Interaction between proppant packing, reservoir depletion, and fluid flow in hydraulic fractures

Abstract

Understanding of proppant transport and deposition patterns in a hydraulic fracture is vital for effective and economical production of petroleum hydrocarbons. In this research, a numerical modeling approach, combining Particle Flow Code (PFC) with single-/multiphase lattice Boltzmann (LB) simulation, was adopted to advance the understanding of the interaction between reservoir depletion, proppant particle compression, and single-Zmultiphase flow in a hydraulic fracture. PFC was used to simulate effective stress increase and the resultant proppant particle movement and rearrangement during the process of reservoir depletion due to hydrocarbon production. The pore structure of the proppant pack was extracted and used as boundary conditions of the LB simulation to calculate the time-dependent permeability of the proppant pack. We first validated the PFC-LB numerical workflow, and the simulated proppant pack permeabilities as functions of effective stress were in good agreement with laboratory measurements. Furthermore, three proppant packs with the same average diameter but different diameter distributions were generated. Specifically, we used the coefficient of variation (COV) of diameter, defined as the ratio of standard deviation of diameter to mean diameter, to characterize the heterogeneity of particle size. We obtained proppant pack porosity, permeability, and fracture width reduction (compressed distance) as functions of effective stress. Lfnder the same effective stress, a proppant pack with a higher diameter COV had lower porosity and permeability and larger fracture width reduction. This was because the high diameter COV gave rise to a wider diameter distribution of proppant particlcs: smaller particles were compressed into the pore space between larger particles with the increasing stress, leading to larger compressed distance and lower porosity and permeability. Using multiphase LB simulation, relative permeability curves were obtained, which are critical for larger-scale reservoir simulations under various effective stresses. The relative permeability of oil phase was more sensitive to changes in geometry and stress, compared to the wetting phase. This was due to the fact that the oil phase occupied larger pores; compression of the proppant pack impacted the structure of the pores, since the pores were further from the grain contacts and thus more susceptible to collapse. It is also interesting to notice when effective stress increased continuously, oil relatively permeability increased first and then decreased. This nonlinear behavior was due to the nonlinear development of pore structure and oil connectivity under increasing stress. Show more