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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 …