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Abstract
This paper expounds a simple, fundamental theory for predicting sedimentation particulate fouling thresholds for horizontal flows inside heat exchanger tubes. The velocities and shear stresses at the tube wall predicted by this theory for keeping particulate matter suspended compare favorably with industrial experience and proprietary Chevron data. This theory is also not inconsistent with the literature in that the shear stress required for sedimentation fouling mitigation is roughly 4–6 Pa. However, the situation where small particles become encapsulated in the viscous sublayer cannot be resolved with a simple sedimentation particulate fouling threshold theory at this time, necessitating future research.
ACKNOWLEDGMENTS
The author gratefully acknowledges Chevron for permission to publish this work. The critical review performed by Les Jackowski of Chevron was very helpful and most appreciated.
NOMENCLATURE
| CD | = | drag coefficient, dimensionless |
| Di | = | inside diameter of the heat exchanger tube, m |
| Dp or Dparticle | = | particle diameter, μm |
| Dp+ | = | dimensionless particle diameter, dimensionless |
| f | = | Blasius/Moody/Darcy friction factor, dimensionless |
| FBrownian | = | force of Brownian motion, N |
| Fbuoyancy | = | force of buoyancy, N |
| Fdrag | = | force of drag, N |
| Fgravity | = | force of gravity, N |
| Ftotal | = | total sum of forces, N |
| g | = | acceleration of gravity, 9.81 m/s2 |
| I | = | turbulence intensity, dimensionless |
| kB | = | Boltzmann constant, 1.381 (×10−23) J/K |
| Rebulk | = | Reynolds number of the tubeside fluid based on Vbulk, dimensionless |
| Rep | = | particle Reynolds number, dimensionless |
| Tb or Tbulk | = | bulk fluid temperature, °C |
| tp+ | = | dimensionless relaxation time, dimensionless |
| Vbulk | = | average velocity of the bulk fluid flow, m/s |
| Veddy | = | instantaneous velocity of a turbulent eddy, m/s |
| Vsusp | = | bulk velocity required to suspend a particle in a horizontally flowing fluid, m/s |
| x | = | x-direction (abscissa) in the Cartesian coordinate system, m |
| y | = | y-direction (ordinate) in the Cartesian coordinate system, m |
| yvs | = | viscous sublayer thickness, μm |
Greek Symbols
| μf | = | fluid viscosity at bulk temperature, cP |
| ρf | = | fluid density at bulk temperature, kg/m3 |
| ρp | = | particle density, kg/m3 |
| τw | = | shear stress applied to the heat exchanger tube inner wall in the direction of the flowing fluid, Pa |
Additional information
Notes on contributors
Christopher A. Bennett
Christopher A. Bennett earned a B.S. in chemical engineering with a minor in chemistry, specializing in physical chemistry, from the University of Toledo, Ohio, and then an M.S. and a Ph.D. in chemical engineering from the University of Michigan, Ann Arbor. His research in graduate school focused on the synthesis, characterization, and catalytic evaluation of mono- and bimetallic early transition metal nitrides, from which he concluded that the catalytic sites for n-butane dehydrogenation over vanadium nitride were nonmetal vacancy defects. He then entered industry as a researcher working for Heat Transfer Research, Inc. (HTRI), where he applied his knowledge of characterization, heat transfer, and fluid dynamics to fouling, specializing in crude oil fouling. He was consequently the first to report the manifestation of the isokinetic/compensation effect in high-temperature crude oil fouling, and because the laboratory observations parallel industrial experiences observed in multiple crude oil preheat trains, he can assure readers that at least this manifestation of the isokinetic/compensation effect is not the result of experimental errors. During his tenure at HTRI he also chaired the Crude Oil Fouling Task Force (COFTF) and co-chaired the Exchanger Design Margin Task Force (EDMTF). He is currently a heat exchanger specialist at Chevron Energy Technology Company, where he continues his study of fouling.