Lost circulation material (LCM) is commonly used to stabilize formations and inhibit fluid losses from the wellbore during drilling. Mud loss records and wellbore downhole image logs often reveal existence of multiple natural and drilling-induced fractures in the wellbore vicinity. Appropriate particle size distribution (PSD) for the LCM blend should be designed so that lost circulation from all near-wellbore fractures is contained.

This paper presents a novel design scheme for multi-modal PSD of LCM blends applicable to the likely cases of lost circulation from multiple near-wellbore fractures. The design scheme takes advantage of an analytical solution which estimates the fracture widths of an arbitrary number of fractures around inclined wellbores when subjected to the three principal stresses of the subsurface. The LCM blend design involves dividing the blend into subcategories of various sub-blends sizes. Each sub-blend has distinct particle size distribution, when combined, satisfying the size distribution criteria on the quantile distribution basis. The fractures apertures widths, which are a crucial input for LCM blend selection, are determined from an analytical solution of the related wellbore geomechanics problem. The solution is derived from the dislocation-based formulation of fracture opening profile in an infinite poroelastic medium. The effects of overburden stress, anisotropic horizontal stresses, wellbore inclination and azimuth as well as the mechanical interaction between the cracks are incorporated in the analysis. Further, a systematic method to characterize mud cake parameter is employed. Mud cake efficiency is shown to cause considerable influence on fractures aperture width and consequent composition of the LCM blend.

A synthetic study case mimicking typical depleted sand drilling environments is used to determine the optimal LCM blend design. The poroelastic back-stress effect is considered in the test cases, suggesting substantial changes in fracture initiation pressure and fractures apertures compared to the corresponding elastic solution. Furthermore, the sensitivity of fractures widths to geomechanical parameters is analyzed. The results indicate an interesting interaction between fractures as they induce a compressive hoop stress on one another, limiting the width growth of other fractures. Consequently, the multi-fracture wellbore problem introduces a variation in fraction width, thus causes different LCM sub-blend recommendations tailored to individual fractures. A combination of these sub-blends, each of which only covering a narrow range of fracture width, suggest a novel treatment of fluid loss in multi-fractured wellbore by forming a super-blend which covers the whole range of width distributions.

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