A new constitutive model for calculating the loading-path dependent proppant deformation and damage analysis of fracture conductivity

The conventional mechanical and permeability models for proppant pack consider proppant as an elastic material, however, loading stresses cause proppant rearrangement and crush, leading irreversible material hardening, structure damage of proppant pack, strong reduction of pore space and damage of fracture conductivity. In this work, a confined compression and conductivity test on proppant pack was conducted. According to the experimental results, a new constitutive model for calculating the loading-path dependent proppant deformation and permeability was developed. In the proposed model, a simple yield equation and a non-associated potential equation were applied to derive the irreversible plastic deformation which is further used to calculate the material hardening parameter and the permeability damage. The model was validated by the experimental data and coupled into a reservoir simulator to investigate the impact of the stress shadow effects caused by the current stimulated fracture on the deformation and permeability of the placed proppant in the previous generated fracture. The modeled results revealed that the current fracturing operation damages the conductivity of the previous generated fracture, which must be taken into account for production prediction.