Effect of longitudinal proppant placement and engineering parameters on fracture conductivity

Uncertainty regarding the factors affecting fracture conductivity is a core issue in hydraulic fracturing, and previous conductivity studies have not considered the effects of longitudinal proppant placement and engineering parameters on conductivity. In this study, a proppant transport model for engineering-scale fractures was developed using the Eulerian–Eulerian method. The conductivity model distinguishes between propped and unpropped regions in the longitudinal direction of the proppant. Proppant embedding and deformation in the propped region are calculated based on Hertz's elastic contact theory, whereas the permeability is estimated using the Kozeny–Carman formula. The unpropped region defines the degree of residual tensile opening, and the permeability is calculated using the cubic law. The results indicate an optimal ratio of proppant bed height to fracture height of ∼13/40, which maximizes the conductivity. This study provides critical insights for optimizing fracture conductivity and provides a workflow that integrates proppant placement and conductivity. The influence of engineering parameters on the morphology and conductivity of sand packs was also investigated.