Scaling-up correlations for drag reducing surfactants

Measurement of temperature profiles in turbulent pipe flow of polymer and surfactant drag-reducing solutions

“…It was further shown that fluids exhibiting a ⌬B + -type profiles do scale according to the DR versus velocity correlation, and those fluids exhibiting a fan-type velocity profile scaled according to the w versus velocity correlation. Interestingly, the velocity profile measurements carried out by Bewersdorff and Ohlendorf 16 for CTAB surfactant solutions showed an apparent fan-type velocity profile analogous to the fan-type temperature profiles that we measured for the same fluid that Schmitt et al 42 used to show the validity of the w versus velocity scaling procedure. This finding does strengthen our conclusion of a relationship between ⌬B + -type profiles with the DR versus velocity scaling correlation, versus-on the other hand-fan-type profiles with the w versus velocity scaling correlation.…”

“…Another implication may be related to scaling correlations. 35 We have shown that a 4000 ppm solution of the same SPE 95285 surfactant did not follow the scaling correlation based on DR versus flow velocity-which most polymers and the cationic surfactant solution complied with-but rather an alternative one given by w versus velocity, as also proposed by Schmitt et al, 42 supposedly for all surfactant solutions. An analysis of the differences between these two correlations was undertaken by Aguilar.…”

An improved diameter scaling correlation for turbulent flow of drag-reducing polymer solutions

“…Recently, however, drag-reducing surfactant solutions have become of particular interest due to their greater potential for industrial applications, and in the midst of surfactant studies, the diameter effect problem has been revisited somewhat. Schmitt et al [19] proposed two different empirical correlations for surfactants depending upon the shear stress level: DR vs. ( w for high stresses and ( w vs. V for low stresses. The former is the same as the procedure proposed by Whitsitt et al for polymer solutions, but the ( w vs. V approach is not and would lead to large errors in friction prediction for most polymer solutions.…”

Evaluation of Surfactant Drag Reduction Effect in a District Heating System

“…This is the so-called “correlate model of DR and u p * .” This procedure has the drawback that both variables (DR and u p * ) contain the unknown parameter ( τ w ), and an iterative procedure is therefore necessary to predict the DR of the solution. A number of other researchers, for example, Astarita et al [9], Lee et al [10], and Savins and Seyer [11], then simplified Whitsitt's procedure by using the solvent friction velocity ( u w * ) instead of the solution friction velocity ( u p * ) and proposed “correlate model of DR and u w * .” After that, Schmitt et al [12] proposed two different empirical correlations for surfactants depending upon the shear stress level: DR versus τ w for high stresses and τ w versus V (bulk velocity) for low stresses. Gasljevic and Matthys [13] proposed a new correlation model on the diameter effect of drag-reducing flow by correlating drag-reduction level (DR) with bulk velocity.…”