Method is provided for drilling of formations containing carbonate minerals with flexible tubing capable of being turned in a very short radius. The very flexible tubing may be placed inside a work string in a well with coiled tubing and a micro-jet bit on the tubing be diverted to a selected direction and depth. Acidic drilling fluid pumped through the micro-jet bit allows high rates of drilling with hydrochloric acid. A slip joint between coiled tubing and the flexible tubing may be used to allow jet drilling without movement of the coiled tubing and use of a jet bit with forward-facing jets. Mixing of acid and base solutions downhole may be used to provide hotter acid solutions for drilling.