Type curves for circular uniform-flux fractures in unbounded single-layer reservoirs were presented in the literature several decades ago. Unfortunately, these results have restricted validity since the simple uniform-flux inner-boundary condition will cease to be physically meaningful when significant boundary effects from the top and bottom of the formation start to affect the data. This is especially important for large fractures in formations of limited thickness. For horizontal fractures it is therefore important to include finite conductivity as part of the fracture model. Solutions addressing these issues are presented in this paper along with examples highlighting effects of different modeling options. The solutions include both compressible and incompressible flow inside the fractures.
The solutions have also been extended to multi-layer reservoirs through a decoupling approach, with both unbounded and bounded circular models used in examples. Solutions for layered reservoirs are important because layering is common with obvious effects on productivity and because layering can create unusual pressure-transient characteristics during buildups if there are shale streaks or other low-permeability flow barriers between layers acting as partially sealing boundaries.
Horizontal fractures are becoming more important due to an increasing number of shallow-depth disposal wells, for instance as part of carbon capture and storage developments. Shallow gas developments with fracturing needed to obtain sufficient productivity are also adding to the importance of these fracture models. Both for producers and disposal wells, layering will be an issue and has to be addressed.