• porothermoelasticity;
  • anisotropy;
  • hydraulic fracturing;
  • analytical solution


In this study, the effects of the temperature difference between hydraulic fracturing fluid and rock formation on the time-dependent evolution of fracture width were investigated using a newly derived one-dimensional anisotropic porothermoelastic analytical solution. The solution is shown to correctly reproduce existing solutions for special cases and corrections for an earlier publication are provided. An analysis of time-dependent fracture width evolution using Woodford Shale data was also presented. It was found that when the fracturing fluid has the same temperature as the shale formation, the fracture gradually closes back after the initial opening due to the invasion of the fracturing fluid. Practically, in this scenario, proppants should be pumped into the fracture as soon as possible to obtain maximum fracture conductivity. On the other hand, with a fracturing fluid 60 °C colder than the formation, the thermal contraction of the rock dominates the fracture aperture evolution, resulting in a fracture aperture approximately 70% larger than that produced by the hotter fracturing fluid. Consequently, in this case, it is beneficial to delay proppant placement to take advantage of the widening fractures. Finally, it was found that the fracture aperture is directly controlled by the spacing of natural fractures. Therefore, the presence of natural fractures in the shale formation and their spacing influence not only the type of hydraulic fractures created but also what kind and size of proppants should be used to keep them open. Copyright © 2013 John Wiley & Sons, Ltd.