SETTLING AND SLUMPING IN A NEWTONIAN SLURRY, AND IMPLICATIONS FOR PROPPANT PLACEMENT DURING HYDRAULIC FRACTURING OF GAS-WELLS

Analytical estimates of the amount of gravity-driven vertical motion of proppant which can occur within a hydraulic fracture during placement are derived, and used to investigate the conditions under which large gravity driven Rows can occur. Two major types of gravity-driven rearrangement are considered; settling and slumping. Slumping refers to motion driven by large scale density differences within an effectively single phase but inhomogeneous fluid. Settling is the well known downward motion of heavy proppant particles with slip relative to the lighter suspending fluid. The Row of slurry within the fracture is described using a set of equations formulated in terms of cross-fracture averaged fluxes. These permit the effects of non-uniform proppant concentration across the fracture width to be investigated, under the assumption that the time scale for development of cross slot structure is short compared with that for large scale flow. Constitutive functions are calculated for homogeneous flow, and for Row in which some process has caused all the proppant to migrate into a close packed sheet at the fracture centre. The initial motion of a sharp interface between two regions of different solids concentration is studied, and it is found that both settling and slumping can lead to significant vertical transport of proppant, under practical conditions. Rearrangement rates are larger, by a factor of about four, and occur over a wider range of conditions, if the proppant has migrated into a central sheet than if the solids distribution remains homogeneous. The rates of settling and slumping are similar. It is further shown that broadening of the interface slows down gravity currents, but the zone of concentration variation can be almost as wide as the fracture is tall without seriously reducing rates from those expected for a step concentration change.