The effects of turbulence on the behavior of hydraulically fractured gas wells

Abstract

Laminar flow of fluid through reservoir rock can be described using Darcy's Law. If the flow is not laminar, the Forchheimer equation should be used to describe the system. The Forchheimer equation contains a term, β, which corrects for both turbulent flow and inertial resistance. Non-Darcy flow through reservoir rock has been studied for many years, and several authors have been published empirical correlations between the β-factors for gas flow in packed, hydraulic fractures were measured. The data published from that work indicate that the pressure drop in fractures can be much larger than the value calculated using Darcy's Law. In this research, a two dimensional, single phase model was used to analyze the behavior of fractured gas wells. An empirical correlation for turbulent flow in the fracture was included in the model; therefore, the correct pressure gradients under non-Darcy flow conditions could be calculated. Computer runs were made for a wide range of fracture and reservoir parameters. It was found that substantial turbulence in the fracture will exist even at flow rates as low as 300 MCF/day. The effects of turbulence on the gas well productivity index were determined to be a function of both proppant type and relative conductivity. The effect of turbulent gas flow in the fracture on the shape of pressure buildup curves was also investigated. The results indicate that turbulence can cause significant error in the analysis of pressure buildup data for fractured gas wells.