On steady homogeneous sand–water flows in a vertical conduit

In this paper, an idealized model of the steady‐state phase of the flow in a vertical conduit leading to a sand volcano eruption is developed from first principles. The model assumes that a sand–water mixture flows upwards, driven by an overpressure at the base of a vertical cylindrical conduit (or a two‐dimensional fracture) and opposed by gravity, viscous resistance and turbulent drag. The conditions for flow are analysed in detail, and the mechanisms controlling the eruption rates are studied quantitatively. The flow predictions are in accordance with our observations of analogous vigorous sand eruptions at deepwater oil fields. For sufficiently high flow velocities (u > 10u_T) and small sand fractions (s < 0·2), the flow may be well mixed and homogeneous. If these conditions are not met, the flow may either become two phase or does not develop. Combining geological considerations with the steady homogeneous model, it is possible to predict the behaviour of the vigorous quasi‐steady stage of a sand volcano eruption. It is shown that, based on the average density of the overlying sediments, there are a range of overpressures for which sand volcanoes may develop.