Tensile Failure and Fracture Width of Partially Permeable Wellbores with Applications in Lost Circulation Material Design

Estimation of near-wellbore fracture widths remains central to designing the particle size distribution (PSD) and composition of lost circulation material (LCM) blends. Although elastic rock models are often used for this purpose, they fall short in capturing the substantial effect of pore fluid pressure on the fracture width. The problem is addressed in this paper by incorporating the poroelastic back stress in width estimation of axial fractures nearby an inclined wellbore. The poroelastic back stress is caused by a nonideal drilling fluid filter cake allowing for fluid pressure communication between the wellbore and pore space of the rock surrounding the wellbore. In this aspect, a proper definition of the filter-cake efficiency is made in terms of the wellbore pressure, far-field pore fluid pressure, and pore fluid pressure of the rock surrounding the wellbore. The value of this parameter is estimated from the standard drilling fluid filtration test results, as well as the formation rock permeability. The filter-cake efficiency is next used to develop the long-time, asymptotic analytical solution for the poroelastic stress of an inclined wellbore. By accounting for the obtained poroelastic back stress, an improved estimation of the wellbore tensile limit that depends on the filter-cake efficiency parameter is developed. For wellbore pressures beyond the wellbore tensile limit, the width of the near-wellbore fractures is estimated. The fracture width estimation is made through an analytical, dislocation-based fracture mechanics solution to the integral equation describing the nonlocal stress equilibrium along the fracture faces. The commonly practiced scheme for geometric design of LCM blends is enhanced by using the presented improvement in estimation of the near-wellbore fracture width. A case study is used to demonstrate the substantial effect of drilling fluid filtration properties and the resulting poroelastic back stress on the wellbore tensile limit, estimated fracture width, and consequently, composition of the recommended LCM blend.