An optimized stimulation design not only achieves high productivity during early times, but also necessitates maintaining conductive flow paths during the life of a well. Because of proppant settling and bridging, proppants are not uniformly distributed within developed fracture networks. Moreover, no fractures retain original conductivity during long term depletion, due to proppant embedment and crushing. This paper introduces a model that analytically predicts the proppant deformation and fracture closure behavior, and forecasts production performance.

This model is based on contact mechanics to simulate the mechanical interaction between the proppant pack and formation rock. The fracture aperture can be calculated and updated by taking into account the proppant concentration, non-uniform proppant distribution and in-situ stress conditions. The proppant pack permeability is analytically modelled according to its mechanical properties (size and density) and effective normal stress acting on the fracture surface. In this way, the fracture conductive variation caused by reservoir depletion can be quantified and imported into a reservoir model to forecast production.

This paper presents a new analytical model to describe dynamic fracture closure and its impact on production performance, which varies significantly with the proppant mechanical properties, proppant concentration, proppant distribution, stress condition and formation types. Under different conditions, conductivity evolution of propped fractures can be obtained from the presented model and matched well with multiple experimental tests. Sensitivity of proppant properties, reservoir attributes, and operational parameters are discussed in this study. Production results from these sensitivity analyses can be used to compare and contrast different design scenarios.

This model enables an efficient and reliable prediction of the fracture dynamic closure behavior and identification of controlling parameters to mitigate premature fracture closure. This model honors heterogeneous proppant distribution and related fracture closure, and hence captures more realistic reservoir performance. By integrating stress-dependent fracture conductivity and production analysis in this model, an operational guideline can be provided to maximize the productivity of fractured formations.

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