Estimating the Coefficient of Inertial Resistance in Fluid Flow Through Porous Media

Journal Paper| October 01 1974 Estimating the Coefficient of Inertial Resistance in Fluid Flow Through Porous Media J. Geertsma J. Geertsma Koninklijke/Shell Exploratie en Produktie Laboratorium Search for other works by this author on: This Site Google Scholar SPE J. 14 (05): 445–450. Paper Number: SPE-4706-PA https://doi.org/10.2118/4706-PA Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn Email Get Permissions Search Site Citation Geertsma, J.. "Estimating the Coefficient of Inertial Resistance in Fluid Flow Through Porous Media." SPE J. 14 (1974): 445–450. doi: https://doi.org/10.2118/4706-PA Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAll JournalsSociety of Petroleum Engineers Journal Search Advanced Search AbstractThe object of this paper is to introduce an empirical, time-honored relationship between inertia coefficient - frequently misnamed "turbulence factor" - permeability, and porosity, based on a combination of experimental data, dimensional analysis, and other physical considerations. The formula can be used effectively for, among other things, the preliminary evaluation of the number of wells in a new gas field and the spacing between them.IntroductionIt has long been recognized that Darcy's law for single-phase fluid flow through porous media,Equation 1in which ?=superficial velocityµ=fluid viscosityk=formation permeabilityp=pressure head,is approximately correct only in a specific flow regime where the velocity ? is low. Single-phase fluid flow in reservoir rocks is often characterized by conditions in favor of this linearized flow law, but important exceptions do occur. They are in particular related to the surroundings of wells producing at high flow rates such as gas wells.For the prediction or analysis of the production behavior of such wells it is necessary to apply a more general nonlinear flow law. The appropriate formula was given in 1901 by Forchheimer1; it readsEquation 2in which ?=densitya=coefficient of viscous flow resistance 1/kß=coefficient of inertial flow resistance.This equation indicates that in single-phase fluid flow through a porous medium two forces counteract the external force simultaneously - namely, viscous and inertial forces - the latter continuously gaining importance as the velocity ? increases. For low flow rates the viscous term dominates, whereas for high flow rates the inertia term does. The upper limit of practical applicability of Darcy's law can best be specified by some "critical value" orf the dimensionless ratio.Equation 3which has a close resemblance to the Reynolds number. Observe that ß/a has the dimension of a length.Inertia and TurbulenceAs the Reynolds number is commonly used as an indicator for either laminar or turbulent flow conditions, the coefficient ß is often referred to as the turbulence coefficient. However, the phenomenon we are interested in has nothing to do with turbulence. The flow regime of concern is usually fully laminar. The observed departure from Darcy's law is the result of convective accelerations and decelerations of the fluid particles on their way through the pore space. Within the flow range normally experienced in oil and gas reservoirs, including the well's surroundings, energy losses caused by actual turbulence can be safely ignored. Keywords: production monitoring, Upstream Oil & Gas, correlation, diameter, Reservoir Characterization, production logging, inertial flow resistance, experiment, Reservoir Surveillance, Fluid Dynamics Subjects: Flow in porous media, Production logging, Reservoir Characterization, Reservoir Fluid Dynamics, Well & Reservoir Surveillance and Monitoring 1974. Society of Petroleum Engineers You can access this article if you purchase or spend a download.