One implementation of the disclosure provides a computer implemented method for underbalanced drilling. The implementation may include determining an initial 2D UBD operation envelope based on a set of initial operating points for a selected TVD or time, displaying the initial 2D UBD operation envelope on a computer display, providing at least one data point representing actual data from a well, determining at least one actual UBD operation point using the at least one data point and displaying it on the computer display along with the 2D UBD operation envelope, selecting an optimization parameter, determining a set of optimized operating points based on the optimization parameter, and displaying the set of optimized operating points on the computer display along with the 2D UBD operation envelope.