The influence of fracture stiffness and the in situ stress field on the closure of natural fractures

Abstract

The extent to which the aperture of natural fractures is reduced, and they are rendered closed and unproductive by the in situ stress field in the subsurface, is critical to planning the exploitation of naturally fractured reservoirs. The semi-log relation between stress and the reduction of natural fracture aperture is combined with the effective normal stress acting on fractures of varying alignment with respect to the horizontal stresses to yield the relation: δ=1/qlog(n+1/2n+n-1/2ncos2θ)+logσ′H/q-P/q, where δ is the reduction of fracture aperture (fracture closure), p and q are constants in the semi-log fracture closure/stress relation, σH′ is the maximum effective horizontal stress magnitude, n is the ratio between the maximum and minimum effective horizontal stress magnitudes, and θ is the angle between the normal to the fracture and the σH direction. Key conclusions from this relation are: (i) for a given fracture, the sensitivity of fracture closure to the anisotropy of the in situ stress field can be constrained by the effective horizontal stress ratio; (ii) natural fracture closure is very sensitive to fracture alignment with respect to σH where the effective horizontal stress ratio is high; (iii) the sensitivity of natural fracture closure to its alignment with respect to σH decreases markedly as the effective horizontal stress ratio drops; (iv) except where the effective horizontal stress ratio is infinite, the rate of change of closure with changing alignment is relatively low at very low and at high misalignment angles, and much greater at intermediate angles. The above relation is applied to a number of fractures for which the closure/ stress relations have been determined. With varying alignment with respect to σH, less stiff fractures show up to four times more closure than stiff fractures.