Improving basic relationships of pipe hydraulics

This communication presents the approaches set up for processing spinner flowmeter well logs in vertical wells with a single fluid phase, which is the most widely used in assessing wells productivity. These focus on improving the pipe hydraulics relationships so that the different fluid inputs throughout the well can be quantified. Since vertical flow inside wells varies with depth between laminar flows (very low Reynolds number, i.e. Re < 10³) and turbulent (Re > 4·10³) the aim has been to reduce the uncertainty in the transition interval. Starting from bibliographical data and/or well-known formulas for laminar and for turbulent flow, several continuous relationships have been developed for any regime: 1) an expression for the radial distribution of velocity inside the pipeline (velocity profile) was developed. 2) A relationship between the average velocity and the velocity at the axis (velocity factor) was created. 3) A third equation was generated to obtain the friction factor in smooth pipes (and starting from this, a new explicit equation for rough pipes). The purpose has been to have a set of empirical expressions of easy and continuous application for any regime, as an alternative to the use of computer simulations.