The method of micro-sized graded proppant injection has been proposed in the industry to increase the size of the stimulated zone in naturally fractured reservoirs, especially CBM. However, big discrepancies between the modelling results of graded proppant injection and the experimental results have been observed. An analytical model of graded proppant injection with consideration of proppant embedment and deformation is established in this paper, and the influences of proppant embedment and deformation are investigated.

An analytical model of calculating the permeability of a fracture filled with partial monolayer proppant is established, and a linear elastic model of calculating proppant embedment and deformation is coupled into it to investigate the influences of proppant embedment and deformation on propped fracture permeability. The influences of proppant embedment and deformation on propped fracture permeability and the optimal proppant packing ratio are investigated. The influences of properties of proppant and rock on propped fracture permeability and the optimal proppant packing ratio are also studied. The graded proppant injection schedules with and without consideration of proppant embedment and deformation are compared and practical understandings are obtained.

The results show that the propped fracture permeability is reduced by more than 50% when the embedment or deformation extent reaches 18%. Neglecting proppant embedment and deformation will lead to an under-estimation of 15%-18% for the optimal proppant concentration during graded proppant injection. Proppant diameter has little influence on the optimal proppant packing ratio. Lower Elastic Modulus in the proppant or rock and/or smaller proppant particles leads to a higher optimal proppant packing ratio and lower permeability correction factors. Poisson's ratio of proppant or rock has very little influence on both optimal proppant packing ratio and permeability correction factor. Proppant concentrations at different stages of graded proppant injection with consideration of proppant embedment and deformation are 21.8% higher than those neglecting the two factors. Proppant embedment and deformation must be considered during planning of the graded proppant injection schedule.

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