Viscoelastic Stress Relaxation for Estimating Shmin Magnitude in Deep Sedimentary Formations
Authors: Mandal P. P. , Sarout J. , Rezaee R. , Finkbeiner T. 
Published: September 2022

ABSTRACT:
General adaptability of viscoelastic stress relaxation from laboratory time-dependent deformation (creep) measurement to derive the least principal stress Shmin magnitudes at depths in sedimentary rocks is proposed. It is based upon a simple viscous rheological model and steady-state tectonic strain loading. Creep data reveals different viscoelastic behavior of rocks mostly controlled by the varying mineral composition and the direction of creep measurement (perpendicular/parallel to the bedding plane). First, this approach is applied in a vertical drilled well then verify in another vertical well located in the Canning Basin where the target resources are ultralow permeable unconventional gas shale reservoirs. A continuous Shmin magnitude profile at depth is obtained from wireline logs through the following: (i) combination of laboratory power-law fitting coefficients, (ii) geological horizontal stress accumulation by constant tectonic loading, and (iii) relatively uniform stress variation of principal stress components (Equation) along with depth. Eaton’s extended model could not capture the stress layering effect precisely and may introduce more uncertainty because of its dependency on several unpredictable parameters while the proposed rheology model relies upon laboratory constituent parameters (B, n) where B is the inverse of static Young’s modulus E and n describes time dependency of rock deformation under a given stress.

1. INTRODUCTION
Realistic estimation of least principal stress Shmin magnitude at depth in sedimentary rocks has significant importance in underground mining, exploration, and extraction of petroleum, and geothermal resources. In-situ stresses are accumulated over large geological time scale through physio-chemical, thermal, and mechanical processes (Kumar et al., 2018) . Accurate Shmin profile at depth assist in efficient hydraulic fracturing design and constrain fracture growth beyond the zone of interest in ultra-low permeable gas shale reservoirs. In petroleum reservoirs, the Shmin is directly measured by mini-frac, leak-off test (LOT) and diagnostic fracture injection test (DFIT) while in the mining field, the measurements of horizontal stress components are relying upon overcoring or hydraulic fracturing method (Heidbach et al., 2016; Kumar et al., 2018). These methods provide a reasonable Shmin value at a particular depth but are limited to the target depth. Petrophysical logs are routinely deployed to build a continuous profile of stress magnitudes along the well path following calibration with direct field measurement. Eaton’s method and its modified version are commonly utilized in deriving stress magnitudes in sedimentary rocks (Eaton, 1969; Thiercelin and Plumb, 1994). The original Eaton’s method considered that the horizontal stress Sh originated from instantaneous gravitational loading of vertical stress Sv and a linear relationship is proposed between vertical and horizontal stresses assuming a linear isotropic elastic medium (Equation 1).