A proper wellbore stability analysis is necessary to avoid trespassing the limits of mud weight window especially in off-shore drilling. Wellbore strengthening is a mechanism to enable safe and cost-effective drilling operation by means of increasing the fracture pressure of the rock. This paper presents a model illustrating the relationship between wellbore strengthening and HPHT filtration for different permeabilities. Data were collected from previous experiments on shale and sandstone cores to increase fracture pressure by utilizing calcium-based, iron-based nanoparticles (NPs) and graphite in oil based mud. A differential evolution algorithm was used to find a poly-variate, polynomial model for breakdown pressure increase and HPHT fluid loss reductions for different permeable media. Sensitivity analysis were done to test the robustness of the results of the model and to reduce uncertainty. Based on the results, filtration reduction is dominant parameter on wellbore strengthening. The correlation shows permeability has a limited influence on increasing fracture pressure. By decreasing filtration using calcium-based and iron-based NPs in drilling fluid, fracture pressure increase in both high and low permeable formations.

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