With the design charts presented here, and nothing more elaborate than aslide rule, it is possible to predict the dimensions of either a linearly or aradially propagating, hydraulically induced fracture around a wellbore.


During the hydraulic fracturing treatment of an oil or gas well the liquidpressure in the borehole is increased until tensile stress in the surroundingrock exceeds tensile strength. Once a tensile fracture is initiated, it ispenetrated by liquid from the borehole and fracture propagation undercontinuous hydraulic action takes place. The fracturing liquid carries apropping agent to ensure a highly permeable flow propping agent to ensure ahighly permeable flow channel after pressure release. Field results range fromfailure to obtain increased production to outstanding success. In all cases, production to outstanding success. In all cases, however, it unfortunatelyremains uncertain whether the values chosen for the operational parameters, such as injection rate, pumping time and fluid viscosity, were in fact theideal ones. Though experience provides a lead, a more satisfactory way topredict results would seem to be the subject the fracture propagation processto a theoretical analysis that (1) makes the maximum use of the relevantphysical information and (2) so simplifies the resulting calculations that thefield engineer gets practical data that he can handle comfortably.

We areattempting here to do this in connection with the prediction of fracture widthand areal extent before pressure release. What remains of the fractureafterwards depends on the distribution of the propping agent between thefracture walls, and that is a propping agent between the fracture walls, andthat is a separate story.

Idealization of the Problem

To keep the problem tractable, a number of simplifying assumptions have hadto be made:

  1. The formation is homogeneous and isotropic as regards those ofits properties that influence the fracture-propagation process.

  2. Thedeformations of the formation during fracture propagation can be derived fromlinear elastic stress-strain relations.

  3. The fracturing fluid behaves like apurely viscous liquid; i.e., any peculiar flow behavior due to the addition ofgelling agents or other additives is neglected. Moreover, the effect of thepropping agent distribution on the distribution of fluid viscosity in thefracture is not taken into account.

  4. Fluid flow in the fracture is everywherelaminar.

  5. Simple geometric fracture-extension patterns are assumed - eitherradially symmetrical propagation from a point source (Fig. 1A) or rectilinearpropagation originating from a line source (Fig. 1B). In the first case theperiphery of the fracture is circular, in the second case it is rectangular.

  6. A rectilinear propagation mode can be accomplished only by injection over alarge perforated interval, thus forming a line source.

Such a rectilinearfracture must therefore be located in the vertical plane. A circularpropagation mode might be expected from injection through propagation modemight be expected from injection through a narrow band of perforations. Thisforms a point source.


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