Stress determination from hydraulic fracturing tests: the system stiffness approach

Hydraulic fracturing tests with mud is the most inexpensive method for determining the minor in situ horizontal stress in deep petroleum wells. This paper presents a unified model of pump-in/shut-in and pump-in/flowback tests. The key element of the model is the system stiffness resulting from the stiffness of the fluid volume pressurised, and the stiffness due to the fracture. It is shown that the change in system stiffness at fracture closure is observed in both kinds of tests. The model is used directly in the design and interpretation of the flowback tests, where direct measurement of pressure versus flowback volume, and hence system stiffness is possible. However, the model also predicts the time development of pressure, and suggests methods for the analysis of the pressure versus time curve for both flowback and shut-in tests. We argue that the character of the pressure versus time curve in a shut-in test with mud may be significantly influenced by the low permeability of the mud cake which is formed on the face of permeable formations. This invalidates the traditional interpretation procedures, making new analysis methods outlined in the paper necessary for a successful interpretation of such tests. The model calculations are supported by extensive field data from offshore Norway.