Experimental characterization of the Barree and Conway (2004) single-phase non-Darcy flow model in various hydraulic fracturing sands

Abstract

The aim of this dissertation is to experimentally investigate the effect of non-Darcy flow through fracturing sand and irregular shaped materials on the parameters of the Barree and Conway (2004) non-Darcy single-phase flow model. It also investigates the existence of the minimum permeability concept. Several modifications were made to the laboratory data acquisition to ensure the quality of the captured data. A new apparent permeability computational method was developed which involves the integration of Darcy's Law to take into account the variations in the flowing fluid velocity as well as the fluid properties. Detailed procedures were put into place to ensure consistency between flow cells of the same granular material. A series of laboratory flow experiments were conducted under confining stresses from 1000 psi to 5000 psi on five sizes and types of fracturing sand (resin coated and uncoated) and crushed turquoise. Three flow cells were built from each granular material. Each cell was designated for a single-phase flow. In addition, fracturing sand characterization such as sieve analysis and sphericity and roundness tests were performed. Apparent permeability experimental data was captured over a large range of pseudo-N[subscript Re] (1- 2021 100/cm). The experimental results show that the evolution of the pressure drops points out limitation to the validity of the Forchheimer equation. The Barree and Conway non-Darcy single-phase model fits the experimental data across the entire range of the pseudo-N[subscript Re] experimentally obtained. The minimum permeability could not be verified due to pressure limitations of the nitrogen generation system. Results also show that the transitional constant ([tau]) in the Barree and Conway single-phase non-Darcy flow model along with the coefficient (E) decreases with confining stress while the coefficient (F) that control the rate at which the apparent permeability drops from Darcy permeability increases. The analysis shows a direct relationship between [tau] and the average grain diameter while F and E are also strongly related.