Simultaneous Optimal Estimation of Roughness and Minor Loss Coefficients in a Pipeline

Ildeberto Santos-Ruiz,Vicenç Puig,Guillermo Valencia-Palomo,Francisco-Ronay López-Estrada

doi:10.3390/mca25030056

Abstract

This paper presents a proposal to estimate simultaneously, through nonlinear optimization, the roughness and head loss coefficients in a non-straight pipeline. With the proposed technique, the calculation of friction is optimized by minimizing the fitting error in the Colebrook–White equation for an operating interval of the pipeline from the flow and pressure measurements at the pipe ends. The proposed method has been implemented in MATLAB and validated in a serpentine-shaped experimental pipeline by contrasting the theoretical friction for the estimated coefficients obtained from the Darcy–Weisbach equation for a set of steady-state measurements.

Highlights

Pipelines are one of the most economical means of transporting liquids
The best fit of the measurements to the Colebrook–White equation was obtained for a roughness coefficient ε = 3.4652 × 10−4 and a total length L = 112.2238 m
The roughness coefficient estimate is more sensitive to measurement noise than the minor loss coefficient estimate by almost one order of magnitude

Summary

Introduction

Pipelines are one of the most economical means of transporting liquids. They are widely used to carry water, fuels, and other substances in the process industries. To diagnose leaks through pressure variations, it is essential to know how much pressure variation is caused by a reasonable pressure drop due to friction in the pipeline, which is only possible if the roughness and head loss coefficients of the pipe are known [4,5]. There is a general assumption that the head loss (h f ) due to friction depends on the inner diameter (D) of the pipe, the length (L) in which the head loss is measured, the average flow velocity (V), the absolute roughness of the pipe wall (ks), the gravity acceleration (g), and the density and the viscosity of the fluid. 2020, 25, 56 where Re is the Reynolds number, which measures flow turbulence as a function of viscosity and velocity, and ε = ks/D is the so-called relative roughness coefficient. Equation (1) is represented in the following simplified form called the Darcy–Weisbach equation [21,23]:

Methods

Results

Conclusion