Accurate prediction of the least principal stress at depth can improve the efficiency of hydraulic fracturing design and mitigate the risk of unnecessary vertical growth of fractures beyond the reservoir interval. Here, we demonstrate that a viscoelastic stress relaxation model can predict the variation of the least principal stress in a vertical well of the Perth Basin. Creep response of clay- and carbonate-rich shales have been recorded in the laboratory for a duration of ~ 6 hours under simulated in-situ stress conditions. A simple power-law captures the primary creep response, and an empirical relationship is established between the inverted creep parameters. To compute the least principal stress magnitude at depth, we combined gravitational loading, horizontal tectonic stress accumulation at a predefined loading rate via the viscoelastic rheology, and uniformity of the relative stress magnitude along depth, with the necessary wireline log curves (Fig.1). The derived stress magnitude matches well the Instantaneous shut-in pressure (ISIP) stimulation data from hydraulic fracturing in the field. Finally, it is shown by performing a 3-dimensional planar hydraulic fracture simulation through Baker Hughes's MFrac that stress layering can either act as a fracture barrier or a propagator, depending upon the differential stress contrast between layers.

1. Introduction

Accurate estimation of the magnitude of the least principal stress Shmin across lithological layers has paramount importance in petroleum or deep mining exploration. Artificial fractures can be generated by fluid injection when the fluid pressure Pf overcomes the magnitude of Shmin, which is defined as hydraulic fracturing (HF). In unconventional gas shale reservoirs, discontinuity in the Shmin profile with depth can either inhibit or promote the vertical propagation of a hydraulic fracture from the producing reservoir interval into adjacent layers. In this context, multiple researchers (Ma and Zoback, 2017; Singh et al., 2019; Sone and Zoback, 2014b; Xu et al., 2019) reported a correlation between the changes in the least principal stress value with depth and the variations in the composition of lithological layers. The often reported geological heterogeneity of gas shale reservoirs is a source of additional complexity when attempting to identify the actual root causes of these variations. Sone and Zoback (2014b) first proposed a viscoelastic model for the estimation of the principal horizontal stress in a vertical well in the Barnett shale formation. Their model can mimic the observed downward propagation of hydraulic fractures in the limestone formation below the perforated interval, driven by a lower magnitude of Shmin in that layer. Mandal et al. (2021a) recently evaluated several possible mechanisms to explain such behavior in the Goldwyer shale formation, e.g., contrast in frictional strength properties, viscoelastic stress relaxation, change in pore pressure. Because the creep rate is a key ingredient for estimating the variation in magnitude of Shmin with depth using viscoelasticity, additional laboratory investigations have been initiated focusing on creep measurements in clay- and carbonate-dominated gas shales under constant axial stress load.

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