Viscous relaxation model for predicting least principal stress magnitudes in sedimentary rocks

We propose a new method for estimating stress magnitudes as a function of depth in sedimentary formations based on a laboratory constrained viscous rheology and steady tectonic loading. We apply this method to a well drilled in the Barnett shale in the Fort Worth Basin, Texas. Laboratory experiments show that shale gas reservoir rocks exhibit wide range of viscoplastic behavior mostly dominantly controlled by its composition. Stress relaxation in these formations is described by a simple power-law (in time) rheology. We demonstrate that a reasonable profile of the principal stress magnitudes can be obtained from geophysical logs by utilizing (1) the laboratory power-law constitutive law, (2) an estimate of the horizontal tectonic loading, and (3) the assumption that the ratio of principal stress differences ([S2−S3]/[S1−S3]) is relatively uniform with depth. Profiles of the principal stress magnitudes generated based on our proposed method for a vertical well in the Barnett shale generally agree with the occurrence of drilling-induced tensile fractures in the same well. Also, the predicted decrease in the least principal stress (fracture gradient) in the limestone formation underlying the Barnett shale appears to explain the downward propagation of hydraulic fractures observed in this region. This stress change is not captured by the extended Eaton (instantaneous loading) model even when incorporating formation anisotropy. We believe our approach is more consistent with the time-dependent processes associated with stress accumulation over the course of geological time and thus may provide a new method to predict vertical hydraulic fracture growth in targeted reservoirs.