Multi-walled carbon nanotube (MWCNT) and graphene nanoplatelet reinforced thermoplastic poly(lactic acid) (PLA) biodegradable nanocomposites were designed and prepared using solution casting techniques. The prepared biodegradable polymers are expected to provide an environmentally friendly alternative to petroleum-based polymers. Both nanocomposite systems exhibited better thermal stability and improved mechanical performance over the unreinforced polymer exhibiting excellent strength and degradability. The addition of graphene nanofiller in varied amounts was aimed to enhance the thermal and mechanical properties of the nanocomposites even further and incorporate the outstanding characteristics of graphene nanoplatelets into the nanocomposites. The polymeric nanocomposites showed also superior advantages for oil drilling relevances, automotive lubricating purposes, membrane technology and food packaging. Scanning electron microscopy images indicated a homogeneous dispersion of the nanofiller within the polymeric matrix at low filler loadings and a cluster formation at higher loadings that could be responsible for the polymeric matrix movement restrictions. The enthalpy of mixing (the polymer and the nanofiller) measured could explain the cause of the repulsive interactions between the nanoparticles and the polymeric chains, which created an additional excluded volume that the polymeric segments were restricted to occupy, thus forcing the conformational characteristics of the polymeric chains to deviate away from those of the bulk chains. The prepared polymeric nano composites (poly lactic acid carbon nano tube and poly lactic acid graphene nanoplatelets) were utilized in the formulation of oil-base mud as a viscosifier. The rheological, filtration properties and electrical stability of the oil based mud formulation with the new polymeric nanocomposite were studied and the result compared to the oil-based mud formulation with commercial viscosifier.