In the current global scenario, safe disposal of waste is a major challenge, so numerous subsurface waste disposal methods are used. However, they risk resulting in leachate formation. This leachate produced from toxic waste materials leaks into the groundwater resulting in its contamination. For the decontamination of groundwater, it is therefore important to understand the behaviour of such plumes in porous media. Many studies have been performed on finding dispersion coefficient, sorption behaviour, etc., but not much work has been done on understanding plume morphology and its extent of spread. The objective of the current study is to quantify the leakage profile of a contaminant in a saturated porous medium. Here, we use cesium nitrate as our solute for the experiments which is a major contaminant, generated from nuclear waste. This experimental investigation focuses on the length and volume of the plumes and our results show that their developments exhibit power law behaviour on time. Our experiments are performed with different permeability, solute concentration, and volumes. Results from this work are expected to help us better understand the problem of nuclides transport.