Natural fractures are oftentimes not orientated in the direction of in-situ principal stresses. When developing naturally fractured reservoirs, the complex fracture network is affected by the shear stresses acting on the fracture surfaces. In some rare cases, the main fracture may not align with the principal stresses. Under such circumstances, shear stresses and displacements during fracture closure will impact the overall conductivity, especially for acid fracturing treatment, where flow paths are supported by the roughness of unevenly acid-etched fracture walls.

In this paper, we present a new approach to model acid fracture conductivity by allowing combined normal and shear loading on fracture walls. The closure of rough surfaces is modeled as elastic deformation of asperities. The model considers the mechanics of asperity contacts and statistical descriptions of interface roughness and asperity contact orientation for shear slippage between asperities. A numerical simulation algorithm is implemented to evaluate the fracture displacement under complex loading conditions. The overall conductivity is then obtained from numerical simulation based on deformed fracture apertures. The model was validated with the experimental observation under normal closure condition. A parametric study was carried out to evaluate the rock mechanical properties and fracture geometries on the conductivity behavior of acid fracturing.

Modeling results show that the interface closure behavior can be significantly affected by the asperity contact orientations. If slipping among asperities is considered, larger deformations during fracture closure are observed from simulation comparing to results from conventional fracture closure models based on summit-to-summit asperity contact. Sensitivity analysis indicates that the overall conductivity of a fracture depends on mechanical properties of the rock, distribution of asperity contact orientation, and shear loading conditions.

The new approach proposed in this paper provides access to acid fracture conductivity estimation under various in-situ stress conditions and fracture orientations. This model can be helpful in evaluating fracture treatment in reservoirs with natural fractures or complex subsurface structures.

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