Analysis of Intra-Reservoir Stress Variations in Shale Gas Reservoirs Based on the Variation of Viscoelastic Properties

We studied the time-dependent deformation of various shale gas reservoir rocks through laboratory triaxial creep experiments. Upon stepwise loading of axial differential stress, samples exhibit instantaneous elastic deformation followed by time-dependent creep behavior. The total elastic and creep strain response is approximately linear against the applied differential stress which evokes a linear viscoelastic behavior against differential stress. We find that the total strain response can be expressed by a power-law creep compliance function, e=Btⁿ, where B and n are characteristic constitutive parameters. B and n range between 0.015-0.06 [GPa^-1] and 0.01-0.08, respectively, thus viscoelastic behavior of these rocks vary significantly between and within reservoirs. Using linear viscoelasticity, we attempt to obtain a profile of horizontal stress difference along a vertical well from Barnett shale assuming a simple tectonic loading history. The profile of B along the well was estimated from sonic logs and the profile of n was estimated from an empirical relationship between B and n we observed from Barnett shale samples. Results suggest that the horizontal stress difference along the well can vary by up to 10 MPa within the shale reservoir, consistent with fluctuations in stress difference inferred from observations of wellbore failures in the same well.