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In order to evaluate naturally fractured reservoirs, it is critical to assess whether natural fracture sets believed to exist at depth (eg, from surface mapping and/or seismic data) are likely to be open and productive or closed and nonproductive. The semi-log relation between stress and the closure of natural fractures is combined with the effective normal stress acting on fractures to yield:
which relates fracture closure (8), the constants in the semilog fracture closure/stress relation (k and s), and maximum effective horizontal stress (oH) magnitude with the effective horizontal stress ratio (n), and the angle between the normal to the fracture and the o"h direction (0).
This relation shows that: (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 (n); (ii) natural fracture closure is sensitive to fracture orientation with respect to the in situ stress field where n is high; (iii) the sensitivity of natural fracture closure to its orientation with respect to the in situ stress field decreases markedly as n drops; and (iv) the rate of change of closure with changing orientation is relatively low at very low and very high misalignment angles, and much greater at intermediate angles.