A two-scale model is developed to characterize drilling mud flow in fractured formations. At the microscale the flow in the fractures is modelled as a viscous fluid. A Darcy flow is used to the equation for the matrix, which is assumed to hold on the macroscopic scale. The mud leak-off from the fracture surface into the formation is quantified by reducing dimensionality and type of flow in the fractures. The case of a complex fracture network is generated with the aim of considering a more practical engineering phenomenon. By selecting appropriate asymptotic functions to locally enrich the conventional finite-element approximation space, the position and direction of the fractures is independent from the underlying simulation elements. Several parametric studies are presented to demonstrate the distribution of fracture aperture and the effect of mud leak-off on the fluid invasion depth and mud loss volume. It is shown that the mud loss volume may be significantly influenced by the multi-scale distribution of the fracture aperture and leak-off effect. It is also shown that consideration of fracture networks and mud leak-off effect can significantly improve the accuracy of the mud loss prediction, and thereby results in a more realistic characterization of naturally fractured reservoirs.

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