Real-time analysis of drilling mud loss data is an effective tool to characterize the size, distribution and permeability of natural fractures. The estimated properties of natural fractures can then be used to modify the drilling fluid properties and design remedial mud loss treatment to stop further drilling fluid loss. Moreover, characterization of natural fracture provides crucial information for the design and application of reservoir stimulation operations. In this paper, we present a theoretical model to simulate the invasion of the drilling fluid into natural fractures. Mathematical modelling was performed for two types of rheology constitutive models which are commonly used for drilling fluids, namely Bingham Plastic and Herschel-Bulkley. The fluid leak-off into the formation is modelled using Carter's model. Moreover, a simplified local elasticity equation is used for the fracture width variation due to fluid pressure. A forward finite-difference numerical scheme is used to solve the pressure drop equation. The developed model is then validated against well-known analytical solutions and numerical simulations. Parametric studies were conducted to evaluate the impact of the fracture deformability, formation leak-off properties, drilling fluid rheology, and the pore fluid contribution. Finally, the output of the developed model is compared with the field data of a welldocumented mud loss incident. The obtained results indicate that the incorporating the effect of the fluid leak-off may significantly increase the rate of mud loss volume. Therefore, for highly permeable formations (such as carbonates), considering the impact of the fluid leak-off effect seems necessary for a realistic characterization of the mud loss problem. Fracture deformability affects the mud loss volume, with higher deformability leading to a larger mud loss volume. Also, the numerical results confirmed that the rate and magnitude of mud loss volume is significantly affected by the rheological properties of the drilling fluid, in particular the yield stress. In contrast, the effect of pore fluid seems relatively negligible for typical formation fluid types. Comparing the results of our simulation with mud loss field data shows that the developed model can accurately predict the rate and total volume of mud loss into the fractures. Moreover, it shows that incorporating the impact of the fluid leak-off and the fracture stiffness may significantly affect the fracture width prediction. Therefore, these factors should be considered to obtain an accurate estimate of the natural fracture aperture.

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The propagation path of hydraulic fracture is significantly affected by the properties of cemented natural fractures (i.e., veins), such as, stiffness, tensile and shear strength, and flow characteristics. Moreover, the magnitude of stress anisotropy can control the results of hydraulic fracture crossing or diverting into the vein. To study the effect of vein properties and the differential stress on the interaction of hydraulic fractures with mineral-filled veins, we employed a three-dimensional (3D) Discrete Element Method (DEM) model which couples the fluid flow and the bonded-particle assembly. The hydraulic fracture interaction with the vein was investigated by monitoring the bond breakages and measuring the fracture diversion distance along the vein before kinking back into the rock matrix. Numerical results are in good agreement with the fracture diversion results from the published experimental and numerical SCB tests of Marcellus shale with calcite-filled veins. The propagating hydraulic fracture is more likely to divert into the veins with smaller approach angle. Increasing the differential stress leads to fracture crossing than diversion into the vein. For veins with greater stiffness than the host rock, microcracks were generated in the vein before the hydraulic fracture intersected it. For tight formations with stiffer veins, the vein permeability did not have much influence on the fracture diversion result since the damage induced by the stress concentration ahead of the hydraulic fracture tip dominated the fluid flow in the vein.

Wellbore strengthening (WBS) offers enabling technology for wells that are drilled in geological environments with a narrow drilling margin. Through its deployment, costly lost circulation events may be avoided, casing setting depths may be extended, and, in optimum cases, deeper targets may be reached with a reduced or slimmed-down casing program.The elevation of the fracture gradient offered by WBS is a complex issue that involves the growth of fractures in permeable or impermeable rocks using non-Newtonian drilling fluids that are laden with solids of varying types and sizes. Several plausible (and sometimes contradictory) models have been proposed historically to explain the WBS phenomenon, and the only way to assess the correct explanation is through dedicated experimentation. In this paper, an experimental technique to study WBS under realistic conditions is introduced, and the results of a series of larger-scale fracturing experiments using this technique are presented.The experimental set-up described here consists of a dual flow-loop/ pressure-intensifying system to carry out high-pressure borehole fracturing tests on cylindrical rock samples while maintaining continuous circulation of the drilling fluid within the borehole. The system offers full control over pore pressure, radial confining pressure and, if desired, independent axial pressure. Several injection cycles are performed to characterize the values of the fracture initiation pressure (FIP) and fracture propagation pressure (FPP) and thereby characterize WBS effects. Typical experimental variables included: the type of base fluid (water-based, oil-or synthetic-based), the concentration, type, and particle size distribution (PSD) of lost circulation materials (LCMs) used to achieve WBS effects, and the type of rock tested (sandstone and shale, i.e. permeable and impermeable rock media). Additionally, post-fracturing techniques such as thin-section analysis were employed to study the fracture geometry and deposition structure of plugging solids on the fracture surfaces.The experiments clearly show that for any rock with a given set of rock strength and failure parameters, there is an optimum PSD for maximizing WBS effects. Optimum PSD appears to be of primary importance, almost irrespective of LCM type. The results furthermore show that although a minimum concentration of LCM bridging agents is required for effective WBS, FPP does not increase significantly for concentrations above a certain upper threshold value. Moreover, increasing the injection volume during WBS squeeze treatments above a threshold value may actually lead to lower FPP values. All of these findings have important implications for field application of WBS treatments. In addition, petrographic imaging of the fracture after testing show that fracture plugging occurs in the proximity of the fracture tip and not close to wellbore face, in direct support of the Fracture Propagation Resistance (FPR) model of WBS, and in disagreement with Wellbore Stress Augmentation/ Stress Cage mode...