We investigated numerically, the fracturing process for an infill multi-fracture horizontal well (MFHW) using the indirect boundary element method. Our code initially involved the constant 2D displacement discontinuity method (DDM), the higher-order 2D HDDM, and the 2D HDDM+ (involving square root tip elements) numerical schemes, all of which were validated against the analytical solution of Sneddon and Elliot (1946). The improved accuracy and computational efficiency obtained using the 2D HDDM and 2D HDDM+ numerical schemes led to further enhancement of the simulator by the introduction of higher-order elements in the 3D space.

To the authors’ knowledge, this is the first application of the higher-order 3D HDDM to hydraulic fracture modeling since the original development of the method by Shou et al. (1997). The proposed method results in a more accurate estimation of the fracture width than the standard constant 3D DDM method, while preserving the same number of degrees of freedom. Our 3D HDDM method can neglect, without loss of accuracy, the dip-slip shear stress and the displacement components, thus improving the computational efficiency of the method.

The associated fluid mechanics accounts for the pressure drop along the wellbore and across perforations to accurately predict the pressure and fluid flow rate distribution within each fracture. The nonlinear fluid mechanics equations were discretized by the finite difference method and iteratively coupled with the simplified 3D-DDM. The developed numerical scheme was validated against the Perkins-Kern-Nordgren (PKN) (Perkins and Kern, 1961; Nordgren, 1972) and Khristianovic-Geertsma-de Klerk (KGD) (Khristianovich and Zheltov, 1955; Geertsma and de Klerk, 1969) analytical models.

We adopted the analytical solution of Economides and Nolte (2000) that depends on the local DDM results to obtain the fracture width distribution across multiple reservoir layers. Additionally, our simulator implements the fracture height growth methodology suggested by Li (2019).

We conducted simulation studies of non-planar propagation of five simultaneously-induced fractures with variable spacing. Our simulator accurately predicts the fluid flow, pressure, and width distribution within each fracture, and can be an effective tool in the decision-making process of fracturing design in unconventional reservoirs.

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