Multiphase drilling systems and methods

1. A method for drilling a wellbore, comprising:

injecting drilling fluid through a drill string disposed in the wellbore;

rotating a drill bit disposed on a bottom of the drill string, wherein:

the drilling fluid comprises a liquid and a gas,

the drilling fluid is injected at the surface,

the drilling fluid exits the drill bit and carries cuttings from the drill bit, and

returns comprising the drilling fluid and the cuttings flow to the surface via an annulus formed between the drill string and the wellbore; and

drilling through at least a portion of a non-productive formation, wherein an injection rate of at least one of the liquid or the gas is controlled so that an equivalent circulating density (ECD) of the returns is equal to or slightly greater than a stability equivalent mud density (EMD) of the formation.

2. The method of claim 1 , wherein the liquid is injected at a rate so that a liquid velocity of the returns in the annulus is sufficient to transport the cuttings.

3. The method of claim 1 , wherein the injection rate of the at least one of the liquid or the gas is controlled so that the ECD of the returns is substantially less than a pore EMD of the formation.

4. The method of claim 1 , wherein a liquid volume fraction of the drilling fluid at standard temperature and pressure is greater than or equal to 0.01 and less than or equal to 0.07.