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Global monitoring of fluidized-bed processes by means of
microwave cavityresonances
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Measurement: Journal of the International Measurement
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Citation for the published paper:Nohlert, J. ; Cerullo, L. ;
Winges, J. (2014) "Global monitoring of fluidized-bed processes
bymeans of microwave cavity resonances". Measurement: Journal of
the InternationalMeasurement Confederation, vol. 55 pp.
520-535.
http://dx.doi.org/10.1016/j.measurement.2014.05.034
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Measurement 55 (2014) 520–535
Contents lists available at ScienceDirect
Measurement
journal homepage: www.elsevier .com/ locate /measurement
Global monitoring of fluidized-bed processes by meansof
microwave cavity resonances
http://dx.doi.org/10.1016/j.measurement.2014.05.0340263-2241/�
2014 The Authors. Published by Elsevier Ltd.This is an open access
article under the CC BY license
(http://creativecommons.org/licenses/by/3.0/).
⇑ Corresponding author. Tel.: +46 317721710.E-mail address:
[email protected] (J. Nohlert).
Johan Nohlert a,⇑, Livia Cerullo a, Johan Winges a, Thomas
Rylander a, Tomas McKelvey a,Anders Holmgren b, Lubomir Gradinarsky
b, Staffan Folestad b, Mats Viberg a,Anders Rasmuson c
a Department of Signals and Systems, Chalmers University of
Technology, SE-41296 Göteborg, Swedenb AstraZeneca R&D,
Pharmaceutical Development, SE-431 83 Mölndal, Swedenc Department
of Chemical and Biological Engineering, Chalmers University of
Technology, SE-41296 Göteborg, Sweden
a r t i c l e i n f o a b s t r a c t
Article history:Received 16 October 2013Accepted 23 May
2014Available online 19 June 2014
Keywords:Pharmaceutical fluidized-bed processMicrowave
measurement systemPermittivity estimationElectromagnetic
homogenizationFinite element methodSensitivity analysis
We present an electromagnetic measurement system for monitoring
of the effective per-mittivity in closed metal vessels, which are
commonly used in the process industry. Themeasurement system
exploits the process vessel as a microwave cavity resonator andthe
relative change in its complex resonance frequencies is related to
the complex effectivepermittivity inside the vessel. Also, thermal
expansion of the process vessel is taken intoaccount and we
compensate for its influence on the resonance frequencies by means
ofa priori information derived from a set of temperature
measurements. The sensitivities,that relate the process state to
the measured resonance frequencies, are computed bymeans of a
detailed finite element model. The usefulness of the proposed
measurementsystem is successfully demonstrated for a pharmaceutical
fluidized-bed process, wherethe water and solid contents inside the
process vessel is of interest.� 2014 The Authors. Published by
Elsevier Ltd. This is an open access article under the CC BY
license (http://creativecommons.org/licenses/by/3.0/).
1. Introduction scopic methods such as near infra-red (NIR) and
Raman
In the pharmaceutical industry, monitoring and controlof
manufacturing processes are important in order toachieve
high-quality products to a low production-cost. Acommon step in the
manufacturing process for many phar-maceutical products is coating
and drying of particles influidized-bed processes. Measurement
techniques thatare capable of monitoring the material distribution
andmoisture content in this type of process are importanttools for
control, optimization and improved understand-ing of the
process.
Currently available methods for monitoring of moisturecontent in
pharmaceutical fluidized-beds include spectro-
spectroscopy [1,2]. Although these methods yield impor-tant
information on moisture content as well as physicaland chemical
properties of the material, they mainly pro-vide local information
for the region in the very proximityof the measurement probe, which
may be insufficient ormisleading for the estimation of the global
process state.Recently, Buschmüller et al. [3] developed a stray
fieldmicrowave resonator technique for in-line moisture
mea-surements during fluidized-bed drying. However, theirapproach
is based on local fields in the vicinity of theresonator probe and,
therefore, it does not yield globalinformation on the process
state.
At low frequencies, electric capacitance tomography(ECT) can be
applied to regions with high particle density[4]. Although ECT
yields important information on the par-ticle distribution on a
global scale, it suffers from limitedspatial resolution and it is
not suited for the estimation
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Fig. 1. Schematic picture of the process vessel.
J. Nohlert et al. / Measurement 55 (2014) 520–535 521
of dielectric losses, which leads to difficulties in
distin-guishing between material density and moisture content.
In this article, we present a microwave-based measure-ment
technique that exploits electromagnetic eigenmodesthat are
supported by the process vessel bounded by itsmetal walls. The
process vessel is considered as a cavityresonator and the
permittivity distribution inside the ves-sel is estimated based on
measurements of the complexresonance frequencies of the cavity.
This technique resem-bles the well-established cavity perturbation
measure-ment technique, which is regularly used for
accuratemeasurements of dielectric and magnetic properties
ofmaterials at microwave frequencies [5,6]. In contrast
totraditional cavity-perturbation measurements, our tech-nique
exploits several different eigenmodes, which
yieldsthree-dimensional spatial resolution and
measurementinformation at multiple frequencies.
The process vessel is equipped with a set of probes thatare
connected to a network analyzer. Given the scatteringparameters
measured with the network analyzer, we esti-mate the complex
resonance frequencies of the processvessel, where the real part
corresponds to the frequencyof oscillation and the imaginary part
corresponds to thedamping. We exploit a linearization of the
electromagneticresponse of the process vessel and it yields a
relationbetween (i) a perturbation of the resonance frequenciesand
(ii) a perturbation of the complex permittivity insidethe process
vessel. We parameterize the permittivity withspace dependent basis
functions and determine the coeffi-cients by means of solving an
estimation problem based onan over-determined system of linear
equations, where theright-hand side contains the measured
deviations in theresonance frequencies as compared to the empty
vessel.
2. Measurement system
2.1. Process equipment
Fig. 1 shows a schematic picture of a fluidized-bed pro-cess
vessel of Wurster type, which is the type of process weconsider in
this article. This process is used for coating anddrying of
pharmaceutical particles, such as pellets or gran-ules, and the
particular vessel we consider is a custom builtlab-scale device for
batches consisting of up to 1 kg of par-ticles. The particles are
dielectric objects of size that nor-mally range from 250 lm to 1 mm
and in this article, weconsider particles that mainly consist of
microcrystallinecellulose (MCC).
The bottom plate of the process vessel, also referred to asthe
distributor plate, is perforated with a large number ofsmall holes.
An airflow is applied through the distributorplate, which fluidizes
the particles and creates a fluidizedbed. Above the distributor
plate resides a metal tube, whichis referred to as the Wurster
tube. At the center of the dis-tributor plate below the Wurster
tube, a pneumatic spraynozzle injects a rapidly moving mixture of
air and liquid thataccelerates the particles in its immediate
vicinity in anupward motion. The particles move through the
Wurstertube and create a fountain-like flow pattern above the
Wur-ster tube. As the particles exit the fountain region, they
fallback into the fluidized bed outside the Wurster tube.
The liquid injected through the spray nozzle is a solu-tion that
is sprayed onto the surface of the particles. Thesolvent evaporates
mainly inside and immediately abovethe Wurster tube, which results
in a deposited layer ofthe solute on the surface of the particles
[7]. A commonsolvent is water and there is a large variety of
solutes suchas active pharmaceutical ingredients (API), polymers
usedfor film coating and various filler materials. Thus, this
typeof process allows for the manufacturing of
multi-layeredparticles. Here, the different layers provide designed
func-tions such as protection from humidity during storage,delay of
API release in the digestive system and the actualdelivery of the
API.
The water and its distribution inside the vessel for theduration
of the process influence the process state and,consequently, the
quality of the final product. For example,API that are sensitive to
long-term exposure to moisturemay be coated with a film that
protects the API from ambi-ent humidity. In such cases, it is
important to establish thatthe particles are sufficiently dry
before this film is applied.In addition, a too fast drying rate may
have negativeimpact on the coating quality. A more extreme
situationis the undesirable event of excessive amounts of
waterinside the vessel, which can cause extensive particle
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522 J. Nohlert et al. / Measurement 55 (2014) 520–535
agglomeration and eventually process break-down. If sucha
condition can be detected, it is feasible to change the pro-cess
parameters in order to counter-act agglomeration. Thewater inside
the vessel can occur in a number of differentforms: (i) water
vapor; (ii) sorbed water inside the parti-cles; (iii) free water on
the surface of the particles; (iv)water droplets in the air; (v)
condensed water dropletson the vessel walls; and (vi) water in
agglomerates ordense gatherings of particles.
2.2. Measurement principle
From an electromagnetic point of view, the process ves-sel that
we consider is a rather good approximation of amicrowave cavity
resonator. The geometry of the vessel,which is used in the
electromagnetic model described laterin the article, is shown in
Fig. 2. We exploit two magnetic-field probes to excite eigenmodes
supported by the micro-wave resonator and the corresponding
eigenfrequenciesare measured with the same set of probes. A network
ana-lyzer is connected to the two probes and the 2� 2 scatter-ing
matrix is measured as a function of frequency. Themeasured
scattering parameters are used to extract thecomplex resonance
frequencies of a selection of the lowesteigenmodes supported by the
process vessel.
It should be emphasized that although these probes arerather
small in comparison to the microwave resonator,i.e., the process
vessel, the electromagnetic field for basi-cally all eigenmodes
extends throughout most of the pro-cess vessel’s volume. The
eigenfrequencies are influenced
Fig. 2. The process vessel including its two rectangular windows
(W1 andW2) and the cylindrical tube used for loading of particles
(H1). This figurealso illustrates four temperature probes (T1–T4)
and two microwaveprobes (M1 and M2) although these are not part of
the electromagneticmodel.
by the geometry of the process vessel and, more impor-tantly for
this application, the material and its distributioninside the
process vessel. Consequently, importantinformation on the
distribution of particles and theirmoisture content can be derived
from the measuredeigenfrequencies.
2.2.1. Homogenization of a mixture of air and particlesThe
mixture of particles and air influences the electro-
magnetic fields inside the process vessel. The
typicallength-scales associated with the lowest eigenmodes
arecomparable to the size of the cavity and, as a consequence,the
particles are extremely small in relation to the spatialvariation
of the electromagnetic field. Thus, it is beneficialto represent
the mixture of particles and air in terms of aneffective
permittivity, where the possible presence of othersmall dielectric
objects, such as liquid droplets, contributesto the effective
permittivity in the same manner as the par-ticles. Given the
material parameters and geometry of theparticles together with
their spatial distribution, the effec-tive permittivity can be
calculated by means of electro-magnetic mixing formulas [8]. Here,
we focus on thewell-known Maxwell–Garnett mixing formula
�eff � �b�eff þ 2�b
¼ 13�b
XNn¼1
#nanVn
; ð1Þ
where �eff is the effective permittivity and �b is the
permit-tivity of the background medium for a mixture with N
dif-ferent types of inclusions indexed by n. In this article,
weassume that �b is real, i.e., we have a lossless
backgroundmedium. For the inclusions of type n, we have the
polariz-ability an, the inclusion volume Vn and the volume
fraction#n. For homogeneous spherical inclusions with permittiv-ity
�i, we have the polarizability
a ¼ 3�bV�i � �b�i þ 2�b
; ð2Þ
where V is the volume of the particle. Layered
sphericalparticles with a core and an outer shell with different
per-mittivities can also be incorporated into Eq. (1) by usingthe
associated polarizability for this type of inclusions [8].
A dispersive inclusion material yields a dispersivebehavior of
the effective permittivity, although the disper-sion relation of
the mixture may be different from that ofthe inclusions. For
example, air with inclusions that aredescribed as a Debye medium
yields an effective permittiv-ity that also behaves like a Debye
medium, but with differ-ent values of the Debye parameters [9].
Furthermore, airand inclusion particles with non-zero conductivity
yieldsDebye-characteristics of the effective permittivity, due
tothe Maxwell–Wagner effect [10].
2.2.2. Density independent moisture measurementsA feasible way
to extract information about moisture
content of the particles from the estimated complex effec-tive
permittivity �eff ¼ �0eff � j�00eff in the process vessel, isthe
approach of density-independent measurement tech-niques [10]. The
main idea of this approach is that if thematerial density in a
given volume changes, both �0eff and�00eff will be affected in a
similar way, since they both
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J. Nohlert et al. / Measuremen
depend on the total amount of polarizable material in
thevolume.
In a situation where a certain material is dispersed in
abackground medium with permittivity �b, the ratio
g ¼ �00eff
�0eff � �b; ð3Þ
is an example of a density-independent function that hasshown to
be more or less independent on the density formany material
mixtures [11,12]. This is not surprising, andit can be shown using
the Maxwell–Garnett mixing formulaapplied to lossy spherical
inclusions dispersed in a losslessbackground medium, that g is
independent on the volumefraction # in the low-density limit.
Therefore, it is expectedthat measurements of �00eff and �
0eff taken at different material
densities would fall on a straight line that intersects the
ori-gin if �00eff is plotted versus �
0eff � �b, given that the particles
have constant permittivity. The slope g of this line
usuallydepends on the moisture content of the inclusion materialin
a characteristic manner. The slope g may therefore beused as a
density-independent metric of the moisture con-tent, if it is known
how g depends on the moisture contentfor the material considered.
Such relations are usuallyobtained from calibration procedures
which involve mea-surements on material samples with known moisture
con-tent. It should be emphasized that g may depend on manyother
factors as well, such as the physical state of the water(e.g.
whether it is free or bound in the material) and the tem-perature.
In the case of free water, its distribution in thematerial may also
be of importance.
In practical measurement situations, the estimatedeffective
permittivity �eff may be biased by, e.g., tempera-ture variations
of the metal parts of the cavity, or by changesin the permittivity
of the background medium (which isusually air) caused by, e.g., a
varying humidity. In such cases,there may be non-zero residual
components of �00eff and�0eff � �b at zero material density due to
biased estimates of�eff , which makes a direct use of the ratio g
unreliable. Wetherefore make an attempt to extend the classical
density-independent measurement approach to situations wherean
uncontrolled bias of the estimated �eff is present. Ourapproach is
based on the covariance between �00eff and�0eff � �b, which is
computed for a fairly large number of mea-surement samples. The
material (in our case the particles inthe process) is
re-distributed between different samplepoints which yields a
variation in the material density andhence a variation in �00eff
and �
0eff , which is used to calculate
the covariance. As a motivation to this approach, we con-sider a
situation where lossy spherical inclusions with per-mittivity �i ¼
�0i � j�00i are dispersed in a backgroundmedium with permittivity
�b with volume fraction #. If thedispersion is dilute (#� 1) and if
the loss factor of the inclu-sion material is low (�00i =�
0i 6 0:1), the Maxwell–Garnett mix-
ing formula yields the following expressions for the real
andimaginary parts of the effective permittivity
�0eff=�b � 1 ’ 3�0i=�b � 1�0i=�b þ 2
# ð4Þ
�00eff=�b ’ 9�00i =�b
ð�0i=�b þ 2Þ2 #: ð5Þ
If we now assume that #; �0i and �00i vary randomly around
their respective mean values, this will obviously
yieldvariations in �eff . Hence, by studying the covariancebetween
the real and imaginary part of �eff , one mayextract important
information about the parameters #; �0iand �00i and their
variabilities. In particular, we notice fromEqs. (4) and (5) that
both the real and imaginary part of�eff depend linearly on the
volume fraction #, whichexplains the density-independent nature of
the ratio gand the reason why �00eff and �
0eff � �b obtained from differ-
ent volume fractions tend to fall on a straight line.
Devi-ations from this line can be explained by means ofvariations
in �0i and �
00i , since they influence the real and
imaginary part of �eff in different ways, as seen fromEqs. (4)
and (5).
2.3. Experimental setup
The experimental setup is shown in Fig. 3a and itincludes the
process vessel, the process machine and thetwo-port network
analyzer used to perform the microwavemeasurements.
t 55 (2014) 520–535 523
2.3.1. Reduction of undesired lossesThe original process vessel
has a couple of apertures, such
as windows that are used for visual inspection of the
process,and such apertures damp the microwave cavity by means
ofradiation losses. We are interested in measuring the
dampingassociated with the moisture content of the particles
and,thus, we wish to reduce other contributions to the totaldamping
of the cavity. Therefore, we shield the process vesselby covering
the apertures W1, W2 and H1 in Fig. 2 by alumi-num foil, and use a
perforated plate to shield the microwavecavity from the air outtake
in the upper part of the processvessel. In addition, the shielding
mitigates possible problemswith external electromagnetic sources
that may disturb themeasurements. With these arrangements we
obtainunloaded Q-values of the cavity which are in the order
of103—104 for the lowest eigenmodes.
2.3.2. Choice of probes and their designPharmaceutical mixtures
processed in steel containers
often become electrically charged due to the triboelectriceffect
[13,14]. Consequently, the statically charged parti-cles yield a
quasi-static electric field as they move insidethe vessel. In order
to protect the network analyzer frominduced voltages of large
magnitude and electric dis-charges that may occur in the process
vessel, we exploitmagnetic field probes (also referred to as
H-probes) thatare mainly sensitive to the time variations of the
magneticflux that passes through the loop of the H-probe.
Fig. 3b shows the process vessel equipped with two H-probes
located in the upper part of the cavity for measure-ment of the
azimuthal and vertical components of themagnetic field. At these
locations, we can efficiently coupleto the magnetic field of the
lowest eigenmodes that we usefor sensing. In addition, the size of
each loop is chosen suchthat we get sufficiently good coupling to
all of these modes.For industrial usage, it may not be feasible to
let the probeextend into the process vessel. A possible remedy is
to
-
(a) Experimental setup(a) Experimental setup (b) H-probes(b)
H-probes
Fig. 3. Photographs of (a) the process vessel in the
experimental setup and (b) the two H-probes.
524 J. Nohlert et al. / Measurement 55 (2014) 520–535
create a shallow dent in the cavity wall and to cover thisdent
by a dielectric ‘‘radome’’.
2.3.3. Measurement settingsThe network analyzer (Agilent E8361A)
is controlled
from a PC via GPIB interface, in order to perform repeatedscans
of a frequency band that includes the resonancefrequencies of the
sensing modes (0.7–1.7 GHz). This fre-quency band takes
approximately 2 s to scan (for excitationon one of the two ports),
using totally 6400 frequency pointsand the IF bandwidth set to 5
kHz, which means that it takes1–10 ms to scan the frequency band
occupied by a singleresonance. The time between two consecutive
frequencysweeps is set to 10 s, where a substantial part of this
timeis required for data transfer over the GPIB interface. In
thepost-processing of the measurement data, we use a statisti-cal
approach which benefits from a large number of mea-surement
samples. Therefore, a measurement setup thatallows for faster
sampling of the process would be beneficialfor this measurement
technique.
3. Electromagnetic model
For the analysis of the resonance frequencies and
thecorresponding eigenmodes, we use an idealized model ofthe
process vessel: (i) all the metal parts of the process ves-sel are
assumed to be perfect electric conductors (PEC); (ii)all apertures
are completely sealed such that the interior ofthe process vessel
is completely enclosed by a perfect elec-tric conductor; and (iii)
the probes are excluded from themodel. Further, we assume that the
material inside theprocess vessel can be described by relatively
simple disper-sion relations for the frequency band of interest
and, as astarting point, we consider a frequency-independent
per-mittivity that may vary with respect to space. Also, weassume
that the magnetization for the media involved isnegligible and use
the permeability l ¼ l0.
Thus, we consider the eigenvalue problem
r� E ¼ �jxB in X; ð6Þ
r � 1l0
B ¼ ðjx�þ rÞE in X; ð7Þ
n̂� E ¼ 0 on C: ð8Þ
We seek the eigenmodes ðEm;BmÞ and the
correspondingeigenfrequencies xm that satisfy the eigenvalue
problem(6)–(8), where the index m labels the resonancessupported by
the process vessel.
3.1. Weak formulation
The eigenvalue problem (6)–(8) is expressed in theweak form:
Find ðE;B;xÞ 2 H0ðcurl; XÞ � Hðdiv; XÞ � Csuch that
cFLðE;vÞ ¼ �jxm1ðB;vÞ; ð9ÞcALðB;wÞ ¼ jxl0�0m�r ðE;wÞ þ
l0mrðE;wÞ; ð10Þ
for all ðv ;wÞ 2 Hðdiv; XÞ � H0ðcurl; XÞ. Here, we expressthe
real (absolute) permittivity � ¼ �0�r in terms of the
cor-responding relative permittivity. Further, we have thebilinear
forms
cFLðu;vÞ ¼Z
Xðr � uÞ � v dX; ð11Þ
cALðu;vÞ ¼Z
Xu � ðr � vÞdX; ð12Þ
m1ðu;vÞ ¼Z
Xu � v dX; ð13Þ
m�r ðu;vÞ ¼Z
X�ru � v dX; ð14Þ
mrðu;vÞ ¼Z
Xru � v dX: ð15Þ
Finally, we have the spaces
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J. Nohlert et al. / Measurement 55 (2014) 520–535 525
Hðcurl; XÞ ¼ fu : u 2 L2ðXÞ andr� u 2 L2ðXÞg; ð16ÞHðdiv; XÞ ¼ fu
: u 2 L2ðXÞ andr � u 2 L2ðXÞg; ð17Þ
and H0ðcurl; XÞ is the subspace of Hðcurl; XÞ that satisfiesthe
boundary condition (8).
3.2. Finite element approximation
We expand the electric field in terms of curl-conform-ing
elements and the magnetic flux density in diver-gence-conforming
elements, see Ref. [15] for furtherdetails. This yields the
discrete eigenvalue problem
0 �CCT �Z0Mr
� �c0be
� �¼ jx
c0
M1 00 M�r
� �c0be
� �; ð18Þ
where we have scaled the magnetic flux density with thespeed of
light and Ampère’s law with the impedance ofvacuum. This form is
useful since it yields an eigenvalueproblem that is linear in terms
of the eigenvalue jx=c0.Reference [16] contains further details on
the treatmentof eigenvalue problems by means of the finite
elementmethod.
Elimination of the magnetic flux density from Eq. (18)yields the
corresponding eigenvalue problem
CTM�11 Cþ jxl0Mr �x2l0�0M�r� �
e ¼ 0; ð19Þ
formulated in terms of only the electric field. This eigen-value
problem is nonlinear since it is quadratic in termsof the
eigenfrequency x.
For problems with conducting media, it is computation-ally
advantageous to solve Eq. (18). Such situations mayoccur in
pharmaceutical processes that feature solutionswith ions. For dry
processes, the non-conducting back-ground medium with possibly
conducting inclusions, dis-plays a more complicated dispersion for
the effectivepermittivity. Given the somewhat limited
frequency-bandused for the measurements in this article, we choose
toapproximate the effective permittivity by a frequency-independent
function �ðrÞ ¼ �0ðrÞ � j�00ðrÞ. This yields theeigenvalue
problem
CTM�11 C�x2l0 M�0 � jM�00ð Þ� �
e ¼ 0; ð20Þ
which is not particularly attractive for direct computationbut
useful for the sensitivity analysis that follows below.
3.3. Losses due to finite conductivity in the cavity walls
It is possible to approximately determine the losses dueto
cavity walls of finite conductivity based on the electro-magnetic
field solution computed for a PEC boundary. Thistype of approach
yields the quality factor associated with aparticular eigenmode
and, consequently, its damping [17].The losses are given by
Pwall ¼ Re12
ZC
ZCjn̂�Bml0j2dC
� �; ð21Þ
where ZC ¼ ð1þ jÞ=ðrdmÞ is the surface impedance for thewall of
finite conductivity. Here, dm ¼ ð2=ðxml0rÞÞ
1=2 isthe penetration depth for the eigenfrequency xm and
the
magnetic flux density Bm of the corresponding eigenmodeis
computed based on the approximation that the wall con-ductivity is
infinite. Finally, the quality factor is given byQwall;m ¼
xmWm=Pwall;m where Wm is the time-averageenergy stored in the
vessel by the eigenmode ðEm;BmÞ, i.e.,
Wm ¼14
ZX�jEmj2dXþ
14
ZX
1l0jBmj2dX: ð22Þ
4. Estimation procedure
Given the measured scattering parameters, we estimatethe complex
resonance frequencies by means of a sub-space-based multivariable
system identification algorithm[18]. This measurement procedure is
repeated in a regularfashion throughout the entire duration of the
process time,and in the following, we refer to the estimated
resonancefrequencies as the measured resonance frequencies.
First,the vessel is empty and the measured resonance frequen-cies
are denoted �xrefm , where the overline denotes a mea-sured
quantity. Next, the process vessel is loaded withparticles and the
subsequent measured resonance frequen-cies �xm are used to form the
deviations in the resonancefrequencies D �xm ¼ �xm � �xrefm . As
the process evolves, weexploit the relative deviation D �xm= �xrefm
to estimate thestate of the process and, later in this section, we
presentformulas that relate a perturbation in resonance frequencyto
the corresponding perturbations in (i) the materialparameters and
(ii) the shape of the vessel due to thermalexpansion.
The estimation of the material and shape parameters isbased on
minimization of the misfit between the measuredand computed
relative deviations in resonance frequen-cies. Thus, we wish to
minimize the following expression
Xm
Dxmxrefm
� D�xm
�xrefm
��������
2
; ð23Þ
where Dxm ¼ xm �xrefm is the deviation in the computedresonance
frequencies xm as compared to the correspond-ing (computed) result
xrefm for the empty reference case.The computed resonance
frequencies xm are functions ofthe material and shape parameters,
and this dependencymay be expressed according to
xm ¼ xmjLP þX
n
@xm@pnjLPdpn; ð24Þ
for small deviations around a certain linearization point,which
is denoted by the subscript LP. The empty cavitymay be used as
linearization point, but if the permittivityinside the vessel
deviates substantially from vacuum, it isbeneficial to use a
linearization point with higher permit-tivity in certain regions of
the vessel. The perturbationsdpn in the parameters with respect to
the linearizationpoint, are stored in a vector x and we compute an
estimatex̂ of x by means of the regularized approach
x̂ ¼ arg minxjjAx� bjj2 þ cjjLðx� ~xÞjj2: ð25Þ
Here, the elements of the matrix A and the right-hand-sidevector
b are given by
-
526 J. Nohlert et al. / Measurement 55 (2014) 520–535
Amn ¼1
xrefm@xm@pnjLP ð26Þ
bm ¼D �xm�xrefm
�xmjLP �xrefm
xrefm: ð27Þ
The first term in Eq. (25) resembles a system of linearequations
which is over-determined, i.e., the number ofrows in A exceeds the
number of columns. Hence, theresidual jjAx� bjj can be used as a
metric of how wellthe column space of A is able to represent the
data vectorb. The second term in Eq. (25) is a regularization
term,which penalizes solutions x̂ away from a given vector ~xusing
a weighted Euclidean norm. The matrix L in the reg-ularization term
is diagonal with all diagonal elementsequal to unity, except for
the elements that multiply theshape parameters, which are
substantially larger. The bal-ance between the two terms in Eq.
(25), i.e., a solutionwhich makes Ax̂ � b and a solution x̂ � ~x,
is controlledby the regularization parameter c. From a Bayesian
pointof view we can interpret Eq. (25) as the posterior
meanestimate of x under the assumption that the measurementerrors
in b are Gaussian distributed, have zero mean andcovariance matrix
12I and the parameter vector x has aGaussian prior distribution
with mean value ~x and covari-ance matrix ð12=cÞðLTLÞ�1 [19].
For normal process conditions, the losses in the processvessel
are small and, therefore, we compute the sensitivitymatrix A for
linearization points that corresponds to thevessel without losses.
Consequently, the permittivity isrepresented by � ¼ �0LP þ d�0 �
jd�00, where �0LP is the permit-tivity at the linearization point.
Here, the perturbationswith respect to the linearization point are
denoted d�0
and d�00, which are estimated by means of Eq. (25).Thus, we use
the eigenvalue problem (20) with
�0ðrÞP �0 and �00ðrÞ ¼ 0 to compute the eigenfrequenciesand
eigenmodes at the linearization point, which reducesto a special
case of Eq. (18). The computed eigenfrequen-cies and eigenmodes are
also used to compute the sensitiv-ities as described later in this
section. The down-bed regionwith the fluidized particles yields an
effective permittivitythat deviates substantially from vacuum.
Therefore, we usea linearization point
�0LPðrÞ ¼�0bed in the bed region;�0 outside the bed region;
�ð28Þ
where �0bed P �0. We solve the eigenvalue problem for arange of
bed heights hbed and bed permittivities �0bed, wherethe solutions
from the eigenvalue problem together withthe corresponding
sensitivities are stored in a database. Itis noticed that the
resonance frequencies and their sensi-tivities do not change
significantly as hbed decreases, if�0bed is increased to an
appropriate extent. This is reason-able since it merely corresponds
to a redistribution of thebed material to a smaller region. During
the evolution ofthe process, we continuously seek the linearization
point�0LP that yields the best fit with the corresponding
devia-tions in the measured resonance frequencies, where thebed
height is fixed at a representative value hbed ¼ 5 cm.
Hence, this estimation procedure can be used for a pro-cess
where the particles grow significantly in size, by
means of changing the linearization point �0LP. To summa-rize,
Eq. (25) yields reliable estimates of the perturbationsd�0eff and
d�
00eff with respect to the linearization point. This
approach is sufficient for most normal process states.
4.1. Sensitivity analysis
The sensitivity analysis is based on the eigensolutionðEm;Bm;xmÞ
computed for a linearization point with�0ðrÞP �0 and no losses,
i.e., �00ðrÞ ¼ 0 and rðrÞ ¼ 0. Giventhis linearization point, we
formulate the sensitivities thatrelate a small perturbation dxm in
the resonance frequencyxm to perturbations in (i) the material
parameters d�0 andd�00 and (ii) the normal displacement dn of the
cavity’sboundary. Fig. 4a shows a subdivision of the cavity’s
vol-ume that is used for the parameterization of the materialand
Fig. 4b shows the cavity’s wall with a set of basis func-tions used
for the representation of the normal displace-ment, where both
parameterizations are axisymmetric.
4.1.1. Material sensitivitiesBased on the eigenvalue problem
(20), the sensitivity of
the resonance frequency xm with respect to changes in
thematerial parameters p ¼ �0 and �00 is expressed as
dxmxm
¼ �md�0 ðEm;EmÞ � jmd�00 ðEm;EmÞ
2m�0 ðEm;EmÞ; ð29Þ
where we have
mdpðu;vÞ ¼Z
Xdpu � v dX; ð30Þ
for a perturbation dp with respect to the material parameter
p[17,20]. From Eq. (29), we notice that d�0 affects only the
realpart of the eigenfrequencies, and that d�00 only affects
theimaginary part. The discrete version of this linearization
is
dxmxm
¼ � eTm Md�0 � jMd�00½ �em
2eTmM�0em: ð31Þ
4.1.2. Representation of material perturbationsThe perturbation
dp of the material parameter p is rep-
resented in terms of a set of N space dependent basis func-tions
unðrÞ, which are multiplied with the coefficients dpn,according
to
dpðrÞ ¼XNn¼1
dpnunðrÞ: ð32Þ
Here, we subdivide the vessel’s volume X into regions Xnsuch
that Xn do not overlap and
SNn¼1Xn ¼ X. We exploit
piecewise constant basis functions unðrÞ that are equal toone if
r 2 Xn and zero elsewhere. In particular, we associ-ate the basis
functions with three regions: (i) the bedregion of height hbed with
a relatively high density of par-ticles; (ii) a cylinder shaped
volume that coincides withthe core of the fountain; and (iii) the
rest of the processvessel. These regions are formed by combining
the basicsubregions shown in Fig. 4a.
The residual jjAx̂� bjj in the solution to the estimationproblem
(25) is used as a metric of how well these basisfunctions are able
to represent the actual permittivity
-
Fig. 4. Two-dimensional projection of the process vessel showing
(a) the basic subregions that may be combined in different ways to
obtain the materialbasis functions un and (b) basis functions used
to represent shape deformations. All dimensions are in
millimeters.
J. Nohlert et al. / Measurement 55 (2014) 520–535 527
distribution in the experiment. For instance, the height
andradius of the fountain region is chosen such that the resid-ual
is minimized. Based on measurement results presentedlater in this
article, we find that the fountain region indi-cated by gray color
in Fig. 4a yields the best agreementwith the measured resonance
frequencies.
4.1.3. Shape sensitivitiesFor a normal displacement dn of the
vessel’s boundary
C, the resulting perturbation in the resonance frequencyis given
by [17,20]
dxmxm
¼ � ddnðBm;BmÞ=l0 � ddnð�0Em;EmÞ
2Wm; ð33Þ
where Wm is the time-average energy in the cavity givenby Eq.
(22), and
ddnðu;vÞ ¼Z
Cu � v�dndS: ð34Þ
A positive deformation dn > 0 here corresponds to that
thevolume of the cavity increases. We notice that shape
defor-mations only affect the real part of the
eigenfrequencies.
The corresponding discrete formulation of Eq. (33) is
dxmxm
¼ �1l0
bHDdnb� eHD�0dne1l0
bHM1bþ eHM�0e; ð35Þ
where the superscript H indicates conjugate transpose.
4.1.4. Representation of shape perturbationsWe use an
axisymmetric representation of the normal
displacement dn by means of a quadratic hierarchical basisfor
three different parts of the vessel’s boundary: (i) theupper lid;
(ii) the cylindrical surface; and (iii) the conicalsurface. Fig. 4b
shows the basis functions in relation tothe geometry of the vessel.
On each of the three parts ofthe boundary, we exploit the (local)
basis functions
w1ðuÞ ¼ 1� u ð36Þw2ðuÞ ¼ u ð37Þw3ðuÞ ¼ 4uð1� uÞ ð38Þ
where the part of the boundary is parameterized by thelocal
coordinate u such that the interval 0 6 u 6 1 corre-sponds to the
entire part of the boundary.
-
Table 1Computed and measured values of the resonance frequencies
and unloadedQ-values of the lowest eigenmodes in the process
vessel. The variabilities(here represented by one standard
deviation) in the measured quantitiesarise from disassembling and
reassembling the complete vessel.
m Computed Measured
f0 ðMHzÞ Q f0 ðMHzÞ Q
1 759 5100 761 ± 0.07 5400 ± 1002 894 5800 894 ± 0.05 5100 ±
4003 928 5900 930 ± 0.02 4400 ± 4004 1008 6000 1009 ± 0.03 3200 ±
8005 1051 6100 1051 ± 0.06 4700 ± 2006 1149 6300 1150 ± 0.03 3400 ±
7007 1207 5600 1206 ± 0.08 3500 ± 3008 1495 9800 1498 ± 0.05 10,300
± 400
528 J. Nohlert et al. / Measurement 55 (2014) 520–535
In order to constrain the number of degrees of freedomassociated
with the cavity’s shape to a number that is prac-tical, and to
suppress non-physical shape deformations, weform two new basis
functions by linearly combiningdn1—dn8 according to
dnlid ¼ 0:97dn6 þ 0:24dn8 ð39Þdncone=cyl ¼ 0:69dn2 þ 0:16dn3 þ
0:71dn4: ð40Þ
Thus, dnlid describes a smooth deformation of the top lidand
dncone=cyl describes a joint deformation of the cylindri-cal and
conical parts of the vessel. The coefficient valuesin Eqs. (39) and
(40) are chosen such that the residualjjAx̂� bjj is minimized,
given only these two independentdegrees of freedom for the
shape.
4.2. Temperature measurements
Before the vessel is loaded with particles, it is
normallypre-heated. We exploit this part of the process to
gaininformation that is used to compute the a priori informa-tion
~x for later parts of the process. During the pre-heatingof the
vessel, the vessel is empty and we perform simulta-neous and
synchronized measurements on (i) the reso-nance frequencies and
(ii) the temperature registered bythe set of temperature probes
shown in Fig. 2. Given thedeviations ydT in the temperatures
(relative to the initialtemperatures) and the shape perturbations
x̂dn estimatedfrom the resonance frequencies for the empty cavity,
weuse the relatively simple model x̂dn ¼ BydT , where thematrix B
is determined by means of linear regression fromthe data acquired
during the pre-heating interval. Thismodel is used to obtain a
priori estimates ~xdn ¼ BydT fromthe measured temperatures during
later parts of the pro-cess, after the particles have been loaded.
In the following,we exploit the a priori information
~x ¼~xd�eff~xdn
� �¼
0BydT
� �; ð41Þ
in the estimation problem (25), where ~xd�eff corresponds toall
the material parameters that are incorporated in theestimation
procedure.
Tests demonstrate that about 95% of the perturbationsin the
resonance frequencies due to thermal expansion ofthe vessel during
heating and cooling can be accountedfor by this model, when the
vessel is empty. This approachis less successful once the vessel is
loaded with particles,since the presence of particles yields a
different tempera-ture distribution in the vessel. However, it is
presumedthat it is feasible to improve the a priori
information,should the metal temperature be measured at more
placeson the vessel’s wall and top lid.
5. Results
In the measurement results presented in the following,we perform
repeated microwave measurements on theprocess vessel as the process
is running. Each processexperiment typically takes a few hours in
total. The exter-nal process parameters such as the flow-rate,
temperatureand humidity of the fluidizing air, the pressure and
flow in
the pneumatic spray-nozzle and the flow-rate of the spray-ing
liquid, are controlled from the user interface of the pro-cess
machine. These external process parameters togetherwith measured
temperatures at the locations indicated inFig. 2, are logged by the
process machine.
5.1. Cavity without particles
Among the eigenmodes hosted by the process vessel wehave
identified eight modes that are feasible to use forsensing. These
modes are listed in Table 1 together withtheir resonance
frequencies and unloaded Q-values. Allthese modes have similarities
with the TE and TM modeshosted by a circular cylindrical cavity. In
particular, themodes m ¼ 1;2;5 and 7 resemble the
modesTE111;TE112;TE113, and TE114 of a circular cylindrical
cavity,and the modes m ¼ 3;4 and 6 resemble the modesTM010;TM011
and TM012 respectively. The mode m ¼ 7(TE114) has a strong electric
field in the lower part of thevessel, which makes it well-suited
for probing the permit-tivity in the down-bed region. The mode m ¼
8 resemblesTE011 which has an electric field that is zero on all
cavitywalls, which implies that its resonance frequency is
insen-sitive to dielectric material adhering to the cavity
walls.This mode also has a notably high Q-value.
The loaded Q-values in the experiment can be calcu-lated from
the real and imaginary part of the measuredcomplex resonance
frequency x according to
Q l ¼ReðxÞ
2 � ImðxÞ ; ð42Þ
for the weakly damped cavity modes [17]. Since the cavityis
loaded by two probes with different coupling coeffi-cients, the
following expression is used to calculate theunloaded Q-value
Q u ¼ Q l2
jS11j þ jS22j
; ð43Þ
where the reflection coefficients S11 and S22 are evaluatedat
each resonance frequency [21].
We calculate the Q-value from the electromagneticmodel using the
method described in Section 3.3, and herewe assume that the cavity
walls have a conductivityrc ¼ 106 S=m, which should be
representative for thestainless steel that the vessel is made
of.
-
J. Nohlert et al. / Measurement 55 (2014) 520–535 529
As can be seen in Table 1, the measured and computedresonance
frequencies agree well. There is also a generallygood agreement
between measured and computed Q-val-ues although, for some modes,
the measured Q-value is sig-nificantly lower than the computed. The
latter may be aresult of insufficient electric contact in the joint
betweenthe conical and cylindrical part of the cavity, or at the
alu-minum foil that covers the windows. As the process vesselis
disassembled and reassembled, a certain variability inthe measured
resonance frequencies and Q-values is intro-duced, which is
presented in Table 1. This variability is sig-nificant in relation
to the perturbations in resonancefrequencies caused by changes in
the state of the process.Therefore, the particles are inserted into
the process vesselthrough a small hole (indicated by H1 in Fig. 2)
after thenecessary reference measurements on the empty cavityhave
been collected, in order to eliminate this
variability.Investigations show that the variability introduced
frominserting the particles in this manner is negligible.
5.1.1. Effects from air humidity and sprayIn a Wurster-process,
several different components that
influence the resonance frequencies are present simulta-neously.
The most important of these components are (i)particles, (ii) the
temperature of the vessel (iii) liquid drop-lets from the spray
nozzle and (iv) water vapor in the flu-idizing air. The temperature
of the vessel affects theresonance frequencies mainly via
perturbations of the cav-ity’s shape, whereas the other components
are assumed toinfluence the resonance frequencies via the
permittivity. Inorder to assess how each of these components
contributeto the microwave response, they have been studied
sepa-rately. Some of these components, such as the sprayingliquid
and the temperature, are inherently interconnected,i.e., the
spraying rate cannot be changed without alsoaffecting the
temperature.
The humidity of the fluidizing air can be
controlledindependently using the process machine and
humiditiesranging from 0 to 20 ðg H20Þ=ðkg airÞ, corresponding
todew-points in the range from �30 �C to 25 �C, can beachieved. Our
measurements show that the humidityinfluences only the real part of
the permittivity of the airand hence the resonance frequencies, to
a degree that isclearly detectable.
Water sprayed from the pneumatic spray nozzle (alsoreferred to
as the atomizer) yields similar changes in thepermittivity inside
the cavity as the humidity does. Only�0eff is influenced by the
spray, and if the same amount ofwater is added through the atomizer
as via the fluidizingair, the change in �0eff is very similar. The
contributions tothe permittivity of the air from humidity in the
fluidizingair and from water spray are additive, as long as the
spray-ing rate is sufficiently low to allow for complete
evapora-tion of the liquid droplets.
5.2. Measurements with particles
In the following, we present measurement results forprocesses
involving particles. The particles used are madeof MCC (Cellets
�brand) and have diameters in a distribu-
tion from 500 to 700 lm. A batch consisting of 200 g of
particles is used in all of the following experiments.
Allprocess settings are identical in the following
experiments,except for the type of spraying solution and the
sprayingrate. The fluidization flow is set to 30 Nm3=h (where
Ndenotes normal temperature and pressure) with an inlettemperature
of 70 �C. The atomizer pressure is 2:0 barand the associated
atomizer flow is 2:0 Nm3=h.
The spraying liquid used in the experiments is watercontaining
either (i) Mannitol or (ii) NaCl. The permittivityof these spraying
liquids is measured using the dielectricprobe kit 85070E from
Agilent Technologies, and theresults are shown in Fig. 5.
In the beginning of each experiment, the vessel is pre-heated
and the particles are loaded, before the experi-ment-specific part
of the process (e.g. coating) is initiated.In the results presented
in the following, we omit the pre-heating interval and focus on the
experiment-specific parts.
The average error between the model and measurementis computed
as the root-mean-square of the differencebetween measurements (b)
and model fit (Ax̂), averagedwith respect to the number of sensing
modes M. With par-ticles present in the vessel, this average error
is in the orderof 10�5 during normal process conditions (no
extensiveagglomeration, etc.) which should be compared with
theaverage magnitude of the measurement response(jjbjj=M), which is
in the order of 10�3.
According to the sensitivity analysis in Section 4.1,
per-turbations in the real part of the resonance frequencies
arerelated to both d�0eff and dn. Similarly, a perturbation in
theimaginary part of the resonance frequency is related tod�00eff .
As described in Section 4.2, dn is to a large extent deter-mined
based on a priori information that exploits tempera-ture
measurements. An error in the a priori information mayyield a
corresponding error in d�0eff , which varies on a time-scale that
is significantly slower than the fast timescalesassociated with the
fluid-dynamics of the process. Basedon these two time-scales, we
make the assumption�eff ðtÞ ¼ �eff ;slowðtÞ þ �eff ;fastðtÞ, where
�eff ;fastðtÞ representsfast random fluctuations and �eff ;slowðtÞ
represents slowchanges in the permittivity caused either by errors
in the apriori information or by changes in the actual process
state(such as particles growing in size or accumulation of
mois-ture in the particles). We model �eff ;slowðtÞ by a
low-orderpolynomial with respect to time t, and this polynomial
isdetermined by means of linear regression based on the esti-mated
�eff ðtÞ. Furthermore, we compute the covariancematrix from the
real and imaginary part of �eff ;fastðtÞaccording to C ¼ covðz1;
z2Þ where z1 ¼ ½�0eff ;fastðtnÞ=�0 � 1�
T
and z2 ¼ ½�00eff ;fastðtnÞ=�0�T are vectors containing samples
of
�eff ;fast taken at discrete time instants tn. If the
eigenvectorsof C are scaled by the square root of its eigenvalues
(i.e.the standard deviations), they define the major and
minorsemi-axes of an ellipse that represent the co-variation ofthe
data. Such ellipses are included in the scatter-plots inthe
presentation of the following measurement results.Variations in
�eff ;fastðtÞ along the eigenvector associated withthe largest
eigenvalue of C, are mainly attributed to fluctua-tions in the
particle volume fraction #. Therefore, we takethe slope of this
eigenvector (i.e. the major semi-axis ofthe ellipse) as a
density-independent ratio which is equiva-lent to the ratio g in
Section 2.2.2.
-
0.5 1 1.5 20
10
20
30
40
50
60
70
80
f [GHz]
/0
and
/0
[-]
(a) Mannitol
0.5 1 1.5 20
10
20
30
40
50
60
70
80
f [GHz]
/0
and
/0
[-]
(b) NaCl
Fig. 5. Relative permittivity of distilled water at room
temperature that contains (a) Mannitol (13.5%) and Kollicoat
IR�
(1.5%), and (b) NaCl (0.5%). Solidcurves represent �0=�0 and
dashed curves �00=�0.
530 J. Nohlert et al. / Measurement 55 (2014) 520–535
The relationship between this slope and underlyingphysical
parameters such as the moisture content of theparticles and the
concentration of salt (NaCl) in the spray-ing liquid, have been
studied by means of Monte-Carlosimulations. These simulations are
based on measure-ments of the complex permittivity of MCC [11] and
empir-ical models for the permittivity of water with and
withoutsalt [10], together with the mixing formulas described
inSection 2.2.1. Thus, we generate random mixtures of MCCparticles
and air by using statistical normal-distributionsto represent the
volume fraction and water content ofthe particles. The water is
assumed to be either absorbeduniformly in the MCC-particles or
distributed in a uniformwater-layer on the surface of the
particles. The case with apronounced water-layer may be
representative also for sit-uations where the surface of the
particles have a substan-tially higher moisture content than the
core. Based onthese simulations, we observe the following
trends:
1. An increase in the moisture content of the MCC parti-cles
(absorbed water) increases the slope, if the initialmoisture
content is less than around 7%. For highermoisture contents, the
slope instead decreases withincreasing moisture content.
2. Pure water distributed on the surface of the
particlesdecreases the slope.
3. Water containing salt distributed on the surface of
theparticles increases the slope if the salt concentrationexceeds
1%.
4. The slope is not affected by changes in the volume frac-tion,
if the volume fraction is sufficiently low (around5% or lower),
whereas at higher volume fractions, theslope increases with
increasing volume fraction.
5.2.1. Fast coating processHere, we present results from a
process where MCC par-
ticles are coated with a mixture of Mannitol (a sugar) and
apolymer labeled Kollicoat IR
�(ethylene glycol vinyl acetate
grafted polymer), where the Mannitol and the Kollicoat IR
are dissolved in de-ionized water. The dry content of
thesolution (the fraction that ideally stays on the surface ofthe
particles) is 15 mass% (13.5% Mannitol and 1.5% Kolli-coat IR). The
complex relative permittivity for this solutionis shown in Fig. 5a,
and here we notice that the response issimilar to that of pure
water. In this experiment, a rela-tively high spraying rate is used
to obtain fast build-up ofthe coating layer. First, the spraying
rate is set to 11.3 g/min and kept constant during approximately 15
min. Next,the spraying rate is increased even further to 14.4
g/min,which eventually leads to extensive agglomeration
andparticles adhering to the walls of the vessel.
Fig. 6 shows the estimated permittivity in three differ-ent
regions: (i) the down-bed region; (ii) the fountainregion above the
Wurster tube; and (iii) the rest of the vol-ume above the down-bed
region, as function of processtime in hours. At t = 0.9 h, the
particles are fluidized inthe process with the fountain off, and
the temperature isin equilibrium. The following changes in process
settingsare marked with dashed vertical lines: at t = 1.04 h
thefountain is switched on; in the interval 1.2 h < t < 1.26
hthe spraying rate is successively increased to 11.3 g/min;at t =
1.51 h the spraying rate is increased to 14.4 g/min.Some
interesting features can be observed in these figures:
1. The estimated permittivities fluctuate substantially,which is
reasonably caused by the continuous re-distribution of the
particles in the process which occurson a short time scale (
-
1 1.2 1.4 1.6
0.1
0.2
0.3
0.4
0.5
t [h]
eff/
0-
1an
deff
/0
[-]
(a) Bed
1 1.2 1.4 1.6
0
0.01
0.02
0.03
0.04
0.05
t [h]
eff/
0-1
and
e ff/
0[-]
(b) Fountain
1 1.2 1.4 1.6
−2
0
2
4
6
8
x 10−4
t [h]
eff/
0-
1an
deff
/0
[-]
(c) Volume
Fig. 6. Estimated permittivity as a function of process time in
the fast coating process. Black lines represent �0eff=�0 � 1 and
gray lines �00eff=�0. The dashedblack curve in (a) shows the
permittivity in the bed region at the current linearization
point.
J. Nohlert et al. / Measurement 55 (2014) 520–535 531
compensation for temperature variations, but it couldalso be due
to a lower particle density in the fountainas the spraying starts.
The estimated permittivity inthe remaining volume increases as the
spraying starts,reasonably due to increased air humidity inside
thevessel.
4. During the interval 1.5 h < t < 1.75 h, extensive
agglom-eration occurs in the process and the particles start
tobuild up dense layers on parts of the cavity walls, as aresult of
the high spraying rate (this could be observedvisually after the
experiment was finished). This pro-cess is clearly reflected in the
estimated permittivities,which are changing dramatically during the
agglomera-tion interval.
In situations similar to the agglomeration intervaldescribed in
item 4 above, i.e. at very moist process condi-tions that yields
material build-up on the vessel walls, werepeatedly observe a
larger discrepancy between themodel and measurements, i.e. an
increasing residualjjAx̂� bjj. Thus, a model that allows only for a
constantpermittivity in the bed, fountain and remaining
volumeregions, is unable to accurately represent the material
dis-tributions formed during extensive agglomeration. Thisindicates
the possibility of detecting anomalous processconditions based on
the residual. Studies show howeverthat it is possible to maintain a
low residual also duringextensive agglomeration if the cavity is
divided into sub-regions that better represent the actual material
distribu-tion. The sub-regions in the direct vicinity of the
cavitywalls shown in Fig. 4a may be well-suited for this
purpose.
Fig. 7 shows scatter plots of �00eff=�0 versus �0eff=�0 � 1
in
the three regions before and after spraying starts. The
ellip-ses in these scatter plots represent the co-variation of
thedata, where the length of each semi-axis is three
standarddeviations. All ellipses are highly elongated and the
varia-tions along the major semi-axis is assumed to be caused
byvariations in material density, according to the discussionon
density-independent functions in Section 2.2.2. Theslopes in the
scatter plots are shown in Table 2. Here wenotice that (i) the
slope is higher in the bed region, as com-pared to the fountain and
volume regions and (ii) the slopedecreases in the fountain and in
the volume after the
spraying starts, but remain unchanged in the bed. Accord-ing to
the results from the Monte-Carlo simulationsdescribed previously,
the decreasing slope in the fountainand volume regions could
indicate that the moisture con-tent at the surface of these
particles increases during thespraying interval. The higher slope
in the bed is in agree-ment with the Monte-Carlo simulations, since
the volumefraction in the bed is substantially higher than in the
otherregions.
5.2.2. Slow coating processIn this experiment, MCC particles are
coated with Man-
nitol and Kollicoat IR�
with the mixing ratio described inSection 5.2.1, under
relatively dry process conditions, i.e.,a relatively low spraying
rate of 6:6 g=min is used.
Fig. 8 shows the estimated permittivity in the bed, foun-tain
and remaining volume regions, as function of processtime in hours.
The time interval 0 h < t < 0.9 h, which hasbeen omitted,
includes pre-heating of the vessel and load-ing of particles, so at
t = 0.9 h, the particle fountain isswitched on and the temperature
is close to equilibrium.The process conditions are changed at the
time instantsindicated by the dashed vertical lines: at t = 0.89 h
spray-ing (coating) starts with a spraying rate of 4.6 g/min; att =
0.96 h the spraying rate is increased to the final value6.6 g/min;
at t = 1.13 h the temperature is considered sta-ble and at t = 1.78
h the spraying ends. In these figures,some interesting features can
be observed:
1. The estimated permittivity in the bed increases slowlyduring
the coating interval 0.90 h < t < 1.78 h, whereasthe
permittivities in the fountain and the remainingvolume regions
remain fairly constant. This may beexplained by particles growing
in size as a result ofthe coating, which results in more dielectric
materialthat accumulates mainly in the bed region. The growthin
particle size was verified by means of sieving andweighing the
particles after the coating process wasfinished, and the
mass-increase was found to beapproximately 25%. A bed that grows in
size in theexperiment is interpreted by our model as an increasein
the effective permittivity in the bed-region, whichhas a fixed
size. This effect can however not be clearly
-
0.27 0.3 0.33 0.36 0.39 0.420.01
0.03
0.05
0.07
0.09
eff / 0 - 1 [-]
eff/
0[-]
0.012 0.014 0.016 0.018 0.02 0.022−2−101234 x 10
−3
eff / 0 - 1 [-]
eff/
0[-]
2.1 2.4 2.7 3 3.3 3.6x 10−4
1
3
5
7
9x 10−5
eff / 0 - 1 [-]
eff/
0[-]
0.22 0.28 0.34 0.4 0.46−0.02
0.01
0.04
0.07
0.1
eff / 0 -1 [-]
eff/
0[-]
0.004 0.008 0.012 0.016 0.02
−3
−1
1
3
5x 10−3
eff / 0 -1 [-]
eff/
0[-]
6.6 6.9 7.2 7.5 7.8 8.1x 10−4
01234567
x 10−5
eff / 0 - 1 [-]
eff/
0[-]
Fig. 7. Scatter plots of �00eff=�0 versus �0eff=�0 � 1 in the
fast coating process. Values inside parentheses are the slopes of
the major semi-axis of the ellipses.
The black lines starting with squares represent the slowly
varying component �eff ;slow of the estimated permittivity.
Table 2Slopes of the major semi-axis in the scatter plots of
�00eff versus �
0eff � 1.
Bed Fountain Volume
Spraying off 0.314 0.245 0.247Spraying 11.3 g/min 0.313 0.228
0.211
532 J. Nohlert et al. / Measurement 55 (2014) 520–535
observed in the fast coating experiment described inSection
5.2.1, which is somewhat surprising given thatwe use the same
coating solution in both processes.
2. The permittivity in the remaining volume region (Fig.
8)increases as the spraying starts, it increases further asthe
spraying rate increases and drops as the sprayingis stopped. This
may be attributed to changes in the per-mittivity of the air, due
to increased humidity caused bythe evaporating water in the
spray.
1 1.2 1.4 1.6 1.8
0.1
0.2
0.3
0.4
0.5
0.6
0.7
t [h]
eff/
0-
1an
de ff
/0
[-]
(a) Bed
1 1.2
0
0.005
0.01
0.015
0.02
t
eff/
0-
1an
de ff
/0
[-]
(b) F
Fig. 8. Estimated permittivity as a function of process time in
the slow coatindashed black curve in (a) shows the permittivity in
the bed region at the curren
Fig. 9 shows scatter plots of �00eff=�0 versus �0eff=�0 � 1
for
the tree regions, during the coating interval. Here, wenotice
that the slope is higher in the bed as compared tothe other two
regions, which is reasonable given the highervolume fraction in the
bed. We also notice how the slowlyvarying component �eff ;slow
shown by black lines in Fig. 9,varies substantially in the bed
region, reasonably due tothe growth in particle size.
5.2.3. Particles sprayed with salt waterIn this experiment, MCC
particles are sprayed with salt
water (0.5 mass% NaCl dissolved in distilled water at
roomtemperature). The complex relative permittivity for
thissolution is shown in Fig. 5b and here we notice a
significantincrease in �00 at low frequencies due to the
conductivity
1.4 1.6 1.8
[h]
ountain
1 1.2 1.4 1.6 1.8
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10−4
t [h]
eff/
0-
1an
deff
/0
[-]
(c) Volume
g process. Black curves represent �0eff=�0 � 1 and gray curves
�00eff=�0. Thet linearization point.
-
0.32 0.39 0.46 0.53 0.6−0.01
0.02
0.05
0.08
0.11
0.14
eff/ 0 1 [-]
eff/
0[-]
0.006 0.01 0.014 0.018 0.022−4
−2
0
2
4
x 10−3
eff / 0 1 [-]
eff/
0[-]
3.5 3.8 4.1 4.4 4.7 5x 10 −4
12345678
x 10−5
eff / 0 1 [-]
eff/
0[-]
Fig. 9. Scatter plots of �00eff=�0 versus �0eff=�0 � 1 in the
slow coating process. Values inside parentheses are the slopes of
the major semi-axis of the ellipses.
The black lines starting with squares represent �eff ;slow, i.e.
the slowly varying component of the estimated permittivity.
1.9 2 2.1 2.2 2.3 2.4
0.1
0.2
0.3
0.4
0.5
t [h]
eff/
01
and
eff/
0[-]
(a) Bed
1.9 2 2.1 2.2 2.3 2.4
0
0.01
0.02
0.03
0.04
t [h]
eff/
01
and
e ff/
0[-]
(b) Fountain
1.9 2 2.1 2.2 2.3 2.40
2
4
6
8
10
x 10−4
t [h]
eff/
01
and
e ff/
0[-]
(c) Volume
Fig. 10. Estimated permittivity as a function of process time in
the salt water experiment. Black curves represent �0eff=�0 � 1 and
gray curves �00eff=�0. Thedashed black curve in (a) shows the
permittivity in the bed region at the current linearization
point.
0.27 0.31 0.35 0.39 0.43 0.47
0.01
0.03
0.05
0.07
0.09
0.11
eff/ 0 1 [-]
eff/
0[-]
0.012 0.015 0.018 0.021 0.024
−2−1
01234
x 10−3
eff / 0 1 [-]
eff/
0[-]
2.4 2.6 2.8 3 3.2 3.4x 10−4
1
2
3
4
5
6
x 10−5
eff / 0 1 [-]
eff/
0[-]
0.23 0.29 0.35 0.41 0.47 0.530
0.03
0.06
0.09
0.12
0.15
eff/ 0 1 [-]
eff/
0[-]
0.003 0.007 0.011 0.015 0.019 0.023−4
−2
0
2
4
6x 10−3
eff/ 0 1 [-]
eff/
0[-]
8.1 8.5 8.9 9.3 9.7x 10−4
2
4
6
8
10
x 10−5
eff/ 0 1 [-]
eff/
0[-]
Fig. 11. Scatter plots of �00eff=�0 versus �0eff=�0 � 1 in the
salt water experiment. Values inside parentheses are the slopes of
the major semi-axis of the ellipses.
The black lines starting with squares represent the slowly
varying component �eff ;slow of the estimated permittivity.
J. Nohlert et al. / Measurement 55 (2014) 520–535 533
introduced by the salt. Two different spraying rates arestudied,
namely 11:6 g=min and 13:3 g=min.
Fig. 10 shows the estimated permittivity in the bed,fountain and
remaining volume regions, as function of
process time in hours. At the first time instant shown inFig.
10, the particles are fluidized, the fountain is on andthe
temperature is stable. The following changes in processsettings are
marked with dashed vertical lines: at t = 1.84 h
-
Table 3Slopes of the major semi-axis in the scatter plots of
�00eff versus �
0eff � 1 for
the salt water experiment.
Bed Fountain Volume
Spraying off 0.327 0.248 0.235Spraying: 11.6 g/min 0.374 0.299
0.307
534 J. Nohlert et al. / Measurement 55 (2014) 520–535
the spraying starts (11.6 g/min); at t = 2 h the temperatureis
considered stable; at t = 2.24 h the spraying rate isincreased to
13.3 g/min which yields very moist processconditions and presumed
initiation of extensive agglomer-ation. The increase in spraying
rate to 13.3 g/min is fol-lowed by clear changes in the estimated
permittivities,possibly due to free water (with salt) on the
surface ofthe particles in the fountain region and/or
agglomerationwith particles adhering to the walls of the
vessel.
Fig. 11 shows scatter plots of �00eff=�0 versus �0eff=�0 � 1
in
two intervals: (i) no spray and (ii) spraying at 11.6
g/min(which does not yield agglomeration). The slopes of themajor
axis for the three regions is also presented in Table 3.Here, it is
interesting to notice how the slopes in all regionsclearly increase
after the spraying is switched on. This isexpected, given the high
dielectric losses of the salt waterin the frequency range of the
cavity resonances, and it isalso in agreement with the Monte-Carlo
simulations pre-sented previously.
6. Conclusions
We have presented a microwave measurement tech-nique for
industrial processes contained in closed metalvessels, which
exploits a number of electromagnetic reso-nances of the metal
vessel to estimate the process state.In particular, we estimate the
effective permittivity insidea vessel that hosts a pharmaceutical
fluidized-bed process,which is used for particle coating. This
process involvesspraying a solution onto the particles, where water
actsas the solvent for different types of coating substances.For
this particular application, it is important to monitorthe moisture
content of the particles and the particle dis-tribution.
Electromagnetic waves interact strongly withwater in a non-invasive
and non-destructive manner,which makes this type of measurement
technology veryattractive. In addition, our measurement system is
sensi-tive to changes in permittivity throughout the process
ves-sel and, thus, it can be considered to perform a
globalmeasurement of the process state, which is challengingfor
more conventional techniques.
We exploit two magnetic field probes and measure thescattering
parameters as function of frequency using a net-work analyzer. The
complex resonance frequencies areestimated from the scattering
parameters and these arerelated to a reference measurement of the
empty vesselin order to achieve relative changes in the resonance
fre-quencies. The perturbations in the resonance frequenciesare
related to (i) the perturbations in the complex
effectivepermittivity inside the vessel and (ii) the thermal
expan-sion of the vessel caused by variations in the temperature.We
exploit an estimation algorithm with regularization to
estimate the effective permittivity and the shape of thevessel,
where the unknown effective permittivity andshape is parameterized
with the aid of spatial basis func-tions. The real and imaginary
part of the effective permit-tivity are assumed to be
frequency-independent in thefrequency band of the used resonance
frequencies. Wemodel the vessel by means of the finite element
methodand the computed eigenmodes and eigenfrequencies areused to
calculate sensitivities with respect to changes inthe material
parameters and the shape of the vessel. Theestimation incorporates
a priori information that is col-lected from probes that measure
the temperature of thevessel’s metal walls and the air that flows
through thevessel. This approach accounts for substantial parts of
thetemperature variations but it is believed that it can
besignificantly improved.
The measurement technique performs well for the esti-mation of
the effective permittivity that is parameterizedfor a small number
of sub-regions. The re-distribution ofmaterial occurring when the
particle fountain is switchedon, is clearly reflected in the
estimated permittivity in allthese sub-regions. The effect of
particles that grow in sizeduring coating processes can be observed
in the estimatedpermittivities, and we have also shown that
material build-up on the cavity walls can be clearly detected. We
haverelated the real part of the effective permittivity to
itsimaginary part by means of scatter plots and covariancematrices,
where measurements taken at different timeinstants fall
approximately on a straight line. This line isdefined by the
eigenvector associated with the largesteigenvalue of the covariance
matrix, and the slope of theline is affected by the liquid sprayed
onto the particles inthe process. In particular, the slope of this
line clearlyincreases if the particles are sprayed with a liquid
thatfeatures substantial dielectric losses.
Acknowledgements
Livia Cerullo was financially supported by AstraZeneca.In
addition, Johan Winges was financially supported by theSwedish
Research Council (dnr 2010-4627) in the project‘‘Model-based
Reconstruction and Classification Based onNear-Field Microwave
Measurements’’. The computationswere performed on resources at
Chalmers Centre for Com-putational Science and Engineering (C3SE)
provided by theSwedish National Infrastructure for Computing
(SNIC).
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Global monitoring of fluidized-bed processes by means of
microwave cavity resonances1 Introduction2 Measurement system2.1
Process equipment2.2 Measurement principle2.2.1 Homogenization of a
mixture of air and particles2.2.2 Density independent moisture
measurements
2.3 Experimental setup2.3.1 Reduction of undesired losses2.3.2
Choice of probes and their design2.3.3 Measurement settings
3 Electromagnetic model3.1 Weak formulation3.2 Finite element
approximation3.3 Losses due to finite conductivity in the cavity
walls
4 Estimation procedure4.1 Sensitivity analysis4.1.1 Material
sensitivities4.1.2 Representation of material perturbations4.1.3
Shape sensitivities4.1.4 Representation of shape perturbations
4.2 Temperature measurements
5 Results5.1 Cavity without particles5.1.1 Effects from air
humidity and spray
5.2 Measurements with particles5.2.1 Fast coating process5.2.2
Slow coating process5.2.3 Particles sprayed with salt water
6 ConclusionsAcknowledgementsReferences