The Application of the Cubic and Quadratic Forchheimer Equations in the Design of High-Rate, Gravel-Packed Gas Well Completions

Abstract

The Application of the Cubic and Quadratic Forchheimer Equations in the Design of High-Rate, Gravel-Packed Gas Well Completions R.S. Buell; R.S. Buell Colorado School of Mines Search for other works by this author on: This Site Google Scholar J.W. Crafton J.W. Crafton Colorado School of Mines Search for other works by this author on: This Site Google Scholar Paper presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, September 1985. Paper Number: SPE-14448-MS https://doi.org/10.2118/14448-MS Published: September 22 1985 Cite View This Citation Add to Citation Manager Share Icon Share Twitter LinkedIn Get Permissions Search Site Citation Buell, R.S., and J.W. Crafton. "The Application of the Cubic and Quadratic Forchheimer Equations in the Design of High-Rate, Gravel-Packed Gas Well Completions." Paper presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, September 1985. doi: https://doi.org/10.2118/14448-MS Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex Search nav search search input Search input auto suggest search filter All ContentAll ProceedingsSociety of Petroleum Engineers (SPE)SPE Annual Technical Conference and Exhibition Search Advanced Search AbstractThe addition of the cubic term to the quadratic Forchheimer equation is evaluated in the design of high-rate, gravel-packed, gas well completions. The impact of the cubic term on the Rawlins and Schellhardt1 back pressure plot, non-Darcy plot as used by Jones et al.2 and Himmatramka,3 and the rate sensitive skin plot as used in references 4 and 5, is evaluated. The authors conclude that high-rate, gravel-packed gas well completions can be designed with sufficient accuracy under field conditions without the inclusion of the cubic term. An example calculation is done using the cubic term to illustrate its effect. A design procedure is presented for inside casing gravel pack design.IntroductionForchheimer6 observed that at higher velocities, the pressure loss was significantly different from that predicted by the Darcy laminar flow relationship. As a first approximation, the Forchheimer quadratic expression1 is often used.Equation 1The deviation from Darcy flow begins when viscous-shear and inertial forces become significant. For even higher velocities, Forchheimer found that adding a cubic term improved the fit of his data, and Equation (2) was suggested. The need for the cubic term is attributed to the onset of turbulence. The following equation is the expression which incorporates Darcian behavior, visco-inertial effects and turbulence.Equation 2The need for a cubic term has been suggested by others7–9 based on their laboratory investigations. The Firozabadi and Katz nomenclature are used for â??Î3â?¿ and â??Î2â?¿.9 Turbulence in porous media should not be confused with turbulent pipe flow. In porous media, fully established eddies do not usually exist during turbulent flow. Turbulence in porous media usually begins when Reynolds' numbers are from one to ten. The need for the cubic term has also been derived from theoretical considerations.7 Keywords: reservoir, upstream oil & gas, ezeudembah, cubic term, spe 14448, mmcf day, pressure loss, drillstem/well testing, equation, society of petroleum engineers Subjects: Formation Evaluation & Management, Drillstem/well testing This content is only available via PDF. 1985. Society of Petroleum Engineers You can access this article if you purchase or spend a download.