The article presents technical approach to keeping preset differential pressure on the formation in the course of well foam washing, developed on the basis of field hydrodynamic research. The authors have developed an advanced technology of removing argillo-arenaceous plugs from the well bottomhole in the conditions of the abnormally low pressure, defined boundary conditions for keeping depression in the "well- formation" system in the process of removing argillo-arenaceous plugs with the use of a coiled tubing unit and offered a mathematical model and suitable software for defining pressure and foam velocity in all elements of the circulation system.