Experiments versus theory for the initiation and propagation of radial hydraulic fractures in low-permeability materials

We compare numerical predictions of the initiation and propagation of radial fluid-driven fractures with laboratory experiments performed in different low-permeability materials (PMMA, cement). In particular, we choose experiments where the time evolution of several quantities (fracture width, radius, and wellbore pressure) was accurately measured and for which the material and injection parameters were known precisely. Via a dimensional analysis, we discuss in detail the different physical phenomena governing the initiation and early stage of growth of radial hydraulic fractures from a notched wellbore. The scaling analysis notably clarifies the occurrence of different regimes of propagation depending on the injection rate, system compliance, material parameters, wellbore, and initial notch sizes. In particular, the comparisons presented here provide a clear evidence of the difference between the wellbore pressure at which a fracture initiates and the maximum pressure recorded during a test (also known as the breakdown pressure). The scaling analysis identifies the dimensionless numbers governing the strong fluid-solid effects at the early stage of growth, which are responsible for the continuous increase of the wellbore pressure after the initiation of the fracture. Our analysis provides a simple way to quantify these early time effects for any given laboratory or field configuration. The good agreement between theoretical predictions and experiments also validates the current state of the art hydraulic fracture mechanics models, at least for the simple fracture geometry investigated here.