A geomechanical model is presented to characterize the flow of solid-laden fluids into pre-existing penny-shaped fractures. The model incorporates the impacts of the fluid leak-off, fracture deformability, fluid rheology, and the solid content of the fluid in a coupled manner. Mathematical derivations pertaining to the different elements of the model are presented. The model yields a coupled system of non-linear partial differential equations (PDEs), which is solved using an implicit finite difference scheme. The developed solution enables simulating the impact of the solid content of the fluid in plugging of fractures. It is shown that formation of a plugged zone can significantly affect the rate and depth of fluid invasion in fractures. In fact, it can be shown that for fluids which are heavily loaded with solids (e.g., drilling fluids), it is necessary to consider the impact of the fracture plugging effects on the fluid invasion problem. Sensitivity analyses were conducted to investigate the impact of the solid concentration, filtration rate, and borehole overpressure. The results show that a higher solid concentration will result in a faster plugging of the fractures, and thereby lower volume of fluid invasion in fractures. This study confirms that solid plugging of fractures requires a minimum level of leak-off volume, and no effective fracture plugging is expected in impermeable formations. From a practical standpoint, the developed model may be used in well construction applications to avoid severe lost circulation problems in fractured formations.

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