These are the datasets and modeling information for the future publication, "Adsorption Modeling and Experiments on Novel Materials to Remove Ammonia and Heavy Metals from Aquaponic Systems and Wastewater." This data is from the research performed on adsorbent materials successfully removed dissolved metals from aquaponic environments. Combined with data optimized using MINEQL+, a multitude of conditions were examined to determine the best operating range of zeolites, silica gel, activated carbon, and arcillite to absorb the bioaccumulating ions of ammonium and nickel in aqueous solutions. After reaching steady-state conditions, the data were fitted successfully to a Freundlich isotherm model.