A permeability model for the hydraulic fracture filled with proppant packs under combined effect of compaction and embedment

Hydraulic fracture is the main flow path for gas transport. The proppants are man-made material that filled in the hydraulic fractures to keep them open and allow gas flow through. The permeability change of hydraulic fracture is controlled by the combined effect of compaction and embedment. In this study, we modeled the proppant embedment as a function of effective stress by a transformed Hertz contact model and a proposed power law model which is analogous to the Oliver-Pharr model. The results illustrate that the power law relationship could better fit the experimental data, because the Hertz model becomes invalid when the embedment is large compared to the proppant size. By incorporating the power law correlation into an existing theoretical permeability model as a function of effective stress, a permeability model for the hydraulic fracture filled with proppant packs under combined effect of compaction and embedment is developed. The new model is able to adequately describe the permeability data of proppant packs confined by rock core slices. Although this study puts forward the theoretical basis of the hydraulic permeability modelling under combined effect of compaction and embedment, more fundamental studies are required to investigate the contact behaviour between the proppant packs and the fracture face under various conditions. Therefore, the permeability model could be further improved by introducing the new advanced proppant embedment correlations.