Well productivity evaluation in deformable single-fracture media

Evaluations and interpretations of reservoir productivity are frequent in geothermal, groundwater and hydrocarbon research and applications. In this study, we consider the closure of fractures around production wells due to compaction that can affect the productivity value, i.e. the ability of subsurface formations for transporting the desired fluid to a borehole. We introduce analytical tools to evaluate and predict changes in the productivity of a deformable fractured porous media. We propose analytical models for three geometries: a rectangular fracture with zero/non-zero orientation and a circular fracture with zero orientation to maximum horizontal stress. An advanced numerical model is utilised to evaluate the impact of spatial variation of fracture aperture induced by the fracture deformation on well productivity. The developed analytical solutions using a uniform fracture aperture always either over- or underestimate the production rate. Hence, an equivalent aperture model is developed for the fracture with aperture distribution under variable contact stresses to circumvent this problem. The proposed equivalent aperture model reduces the average and maximum errors of production-rate prediction from 28% to 0.6% and from 116% to 25%, respectively. We further employ the proposed model for sensitivity analyses to illustrate the impacts of in-situ and human-controlled parameters on productivity reduction. These analyses present that the interactions among initial reservoir pressure, fracture orientation, fracture stiffness, and well pressure control productivity reduction behaviours and the maximum productivity reduction values.