The paper presents three-dimensional numerical model for multiple fracture propagation from the horizontal wells. A 3D numerical model is developed using a combination of the displacement discontinuity method and the finite element method. The reservoir rock mass is assumed homogenous, isotropic, and linear elastic. The fluid flow inside the fracture is assumed laminar flow and the fluid follows Newtonian behavior. The Galerkin’s finite element approach is used for the fluid flow modeling, the rock mass deformation is simulated using the elastic displacement discontinuity method, and the crack tip displacement approach is implemented for mixed-mode fracture propagation. Details of mathematical formulations and methodology for numerical implementation are presented first. Then, the numerical model is verified with some known analytical and semi-analytical solutions. Finally, numerical examples of planar and non-planar multiple fracture propagation in case for sequential and simultaneous fracturing procedure in the Niobrara Chalk formation have been presented. The results demonstrate the effects of in-situ stress, rock and fluid properties, and the "stresses shadowing" effect which mainly depends on the spatial interval between the fractures plays a critical role in the multiple fracture propagation.


Horizontal well fracturing is applied to improve well productivity from lower quality reservoirs that could not have been economically developed using the conventional fracturing methods. The idea of simulation by hydraulic fracturing is to create a large volume of fractured rock with enhanced permeability with multistage fracturing. The multi-stage fracturing is carried out either in simultaneous or sequential manner from perforation clusters. In case of simultaneous fracturing, the multiple fractures are created and propagated at same time from clusters, whereas in case of sequential fracturing, the fractures are created from one cluster after another usually by keeping the previously created fracture either propped or pressurized with fluid [1].

Several numerical models have been presented to study multiple and multistage fracturing from the single and multiple horizontal well. Most are based on analytical stress analysis method [2, 3], semi-analytical method [4], 2D numerical fracture mechanics models [1, 5] or planar 3D model [6]. Stephen et al. [7] have presented a 3D model based on boundary element method for simultaneous propagation of multiple fractures from a single horizontal well. In this paper, we present a 3D boundary element model with capabilities to simulate any number of fractures in case of simultaneous or sequential propagation schemes from a single or multiple horizontal wells. The main emphasis have been given to evaluate the influences of induce stresses change or "stress shadowing" effect on the multiple fracture propagation.

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