Deviation of hydraulic fractures through poroelastic stress changes induced by fluid injection and pumping

This paper presents an analysis of the deviation of hydraulic fractures associated with the poroelastic change of the in situ stress field caused by fluid injection and pumping in the reservoir. This mechanism is studied within the confines of a simple model involving one injection and one pumping well, and a hydraulic fracture propagating along the path initially equidistant from the two wells. Analysis of the fracture deviation from its straight-ahead path and determination of the conditions leading to attraction of the fracture by the injection well are both based on a theoretical study of the stress trajectories. Comparison of the analytical prediction of the fracture path with the computed path using a numerical technique shows excellent agreement between the two methods, provided that a certain dimensionless toughness is small. The principal results of this study can be summarized as follows. First, a fracture propagating along a path, initially midway between an injection and a pumping well, will always be deviated by the injection well due to the shear stress induced by fluid injection and pumping along the initial path. Second, the injection well acts as an attractor of hydraulic fractures propagating within its "attraction basin". Then, the fracture will propagate toward the injection well rather than simply be deviated by it. One of the features of this attraction basin is the existence of a "fracture barrier" characterized by a 90° rotation of the principal stress directions, with respect to far-field principal directions. Third, fracture deviation and attraction towards the injection well appears to be primarily controlled by only two dimensionless quantities: ∏ = S₀/σ*, the ratio of the stress deviator at infinity over the characteristic stress σ* associated with injection and pumping of fluid; and τ = 4ct/L², a dimensionless time (where c is the diffusivity and L is the half-distance between the two wells). The number of significant parameters is thus remarkably less than expected from a dimensional consideration. Only in the region close to the injection well is there an influence of an additional number ∏₁ = (P₀ - p₀)/σ*, the ratio of the difference between the mean pressure at infinity and initial pore pressure to the characteristic stress σ*.