Impact of stress-dependent Young's moduli on hydraulic fracture modeling

Hydraulic fracturing simulators currently model rocks as linear elastic materials with a linear stress-strain relationship. Although many formations do behave in a linear elastic manner when fractured, other soft rocks have been studied in triaxial and plane-strain compression tests that show a highly stress-dependent Young's modulus even at low strain levels. Fundamental stress-strain relationships for fracture design and the importance of distinguishing between the tangential and secant Young's modulus are discussed. Various stress-strain constitutive models are presented for nonlinear elastic and elastic-plastic behaviors of materials. The first order impact of a stress-dependent Young's modulus on the fracture geometry and pressure behavior is discussed. Various examples of stress-dependent Young's modulus are presented that illustrate the importance of including non-linear stress-strain behavior in hydraulic fracture modeling. Parametric studies of limiting non-linear elastic behaviors using analytical 2-D fracture propagation solutions and numerical simulation results are presented. Numerical hydraulic fracturing solutions for a stress-dependent Young's modulus in soft rock fracturing are discussed. Finally, general conditions identifying when nonlinear elastic and plastic behavior should be included are addressed.