I have started working on the above mentioned model, I would like if someone can guide me on this, how to pursue this modelling by use of some kind of software.
For a 3-D numerical model, you can model groundwater hydraulics with MODFLOW. Then, that output can be used to model contaminant transport with MT3DMS. Both models are freely available from USGS. However, it is advisable to use a GUI to operate the models. Commercial software for this exists. For example, GroundwaterVistas. The licenses are expensive, though. USGS offers some free operating software (MODELMUSE), but they won't be as easy as commercial GUI (but free!). Check out USGS website: https://water.usgs.gov/nrp/software.php