Correlations between porous medium flow data and turbulent tube flow results for aqueous hydroxypropylguar solutions (Part 2)

Abstract

Turbulent tube flow and the flow through a porous medium of aqueous hydroxypropylguar (HPG) solutions in concentrations from 100 wppm to 5000 wppm is investigated. Taking the rheological flow curves into account reveals that the effectiveness β in turbulent tube flow and the efficiency κ for the flow through a porous medium both start at the same onset wall shear stress of 1.3 Pa. The similarity of the curves β = β(τ _w ) and κ = κ(τ _w ), respectively, leads to a simple linear relation β/κ =k, where the constantk or proportionality depends uponc. This offers the possibility to deduce β (for turbulent tube flow) from κ (for flow through a porous medium). In conjunction with rheological data, β will reveal whether, and if yes to what extent, drag reduction will take place (even at high concentrations).

The relation of our treatment to the model-based Deborah number concept is shown and a scale-up formula for the onset in turbulent tube flow is deduced as well.