Radio-frequency slurry-density measurement for dredging pipelines

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Radio-frequency slurry-density measurement for dredging

pipelines

Citation for published version (APA):

van Eeten, M. J. C. (2011). Radio-frequency slurry-density measurement for dredging pipelines. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR712707

DOI:

10.6100/IR712707

Document status and date: Published: 01/01/2011

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Radio-Frequency

Slurry-Density Measurement

for Dredging Pipelines

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Radio-Frequency Slurry-Density Measurement

for Dredging Pipelines

PROEFONTWERP

ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de rector magnificus, prof.dr.ir. C.J. van Duijn, voor een

commissie aangewezen door het College voor Promoties in het openbaar te verdedigen

op dinsdag 21 juni 2011 om 16.00 uur

door

Marius Johannes Cornelis van Eeten

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prof.dr. H.C.W. Beijerinck en

prof.dr. A.G. Tijhuis

A catalogue record is available from the Eindhoven University of Technology Library.

van Eeten, M.J.C.

Radio-Frequency Slurry-Density Measurement for Dredging Pipelines / by Marius Johannes Cornelis van Eeten. –

Eindhoven: Technische Universiteit Eindhoven, 2011. – Proefontwerp.

ISBN: 978-90-386-2513-3 NUR: 926

Subject headings: dredging / slurry density measurement / electromagnetic waves / radio frequency / transmissometry.

Cover: simulated electric field strength inside an RF slurry-density measurement pipe (p. 58).

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopy-ing, recording or otherwise, without the prior written permission from the copyright owner.

The work presented in this thesis has been performed at IHC Systems and financed by IHC Systems.

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Acknowledgements

This thesis is the result of a project that started in 2004. As it was a truly multidisciplinary project, I needed and found a helping hand along the way many times.

Foremost, I would like to thank my promotor prof.dr. Herman Beijerinck, for keeping faith in me, recognizing and cultivating my potential. At times when success seemed further away than ever, and Physics seemed to play tricks with me, he provided positive guidance, pointing out that we were still making progress. At times when I thought the result was looking good, he pushed me to take the extra step to make it better. He also helped me tremendously with my reporting skills, making the writing of this thesis less of a struggle than anticipated. Without doubt, there is no one who has supported me in my professional life like you have.

Secondly, I would like to thank my second promotor, prof.dr. Anton Tijhuis, for the helpful meetings and discussions that we had about patch antennas, near-fields and wave propagation. Even though he has an unbelievably busy schedule, he made time for me whenever I had questions on his field of expertise.

I would also like to thank ir. Cees de Keizer, manager Research & Development at IHC Systems, for keeping faith in me and the project. I remember the times when we thought we were almost there, after which yet another issue popped up. Somehow, these critical phases of a project always seemed to coincide with the budget planning. Yet each time, he maintained faith in a positive outcome and managed to get a green light for the upcoming year.

During the last year of the project, I had great help from ir. Gabriel Squillace, PDEng trainee from Eindhoven University of Technology, who helped with the development of new electronics.

Of course I like to thank ir. Krzysztof Zych, also PDEng trainee from Eindhoven University of Technology, who continued doing tests and measurements while I was working on the reports and thesis. I have truly appreciated our many discussions on wave propagation and diffusion. Continuing the measurements is one thing, but the value of discussion exceeds this by far.

I also like to thank prof.dr.ir. Bart Smolders, dr.ir. Huib Visser and dr.ir. Bas de Hon, all three from the Electromagnetics group of the department of Electrical Engineering at Eindhoven University of Technology, for their discussions and input on large ‘microstrip’ antennas.

Then there is Remco Fischbuch, electronics engineer disguised as ‘tech. support’ at IHC Systems. Thank you for helping me with the measurement electronics. We spent quite a lot of time together debugging the electronics and the code, and I learned a lot from you on the field of noise reduction.

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Moreover, I thank Robert van Leuveren for putting up with me and my large setup in the RA workshop, where I performed my static tests, and for becoming a good friend. We have had some interesting discussions on politics, current events, and the sound from Detroit and Chicago, which I really appreciate. I would also like to thank Cees Quick, for providing me with constructive advice (literally and figuratively).

Thanks to Ron de Poorter from IHC Beaver Dredgers, for making the tests at the Haringvliet possible, and Yarno Ketting and ir. Jort van Wijk, both from MTI Holland, for the use of their test facilities and the construction of a new and very valuable setup. I would like to thank all my friends, relatives and colleagues who were interested in my work. In particular, I would like to thank my parents, Jan en Willemien, for their continuing support during all my years at Eindhoven University of Technology— probably a few more than they had anticipated—and my sister Yvonne, for her support and proof reading.

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Summary

Radio-Frequency Slurry-Density Measurement

for Dredging Pipelines

Hydraulic dredgers make use of a density meter to measure the instantaneous density in the slurry transport pipeline, primarily for process control and production calculation. The current ‘golden’ standard for slurry density measurement is the radioactive density meter. It is based on a slurry density-dependent absorption of gamma radiation. As such, it contains a radioactive source.

The use of a radioactive source is legally justified [72], as long as there are no suit-able effective non-radioactive alternatives. Moreover, transport and handling of devices containing radioactive material is often difficult and costly due to governmental reg-ulations, certified personnel is required to operate radioactive devices, and the use of radioactive sources is a sensitive issue in society. The motivation for this research is to find a non-radioactive alternative for this slurry density meter.

In this project, we have developed a prototype of an alternative density meter, based on transmission of electromagnetic waves through the slurry: the Radio Frequency (RF) density meter. The electromagnetic slurry density measurement relies on the differences in (electrical) permittivity and conductivity of water and soil, which result in a change in propagation time and amplitude of an electromagnetic wave, as it travels through the slurry. Though the permittivity of the soil varies slightly for different soil-types, this variation will only have a limited influence on the density measurement, due to the large difference in permittivity between water and soil.

The operating window of the radioactive density meter covers the entire practical density range ρ = [1.0, 1.8] ton/m3. It is insensitive to the electrical conductivity of the slurry, and is commercially available for pipe diameters up to 1.3 m.

In contrast, we restrict the operating window of the prototype RF density meter to densities in the range ρ = [1.0, 1.8] ton/m3and an electrical conductivity in the range σ = [0.05, 1.0] S/m. Though the prototype has a 0.5 m diameter, the pipe diameter is primarily limited by the availability of high powered RF amplifiers.

In the course of the project, we built and tested two prototypes. Both prototypes are ‘hybrid’ density meters: they also contain a standard radioactive density meter, which enables us to make a direct comparison between the two methods. To measure the change in propagation time as a function of varying density (and conductivity), we developed an amplitude-modulated continuous-wave phase-shift measurement circuit. Conceptually, an electromagnetic density measurement seems an easy task: electro-magnetic waves are transmitted through the slurry. The permittivity of the slurry

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deter-mines the propagation velocity of electromagnetic waves and its conductivity attenuates the waves. By measuring these two parameters, we can calculate the sand volume-fraction and thus the density of the mixture.

However, complications arise from the interactions of the electromagnetic waves with the metal pipe, the near-field behavior of the electromagnetic waves, and the gradual transition from propagation to diffusion. Moreover, the conductivity of the slurry does not only attenuate the signal, it also induces a significant phase-shift. The first prototype contained an abrasion resistant polyurethane coating, which yielded yet another unan-ticipated side effect: a whispering-gallery mode. Therefore, the second prototype has a bare metal pipe wall.

Real-life tests of the second prototype at a cutter dredger uncovered some serious issues with the RF density meter. It was only after we constructed a new test setup, which enabled us to vary both the density and the conductivity of the slurry, that we discovered the source of these problems: the third-harmonic of the RF signal was interfering with the phase-shift measurement.

The construction of this new test setup was an important step in the development of the RF density meter: not only can it be used to test the density meter under controlled conditions with a wide variety of densities, soil types, and conductivities; it can also be used as a calibration tool for the first production series of RF density meters.

An accurate measurement of the conductivity of the slurry turns out to be vital for a proper RF density measurement. For this purpose, we have developed a conductivity sensor, a flange probe which can be mounted flush with the pipe wall. Because the measured conductivity exhibits hysteresis with respect to the phase-shift that it induces, we have tried to use the built-in conductivity measurement of a magnetic flow meter. Though the measured conductivity of the flow meter exhibits no visible hysteresis, its standard deviation is much larger than from the flange probe. Eventually, we have switched to a model which uses a measurement of the attenuation of the electromagnetic wave instead of a conductivity measurement.

Using the new laboratory setup, we have tested the second prototype with the im-proved phase-shift measurement electronics, varying the density and the conductivity within the operating window. Using a curve-fitting procedure, we obtain an RF density measurement with a standard deviation of 0.043 ton/m3as compared to the radioactive density meter, for ρ = [1.0, 1.8] ton/m3and σ = [0.05, 1.0] S/m. Within the reduced operating window ρ = [1.0, 1.6] ton/m3and σ = [0.05, 0.3] S/m, which corresponds to the circumstances observed during real-life tests at the Haringvliet, this standard deviation improves to 0.014 ton/m3.

In order to transform the second prototype to an operational device with the required robustness, that can be sold to customers of IHC Systems as a reliable tool for river-water operated dredgers, the complexity of the construction should be reduced, abandoning the concept of replaceable antennas. Also the electronics should be revised, making these more reliable.

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Samenvatting

Hydraulische baggerwerktuigen maken gebruik van een concentratiemeter om de instan-tane concentratie in een baggertransportleiding te meten, hoofdzakelijk voor regeling van het proces en productieberekening. Momenteel wordt de radioactieve concentratiemeter beschouwd als de ‘gouden standaard’. Deze is gebaseerd op een concentratieafhankelijke absorptie van gammastraling. Om die reden bevat het een radioactieve bron.

Het gebruik van een radioactieve bron is wettelijk gerechtvaardigd [72], zolang er geen geschikte en effectieve niet-radioactieve alternatieven bestaan. Daarbij is het transport van en het omgaan met apparaten waarin een radioactieve bron zit veelal lastig en duur wegens overheidsregelingen, is gecertificeerd personeel vereist voor de bediening ervan, en ligt het gebruik van radioactieve bronnen maatschappelijk gevoelig. De motivatie voor dit onderzoek, is het vinden van een niet-radioactief alternatief voor deze concentratiemeter.

In dit project hebben we een prototype van een alternatieve concentratiemeter ontwik-keld, welke is gebaseerd op doorstraling van het baggermengsel met electromagnetische golven: de radiofrequente (RF) concentratiemeter. De electromagnetische concentratie-meting maakt gebruik van de verschillen in elektrische permittiviteit en geleidbaarheid van water en grond, welke resulteren in een verandering in de voortplantingstijd en amplitude van een uitgezonden electromagnetische golf terwijl deze door het bagger-mengsel propageert. Ofschoon de elektrische permittiviteit van grond enigszins varieert voor verschillende grondsoorten, zal dit slechts een beperkte invloed hebben op de concentratiemeting, vanwege het grote verschil in permittiviteit tussen water en grond. Het werkgebied van de radioactieve concentratiemeter bestrijkt het gehele concen-tratiebereik ρ = [1.0, 1.8] ton/m3. Daarbij is het ongevoelig voor de elektrische geleid-baarheid van het baggermengsel, en is verkrijgbaar voor pijpdiameters tot 1.3 m.

Het werkgebied van het prototype RF concentratiemeter beperken we tot concentra-ties in het gebied ρ = [1.0, 1.8] ton/m3en een elektrische geleidbaarheid in het bereik σ = [0.05, 1.0] S/m. Alhoewel het prototype een diameter heeft van 0.5 m, wordt deze diameter hoofdzakelijk beperkt door de verkrijgbaarheid van hoog vermogen RF verster-kers.

In de loop van het project hebben we twee prototypes gebouwd en getest. Beide prototypes zijn ‘hybride’ concentratiemeters: ze zijn uitgerust met een standaard radio-actieve concentratiemeter, welke ons in staat stelt de twee methodes direct met elkaar te vergelijken. Om de verandering in voortplantingstijd te kunnen meten als functie van de concentratie (en geleidbaarheid), hebben we een meetcircuit ontwikkeld welke de faseverschuiving van een amplitude gemoduleerde golf kan meten.

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gezicht vrij eenvoudig: electromagnetische golven worden door het baggermengsel gezonden. De permittiviteit van het mengsel bepaalt de propagatiesnelheid van de golven en de geleidbaarheid zorgt ervoor dat ze worden verzwakt. Door beide parameters te meten, kunnen we de volume-fractie van het zand bepalen, en dus de concentratie van het mengsel.

Echter, interacties tussen de electromagnetische golven en de metalen buiswand, het gedrag van de golven in het nabije veld, en de geleidelijke overgang van propagatie naar diffusie maken de zaak een stuk ingewikkelder. Daarbij zorgt de geleidbaarheid van het baggermengsel niet alleen voor een verzwakking van het signaal, het veroorzaakt ook een significante faseverschuiving. Het eerste prototype was aan de binnenkant van de buis voorzien van een slijtagebestendige polyurethaan coating. Deze coating zorgde voor een onverwacht neveneffect: een zogenaamde ‘whispering gallery mode’. Om dit effect te voorkomen, heeft het tweede prototype een buiswand van onbehandeld staal gekregen. Praktijktests met dit tweede prototype aan boord van een snijkopzuiger, brachten een aantal ernstige problemen aan het licht. Pas nadat we een nieuwe testopstelling hadden gebouwd, welke ons in staat stelde om zowel de concentratie als de geleidbaarheid van het baggermengsel te variëren, ontdekten we de oorzaak van deze problemen: de derde harmonische van het RF signaal verstoorde de meting van de faseverschuiving.

De constructie van deze nieuwe testopstelling is een belangrijke stap geweest in de ontwikkeling van de RF concentratiemeter: we kunnen deze niet alleen gebruiken om de concentratiemeter gecontroleerd te testen met een variëteit aan concentraties, grondsoorten, en geleidbaarheden; het kan ook worden gebruikt als een ijkinstrument voor de eerste productiemodellen van de RF concentratiemeter.

Een nauwkeurige meting van de geleidbaarheid van het baggermengsel blijkt essenti-eel te zijn voor een correcte concentratiemeting. Daarom hebben we voor dit doel een geleidbaarheidssensor ontwikkeld, een flensprobe welke vlak aan de buiswand kan wor-den gemonteerd. Omdat de gemeten geleidbaarheid, als functie van de fase-verschuiving die het veroorzaakt, hysterese vertoont, hebben we geprobeerd de ingebouwde geleid-baarheidsmeting van een magnetische flowmeter te gebruiken. Alhoewel de gemeten geleidbaarheid geen waarneembare hysterese vertoont, is de standaarddeviatie veel groter dan met de flensprobe. Uiteindelijk zijn we overgestapt op een model dat gebruik maakt van een meting van de verzwakking van de electromagnetische golven, in plaats van een geleidbaarheidsmeting.

We hebben het tweede prototype getest in de nieuwe laboratoriumopstelling, waarbij we de concentratie en de geleidbaarheid hebben gevarieerd in het vastgestelde werkgebied. Door gebruik te maken van curve fitting, verkrijgen we een RF concentratiemeting met een standaarddeviatie van 0.043 ton/m3vergeleken met de radioactieve concentratieme-ter, voor ρ = [1.0, 1.8] ton/m3en σ = [0.05, 1.0] S/m. Binnen een beperkter werkgebied ρ = [1.0, 1.6] ton/m3

en σ = [0.05, 0.3] S/m, wat overeenkomt met de omstandigheden zoals we die tijdens de praktijktests op het Haringvliet hebben waargenomen, verbetert deze standaarddeviatie tot 0.014 ton/m3.

Om vanuit het tweede prototype tot een werkende concentratiemeter met de vereiste robuustheid te komen, zodat deze kan worden verkocht aan klanten van IHC Systems als een betrouwbaar instrument voor baggerwerktuigen die op rivierwater werkzaam zijn, moet de complexiteit van de constructie worden gereduceerd. Hierbij komt de verwisselbaarheid van de antennes te vervallen. Ook moet de elektronica worden herzien, zodat de werking betrouwbaarder wordt.

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1

Introduction

The slurry density meter is an important instrument for dredge operators. Combined with a flowmeter, it allows for the measurement of production. The current ‘golden standard’ for slurry density measurement is the radioactive density meter.

The subject of this thesis is the development of a prototype of an alternative density meter, based on transmission of electromagnetic waves through the slurry: the Radio Frequency (RF) density meter. In this chapter, we provide a short introduction to this project, starting with an explanation of hydraulic dredging (Sec. 1.1) and slurry density (Sec. 1.2).

In Sec. 1.3, we present the objective of this research, which we motivate in Sec. 1.4. Finally, we give a short explanation of the operating principle of the RF density meter (Sec. 1.5) and present a short historical overview of the project.

1.1 Dredging

Dredging can be defined as the removal of material from the bottom of a body of water. In the past, it used to be a purely mechanical process using buckets, but nowadays most dredging vessels use a hydraulic process for the transport of soil—though the excavation may still be mechanical. These hydraulic vessels all operate on the same principle, which is outlined in Fig. 1.1. The central process in a hydraulic system is the so-called ‘slurrification’: the mixing of the soil with water to create a fluid mixture. The creation of this mixture, called ‘slurry’, enables soil transport using a pipeline and one or more pumps.

World market leader in the construction of specialist dredging equipment is IHC Mer-wede, a Dutch company, based in Sliedrecht, with currently over 3000 employees.

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Figure 1.1: Hydraulic transport of slurry. The material on the bottom of a body of water can be excavated using a variety of tools, such as the draghead, cutterhead and cutterwheel. Then, the excavated material is mixed with water to create a fluid mixture, which is transported by the hydraulic system, consisting of a pipeline and one or more pumps.

IHC Systems is a business unit owned by IHC Merwede and Imtech Marine & Off-shore, turnkey contractor in marine technology.

IHC Systems is dedicated to efficient dredging. Whether efficient means the largest production ‘with the least amount of energy’ or ‘in the shortest amount of time’, knowing the production is crucial. For this purpose, IHC Systems has developed a range of instruments and automatic controllers. These provide the information necessary for a smooth, efficient dredging process, relieving the dredging master of repetitive, low-intelligence duties (his role becoming one of supervision) and achieving maximum operational efficiency of the vessel and its crew.

1.2 Slurry density

The production P is defined as the quantity of dredged material per unit of time and is calculated from the simultaneous measurement of density ρ (ton/m3)_{and flow rate} Q (m3_/_{s). Combined with the density of the dry solids ρ}

s(typically 2.65 ton/m3) and

the density of the water ρw(typically 1.0 ton/m3), the ‘production of solid material’

Pt(ton/h) is calculated as:

P_t=α_T⋅ ρ − ρ_w ρ_s−ρ_w

⋅ρ_s⋅Q ⋅ 3600. _(1.1)

with αTthe ‘transport factor’ or ‘slip ratio’, accounting for the difference in flow velocity

of the water and the solid material. Alternatively, the ‘production of in-situ material’ P_s(_m3/_{h) can be calculated as:}

P_s=α_T⋅ ρ − ρ_w ρ_is−ρ_w

⋅Q ⋅ 3600, (1.2)

with ρisthe density of the material in-situ. By density in-situ, we refer to the wet bulk

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1.2 · Slurry density

The flow rate Q is the product of velocity v (m/s) and pipe cross-section A (m2). The density during dredging typically varies between ρ = 1.2 ton/m3and ρ = 1.8 ton/m3, and the transport velocity in the pipe varies between v = 3 m/s and 10 m/s. The typical diameter of slurry transport pipelines varies between D = 0.5 m and D = 1.3 m. The lengths of these pipelines vary between a few tens of meters and more than 10 km. A failure to keep track of the density and velocity of the mixture in such a long pipeline can easily result in clogging, which can be very time consuming, and thus costly, to resolve.

Figure 1.2: Typical installation of a radioactive density meter on board of a dredger. The large leaden source container is marked with warning signs for ionizing radiation. The receiver unit is positioned exactly on the opposite side, and thus not visible here.

Turbulent flow

As shown below, the flow in a slurry transport pipe is turbulent. This turbulence is actually necessary: if the turbulence in the transport pipe drops below a certain threshold, sedimentation can occur in horizontal pipe sections. Generally, the dimensionless ‘Reynolds number’ is used to determine whether the flow inside a pipe will become

turbulent or remain laminar.

To obtain an order-of-magnitude estimate of the Reynolds number, we treat the slurry as a Newtonian fluid. This is appropriate for water and slurries containing only a limited fraction of fine (non-settling) sand particles [1]. The Reynolds number for a Newtonian fluid in a pipe is given by:

Re = ρ ⋅ v ⋅ D_η , (1.3)

with ρ the density of the medium, v the transport velocity, D the diameter of the pipe and η the dynamic viscosity of the medium. A laminar flow is assumed for Re < 2300, a turbulent flow for Re > 4000, and a transient flow in between.

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An estimation of the Reynolds number for a water flow, using a density ρ = 1.0 ton/m3, a typical transport velocity v = 5.0 m/s, a small pipe diameter D = 0.5 m and the viscosity of water at a temperature of 0○C which is η = 1.78⨉10−3Pa ⋅ s, yields:

Re = 1.4⨉106. (1.4)

For a slurry flow with a density ρ = 1.8 ton/m3, the dynamic viscosity becomes about a factor of ten higher [1], resulting in a substantially lower Reynolds number:

Re = 0.25⨉106, (1.5)

under the same conditions. Still, the Reynolds number is large enough to ensure the formation of a turbulent flow inside the slurry transport pipe. The transport velocity at which the sand grains start to settle is called the critical velocity, which is a density-dependent parameter.

1.3 Objective

The current standard slurry density meter is based on a density-dependent transmission of gamma radiation. As such, it requires a radioactive source. An example of a radio-active density meter from IHC Systems, mounted in the pump room of a hopper dredger, is shown in Fig. 1.2. The objective of this research project is to develop a prototype of a non-radioactive density meter, based on transmission with Radio Frequency (RF) electromagnetic waves: the RF density meter.

The RF slurry density measurement relies on the differences in permittivity and/or conductivity of water and (dry) sand. Slightly simplified: electromagnetic waves are transmitted through the slurry. The permittivity of the slurry determines the propagation velocity of electromagnetic waves and its conductivity attenuates the waves. By measuring the propagation velocity and the attenuation, we can calculate the sand volume-fraction and thus the density of the mixture.

We recognize that for the RF density meter to replace the radioactive density meter, it should be at least as accurate, and applicable under the same operating conditions, as the standard radioactive density meter. Thus far, the prototypes we have developed in this research project have been limited to a pipe diameter D ≤ 0.5 m, and the conductivity of the water has been limited to σ ≤ 1 S/m, which is a quarter of the typical conductivity of sea water. These limitations are explained in Sec. 2.3.

Despite these two limitations, the alternative density meter can still serve a substantial subset of the dredging market: many of the smaller dredgers, with smaller pipe diameters, do not operate at sea. This makes the limited conductivity range less of an issue. The administrative burden and certified personnel requirement of radioactive density meters pose a greater problem for the usually smaller dredging companies that purchase these smaller dredgers. Thus, a low-cost non-radioactive density meter can be an interesting alternative—even when its operating window is limited.

An assessment of the possibility and consequences of extension of this operating window to the whole operating window of the radioactive density meter, requires addi-tional research. We expect that this addiaddi-tional research will be greatly facilitated by the insights gained during the research of the limited-conductivity density meter.

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1.4 · Motivation

1.4 Motivation

The motivation for this research is to find an alternative for the slurry density meter, which is currently based on gamma ray absorption. Since the year 1960 IHC Systems has delivered over 1250 of these radioactive density meters. The use of a radioactive source is legally justified [72], as long as there are no suitable effective non-radioactive alternatives.

The operating principle of the radioactive density meter is very straightforward: a beam of gamma radiation is sent through the pipe and detected by a Geiger-Müller tube or a scintillation detector. The higher the density, the higher the absorption of radiation by the slurry.

ALARA

The radioactive source inside the density meter is deployed according to the ALARA principle, which stands for ‘as low as reasonably achievable’. In practice, this means that the source in a 0.3 m diameter density meter can have a relatively low activity of 1.85 GBq, whereas the source in the largest diameter radioactive density meters can have an activity of 222 GBq. Despite this high activity, the maximum measured dose-rate at the surface of the density meter is kept below 10 µSv/h due to its thick lead and tungsten shielding. The dose-rate decreases with the square of the distance, and at a distance of about one meter the dose-rate of the radioactive density meter is no longer measurable against the background radiation.

To put this dose-rate in perspective: the average annual dose due to cosmic radiation, naturally-occurring radioactive materials, and medical applications, is 2.5 mSv in the Netherlands [50]. The maximum allowed additional dose for employees, due to the use of a radioactive density meter, is 1 mSv/yr [73]. Provided that safety regulations are properly adhered to, this dose limit is never reached.

Disadvantages

The disadvantages of these density meters, which all arise from the use of a radioactive source, include:

1. transport and handling of devices containing radioactive material is more difficult and costly due to governmental regulations;

2. certified personnel is required to operate radioactive devices;

3. the use of radioactive sources is a sensitive issue in society.

Legislation

Due to the high activity of the radioactive sources, their handling is subject to govern-mental regulations. In the Netherlands, these regulations are established in the ‘Besluit stralingsbescherming’ (Bs) [73], which is based on the 96/29/EURATOM directive. Trans-portation of radioactive sources has to comply with the ‘Besluit vervoer splijtstoffen, ertsen en radioactieve stoffen’. Compliance with these regulations is strictly monitored

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by the government, e.g. [53]. In some countries, such as India, Pakistan and Morocco, importing a radioactive density meter is prohibitively difficult. Consequently, some dredging companies have decided to operate without density meter in these countries.

Authorization

The handling of a radioactive density meter is governed by different authorization levels. In the Netherlands, these levels range from ‘certificate of instruction’, unofficially called ‘level 6’, up to Radiation Protection level 2. Each of these levels require training and official certification. These authorization levels determine who may operate the radio-active density meter (level ‘6’), who may service it (level 5a), who is allowed to operate on the source capsule contained within the density meter (level 4a), and who is allowed to operate on the material inside the sealed source capsule (level 4b).

Dredging equipment is often deployed in very remote areas. To ensure an evenly distributed wear of the lining of a density meter, it is necessary to dismount, rotate and remount the pipe periodically. Dutch governmental regulations require such operations to be performed or supervised by a level 5a certified radiation worker. Because it is usually not economically feasible to have a permanent radiation worker on-site, this requirement can result in a significant delay of the dredging project.

Public perception

During discussions with untrained dredging crews, it came to light that they are unaware of the difference between radioactive irradiation and radioactive contamination, and many fear that the slurry that has passed through a radioactive density meter has become (at least slightly) radioactive—which is of course not the case. In reality, the use of a radioactive density meter is very safe, as long as the safety guidelines are properly adhered to.

Even worse, when it comes to radioactive materials, the typical frame of reference for the general public is formed by nuclear power plants. The negative image surrounding nuclear power plants also affects the public opinion towards radioactive sources in general. The general public is unaware of the difference between the activity levels involved in nuclear power plants and the activity of the radioactive source inside a radioactive density meter.

In this perspective, the use of a non-radioactive density meter on board of dredgers may contribute to the dredging company’s positive image.

Cost

The current radioactive density meter is frequently considered to be a rather expensive sensor by clients of smaller, relatively low-cost, dredgers. The selling price of a radio-active density meter starts at € 20,000.00, increasing with size. Various abrasion resistant linings, such as alumina tiles which are commonly used for rock cutter dredgers, also increase the price. Regarding the cost of an alternative density meter, we can discern two workable scenarios:

1. it costs significantly more and its performance is significantly better, i.e. more accurate and applicable under all conditions, or it requires less maintenance;

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1.4 · Motivation

2. it costs significantly less and it may be less flexible and/or less accurate and/or require more maintenance.

For the development of a prototype RF density meter, aiming for a ‘low-cost’ approach does not help to achieve our goal as we discovered during the design of the first prototype (Sec. 3.3). Because the technical feasibility already proved to be enough of a challenge, we have not focussed on the cost price of the alternative density meter during the development of the second prototype. We consider cost reduction to be part of the subsequent transition from prototype to commercial product.

Strengths

Although the motivation for this research project stems from the disadvantages of the radioactive density meter, the radioactive method also has its strengths that any alternative has to compete with:

1. accuracy;

2. reliability.

The accuracy of the radioactive density meter has been accepted by the dredging industry as the ‘golden standard’. This entails that any competitor or proposed successor will be compared to it. Still, by lack of an independent measurement, the accuracy of the radioactive density meter across the entire density range has never been verified.

Secondly, when calibrating the radioactive density meter with glass-packs (silica, ρ = 2.65 ton/m3

) of varying thickness, small variations in the resulting calibration constant are found. As explained in Sec. 4.5 and [15], deviations between the actual density and the reported density are likely to occur when the density profile across the diameter of the pipe is not uniform.

In practice, the accuracy of the production measurement system can be assessed on a hopper dredge by comparing the measured production with the hopper load. However, the largest deviation between these two values stems from the velocity meter: a magnetic flow meter measures the transport velocity of the water, which is usually higher than the transport velocity of the sand grains inside the water, due to gravity, friction, and sedimentation (in a horizontal pipeline). In a production calculator, this difference is compensated for by using an empirical slip factor.

The reliability of the detector unit of the radioactive density meter depends on the detector that is used: Geiger-Müller tubes are very robust, whereas a scintillation detector with an inorganic crystal (commonly a CsI crystal) as scintillator can become damaged quite easily due to shocks or moisture. Plastic scintillators typically have a lower efficiency, but are less fragile. Moreover, scintillation detectors are known to deteriorate quickly under intense illumination, due to heating and ion bombardment of the cathode inside the photomultiplier tube [57]. Geiger-Müller tubes are also known to exhibit (temporary) fatigue under high-intensity illumination [65]. In practice, this is prevented by switching off the power to the detector unit in case of an empty pipe.

The source in a radioactive density meter needs replacement after one half-value time. After one half-value time, the count rate at the highest density is no longer sufficient to meet the specified accuracy. In case of a137CS source, this half-value time is t1⁄2=30 yr

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and for60Co it is t1⁄2 =5 yr. Though a radioactive density meter with a137CS source

has a much longer operational lifetime, this source can only be used for the smallest diameter pipes because its gamma radiation has a much lower energy (Eγ=_{0.66 MeV)} compared to the60Co source (Eγ= {_{1.17, 1.33} MeV). Though a source with a much} higher activity would theoretically enlarge the operating lifetime of a radioactive density meter, the ALARA principle prevents us from using a source with an activity that is higher than necessary.

1.5 RF density measurement

Gamma absorption is directly related to the density of a specific material. In comparison, a density measurement using electromagnetic waves is a much more indirect method: water, with a density of 1.0 ton/m3, has a relative electric permittivity εwr =79, and sand,

with a density of 2.65 ton/m3, has a relative electric permittivity between εsr =4 and

εs

r=6, depending on the type of soil. The permittivity of the slurry is governed by mixing

rules, and must lie in between these extremes, depending on the relative fractions of sand and water, i.e. the density of the slurry.

We expect the soil-type dependent variation in the permittivity of the sand εsrto

have only a limited influence on the density measurement due to the large difference in permittivity between water and sand [14]: ∆ρ/(ρ − 1) = ±0.05 in river water. Still, the RF density meter can be calibrated for a specific soil-type if a better accuracy is needed and the soil-type remains constant.

Permittivity measurement

There is no direct method to measure the permittivity of a material. Again, we have to use an indirect measurement method. The permittivity of a material is defined as the linear response (called ‘polarization’) of this material to an applied electric field [54]. Thus, we should apply an electric field and measure this response. Two options come to mind:

1. we can can form an electric field in the slurry using two conducting plates at opposing sides. These plates form a capacitor and we can measure its capacitance;

2. we transmit an electromagnetic wave through the slurry and measure a change in the propagation time and/or attenuation of these waves.

A quick literature scan of these two methods reveals that a permittivity measurement method using two conducting plates is affected by electrode polarization effects, especially for conductive media [58, 59]. Moreover, capacitance measurements are highly sensitive to external factors, due to parasitic capacitances in the wiring.

In contrast, wave propagation bears resemblance to ground-penetrating radar (GPR), which has been used before to measure water content in soil [68], and the permittivity of concrete as a function of moisture and conductivity [66]. Moreover, an accurate measurement of the change in propagation time and attenuation of a continuous-wave is expected to be less difficult than an accurate capacitance measurement. Thus, the wave propagation method is expected to have best chance of success.

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1.6 · Project description

1.6 Project description

The research started with an investigation of various potential slurry density measurement methods [4]. From the list of 14 potential methods—which will not be discussed here— the electromagnetic wave transmission turned out to be the most promising alternative for slurry density measurement. The runner-up is the so-called pump model, which is expected to be useable as a low-cost simple-design solution, but only when a limited accuracy is acceptable.

The development of an electromagnetic slurry density meter is expected to require considerable investment in time and resources. In contrast, a density measurement using a pump model only reeds pressure sensors before and after the pump, which are typically already present on dredgers, and some algorithm. Because it is important that a new measurement technology is patentable, in order to maintain a competitive advantage, and patents on (software) algorithms are very hard to protect from infringement, the electromagnetic wave transmission is the only alternative worth investing in.

Feasibility

Subsequently, the feasibility of electromagnetic slurry density measurement was inves-tigated using a static measurement setup [13]. Slurry was simulated using sand-packs: wooden frames, covered with anti-root foil, and filled with washed river-sand. By placing these sand-packs in the measurement setup, filled with water of varying conductivity, the effects of sand and water conductivity on the signal transmission were measured. This project led to the conclusion that electromagnetic density measurement is possible, at least under the conditions of limited water conductivity and limited pipe diameter.

Prototypes

The static measurement pipe, used for the feasibility analysis, was not suitable for dynamic tests, because of its fragile construction and because the (dipole) antennas inside the pipe would be exposed to the abrasive slurry.

During the subsequent research, two prototypes were built and tested. The second prototype [21] was built two years after the first prototype [15], applying all insights gained from the first one. Both prototypes were based on a standard radioactive density meter, which makes them drop-in replacements. This is convenient when the prototypes are to be tested on an actual dredger.

A static test setup was constructed at IHC Systems, enabling the analysis of the electro-magnetic fields inside the prototypes as a function of conductivity [15, 32]. Measurements with canvas bags filled with sand, imitating slurry, were also performed with this static setup [71]. However, measurements with the sand-bags and varying conductivity proved to be very irreproducible, due to the slow diffusion of salt in and out of the sand bags.

We tested both prototypes in a test circuit at the laboratory of MTI Holland [15, 30], where a slurry flow with varying density can be generated. Tests with saline water are not allowed at this setup, because the addition of salt tremendously increases the corrosion rate of steel in water. Coating of this setup to prevent corrosion, was calculated to be prohibitively expensive.

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After the dynamic tests at the laboratory, the second prototype was also tested in real-life conditions at a cutter dredger from IHC Merwede, during its commissioning at the Haringvliet [31]. These tests allowed us to assess the performance of the RF density meter with both varying density and varying conductivity.

The tests at the cutter dredger revealed some serious issues with the RF density meter: both the electronics and the measurement pipe required a thorough re-evaluation. Support in the re-design of the electronics was provided in the form of an internship by Squillace. This support was continued as an internship by Zych, who also performed the subsequent static and dynamic tests with the modified prototype.

To be able to measure the response of the RF density meter under conditions of both varying density and varying conductivity, a new, smaller dynamic test setup was created at the laboratory from MTI Holland. The possibility to test the prototype RF density meter in real-life conditions, including a controlled variation of the conductivity, proved to be indispensable. Another advantage of this setup is that it is permanently at our disposal: there are no setup times, contrary to the standard dynamic test setup which is frequently used and modified by others. Most important, it enabled us to recreate the issues that came to light during the tests at the Haringvliet, and to find their cause.

Patents

Several aspects of electromagnetic measurement systems were reported by the “Neder-landsch Octrooibureau” (Dutch Patent Office) to be patented in the United States [63] and Japan [76, 75]. However, our approach is sufficiently different from these patents to acquire a patent on the distinguishing aspects of our RF density meter [49].

Readers expecting a short description of the contents of the thesis here, are asked for a little more patience. In the next chapter, we will first present the design constraints. The contents of this thesis follow at the end of Chap. 2.

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Design constraints

The RF density meter is intended as a replacement for IHC Systems’ radio-active density meter. As such, it should work under the same operating condi-tions. In this chapter, we will first identify the deployment range of the current radioactive density meter (Sec. 2.1).

Consequently, we will show what electromagnetic boundary conditions limit this deployment range for the RF density meter (Sec. 2.2). In Sec. 2.3, we establish the operating window for the first prototypes of the RF density meter.

In Sec. 2.4 we look at the timing resolution needed to measure slurry density based on an electromagnetic wave propagation time measurement. Finally, in Sec. 2.5 we look back on how we started with this project, and in Sec. 2.6, we mention a few alternative attempts at a non-radioactive slurry density meter.

2.1 Deployment range

The radioactive density meter is based on gamma-ray absorption: a beam of gamma radiation is sent through a slurry transport pipe, and detected by a Geiger-Müller tube or a scintillation detector. The higher the density of the slurry within the pipe, the higher the absorption of radiation, and the lower the count-rate at the detector. The density range of the radioactive density meter is limited by the point where the gamma count-rate becomes on the same order of magnitude as the background radiation.

At the current state of technology, radioactive density meters can be used for slurry density measurements for a density range up to ρ = 2.0 ton/m3for smaller diameter pipes and up to ρ = 1.8 ton/m3for the largest pipe diameters (1300 mm). Government regulations prevent the use of radioactive sources with a higher activity to overcome this limit for the largest pipe diameters. Currently, the most common type of

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radio-active density meter from IHC Systems has a density range up to ρ = 1.6 ton/m3. Its accuracy is specified as ‘±5% fsd. or better’ [9], where ‘fsd.’ stands for ‘full-scale deflection’. This translates to a maximum error ∆ρ = ±0.09 ton/m3. The processing electronics continuously calculates the density of the slurry, with an adjustable moving-average window. The time-constant of this moving-average window is set to five seconds by default.

As a replacement of the radioactive density meter, the RF density meter should at least cover the same density range. In Sec. 2.2, we will see that we can achieve the full density range of the radioactive density meter, but we have to restrict the conductivity range of the slurry.

2.2 Boundary conditions

An electromagnetic wave within a metal pipe is subject to boundary conditions. Also the slurry with varying conductivity inside the pipe influences its propagation, and limits the usable frequency range. In this subsection, we will look at signal attenuation, the transition from propagation to diffusion, the wavelength of the electromagnetic waves, and the transition from near- to far-field. The focus will be on a pipe with a diameter D = 0.5 m, but we will also show how the picture changes for other diameters.

Signal attenuation

A tt. (dB ) f (MHz) 0 50 100 150 200 20 40 60 80 100 120 140 160 180 200 σ (S/m) 0.0 0.5 1.0 4.0 84 dB 89 dB

Figure 2.1: Attenuation of a plane electromagnetic wave, in water with conductivity in the range σ = [0, 4] S/m, for a distance x = 0.5 m. The 89 dB and 84 dB dynamic ranges are indicated (dashed lines). The dark areas indicate a challenging attenuation.

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2.2 · Boundary conditions

The principle salt in sea water is NaCl, and sea water can be reasonably approximated by an aqueous NaCl solution [14]. The introduction of salt in water makes it conductive. Consequently, electromagnetic waves are attenuated in saline water.

The conductivity of natural water varies between σ = 0.05 S/m (fresh water) and σ = 4.0 S/m (sea water). The maximum conductivity limit of river water is somewhat arbitrary, as it gradually increases in estuaries. In [14] we have assumed that river water has a maximum σ = 0.65 S/m, but to be on the safe side, we raise this limit to σ = 1.0 S/m here.

Power is lost at several stages from power amplifier to receiver circuit: in the cables, the antennas, and in the slurry. The power loss in the cables is constant, and the loss in the antennas varies only moderately with conductivity. Assuming that we make a proper choice of cabling and tune the antenna to the desired operating frequency, the frequency dependence of the power loss in the antennas is zero. We have estimated that cables and antennas introduce a 9 dB power loss with fresh water, and 14 dB with sea water [38].

The power loss in the slurry has a much stronger dependence on frequency and conductivity. We assume that sand by itself is non-conductive, so the addition and mixing of sand in water reduces it conductivity. For a worst-case estimation of power loss, we calculate the attenuation in saline water.

We assume that the attenuation in the medium varies linearly with pipe diameter. A plot of the attenuation of a plane electromagnetic wave, as function of frequency, in water with various conductivities, is shown in Fig. 2.1 for a distance of 0.5 m. We see that the key to reducing the attenuation is lowering the operating frequency, especially at high conductivity.

To compensate for the signal attenuation inside the pipe, we need amplification—at the transmitter side, at the receiver side, or both. A 50 dB power amplification at the transmitter side, and a 48 dB gain at the receiver side is available using commercial off-the-shelf equipment. So a 98 dB gain is achievable without too much effort. Subtracting the power loss in cables and antennas, we obtain a feasible dynamic range of 84 dB with sea water and 89 dB with fresh water. We have indicated these levels in Fig. 2.1 so that we can compare them to the attenuation in saline water.

Clearly, the attenuation in river water is not problematic for a 0.5 m diameter pipe, but for detection of an electromagnetic signal in sea water, or for larger pipe diameters, we will have to invest in high dynamic-range, low-noise RF amplifiers.

Propagation – diffusion

The initial theoretical model of the RF density meter was based on a difference in relative permittivity between water (εr≈79) and sand (εr≈4). The conductivity of the water

was assumed to be a secondary effect. However, if we look at the plane harmonic wave equation for the electric field_{E in a material with constitutive parameters (ε, σ), which}⃗ is given by [39]: ∇2E + µε ω⃗ 2E⃗ ´¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¶ propagation +jµωσ ⃗E ´¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¶ diffusion =_0, _(2.1)

with µ the magnetic permeability and ω = 2π f the angular frequency of the electro-magnetic wave, we observe a ‘propagation’ term and a ‘diffusion’ term. For low conduc-tivity the propagation term dominates, whereas for higher conducconduc-tivity the diffusion

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term prevails: ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ σ

εω≪1 ⇒ propagation ∶ permittivity dominates σ

εω≫1 ⇒ diffusion ∶ conductivity dominates.

(2.2)

In the propagation domain, the behavior of the electromagnetic wave is primarily determined by the permittivity of the medium, while in the diffusion domain, the conductivity has the largest influence. For a continuous wave with frequency in the range f = [10, 100] MHz in saline water, the transition point from propagation to diffusion is thus obtained at a conductivity:

σ = εω = [0.04, 0.4] S/m. (2.3)

This boundary is within the conductivity range of interest. Though the basic principle of the RF density meter is that we measure a shift in propagation time, caused by a change in permittivity, we have to compensate for the change in phase velocity when the conduc-tivity increases, due to the transition from propagation to diffusion (Fig. 2.2). At zero conductivity, the phase velocity is given by:

v_ph∣_σ₌₀= c₀

√ε_r, (2.4)

with c0the speed of light in vacuum, and the approximate phase velocity for high

conduc-tivity is given by:

v_ph∣_σ≫εω≈ √

2 ⋅√ ω_{µσ .} (2.5)

Clearly, in the high conductivity regime, the propagation velocity does not depend on the permittivity of the propagation medium, but on the conductivity.

Wavelength

The wavelength of electromagnetic waves in a propagation medium is defined as:

λ = 2π

β , (2.6)

where β is the real part of the complex wavenumber k. For the plane harmonic of Eq. (2.1), this wavenumber is given by:

k =√µεω2₊jµωσ . _(2.7)

Consequently, the wavelength depends not only on the permittivity εof that medium, but also on its conductivity σ . When the distance between transmitter antenna and receiver antenna is significantly less than half a wavelength, the field inside the pipe looks more like an electric field inside a capacitor, than a propagating wave. Therefore, we

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2.2 · Boundary conditions 0 0.02 0.04 0.06 0.08 0.1 0.12 0 0.5 1 1.5 2 2.5 3 3.5 4 vph / c0 σ (S/m) 50 MHz 100 MHz 1/√εr

Figure 2.2: Phase velocity of an electromagnetic wave in water as a function of the conductivity of water. The approximations in the low and high conductivity limits Eq. (2.4) and Eq. (2.5) are indicated by dashed lines.

λ (m ) f (MHz) 0 0.5 1 1.5 2 2.5 3 20 40 60 80 100 120 140 160 180 200 σ (S/m) 0.0 0.5 1.0 4.0 D = 0.5 m

Figure 2.3: The wavelength of electromagnetic waves with frequency f in water with conductivity σ = [0.0, 4.0] S/m. The dashed line indicates the D = λ/2 upper boundary for a pipe with diameter D = 0.5 m.

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require that for a pipe with water, at least half of the wavelength λ fits within the pipe diameter D [14]:

λ/2 ≤ D. (2.8)

For a pipe with diameter D = 0.5 m, this requirement means that the maximum wavelength is λ = 1.0 m (Fig. 2.3). Larger pipe diameters allow the use of lower operating frequencies.

The resonant length of the two antennas inside the pipe, poses a similar lower limit to the frequency. As explained in Sec. 3.1, a quarter-wave patch antenna with a resonance frequency f = 50 MHz will be approximately 0.5 m long—the same size as the diameter of the pipe. The use of lower frequencies is only possible with longer antennas, which do not fit inside a pipe with the dimensions of a standard radioactive density meter.

Resonances

An electromagnetic wave, incident on the metal pipe wall, is reflected with a 180○phase shift. This reflected wave will interfere with the transmitted wave, and at certain frequen-cies a standing wave pattern or ‘resonant mode’ will arise. Consequently, excitation of a resonant mode can have a detrimental effect on the propagation time measurement, as we discovered experimentally with the first prototype (Sec. 4.4).

For an estimation of the resonance frequencies, we assume translational symmetry with respect to the vertical axis, and treat the electromagnetic wave in the pipe as a 2D cylindrical wave in a cross-section of the pipe [48]. The two modes with the lowest resonance frequencies are given by:

f_r= 1 2π

xmc0

√ε_r(D/2), (2.9)

with xm= {_{2.405, 3.832}. Thus, for a 0.5 m diameter pipe filled with water, we estimate} that the two lowest resonance frequencies are fr= {51.6, 82.3} MHz.

Whispering-gallery mode

A similar effect that can occur is the ‘whispering-gallery mode’, which is an electro-magnetic wave guided along the pipe wall [38]. A resonant whispering-gallery mode can occur if an integer number of wavelengths fits along the perimeter of the pipe. The corresponding resonance frequencies are given by Eq. (2.9) with xm= {_{1, 2, 3, . . .}. For a} 0.5 m diameter pipe filled with water, the two lowest whispering-gallery modes are found at fwgm= {21.5, 42.9} MHz. Like the resonant modes, a whispering-gallery mode mode

is only excited when the operating frequency is at (or close to) its resonance frequency.

Near-field – far-field

The dimensions of the prototype density measurement pipe are on the same order of magnitude as the wavelength of the electromagnetic waves in water [22]. The characteris-tics of the electromagnetic field near an antenna are very distinct from the characterischaracteris-tics of the field further away from the antenna. We distinguish two regions: the ‘near-field’

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2.3 · Operating window

and the ‘far-field’. In the far-field of an antenna, both the electric component E and the magnetic component H of an electromagnetic wave are fully developed. In the near field, the electric component prevails in case of an ‘electric’ antenna. In case of a magnetic antenna, the magnetic component dominates. In this definition, the near-field includes the reactive near-field, which is closest to the antenna, and the radiating near-field where the radiation pattern has not completely developed yet [7].

As a measurable response to a changing electric permittivity is a key factor in the RF density meter, we need an electric interaction with the medium in the pipe. Thus, we expect that an ‘electric’ antenna, such as an electric dipole, will respond more to a varying material permittivity than a ‘magnetic’ antenna, such as a loop antenna.

For an antenna with largest dimension L > λ, with λ the wavelength in the propaga-tion medium, several empirical relapropaga-tions exist for the near-field to far-field boundary. According to [3] the most commonly used criterion for the far-field is x > 2L2/λ. For the fresh water case and the largest antenna diameter L ≈ 0.5 m, this near-field to far-field boundary evaluates to x = 0.5 m or half the wavelength. According to this estimation, the electromagnetic field within the measurement pipe is completely in the near-field region (in fresh water).

It is, however, unlikely that we can recognize any near-field behavior in the pipe, as the electromagnetic waves also interact with the metal pipe wall, as simulations have indicated [40]. We expect to find near-field behavior only near the transmitter and receiver antennas, and a guided-wave in the rest of the pipe [47]. This makes the electro-magnetic field configuration in the pipe even more complex than an already complex near-field.

Overview

A collective plot of the boundary conditions that determine the range of suitable op-erating frequencies as a function of pipe diameter, is shown in Fig. 2.4. The optimum configuration for the limited conductivity range σ ≤ 1.0 S/m is indicated by the white region in the plot, while the dashed lines should be avoided. Grey regions are most likely to cause problems

In the optimum case, (1) we have at least half a wavelength in the pipe (filled with water), (2) the operating frequency does not coincide with any of the resonant modes, (3) we do not excite a whispering-gallery mode, and (4) we should have no problem with signal attenuation.

2.3 Operating window

At high water conductivity, the attenuation of electromagnetic waves makes it a major challenge to detect them. Moreover, due to the complete transition from propagation to diffusion, all permittivity-dependence drops out of the wave equation. Because of these challenges, we decide to limit both the diameter of the pipe and the maximum allowed water conductivity. We limit the pipe diameter for the RF density meter prototype to:

D_max=_{0.5 m.} _(2.10)

Consequently, its applicability is restricted to smaller cutter dredgers, such as the Beaver series from IHC Merwede, as explained in Sec. 1.4. We restrict density range of

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f (MH z ) D (m) 0 20 40 60 80 100 120 140 160 180 0 0.2 0.4 0.6 0.8 1 λ/2 f_r f_r fwgm 4 S/m 1 S/m

Figure 2.4: Boundaries in operating frequency f and pipe diameter D. The plot contains the D = λ/2 boundary (solid), the two lowest resonance frequencies frand one whispering-gallery

mode (dashed), and the attenuation bounds for σ = {1.0, 4.0} S/m (dash-dot). The white region indicates the optimum choice for σ ≤ 1 S/m.

the prototype RF density meter to the largest available density range of the radioactive density meter:

ρ = [1.0, 1.8] ton/m3

, (2.11a)

and limit the maximum allowed water conductivity to a range that will keep us away from serious attenuation issues and a complete transition to diffusion:

σ = [0, 1.0] S/m. (2.11b)

Though the prototype will not become a complete replacement for all radioactive density meters, the idea is that by focussing on a subset the challenges, we gain the knowledge we need to make the transition to a full-fledged replacement possible in a subsequent development project.

Density/Conductivity window

The RF density meter does not have a direct limitation of the density range, unlike the radioactive density meter where at a certain density the detectable gamma count rate drops below the background radiation. Instead, the density (and conductivity) range is determined by the corresponding wave propagation. The mathematical relation between

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2.3 · Operating window

density, conductivity, and propagation time is derived as follows [41, 14]: The density of a sand-water mixture as a function of the sand volume-fraction ϕ is simply:

ρ(ϕ) = ϕ ρ_s+ (_{1 − ϕ) ρ}_w_, _(2.12) with ρsand ρwthe densities of solid dry sand and water respectively. Subsequently, the

relation between the electric permittivity of a mixture and the volume fractions of its constituents is governed by mixing models. For the permittivity of a two-phase mixture, various theoretical and empirical mixing models can be found [62, 69].

Two geometrically extreme cases are formed by the upper and lower ‘Wiener bounds’ [55, 64]. For a sand-water mixture, the upper Wiener bound corresponds to the (artificial) situation where alternating flat layers of sand and water are placed parallel to the electro-magnetic field, and the lower Wiener bound corresponds to alternating flat layers of sand and water perpendicular to the electromagnetic field.

Thus, the relation between the electric permittivity of a sand water mixture and the permittivities of the constituents is assumed to obey the complex refractive-index model (CRIM) [6, 56, 51, 41, 14]: √ ε_r(ϕ) = ϕ√εs r+ (1 − ϕ) √ εw r, (2.13)

with εwr and εsrthe relative permittivities of the water and the sand, respectively. For

soil consisting of different components, a weighted average of the permittivities of its constituents can be used [60]. All permittivities can be complex values, but without conductivity they are real valued. The term “refractive index” refers to the index of refraction n, which is defined by n =√εrµr=√εrfor non-magnetic materials.

One could argue that the permittivity of a mixture of sand and water is better rep-resented by the Maxwell-Garnett (MG) model, which treats the two components of a mixture differently: it assumes that there is some uniform background material (water) with spherical inclusions of another material (sand). However, this model is mathemati-cally more cumbersome and does not deviate much from the CRIM model (Fig. 2.5).

For the sake of simplicity, we treat the propagation of a continuous-wave signal inside the measurement pipe as plane-wave propagation. The propagation time tpropof

a plane electromagnetic wave with angular frequency ω = 2π f , traveling a distance x in a medium with relative permittivity εrand conductivity σ , is given by [41]:

t_prop(ε_r, σ ) = _cx 0 √ε_r⋅ √ 1/2 ¿ Á Á Á À ¿ Á Á À 1 + (_ε σ 0εrω ) 2 +_1, _(2.14)

where c0is the speed of light in vacuum, and ε0is the permittivity of free space. At zero

conductivity Eq. (2.14) reduces to twave(ρ) = x c0√εr.

Thus, we find a relationship between tprop and (ρ, σ ) by combining Eqs. (2.12) –

(2.14). The largest change in the propagation time within the limits of ρ and σ is given by: ∆tmax=tprop(ρmin, σmax) −tprop(ρmax, σmin). (2.15)

For a phase-shift detector it is important that the maximum phase-shift is less than one period of the RF signal (see also Sec. 4.1). Figure 2.6 shows which combination of density range ρ = [1.0 ton/m3, ρmax]and conductivity range σ = [0.0 S/m, σmax]yields

exactly a phase-shift of one period of the RF signal, for a distance x = 0.5 m. We see that the operating window Eq. (2.11) keeps us well away from the one-period boundary.

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0 10 20 30 40 50 60 70 80 0 0.2 0.4 0.6 0.8 1 εr,m ix ϕ upper WB lower WB CRIM MG

Figure 2.5: Comparison of the CRIM and MG mixing models for a mixture of sand (εr=4) and

water (εr=_{79), as a function of the sand volume fraction ϕ. The upper and lower Wiener bounds} (WB) are also indicated.

σma x (S /m ) ρ_max(ton/m3) 0 0.5 1 1.5 2 1 1.2 1.4 1.6 1.8 2 2.2 f (MHz) 30 50 70

Figure 2.6: Combination of density range and conductivity range where the maximum phase shift for a distance x = 0.5 m is exactly one period of an RF signal with frequency f = {30, 50, 70} MHz. Our limited density and conductivity range [Eq. (2.11)] (hatched area) remains well below these boundaries.

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2.4 · Timing resolution

2.4 Timing resolution

As a first order approximation of the propagation of the electromagnetic waves in the pipe, we consider it as a continuous plane wave which propagates with phase velocity v_ph:

v_ph= c0

√ε_r. (2.16)

For a slurry-density measurement we need to be able to discriminate between water and slurry. A first order approximation of the difference in propagation time of an electromagnetic wave that is transmitted through the medium, is given by:

∆t = ∆x_c 0 ( √ εs r− √ εw r), (2.17)

with εsrand εwr the relative permittivities of sand and water, respectively. Substituting the

typical permittivity εwr =79 for water and an estimated permittivity εsr=41 for slurry

with a density ρ = 1.6 ton/m3, we find:

∆t = 4.2 ns. (2.18)

Thus, for a 0.01 ton/m3density discrimination, which is on the order of the standard deviation of the radioactive density meter, we can estimate the required timing resolution as:

∆t∣_{∆ρ=0.01 ton/m}3≈0.07 ns. (2.19) While this might seem an easy task, considering the current state of technology, we have to relate this to the period, which is T = 20 ns for a 50 MHz signal. Because of this relatively low operating frequency, the required phase resolution is quite stringent:

∆φ = 0.07 20

⋅₃₆₀○=_1.3○_. _(2.20)

This resolution is on the order of magnitude of the phase-accuracy of many electronic RF components, e.g. [12, 10]. Of course, as long as one phase-shift measurement takes substantially less than five seconds, which is the time-constant of the radioactive density meter, we can use averaging to improve the resolution of the phase measurement.

2.5 Today’s knowledge

At the start of the development of the first prototype, none of the boundary conditions were known—except for the signal attenuation. The wave propagation was assumed to be a simple plane-wave, and knowledge was gathered along the way.

The development of the first prototype (Chap. 4) reflects this—in hindsight—slightly naive approach. Much was learned from this first prototype, like the presence of res-onance and a whispering-gallery mode, and the second prototype (Chap. 5) shows improvements on many of these aspects. Instead of trying to solve all problems at the beginning, we have split the problem into smaller pieces, which made the project more comprehensible.

Radio-frequency slurry-density measurement for dredging pipelines

Radio-frequency slurry-density measurement for dredging

pipelines

Radio-Frequency

Slurry-Density Measurement

for Dredging Pipelines

Radio-Frequency Slurry-Density Measurement

for Dredging Pipelines

Acknowledgements

Contents

Summary

Radio-Frequency Slurry-Density Measurement

for Dredging Pipelines

Samenvatting

C

h

a

p

t

e

r

1

Introduction

1.1 Dredging

1.2 Slurry density

Turbulent flow

1.3 Objective

1.4 Motivation

ALARA

Disadvantages

Legislation

Authorization

Public perception

Cost

Strengths

1.5 RF density measurement

Permittivity measurement

1.6 Project description

Feasibility

Prototypes

Patents

C

h

a

p

t

e

r

2

Design constraints

2.1 Deployment range

2.2 Boundary conditions

Signal attenuation

Propagation – diffusion

Wavelength

Resonances

Whispering-gallery mode

Near-field – far-field

Overview

2.3 Operating window

Density/Conductivity window

2.4 Timing resolution

2.5 Today’s knowledge