Impact of capillary pressure on micro-fracture propagation pressure during hydraulic fracturing in shales: An analytical model

The presence of micro-fractures in shale reservoirs is vital for economic production. While a number of models have been proposed to predict the propagation pressure of pre-existing micro-fractures, few models have considered capillary pressure, which may play a significant role in the presence of micro-fractures with nano-scale width. In this study, a new model was developed to predict the propagation pressure of micro-fractures. It is assumed that pre-existing micro-fractures are arbitrarily intersected with the propagated hydraulic fractures. The model was derived based upon linear elastic fracture mechanics under the condition of mode I fracture propagation coupled with capillary pressure. Furthermore, this paper also conducted sensitivity analyses to predict the micro-fracture propagation pressure as a function of the contact angle, surface tension and the width of micro-fracture. The results demonstrated that decreasing the contact angle reduces the propagation pressure of micro-fractures, implying that a hydrophilic system may yield a lower fracture propagation pressure compared with the hydrophobic counterpart. Moreover, for a hydrophilic system, further decreasing the contact angle shifts the propagation pressure to a negative value, implying that the capillary pressure may induce the propagation of micro-fractures without external fluid injection. The propagation pressure is also affected by the surface tension and the width of micro-fracture.