Fracturing a subsurface formation based on the required breakdown pressure accounting for filter cake

A method for fracturing a formation, the method comprising:

• drilling a wellbore into the formation;
• measuring a time-dependent permeability and a time-dependent thickness of a filter cake formed by a first drilling mud;
• determining a time-dependent permeability model based on the measured time-dependent permeability of the filter cake;
• determining a time-dependent thickness model of the filter cake based on the measured time-dependent thickness of the filter cake;
• measuring a permeability of the formation;
• selecting a breakdown pressure model based on (i) the time-dependent thickness of the filter cake, (ii) the time-dependent permeability of the filter cake, and (iii) the permeability of the formation;
• using the selected breakdown pressure model to predict the breakdown pressure of the formation, wherein using the selected breakdown pressure model comprises using the time-dependent thickness model of the filter cake and the time-dependent permeability model of the filter cake in the breakdown pressure model;
• determining a critical mud weight based on the predicted breakdown pressure;
• and
• pumping a second drilling mud into the wellbore to fracture the formation, the second drilling mud having a mud weight within 10% of the critical mud weight.