Estimation of fracture normal stiffness using wellbore pressure recovery

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SUMMARY Fractures are ubiquitous in Earth’s upper crust and strongly affect its physical properties. Their visibility for elastic waves hinges on their stiffness, a measure of the relation between changes in fracture aperture and applied stress, which itself significantly increases with increasing stress according to laboratory data. We constrained normal stiffness (and its stress dependence) of two fractures intersecting a borehole in the research mine ‘Reiche Zeche’ in Freiberg, Saxony, Germany, from pressure-recovery behaviour observed when the pressure in a double-packer interval enclosing them was briefly released during shut-in sequences. For the evaluation of the pressure recovery, we developed a generic model that accounts for the inherent convolution of mechanical closing of the fracture, fluid flow in the fracture, fluid exchange between fracture and the surrounding rock, here addressed as fracture leakage, and effects associated with finite borehole storage. We address the hydraulic system by considering three different ‘storage containers’, described by non-dimensionless storage parameters: the wellbore with a fixed storage capacity, the fracture with storage capacities related to fluid compressibility and fracture stiffness, and the surrounding rock constituting a container with unlimited storage capacity. To examine the model’s characteristics, we investigated pressure transients predicted for specific cases, such as negligible fracture leakage, and subsequently numerically determined the sensitivity of the model predictions to the involved model parameters. The model’s application to the field data yield estimates of properties of the fractures (length, aperture and stiffness) and of the surrounding rock mass (product of permeability and specific storage capacity). The parameters derived from the modelling compare well with independent constraints. An analysis of currently available fracture-stiffness data shows that the lack of knowledge of the stress dependence of stiffness severely hampers firm conclusions on scale dependence and the bias between methods.