Investigations into the opening of fractures during hydraulic testing\n using a hybrid-dimensional flow formulation

We applied a hybrid-dimensional flow model to pressure transients recorded\nduring pumping experiments conducted at the Reiche Zeche underground research\nlaboratory to study the normal opening behavior of fractures due to fluid\ninjection. Two distinct types of pressure responses to flow-rate steps were\nidentified and numerically modelled using a radial-symmetric flow formulation\nfor a fracture that comprises a non-linear constitutive relation for the\ncontact mechanics governing reversible fracture surface interaction. These two\ngroups represent radial-symmetric and plane-axisymmetric flow regimes from a\nconventional pressure-diffusion perspective. A comprehensive parameter study\ninto the sensitivity of the applied hydro-mechanical model to changes in\ncharacteristic fracture parameters revealed an interrelation between fracture\nlength and normal fracture stiffness that yield a match between field\nobservations and numerical results. Fracture stiffness values increase with\ncorresponding fracture length. Decomposition of the acting normal stresses into\na stresses associated with the deformation state of the global fracture\ngeometry and the contact stresses indicates that geometrically induced stresses\ncontribute the more the lower the total effective normal stress and the shorter\nthe fracture. Separating the contributions of the local contact mechanics and\nthe overall fracture geometry to fracture normal stiffness indicates that the\nlatter, the geometrical stiffness, constitutes a lower bound for total\nstiffness; its relevance increases with decreasing fracture length, too. Our\nstudy demonstrates that non-linear hydro-mechanical coupling can lead to vastly\ndifferent hydraulic responses and thus provides an alternative to conventional\npressure-diffusion analysis that requires changes in flow regime to cover the\nfull range of observations.\n