Abstract
The conductivity of the proppant-pack plays a critical role in the productivity of a hydraulically fractured well. Here we combine the Discrete Element Method (DEM) and the Lattice Boltzmann Model (LBM) to investigate the conductivity of proppant-packs under variable confining stress. Three different proppant-packs including well graded, uniformly graded and poorly graded proppants are used to generate loose packing of spherical rigid particles with no initial contact. We then use a DEM algorithm, with specified confining stress, to compact the proppant-packs. A representative elementary volume of the pack is subsequently used for fluid flow simulations. LBM is used to calculate a detailed flow field at the pore scale and the Darcy-scale permeability is then calculated from the average pore-scale velocity and pressure information. The results show, as expected, that the porosity and permeability of the proppant-pack decreases with increasing confining pressure. The permeability of well graded proppant-packs is more sensitive to the stress while uniformly graded packs are more permeable than poorly graded proppant-packs. The calculated permabilities are in good agreement with available experimental data for a range of confining pressures. In addition, the permeability estimated from the Kozeny-Carman equation based on calculated porosities compares well with calculated permeabilities.
