Interaction Between Proppant Compaction and Single-/Multiphase Flows in a Hydraulic Fracture
Understanding 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 the discrete-element method (DEM) with single-/multiphase lattice Boltzmann (LB) simulation, was adopted to advance understanding of the interaction between reservoir depletion, proppant-particle compaction, and single-/multiphase flows in a hydraulic fracture. DEM was used to simulate effective-stress increase and the resultant proppant-particle movement and rearrangement during the process of reservoir depletion caused by hydrocarbon production. Simulated pore structure of the proppant pack was extracted and used as boundary conditions in the LB simulation to calculate the time-dependent permeability of the proppant pack. We first validated the DEM-LB numerical work flow, 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 particle diameter but different diameter distributions were generated to study the role of proppant-size heterogeneity (variation in particle diameter). 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 (closure distance) as functions of effective stress. Under 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 particles; smaller particles were compressed into the pore space between larger particles with increasing stress, leading to larger closure distance and lower porosity and permeability. With multiphase LB simulation, relative permeability curves were obtained, which are critical for larger-scale reservoir simulations under various effective stresses. The relative permeability of the oil phase was more sensitive to changes in geometry and stress, compared with the wetting phase. This was because the oil phase occupied larger pores; compaction of the proppant pack affected the structure of the pores, because the pores were farther from the grain contacts and thus more susceptible to collapse. It is also interesting to note that when effective stress increased continuously, oil relative permeability increased first and then decreased. This nonmonotonic behavior was the result of the nonmonotonic development of pore structure and oil connectivity under increasing stress.