1. . 
An oil-based mud in which the activity, or vapor pressure, of the brine phase is balanced with that of the formations drilled. Although long shale sections may not have a constant value for vapor pressure, aw, the oil mud will adjust osmotically to achieve an "average" aw value. Dynamic (autopilot) balance of mud salinity and drilled shales is maintained because as water moves into or out of the mud, it also moves out of or into the shale. As water transfer continues during drilling, the mud's water phase will be either diluted or concentrated in CaCl2 as needed to match the average aw value of the shale section and cuttings exposed to the mud.
Reference: Chenevert ME: "Shale Control With Balanced-Activity Oil-Continuous Muds," Journal of Petroleum Technology 33, no. 11 (November 1970): 1370-1378.