Non-Darcy Flow in Hydraulic Fractures
Authors: Bybee Karen 
Published: February 2015

This article, written by Assistant Technology Editor Karen Bybee, contains highlights of paper SPE 96389, "Non-Darcy Flow in Hydraulic Fractures: Does It Really Matter?," by J.L. Miskimins, SPE, and H.D. Lopez-Hernandez, SPE, Colorado School of Mines, and R.D. Barree, SPE, Barree and Assocs. LLC, prepared for the 2005 SPE Annual Technical Conference and Exhibition, Dallas, 9–12 October.
In recent years, the petroleum industry has shown a significant increase in interest in non-Darcy flow, especially in fractures. In hydraulic-fracture stimulation, non-Darcy flow can have a major effect on reduction of a propped half-length to a considerably shorter "effective" half-length, thus lowering the productive capability of the well and overall reserves recovery. These non-Darcy-flow effects in propped fractures typically have been associated with high flow rates in both oil and gas wells. Reductions in flow capacity of 5 to 30% can occur in low-rate wells. Such reductions can be the result of non-Darcy effects.

Introduction
Existence of non-Darcy effects in the flow of fluids through porous media has been known for quite some time; however, characterizing and assessing the magnitude of these effects has proved difficult. Hundreds of papers have been published in the petroleum literature addressing everything from analysis of the effects of non-Darcy flow in pressure-transient analyses to determination of its role in gravel packs. Outside of the petroleum industry, thousands of papers have been published on non-Darcy flow because it affects a diverse range of subjects from irrigation to cigarette-filter development.
The full-length paper demonstrates that non-Darcy-flow effects can influence well productivity across the entire spectrum of flow rates, including low rates experienced in many producing wells. A simple spreadsheet model was developed that, although not as rigorous as a fully 3D reservoir model, can provide engineers with the ability to estimate the effects of non-Darcy flow on production.

Observations of Non-Darcy Flow
In 1856, Henry Darcy developed his now famous flow correlation by flowing water, through sand-pack configurations. Darcy's law describes the linear proportionality involving a constant, k, as related to the potential gradient ∆P/∆L, the fluid viscosity, µ, and the superficial velocity, v. Forty-five years later, Forchheimer observed deviation from the linearity of Darcy's equation at increased flow rates. Forchheimer proposed a second proportionality constant, in addition to k, that would account for this nonlinearity. He called this second proportionality constant β, and the result was the familiar Forchheimer equation, in which kd is the constant Darcy permeability and ρ is the fluid density.
The earliest references to non-Darcy-flow effects in petroleum literature occur in the early 1960s. The effects of non-Darcy flow specifically in hydraulic-fracturing operations were first addressed by Cooke in 1973. Increased attention has been paid to non-Darcy-flow effects in hydraulic-fracturing situations during the past several years as the industry attempts to understand the influence of non-Darcy effects under various producing situations.