Drilling depleted reservoirs is often encountered with a host of problems leading to increase in cost and non-productive time. One of these faced by drillers is lost circulation of drilling fluids which can lead to bigger issues such as differential sticking and well control events. Field applications show that wellbore strengthening effectively helps reduce mud loss volume by increasing the safe mud weight window. Wellbore strengthening applications are usually designed based on induced fracture characteristics (i.e., fracture length, fracture width and plug location within fracture). In general, these fracture characteristics depend on several parameters, e.g., in-situ stress magnitude, in-situ stress anisotropy, mechanical properties, rock texture, wellbore geometry, mud weight, wellbore trajectory, pore pressure, natural fractures, formation anisotropy and among others. Analytical models available in the literature oversimplify fracture initiation and propagation process with assumptions such as: isotropic stress field, no near wellbore stress perturbation effects, vertical or horizontal wells only (no deviation/inclination), constant fracture length and constant pressure within the fracture. For more accurate predictions, different numerical methods, i.e., finite element, boundary element, etc., have been utilized to determine fracture width distribution. However these calculations can be computationally costly or hard to implement in near real time. The aim of this study is to provide a fast running, semi-analytical workflow to accurately predict fracture width distribution and fracture re-initiation pressure (FRIP). The algorithm and workflow can account for near wellbore stress perturbations, far field stress anisotropy, and wellbore inclination/deviation. The semi-analytical algorithm is based on singular integral formulation of stress field and solved using Gauss-Chebyshev polynomials. Proposed model is computationally efficient and accurate. The model also provides a comprehensive perspective on the formation strengthening scenarios; a tool for improved LCM design and how they are applicable during drilling operation (in particular through depleted zones). Sensitivity analysis included in this paper quantifies the effect of different rock property, in-situ stress field/anisotropy and wellbore geometry/deviation on the fracture width distribution and FRIP. Additionally, the case study presented in this paper demonstrates the applicability of the proposed workflow in the field.

Drilling depleted reservoirs often encounters a host of problems leading to increases in cost and nonproductive time. One of these problems faced by drillers is lost circulation of drilling fluids, which can lead to greater issues such as differential sticking and well-control events. Field applications show that wellbore strengthening effectively helps reduce mud-loss volume by increasing the safe mud-weight window. Wellbore-strengthening applications are usually designed on the basis of induced-fracture characteristics (i.e., fracture length, fracture width, and stressintensity factor). In general, these fracture characteristics depend on several parameters, including in-situ stress magnitude, in-situ stress anisotropy, mechanical properties, rock texture, wellbore geometry, mud weight, wellbore trajectory, pore pressure, natural fractures, and formation anisotropy. Analytical models available in the literature oversimplify the fracture-initiation and fracturepropagation process with assumptions such as isotropic stress field, no near-wellbore stress-perturbation effects, vertical or horizontal wells only (no deviation/inclination), constant fracture length, and constant pressure within the fracture. For more-accurate predictions, different numerical methods, such as finite element and boundary element, have been used to determine fracture-width distribution. However, these calculations can be computationally costly or difficult to implement in near-real time. The aim of this study is to provide a fast-running, semianalytical work flow to accurately predict fracture-width distribution and fracture-reinitiation pressure (FRIP). The algorithm and work flow can account for near-wellbore-stress perturbations, far-field-stress anisotropy, and wellbore inclination/deviation. The semianalytical algorithm is modeled after singular integral formulation of stress field and solved by use of Gauss-Chebyshev polynomials. The proposed model is computationally efficient and accurate. The model also provides a comprehensive perspective on formation-strengthening scenarios; a tool for improved lost-circulation-materials design; and an explanation of how they are applicable during drilling operation (in particular, through depleted zones). Sensitivity analysis included in this paper quantifies the effect of different rock properties, in-situ-stress field/anisotropy, and wellbore geometry/deviation on the fracture-width distribution and FRIP. In addition, the case study presented in this paper demonstrates the applicability of the proposed work flow in the field.