A Comparison of the Theories for Predicting Width and Extent of Vertical Hydraulically Induced Fractures

Abstract

Prediction of fracture dimensions during propagation of a hydraulically induced fracture for well stimulation is essential for the design of a stimulation treatment. During the past decade much effort has been spent on the development of a suitable theory for this purpose. Since neither the length nor the width of a hydraulically induced fracture can be measured in situ during a field treatment, this is primarily a mental exercise in applied mechanics. The main measurable quantities that are directly related to the fracture propagation process are the total volume of fracturing fluid injected into the reservoir and the time required to accomplish this. Not surprizingly, various authors have arrived at different theories, depending on the assumed conditions prevailing downhole. In this paper, the assumptions underlying the various theories currently in use for the prediction of fracture dimensions, viz., those of Perkins and Kern, of Nordgren, of Geertsma and De Klerk and of Daneshy, are compared. Rather than take issue for one particular theory, which appeared impossible because none of the theories is perfect, the paper shows what the various theories have in common, where and why they differ from each other and what the practical consequences are in case of application to treatment design.