An integral equation was developed to predict the critical parameters (fracture width and length) associated with the propagation of a vertical hydraulic fracture and a numerical solution procedure was developed. The effects of the classical approximations of pressure and fracture width were investigated both separately and together. It was found that the effects associated with the pressure approximation were relatively insignificant, whereas those associated with the fracture width approximation were significant, particularly when the formation was only moderately permeable. Finally, an exact closed-form solution of the integral equation was developed for a special case. It was shown that when the formation is only moderately permeable, this solution provides a better approximation of the exact solution than the classical solution of Carter [2].

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