New Scale From Non-Darcy Flow Characteristics and Its Use in Aspects of Reservoir Engineering
Authors: Deghmoum A.H. , Hamaz H. 
Published: March 2010

Abstract
This study presents a new concept for the use of non-Darcy flow characteristics in reservoir characterization, development, and well performance. More than 1,000 core samples are analyzed under unsteady-state flow conditions. A universal scale turbulent factor vs. permeability is developed on the basis of the reference base-line of turbulent flow through metallic porous media.
This new scale is used to:Classify reservoirs in terms of permeability heterogeneity; and,Establish an iso-turbulence map for reservoir development by selecting adequate zones to drill new wells.
In this paper, different applications for Algerian reservoirs are outlined and a new concept for the use of a turbulence factor is highlighted.

Introduction
This study develops characteristics related to fluid flow through porous media for a turbulent flow regime (high Reynolds number). It involves laboratory experimental analysis followed by numerical and analytical simulations. Six reservoirs are selected: the Upper Trias Shally Sand (TAGS/UTSS) of Hassi R'Mel; the Lower Trias Shally Sand (TAGI/LTSS) of Ourhoud and Rhourd el Khrouf; the Ordovicien of TFT; the Cenomanian Carbonate of Guerguet El Kihal South; and, the Cambrian of both Gassi and Agreb.
Data related to these reservoirs include production and core description. The flow of helium under pressure blowdown conditions is performed on 1,600 core samples selected from the above defined reservoirs. In addition, artificial and homogeneous metallic porous media, used for permeameter and porosimeter calibrations, are analyzed in order to establish a base-line for turbulent flow through natural cores.
Turbulence factor vs. permeability relationship is developed for each reservoir. A universal scale of these properties is established for improving reservoir characterization in terms of reservoir heterogeneity.
Ini tially, analysis is done on the Hassi R'Mel (HR) and Rhourd El Khrouf (RKF) reservoirs(1). The analysis is then extended to additional reservoirs (Sandstone and Carbonates). Layers of the same reservoir are also characterized in order to validate the universal scale. The results show that this developed scale can be considered as a reliable tool for reservoir characterization. The universal scale was also used in the development of the TFT reservoir and to assist with well performance of the Hassi R'Mel field.

Literature Review
In this section, some ideas that have been developed in the area of non-Darcy flow characteristics are briefly presented. Darcy's pioneering experimental work(2) is well recognized as the key factor in predicting production performance of porous and permeable flow systems. However, in certain circumstances such as the turbulent flow, this law may lead to erroneous results. Forchheimer(3) demonstrated that the pressure gradient to sustain a high flow rate through a porous medium is higher than the one Darcy's equation would predict. As the flow rate increases, the deviation between pressure gradient and flow rate increases. Forchheimer attributed the excess gradient required to inertial flow resistance. As a result, he developed a quadratic form to relate the pressure gradient and fluid flow velocity.