Fracture Gradient Prediction using a characteristic effective stress relationship

A relationship between the effective horizontal stress and the effective vertical stress in a rock was determined in this study. With the known relationship, the fracture gradient was obtained. An exponential relationship was assumed as existing between the stresses, and by mathematical manipulation the relationship was recast into a form which relates overburden stress to pore pressure by use of the Terzaghi`s stress equation. Solution to the derived equation gave values of the constants of proportionality, from where the value of the minimum stress was obtained. This value was then used to obtain the fracture gradient by application of the Hubbert and Willis fracture principle. The result obtained, when tested with data from West Texas wells, compares with those obtained from the conventional methods of Eaton, and Mathews and Kelly.