The embedment of multisize proppant in fractures and the creep behavior of the shale will affect fracture permeability, yet the combination of the two factors has not been well studied and understood. In this work, the impact of graded arrangement of multisize proppant on fracture permeability is studied considering proppant embedment and shale creep in a hydraulic fracture. The Hertz contact theory is used to quantify the depth of embedment for proppant with different particle sizes, and the Burgers model is used to describe the creep behavior of shale. Then, a permeability model considering the effects of multisize proppant embedment with shale creep is developed and verified. The results show that, under the combined effect of shale creep and proppant embedment, the reduction in permeability of the proppant arrangement with equal amount of three particle sizes is about twice that of two particle sizes. It also shows that there is an optimal Young’s modulus ratio that allows for minimal proppant embedment when the Young’s moduli of proppant and shale are in the same order of magnitude. Moreover, creep is positively correlated with loading pressure, loading time, and clay mineral content in the shale and there is a clear correspondence between shale creep, fracture width, and permeability variation. It is suggested that proppant type, size, mixing ratio, and fracturing parameters for shale reservoirs should be optimized by combining reservoir mineralogy and rock mechanics to reduce the cumulative effect of shale creep on long-term productivity. This work is useful for optimizing the hydraulic fracturing design for shale reservoirs and improving the efficiency of hydraulic fracturing to increase permeability.

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