size of the house), once it has all warmed up, the cooling effect would be greatly reduced, until an extended period of non-use occurred so the soil could again cool back down. Anyone who has tried to cool their house in this way has noticed the reduction in cooling effect over time."