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Trine Helle Simmenes, StatoilHydro (Norway)
Agust Gudmundsson, Royal Holloway, University of London (United Kingdom)
Shigekazu Kusumoto, University of Tokai (Japan)
Sonja L. Philipp, University of Gøttingen (Germany)
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Rock-fracture aperture variations are very important for fluid transport in various types of reservoirs. This follows because the fluid flow tends to concentrate on those parts of a fracture where the aperture is largest. Here we present field data on aperture variations, measured along fractures of different mechanical types and sizes. In particular, the field data include (a) several-metres-long mineral veins, (b) several hundred-metres-long tension fractures, and (c) several-kilometres-long gaping normal faults. Mechanically, the mineral veins are driven open by internal fluid pressure, whereas the tension fractures are opened by tensile stresses, and the normal faults by tensile and shear stresses.
All the fractures show variations in aperture along their lengths (strike dimensions). The maximum apertures are about 10 cm for the mineral veins, about 10 m for the tension fractures, and about 60 m for the normal faults. We present numerical models indicating that any variation in Young's modulus (rock stiffness) along the fracture path, even if the applied loading is constant, results in variation in aperture. This is supported by field observations of fractures along their heights (dip dimensions) that cross mechanical layers with different stiffnesses, as is common in fractured reservoirs.
When a fracture is subject to a constant loading, either an internal overpressure or an external driving tensile or shear stress, its aperture variation follows a smooth curve, an ellipse. Here overpressure is the difference between the total fluid pressure inside the fracture and the stress acting perpendicular to the fracture walls. Similarly, driving stress is the difference between the remote applied (tensile or shear) stress and the residual strength (tensile or shear) on the fracture surface after opening or sliding. When the loading is not constant, however, there will be variation in the fracture aperture. Non-constant loadings may result from changes in stiffness along the fracture height or fracture length. In our analytical models, we present the overpressure and tensile stress variations by Fourier cosine series, allowing calculations of the aperture variation as well as the local displacement and stress fields around the facture. The results fit well with the field data and can be used to explain them as a consequence of abrupt overpressure and driving-stress variations along the dip or strike dimensions (or both) of the fractures. The results contribute to our understanding of fracture and permeability development and flow channelling in heterogeneous anisotropic reservoirs of various types, including those holding ground water, geothermal water, gas and oil.
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