Mechanical analysis of idealized shallow hydraulic fracture

The characteristics of hydraulic fractures created at shallow depths are known from excavations and borings, but this understanding has lagged behind the ability to predict fracture growth. This paper describes a simple analysis based on elasticity theory and fracture mechanics that will predict characteristics of shallow hydraulic fractures that are relatively flat lying. The analysis gives closed-form expressions for the injection pressure, fracture aperture, and radial length as functions of time, fracture toughness, and elastic modulus. The analysis is first used to estimate fracture toughness and elastic modulus of shallow formations from field tests of hydraulic fracturing. Those parameters are used to calibrate the model and predict the growth of fractures. The average relative error of the predictions is about 20% and increases with the dip and degree of asymmetry of the fracture.