Effects of overpressure variations on fracture apertures and fluid transport
Abstract For an isolated rock fracture in a homogeneous, isotropic rock subject to constant internal fluid overpressure or constant external driving stress, the ideal opening-displacement (aperture) profile or variation is that of a flat ellipse. For many mineral veins, dykes, tension fractures, normal faults, and other rock fractures, however, the opening-displacements show irregular aperture (thickness) variations very different from that of a flat ellipse. Here we present field data on typical fracture-aperture variations, as well as new numerical and analytical models to explain these data. We present the overpressure variation by Fourier cosine series, a very flexible method that can be used to model abrupt overpressure and driving-stress variations in vertical and lateral sections for fractures of various sizes and types. We calculate the opening-displacements of typical hydrofractures, and discuss the results with reference to mineral veins and dykes. We also present numerical models showing that when a fracture dissects layer, or parts of a single layer (such as a lava flow), with different stiffnesses (Young's moduli), the opening-displacement may show irregular variation even when the overpressure is constant. From the cubic law, the volumetric flow rates in the large-aperture segments of the mineral veins and dykes discussed in the paper may have been as much as 3–5-times the flow rates in the small-aperture segments. We propose that differences in volumetric flow rates are related to irregular opening-displacement variations in feeder-dykes is one principal reason for the development of crater cones, a universal feature of volcanic fissures.