Limit equilibrium analysis of drilling mud loss into an inclined natural fracture

A theoretical model is presented for the worst case scenario of drilling mud loss when an inclined wellbore intersects an arbitrarily oriented natural fracture. The fracture is assumed to have a constant aperture and be bounded by rigid walls. The ultimate invasion profile when cessation of mud flow eventually occurs is solved based on limit equilibrium conditions. Effects of the fluid yield stress and the wellbore and fracture orientations upon the mud loss behaviors are analyzed. In the special case when a horizontal natural fracture is intersected by a vertical wellbore, our analysis shows that the commonly used late time limit solution for radial flow of a yield stress fluid needs to be revised. Excellent agreement is achieved when our theoretical solution is compared with experimental data in the literature in determining the fluid yield stress based on the ultimate invasion radius. The theoretical model can also be applied to provide the lower bound estimates of the fracture aperture and permeability based on the mud loss data from the field.