Appendix 1: The different stress profile scenarios
See Figs. 16, 17, 18, 19.
Fig. 16 Stress profile scenario # 1 (base case).
Fig. 17 Stress profile scenario # 2.
Fig. 18 Stress profile scenario # 3.
Fig. 19 Young’s modulus profile
See Figs. 20, 21, 22, 23.
Fig. 20 Frac design optimization.
Fig. 21 Fracture profile assuming rock mechanic model scenario # 1 (base case) and medium proppant size (16–20).
Fig. 22 Fracture profile assuming rock mechanic model scenario # 2 and medium proppant size (16–20).
Fig. 23 Fracture profile assuming rock mechanic model scenario # 3 and medium proppant size (16–20).
Matrices and vectors involved in Eq. (3) are defined as follows:
In which Ω is the domain and Np, Nu are pressure and displacement shape functions, respectively, and can be defined as follows:
where nx, ny are the x, y components of unit normal vector to the boundary.
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Azim, R.A. & Abdelmoneim, S.S. J Petrol Explor Prod Technol (2013) 3: 21. https://doi.org/10.1007/s13202-012-0038-6
Local grid refinement, it is a widely used expression for the process of dividing one or several grids in the reservoir model into smaller sized grids allowing enhanced grid definition, which is useful for modeling wells or hydraulic fractures and other complex reservoir structures
Department of Energy, governmental department whose mission is to advance energy technology and promote related innovation in the United States
Tailored pulse fracturing
Employed to control the extent and direction of the produced fractures by the ignition of precise quantities of solid rocket fuel-like proppants in the wellbore to create pressure ‘pulse’ which creates fractures in a more predictable pattern
Using foam under high pressure in gas reservoirs. It has the advantage over high-pressure water injection because it does not create as much damage to the formation, and well cleanup operations are less costly
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