The invention concerns a computer implemented method for underbalanced drilling. In one embodiment, the method includes determining a plurality of gas injection rate versus bottom hole pressure curves for a plurality of liquid injection rates for a specified minimum and maximum gas injection rate and a minimum and maximum liquid injection rate. Next, the method determines a set of four interception curves including a minimum motor equivalent liquid rate interception curve, a minimum vertical liquid velocity intercept curve, a minimum horizontal liquid velocity intercept curve, and a maximum motor equivalent liquid rate intercept curve for a specified minimum and maximum mud motor rate range and a minimum horizontal and vertical annulus velocity.