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Frequently, net treating pressures (pressure in excess of closure stress) observed during hydraulic fracturing, are significantly greater than what is predicted by industry fracturing simulators. Elevated net pressures have been attributed to various fracture tip phenomena some of the more popular of these being:

  1. high fracture toughness,

  2. "dry zone," a zone near the fracture tip where injected fluid is excluded,

  3. non- linear or inelastic effects resulting in dilation or reduced fracture widths.

A study of the above effects on fracture widths and pressures was conducted for symmetric radial ("penny") fractures. A rigorous solution method was developed which permitted characterization of the extent of a "dry zone" and it's effect on width and pressure. Results indicated that the size of this zone is largely controlled by the pressure within the zone and by the pressure gradient of the injected fluid that is next to it. Therefore, conditions which promote large pressure gradients such as high viscosity, large moduli and high injection rates, also created larger "dry zones." However, the width and pressure near the wellbore were found to be essentially independent of the size of the "dry zone."

The effects that dilatant behavior, possibly caused by plasticity or micro cracking, might have on elevating fracturing net pressures was simulated using an approximate inelastic solution. This solution method modifies the elasticity equation by a "stiffening" function to effectively reduce the width such that the greatest relative reduction occurs near the crack tip. Net pressures and widths near the wellbore can be considerably greater than those obtained with the elastic solution (widths are still greater even in those cases where toughness is elevated to match the net pressure). Bottom hole pressure data was obtained during extensive fracture testing of shales/mudstones in the North Sea. A radial fracturing model simulating inelastic conditions, was found to better predict fracturing pressure responses than its elastic counterpart.


During the last 40 years, tremendous strides have been made in developing hydraulic fracturing simulation models to help facilitate the economical exploitation of oil and gas reservoirs. Even with the development of sophisticated pseudo and planar 3-D fracturing simulators, there still are questions as to their reliability in modeling the hydraulic fracturing process. Frequently, net pressures (injection pressure minus closure stress) observed during fracturing treatments are considerably larger than predicted by current models [1–6]. The exact causes of these elevated pressures are not known, but are generally thought to be crack-tip related phenomena. A brief discussion of three proposed tip phenomena follows:

  1. Elevated fracture toughness (elevated in that the toughness required to match the observed pressure can be significantly higher than those measure by laboratory test) [8–10]. Shlyapobersky, et al. [1–2]interpreted high net pressures observed during field tests, as support for the existence of elevated fracture toughness.

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