A method and system for drilling a wellbore is described. The system includes a wellbore with a variable density drilling mud, drilling pipe, a bottom hole assembly disposed in the wellbore and a drilling mud processing unit in fluid communication with the wellbore. The variable density drilling mud has compressible particles and drilling fluid. The bottom hole assembly is coupled to the drilling pipe while the drilling mud processing unit is configured to separate the compressible particles from the variable density drilling mud. The compressible particles in this embodiment may include compressible hollow objects filled with pressurized gas an configured to maintain the mud weight between the fracture pressure gradient and the pore pressure gradient. In addition, the system and method may also manage the use of compressible particles having different characteristics, such as size, during the drilling operations.