A new permeability model of fracture containing proppants

Abstract

Flow of fracture containing proppant widely exists in the reservoir stimulation. In this article, a typical channel fracture containing large-size proppant is focused, where the average size of proppant is near the aperture of fracture. The propped fracture has the characters of large porosity and small wetted area. In view of the fact that the traditional permeability models cannot be applied to the present propped fracture placement, a new permeability model is proposed. At first, the main influence factors are identified by theoretical analysis. Then, based on a great number of three-dimensional simulations, a power law model is built by regressive method. The present model relates permeability, normalized by diameter and height of proppant, with porosity and area ratio between the proppant and fracture walls. Compared with the traditional permeability models, the present model can better describe and evaluate the flow capacity of channel fracture containing large-size proppant. Last, to give the application range of model, the critical Reynolds numbers are identified based on the analysis of Darcy and non-Darcy flow. The nonlinear flow properties are discussed for the present propped fracture placements of channel. The critical Reynolds numbers are obtained by the Forchheimer's law and Zimmerman parameter. It is found that the critical Reynolds numbers approximately have a linear relationship with porosity and area ratio. This article provides an innovative idea of proppant-fracture structure with high-permeability property, which provides a promising direction for the high-efficient mining of fluidized minerals.