A model for hydraulic fracture growth across multiple elastic layers

Typical stress conditions in gas reservoirs consisting of multiple thin coal seams interlayed with shales, tuffs and sandstones, often lead to generation of a planar vertical hydraulic fracture. A pseudo-3D model, in which the growth of the planar hydraulic fracture occurs through multiple horizontal layers with different elastic properties, is developed to account for the effects of modulus contrasts on fracture shapes. In this model, plane strain deformation is assumed for pseudo-3D cells that have uniform cross-sectional pressure distribution, and the horizontal fluid flow is simplified to be one dimensional. The vertical and horizontal fracture growth are controlled in the model by two failure criteria, respectively. Viscous fluid friction effects are included for vertical growth and a correction factor is applied to the horizontal failure criterion to adjust the propagation speeds. The numerical results for different values of the correction factor are presented for a vertically planar fracture propagating in a homogeneous rock subject to stress contrasts. Fitting the pseudo-3D results to fully-3D results provides a means to determine the correlation factor that is found to be a function of material constants and cell length. The correlation factor obtained is then extended to hydraulic fracture propagation in a layered rock mass. There are two options in choosing material constants for the correlation factor and their results are examined. Both choices demonstrate the same varying trends for fracture height and propagation speed. The existence of softer coal seams retards upward fracture growth, with a stepwise injection pressure associated with the discontinuous upward growth.