Analysis of Hydraulic Fracturing of High Permeability Gas Wells to Reduce Non-Darcy Skin Effects
Authors: Settari A. , Jones J.R. , Stark A.J. 
Published: March 2010

Abstract
Hydraulic fracturing has become increasingly popular in high permeability gas reservoirs in order to reduce apparent skin and thus improve well productivity. The remaining post fracture rate dependent skin effect varies from case to case and it is unclear whether this is a result of non-Darcy flow in the fracture, the reservoir or both.
This paper presents a study of the effects of reservoir and fracture turbulence in fractured gas wells. A quantification of the fracture length required to eliminate the effects of reservoir turbulence is obtained by means of a numerical study. A similar study with non-Darcy flow in both the reservoir and the fracture results in a correlation of fracture length required to get zero apparent skin at 75﹪ of AOF as a function of reservoir permeability, pressure, fracture conductivity and β factor.

Introduction
As shown first by Forschheimer(1) flow through porous media deviates from the linear Darcy's law and can be described by a quadratic equation with a non-Darcy flow coefficient β in the nonlinear term. The coefficient β has been correlated to reservoir permeability by numerous authors; in general β decreases with increasing reservoir permeability. Experience has shown that the non-Darcy term becomes more significant in higher permeability gas reservoirs. Generally for reservoir permeabilities below 1 mD there is little effect from non-Darcy flow. In higher permeability reservoirs non-Darcy flow can significantly restrict well production rates and may also affect the pressure transient response.
Hydraulic fracturing has become increasingly popular in high permeability gas reservoirs. Normally the goal for hydraulic fracturing high permeability gas wells is to bypass skin damage and thus increase initial flow rates. These 'skin' fractures are generally small in nature and may or may not include high-grade proppants. Prior to performing such a treatment there is often evidence to support a high permeability reservoir and a high apparent positive skin. Unfortunately there is rarely enough data to distinguish if this skin is a true mechanical skin or rate dependent (non-Darcy) skin. Post fracture analysis may show apparent skins ranging from slightly negative to neutral to positive. If a multi-rate post fracture test was performed it is sometimes possible to separate mechanical skin from rate dependent skin.
The basic problem with applying the rate dependent skin analysis to a fractured well is that the rate dependent skin was developed based on the assumption of radial homogeneous flow into the wellbore. By adding a hydraulic fracture the flow regime has been altered and the theory breaks down. It is unclear whether the rate dependent skin is occurring in the linear fracture flow or in the reservoir or in both.
The primary purpose of this study is to quantify when reservoir turbulence is insignificant for a fractured well. The second purpose is to provide a simple method for predicting post fracture rates in high permeability reservoirs taking into account fracture turbulence.

Literature Review
The previous work on non-Darcy flow can be divided into two main categories:what is the exact nature of non-Darcy flow andhow to predict when non-Darcy flow will have a significant effect on production.