Abstract: A steam generator for producing steam in a confined space such that it can be positioned in a borehole for use in secondary and tertiary recovery of hydrocarbons. Fuel is injected axially into a combustion chamber having a reduced orifice in the bottom thereof and oxygen is introduced tangentially from a plurality of ports in the top of the combustion chamber to create a stable vortex flame. A portion of the walls of the combustion chamber are formed from a porous, sintered stainless steel cylinder through which water is pumped to cool the walls of the chamber and to form steam. The combustion products are mixed with a water mist in a steam generating section to form steam.