Determination of Laminar, Turbulent, and Transitional Foam Flow Losses in Pipes
Authors: Blauer R.E. , Mitchell B.J. , Kohlhaas C.A. 
Published: December 2007

This paper was prepared for the 44th Annual California Regional Meeting of the Society of Petroleum Engineers of AIME, to be held in San Francisco, Calif., April 4–5, 1974. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made.
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Abstract
In arriving at a method for predicting friction losses in laminar, predicting friction losses in laminar, transitional, and turbulent flow regimes for flowing foam, it was found Reynolds numbers and Fanning friction factors could be calculated with effective foam viscosity, actual foam density, average velocity, and true pipe diameter. Further, it was found pipe diameter. Further, it was found the relationship between Reynolds number and Fanning friction factor for foam was identical to that of single-phase fluids. The test data were taken under controlled flow in capillary tubes and 1-1/4-inch and 2-3/8-inch oilfield seamless tubing. Friction losses of foam within 2-7/8-inch tubing and 4-1/2-inch and 5-1/2-inch casing during fracture treatments have been accurately predicted using the proposed method.

Introduction
Foam has been used for several years as a wellbore clean-out and drilling fluid and to a very limited extent as a fluid loss, diverting, and fracturing fluid. Applications have been limited because the behavior of the foam could not be confidently predicted. Major problems when using predicted. Major problems when using foam in oilwell treatments were the calculation of friction loss, wellhead pressure, and the resulting density and pressure, and the resulting density and carrying capacities during treatment.
Lockhart and Martinelli, developed the most popular empirical correlation for predicting friction losses of flowing two-phase fluids within horizontal pipes. This method was sufficiently accurate only for pressure losses within pipes smaller than 2-inches in diameter. Other empirical correlations based on mechanical energy or momentum losses proved insufficient also.
Bertuzzi, Tek, and Poettmann's energy dissipation function which has extensive oilfield use for predicting pressure losses within horizontal pipes pressure losses within horizontal pipes for non-uniformly mixed, two-phase fluids was found not reliable for foam.
Failures of these empirical two-phase correlations for the prediction of pressure losses for foam flow may be lodged in the theoretical developments by Einstein and Hatschek. They point out foam should be treated as a point out foam should be treated as a single-phase fluid with viscosities significantly greater than either phase. Mitchell's used these theories to experimentally find viscosities of foam.