Obtaining accurate knowledge of variations in the magnitude of the least horizontal principal stress, S_hmin, with depth is of great practical importance in the oil and gas industry. We demonstrate that accurate knowledge of the magnitude of S_hmin with depth can be obtained utilizing two fundamental concepts. First, frictional faulting constraints place bounds on principal stress magnitudes in relatively stiff (high Young’s modulus) rocks. These bounds depend on depth, pore pressure and whether a site is characterized by a normal, strike-slip or reverse faulting stress state. Second, in more ductile clay-rich formations such as those typical of most US unconventional plays, varying degrees of viscoplastic stress relaxation (VSR) reduces differences between principal stress magnitudes. We focus in this paper on the importance of how layer-to-layer variations of lithology control the magnitude of S_hmin and how the two concepts above can be used to accurately predict variations of the magnitude of S_hmin with depth. It is well established that the effectiveness of multistage hydraulic fracturing is critical to stimulate production in unconventional oil and gas reservoirs. Using several case studies, we illustrate how predictable variations of stress magnitude with depth affect hydraulic fracture propagation. We also demonstrate that widely used elastic loading models do not accurately predict variations with depth. In the context of VSR, essentially complete stress relaxation also helps explain occasional observations of the least principal stress being nearly equal to the overburden stress in some clay-rich formations. In such cases, sub-horizontal hydraulic fracture propagation is expected due to the low tensile strength of bedding planes.

• We review several case studies that document lithology-dependent variations of S_hmin magnitude with depth. These layer-to-layer stress variations, sometimes as large as 10 MPa (~1500 psi), have a profound effect on hydraulic fracture propagation.
• To create continuous estimates of the magnitude of S_hmin with depth, we present a methodology that combines the concept of frictional failure equilibrium in relatively stiff formations with that of viscoplastic stress relaxation in more ductile formations.
• We demonstrate how quantitative estimates of S_hmin magnitude with depth obtained using the concept of viscoplastic stress relaxation significantly improves prediction of hydraulic fracture propagation.
• We demonstrate that this approach yields more accurate estimates of S_hmin magnitude than commonly used elastic loading stress prediction methods.
• We illustrate cases of near-complete stress relaxation (meaning that the three principal stresses become co-equal). In the absence of stress control, hydraulic fracture propagation occurs along weak, sub-horizontal bedding planes.

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