Vertical hydraulic fractures, used to enhance the release of natural gas, can reach thousands of feet in length, while extending only a few hundred feet in height. When a payzone is bounded above and below by zones which have a substantially higher minimum in-situ stress, conditions are optimal for restricting a fracture's vertical growth. By theoretically calculating the height and shape of a fracture, our goal is to study how well higher stress zones adjacent to a blanket payzone confine the vertical growth.

Previously we presented a model1  for fracture expansion which assumed an elliptical fracture perimeter. The fracture height was determined by applying at the wellbore a fracture mechanics criterion, involving a critical stress intensity factor. When this criterion is applied to all points of the fracture perimeter, the entire fracture shape may be determined. This is the approach of this paper. As it turned out, the elliptical fracture shape gave a reasonable approximation for height and bottomhole pressure, and the previous model was able to predict, by way of a parameter study, fracture height growth in a variety of likely situations.

The effects of leakoff, previously neglected, are now included.

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