Technical Notes - Adaptation of Friction Factors to the Flow of Fluids through Censolidated Formations

The friction factor plot presented by Cornell and Katz4 and developed for the flow of fluids through consolidated formations has been directly adapted for handling fluid flow problems involvitrg both linear and radial flow. In this adaptation the friction factor plot is used directly for the solution of problems and thereby eliminates the use of conventional equations which are specific to laminar (Darcy) or turbutent flow. This upproach overcomes the disadvantages inherent in the use of these conventional equations. It eliminates the necessity of checking the type of flow occurring in order to identify the specific equation which must be used. In radial flow problems, because of the increasing mass velocity of the fluids as they approach the wellbore. the type of flow may no longer remain laminar. Consequently, it is necessary to use more than one equation in a problem and to identify the range over which each equation should be applied. Finally, in practice it has been found that much of the flow of gases through consolidated media occurs in a range that is neither laminar or turbulent. For this transitional region, no convenient equations are available. The method and presented friction factor plot are appficahle to both liquids and gases. INTRODUCTION The flow of fluids through unconsolidated media in packed beds has been treated extensively by a number of investigatorsl,2,3,5,7,8 Most of these studies present friction factors as a function of modified Reynolds number similar to those developed for conventional fluid flow through pipes. These friction factor plots are presented for linear flow; however, Elenbaas and Katz have extended these concepts to apply to radial flow. All of these studies on unconsolidated materials require a knowledge of packing properties such as sphericity. porosity, and particle diameter. Sphericity and particle diameter cannot be defined at the present time for consolidated formations such as those commonly found in gas or oil reservoirs. As a result many investigators have not utilized friction factors and Reynolds number in the study of fluid flow through consolidated media. However, Cornell and Katz4 present a plot (Fig. 1) for the flow of fluids through consolidated porous media, in which the friction factor defined as: The turbulence coefficient, P, is related to the formation permeability, K, as presented in Fig. 2. Three different types of flow may exist in the flow ot