Abstract
We applied a hybrid-dimensional flow model to pressure transients recorded during pumping experiments conducted at the Reiche Zeche underground research laboratory to study the opening behavior of fractures due to fluid injection. Two distinct types of pressure responses to flow-rate steps were identified that represent radial-symmetric and plane-axisymmetric flow regimes from a conventional pressure-diffusion perspective. We numerically modeled both using a radial-symmetric flow formulation for a fracture that comprises a non-linear constitutive relation for the contact mechanics governing reversible fracture surface interaction. The two types of pressure response can be modeled equally well. A sensitivity study revealed a positive correlation between fracture length and normal fracture stiffness that yield a match between field observations and numerical results. Decomposition of the acting normal stresses into stresses associated with the deformation state of the global fracture geometry and with the local contacts indicates that geometrically induced stresses contribute the more the lower the total effective normal stress and the shorter the fracture. Separating the contributions of the local contact mechanics and the overall fracture geometry to fracture normal stiffness indicates that the geometrical stiffness constitutes a lower bound for total stiffness; its relevance increases with decreasing fracture length. Our study demonstrates that non-linear hydro-mechanical coupling can lead to vastly different hydraulic responses and thus provides an alternative to conventional pressure-diffusion analysis that requires changes in flow regime to cover the full range of observations.
Highlights
Estimation of a reservoir’s effective hydraulic properties requires a consistent analysis of experimentally determined pressure and flow transients (Muskat and Wyckoff 1937; Fetter 2001)
We focused on one data set of each group, the transient pressure response Map obtained from hydraulic tests at 51.6 m borehole depth, representing the pressure-plateau group, and Mat corresponding to tests conducted at a borehole depth of 24.6 m, representative for the pressure-tangent group, before we used the gained knowledge about the existence of a local error minimum to reduce the computational costs of the numerical fitting procedure for the remaining data sets by focusing on parameter combinations resulting in low error values
We numerically modeled the opening characteristics of fractures during in-situ hydraulic tests using a hydromechanical flow model implemented for radial fractures with non-linear contact mechanics and without leak-off
Summary
Estimation of a reservoir’s effective hydraulic properties requires a consistent analysis of experimentally determined pressure and flow transients (Muskat and Wyckoff 1937; Fetter 2001). Simple analytical models for pressure-diffusion have been applied when their intersection with boreholes classified them as axial or radial (Matthews 1961; Matthews and Russell 1967; Horne 1995; Bourdet et al 1989). Analytical models based on solutions of the diffusion equation for constant flow-rate tests document distinct differences in pressure response for onedimensional and radial flow associated with axial and radial fractures, respectively. Rocks with a dense array of randomly oriented fractures may justify their treatment as porous media, leading to radial flow, too. The full range of responses can be addressed by regarding the dimension of the flow to be a parameter (Barker 1988).
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