Quantitative analysis of factors influencing vertical and lateral fracture growth

This paper presents contributions to the modeling of the vertical and lateral propagation of hydraulic fractures. The first part presents a method for the quantitative analysis of factors controlling vertical height growth in three-dimensional (3D) fracture propagation. Included are confining stress contrast, elastic stiffness contrast, fracture toughness, and influence of settled (or buoyant) proppant on height growth. A composite propagation function was formulated that can be implemented in a pseudo-3D model of fracture geometry or in hand calculations. The second part extends the formulations of the lumped models for lateral fracture growth to handle dynamic conditions existing in the field. The new formulation can handle variable injection rates, fluid rheology changes, and multiple fluids and includes fracture toughness at the tip. The results are presented in the form of dimensionless charts, and their use is explained through an example.