A Radial Turbulent Flow Formula
- Jack R. Elenbaas (University of Michigan) | Donald L. Katz (University of Michigan)
- Document ID
- Society of Petroleum Engineers
- Transactions of the AIME
- Publication Date
- December 1948
- Document Type
- Journal Paper
- 25 - 40
- 1948. Original copyright American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. Copyright has expired.
- 1.2.3 Rock properties, 5.6.4 Drillstem/Well Testing, 5.3.1 Flow in Porous Media, 4.3.4 Scale, 2.4.3 Sand/Solids Control, 4.6 Natural Gas, 5.2.1 Phase Behavior and PVT Measurements
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A radial turbulent flow formula has been developed which permits thecomputation of the pressure drop for radial flow in gas wells whether the flowis laminar, turbulent, or partially laminar and partially turbulent. Using theformula a complete back-pressure curve has been calculated and analyzed by acomparison with existing back-pressure curves. A procedure is presented forcomputing the permeability of the porous media when the porosity, sphericityand average particle diameter are known.
Recent studies on the flow of fluids through porous media have provided newmethods for computing flow under turbulent conditions. The present study wasinitiated as an investigation of pressure-drop computations for flow throughporous sands in gas wells and as an analysis of present-day back-pressuretests.
Although laminar flow exists in the producing formation of gas wells undernormal flow rates, turbulent flow does take place adjacent to the well bore. Asthe flow rate is increased, turbulent flow exists further and further into theproducing formation and under open-flow conditions in relatively deep wells aconsiderable portion of the flow through the sand will be turbulent.
In order to calculate a complete backpressure curve for relatively deep wellswithout resorting to extrapolation of curves drawn from data obtained inback-pressure tests or calculations made in the completely laminar region, itwas necessary to have some means of calculating pressure drop for flow throughporous sands under turbulent conditions. As a result, a radial turbulent flowformula was derived from the equations recently presented by Brownell andKatz.
A rigorous solution of this equation involves a trial and error graphicalintegration. By making the assumptions of average viscosity, temperature andcompressibility factor of the flowing gas, it was possible to graphicallyintegrate the relation for the general case of radial flow of gases through theporous sand of gas wells. A chart has been prepared relating the value of theintegral to the radius of the well bore and to the Reynolds number of theflowing gas. The chart actually performs the graphical integration and thesolution of the formula is then reduced to a simple trial and errorcalculation. A typical back-pressure curve is calculated to show the transitionfrom laminar to turbulent flow.
This paper will briefly describe the procedures for computing flow throughporous media, including a method for predicting sand permeability from porosityand grain size and shape.
Flow Through Porous Media
Brownell and Katz recently reported a correlation for computing flow of fluidsthrough porous media by the use of an enlarged Reynolds number and frictionfactor in which the porosity of the bed is included as an additional primevariable.
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