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.

我们将混合维度流动模型应用于在 Reiche Zeche 地下研究实验室进行的泵送实验期间记录的压力瞬变，以研究由于流体注入而导致的裂缝张开行为。确定了两种不同类型的对流速阶跃的压力响应，它们从传统的压力扩散角度代表径向对称和平面轴对称流态。我们使用径向对称流动公式对裂缝进行数值模拟，该公式包括控制可逆裂缝表面相互作用的接触力学的非线性本构关系。这两种类型的压力响应可以同样好地建模。敏感性研究揭示了裂缝长度和正常裂缝刚度之间的正相关性，这在现场观察和数值结果之间产生了匹配。将作用法向应力分解为与整体断裂几何形状和局部接触的变形状态相关的应力表明，几何引起的应力贡献越大，总有效法向应力越低，断裂越短。分离局部接触力学和整体断裂几何对断裂法向刚度的贡献表明几何刚度构成总刚度的下限；它的相关性随着裂缝长度的减少而增加。