Quantification of Uncertainties of Fracture Permeability Via Mud Loss Information and Inverse Stochastic Modeling

Abstract

Summary This study provides rigorous quantification of uncertainties associated with fracture permeability estimation obtained through stochastic inverse modeling of mud losses recorded while drilling. Fracture characterization is performed in terms of fracture width estimation and is grounded on a stochastic inverse modeling technique. Implementation of the latter rests on a well-defined set of parameters, including drilling fluid, rheological properties, flow rates, pore and dynamic drilling fluid pressure, wellbore geometry. These quantities are generally affected by diverse sources of uncertainty. Drilling mud is modeled as a Herschel–Bulkley fluid. Open fractures are treated as horizontal planes intersecting the wellbore and a simple analytical solution is employed to express mud flow advancement in the fracture as a function of drilling fluid properties and operational conditions. A modern global sensitivity analysis approach is employed to quantify the way uncertain model parameters affect fracture aperture (hence permeability) and extent. Uncertainty propagation from input parameters to model outputs is investigated and quantified through a workflow implemented within a Monte Carlo framework. It is then employed in the context of stochastic inverse modeling of field cases to evaluate posterior probability densities of fracture aperture and to simulate drilling fluid invasion in fractures in quasi-real time during drilling.