Commercial hydraulic fracture software are generally based on the planar 3D model (PL3D) or the Pseudo 3D model (P3D). The PL3D model is more accurate but very CPU intensive, which makes it unsuitable to simulate complex hydraulic fracture networks due to the interaction with natural fractures. The pseudo-3D model is faster but considers separately the vertical and horizontal propagation of the fractures. In recent years, a sophisticated P3D-based complex hydraulic fracture network model, the Unconventional Fracture model (UFM) was developed that can simulate complex physical mechanisms such as interaction with natural fractures, stress shadow and the proppant placement in the complex fracture network. However, one of the main challenges still faced by such simulators is to accurately predict the height growth in formations with heterogeneous mechanical and stress properties.

One assumption of the P3D model is the fracture is being initiated and extended in a lower stress layer than the adjacent layers. In practice, the assumption is not always satisfied, leading to inaccurate or unstable height growth. A comparison of these two models through examples illustrates the situations where P3D model works well and where it does not, and the difficult compromise between accuracy and computational efficiency.

A better compromise can be achieved through a new Stacked Height Growth model (SHG). This model is an enhancement to the P3D model, consisting of multiple rows of elements vertically stacked, to more precisely account for the effect of vertical stress heterogeneity, and to allow multiple horizontal propagation fronts. The width profile and stress intensity factors at the top and bottom depend on the stress and pressure profiles along the stack of elements. The theoretical background of the model is presented. Comparison shows good agreement with the PL3D model for cases that the P3D model cannot accurately simulate, and at a fraction of the computational cost of PL3D. A particularly interesting feature of the SHG model is its flexibility to transition smoothly from a 1D cell-based model such as the P3D model, to a fine scale 2D gridding in the fracture plane. This feature greatly facilitates the implementation of other modeling features into the fracturing simulator.

For example, the SHG model can be used to simulate interaction of hydraulic fractures with Multi-layer Discrete Fracture Networks (MDFN), to better model naturally fractured reservoirs. The SHG model can also be used to model offsets of hydraulic fractures through weak interfaces called ledges. The model can capture the influence of these discontinuities on the proppant placement. Another example, is how a fine 2D gridding using the SHG model can predict proppant placement as accurately as a PL3D model. These extensions of the SHG model have been implemented into the UFM model and are illustrated in this paper through several examples.

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