Bilinear calibration of coaxial transmission/reflection cells for permittivity measurement of low-

loss liquids

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Meas. Sci. Technol. 7 (1996) 1260–1269. Printed in the UK

Bilinear calibration of coaxialtransmission/reflection cells forpermittivity measurement of low-lossliquids

Kjetil Folgerø

Department of Engineering, Stord/Haugesund College, Skaregaten 103,N-5500 Haugesund, Norway and Department of Physics, University of Bergen,Allegaten 55, N-5007 Bergen, Norway

Received 22 February 1996, in final form 13 May 1996, accepted for publication7 June 1996

Abstract. Several parameters describing the quality of petrochemical products canbe revealed from the permittivity spectrum of the product. This requires that thepermittivity be measured with high sensitivity, so the calibration of measurementcells is of great importance. In this work calibration techniques for thetransmission/reflection method for complex permittivity determination of low-lossliquids are studied. It is shown that a bilinear transformation can be used todetermine the scattering parameters at the reference planes from the measuredscattering parameters of a coaxial transmission/reflection cell. The permittivity of asample in the cell can then be calculated with high precision from the referenceplane parameters. The de-embedding procedure consists of determining threecalibration coefficients by measuring three samples with known permittivities.Measurements on low-loss liquids and crude oils confirm the performance of thecalibration procedure. The technique is compared to a simpler calibration methodand the choice of calibration fluids to ensure broad-band measurements isdiscussed.

1. Introduction

In the petroleum refinery industry there is an increasingdemand for on-line determination of product quality.Dielectric spectroscopy has previously been shown tobe a relevant method for quality characterization ofpetrochemical products [1, 2]. Several parametersdescribing the quality of the oil can be found from themeasured permittivity spectrum. Oil has low permittivityand loss, long relaxation times and a broad frequencydispersion region. Hence, the permittivity spectrum has tobe measured with high sensitivity over a broad frequencyrange (typically 1 kHz to 10 GHz), which requires sensitivemeasurement cells and adequate models for calculating thepermittivity.

At low frequencies (1 kHz to 10 MHz) impedancemeasurements of coaxial cells give high-precision measure-ment of permittivity [1]. At radio and microwave frequen-cies, transmission and reflection measurements of coaxialcells using network analysers are a suitable method for fastand broad-band permittivity determination of low-loss liq-uids [3]. The accuracy in the measurements is lower thanthat which is obtained with resonator techniques, but theresonator methods are time-consuming when applied in a

broad range of frequencies [4]. In comparison, a coaxialcell can typically be used over 1–2 frequency decades.

When measuring parameters of petroleum products, arepresentative sample of the flow must be taken. Thevolume of the sample must be large to ensure that possibleimpurities only take up a small part of the measurementvolume. Co-axial transmission/reflection cells have a largesample volume compared with coaxial open-ended probes[5, 6] and coaxial transmission cells of the cut-off variety[7]. In comparison with reflection measurements in coaxialcells [1, 8, 9], transmission measurements are less sensitiveto resonance effects [10]. Hence, longer cells with largersample volumes can be used.

Considering industrial applications of dielectric spec-troscopy, an obvious drawback is that the cell is intru-sive. However, there are severe drawbacks with possiblenon-intrusive sensors as well. Examples are open-endedprobes and microstrip transmission lines which have a verysmall measurement volume and a low sensitivity for low-permittivity samples, antennae and waveguides which typ-ically operate at frequencies above 1 GHz and parallel-plate capacitances which are useful only at low frequencies.Therefore coaxial transmission/reflection cells are the mostsuitable cells for permittivity measurements for frequencies

0957-0233/96/091260+10$19.50 c© 1996 IOP Publishing Ltd

Bilinear calibration of coaxial cells

Figure 1. A sketch of the coaxial transmission/reflectioncell including the temperature control chamber. Thedifference between the network analyser calibration planeand the reference plane of the measurements is indicated.

from 10 MHz to above 1 GHz.Figure 1 is a sketch of a coaxial transmission/reflection

cell with a water chamber for temperature control. Thesample volume is defined by Teflon beads and standardconnectors are placed at both ends of the cell to allowconnection to the network analyser. The reference planefor the measurements differs from the calibration planeof the network analyser, and internal reflections occurdue to mismatch at the Teflon beads and the connectors.In a well-designed cell this mismatch is low and theerror introduced by the end sections of the cell can beregarded as extra phase-shift and loss. This error iseasily compensated for by a reference plane rotation [11].Equations independent of sample length and referenceplane position can then be derived [3] provided thatboth reflection and transmission measurements are done.However, the use of reflection measurements implies thatthe sample length, and therefore the sample volume, mustbe low to avoid quarter-wavelength resonance.

It is difficult to achieve well-matched cells that operateover a broad temperature range and that are stable forlong-term use. The mismatch at the Teflon beads cantherefore not be neglected and the main problem inhigh-sensitivity permittivity measurements is to relate themeasuredparameters to the permittivity. This can bedone by de-embedding the scattering (S) parameters of thereference planes from the measured S-parameters and thencalculating the permittivity from equations for the referenceplane S-parameters.

Several approaches can be used to determine thereference plane parameters. The standard two-portcalibration consists of measuring the reflection from threestandard terminations (open, short and matched load) placedat the reference planes. Another approach is to perform thestandard calibration at the connectors and then de-embedthe reference plane parameters from measurements of ashort termination [12, 13] or a small part of the sample [14]at three different positions in the sample region. The lattermethod is only applicable for solid samples. In additionthese methods require opening of the measurement cell,which can reduce the reproducibility of the measurements.The mismatch of the Teflon beads can also be accounted forby equations that include the position and thickness of thebeads [15]. This requires that the dimensions of the beads

be precisely known, which may not be the case becausewearing of the cells and variations in temperature affectthe Teflon beads.

The aim of this paper is to show that a bilineartransformation can be used to determine the referenceplane S-parameters from the measured S-parameters of atransmission/reflection cell. The permittivity of low-lossliquids can then be calculated with high sensitivity from thereference plane parameters. The de-embedding procedureconsists of determining three calibration coefficients bymeasuring three samples with known permittivities. Furtheron, we derive an explicit bilinear expression for thepermittivity as a function of the measured S-parameters.This explicit expression is equivalent to the bilinearexpression that Cole [16] derived for open-ended coaxialcells. In this model three complex calibration coefficientstake account of all spurious effects. The coefficients aredetermined by measurements on three samples with knownpermittivities.

The bilinear S-parameter transformation is well knownfor reflection measurements, but to my knowledge thisis the first time it has been applied to transmissionmeasurements. The main benefits of this technique are thatthe measurement cell can be calibrated without opening ofthe cell and that re-calibration of the system (such as toaccount for wearing of the cell or changes in operatingtemperature) is easy to perform. Hence, the techniquemay be applicable for calibration of measurement cells inindustrial applications of dielectric spectroscopy in whichrobust cells are required. An advantage of the explicitbilinear calibration procedure derived in this work is that noa priori knowledge of the dimensions of the measurementcell is required (compared for example with the variable-length transmission cell reported in [17], for which thesample length must be known with high precision). Thedrawback of the calibration technique is that three fluidswith permittivities close to that of the sample must beused to achieve high precision. The permittivity of thecalibration fluids must be known with high accuracy, foruncertainties in the permittivities of the calibration fluidswill influence the measured permittivity of the unknownsample. Because a narrow calibration must be used, thepermittivity range of the samples must be known. Thismay be a disadvantage, but the expected permittivity rangeof the samples is often known.

2. Theory

The reference plane S-parameters of a coaxial cell filledwith a sample of complex relative permittivityε∗ = ε′− jε′′

are [18]:

SR11 = SR

22 = 0(1 − z2)

1 − 02z2(1)

SR21 = SR

12 = z(1 − 02)

1 − 02z2(2)

where 0 is the reflection coefficient of an infinitely longsample:

0 = 1 − g√

ε∗

1 + g√

ε∗ (3)

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K Folgerø

z = exp(−γ l) = exp

(− jωl

c

√ε∗

)(4)

where γ is the propagation constant in the sample,c isthe speed of light in vacuum,ω is the angular frequency,l is the length of the sample andg is the characteristicadmittance of the coaxial cell normalized with respect tothe characteristic admittance of the coaxial cables. In thiswork a cell of characteristic impedance 50� is used, henceg = 1.

If no mismatches occur at the connectors and Teflonbeads, the measured S-parameters are given by a referenceplane rotation:

SM11 = SR

11 exp(−2γt l1) (5)

SM22 = SR

22 exp(−2γt l1) (6)

SM12 = SR

12 exp[−γt (l1 + l2)] (7)

SM21 = SR

21 exp[−γt (l1 + l2)] (8)

whereγt = jω√

ε∗t /c is the propagation constant in Teflon,

l1 and l2 are the distances from the reference planes tothe measurement planes andε∗

t is the relative permittivityof Teflon. By normalizing the measurements of the samplewith respect to measurements of a reference fluid, the effectof the phase-shift and the loss in the connector and Teflonis removed:

SM,xij

SM,ref

ij

= SR,xij

SR,ref

ij

(9)

where i ∈ {1, 2}, j ∈ {1, 2}, SM,ref

ij is the meas-

ured S-parameter of the reference fluid andSM,xij

is the measured S-parameter of the sample. Thepermittivity can then be determined from reflection and/ortransmission measurements by solving equation (1) and/or(2) simultaneously with (9).

Equations (5)–(8) do not apply if mismatches occurat the Teflon beads or the connectors and a morecomprehensive calibration is then needed. A bilineartransformation is now assumed to be applicable fortransformation of the S-parameters from the measurementplanes to the reference planes:

SRij = AijS

Mij + Bij

CijSMij + 1

(10)

where Aij , Bij and Cij are found from S-parametermeasurements of three calibration fluids with knownpermittivities. The permittivities of the calibration fluidsshould span the permittivity of the sample and be close tothe permittivity of the sample to ensure high sensitivity.Equation (10) is referred to as the bilinear S-parametertransformation (BST). Figure 2 illustrates the performanceof the transformation on transmission measurements of alow-loss liquid.

The permittivity of an unknown sample is determinedby first calculating the reference plane S-parameters (SR)from the measured parameters (SM ) by the BST methodand then solving (1) or (2) by an iterative method. Themethods of Nicholson–Ross [18] and Weir [11] can alsobe used to calculate the permittivity, but the solution is

Figure 2. The transmission coefficient (S21) for carbontetrachloride measured with the set-up in figure 3 and thecell in figure 1: (a) magnitude and (b) phase; (◦),measured values; (•), estimated values using the bilinearS-parameter transformation technique (equation (10)) withn-decane, p-xylene and toluene as calibration fluids; and(——), theoretical values according to equation (2).

divergent at frequencies corresponding to multiples of onehalf wavelength in the sample.

The calculation of permittivity can be simplified byintroducing the series expansionz = 1 − γ l + 1

2(γ l)2 −16(γ l)3 + · · · into equations (1) and (2). Neglecting termsin third and higher powers gives

SR11 = SR

22 ≈ (1 − g2ε∗)

1 + 2gc

jωl+

(g2 + 2

3gjωl

c

)ε∗

(11)

SR21 = SR

12 ≈2gc

jωl

[1 − 1

6

(jωl

c

)2ε∗

]1 + 2gc

jωl+

(g2 + 2

3gjωl

c

)ε∗

. (12)

A bilinear relation between the permittivity and themeasured S-parameters is found by combining (11) and (12)with the bilinear S-parameter transformation (10):

ε∗ = Aij SMij + Bij

Cij SMij + 1

(13)

whereSMij is the measured S-parameter of the sample and

Aij , Bij and Cij are complex and frequency-dependentcoefficients found from calibration measurements on three

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Bilinear calibration of coaxial cells

Figure 3. The measurement system consists of a networkanalyser, a measurement cell, equipment for temperaturecontrol and a personal computer for data processing andpresentation.

Table 1. Debye parameters for calibration and test fluids at20 ◦C. The Debye model is equivalent to the Cole–Colemodel (equation (14)) with α = 0.

Medium εS ε∞ τ (ps) Reference

Air 1.000 [23]n-Pentane 1.844 [24]n-Heptane 1.924 [24]n-Decane 1.991 [24]p-Xylene 2.270 [23]Carbon tetrachloride 2.238 [25]Toluene 2.391 2.24 7.34 [25]

fluids with known permittivities. Equations (11) and (12)are restricted to low frequencies, but equation (13) isapplicable at higher frequencies if the calibration fluids havepermittivities close to that of the sample. This method isreferred to as the ‘bilinear calibration procedure’ (BCP).Equation (13) can be rearranged to be of the same formas that introduced by Cole [8]. This is a robust techniqueand has been widely used for many years for reflectionmeasurements in open-ended coaxial cells [1, 8] and probes[6]. To my knowledge, this is the first time it has beenapplied to measurements in a transmission/reflection cell.

3. Experimental

The permittivities of carbon tetrachloride and of threecrude oil samples were measured in the frequency range10 MHz to 6 GHz to verify the performance of thesystem. The measurements were performed at 20◦C.Carbon tetrachloride is lossless with permittivityε∗ =2.238. The crude oils were from three different North Seafields. Between each filling the cell was cleaned and dried,and approximately 5 min temperature stabilization time wasused after sample injection. Toluene,p-xylene,n-decane,n-heptane,n-pentane and air in different combinationswere used as calibration fluids. Table 1 gives the Debyeparameters of the fluids.

The measurement system consisted of a measurementcell, a network analyser system (Hewlett Packard 8753Band 85047A), equipment for temperature control and apersonal computer for data acquisition, processing andpresentation (see figure 3). The measurement cell (figure 1)was a coaxial cell of characteristic impedance 50� and

Table 2. Average values and standard deviations in thecalculated permittivity of carbon tetrachloride using thenormalization technique (equation (9)). The values arecalculated from 201 measurement points in the frequencyrange 10 MHz to 6 GHz.

Reference fluid 〈ε ′〉 〈ε ′′〉 σ(ε ′) σ (ε ′′)

n-Pentane 2.2433 −0.0078 0.0137 0.0118n-Heptane 2.2426 −0.0106 0.0097 0.0157n-Decane 2.2440 0.0032 0.0087 0.0084p-Xylene 2.2376 −0.0013 0.0041 0.0048Toluene 2.2352 −0.0013 0.0063 0.0072

Table 3. Average values and standard deviations in thecalculated permittivity of carbon tetrachloride using thebilinear S-parameter transformation procedure(equation (10)). The values are calculated from 201measurement points in the frequency range 10 MHz to6 GHz. n-Decane, p-xylene and toluene are used in thenarrow calibration, whereas n-pentane, n-heptane andtoluene are used in the broad calibration.

Calibration 〈ε ′〉 〈ε ′′〉 σ(ε ′) σ (ε ′′)

Broad 2.2376 −0.0084 0.0105 0.0211Narrow 2.2384 0.0011 0.0043 0.0050

sample length 20 cm. A rather long cell was used to ensurehigh phase-shift and attenuation of the signal, and therebylow uncertainty for measurements of low-loss liquids.

4. Results and discussion

In this section the normalization technique, the BST and theBCP are compared. The permittivity is calculated fromSM

21because the transmitted signal is less sensitive to resonanceeffects than is the reflected signal [10] and because thetransmitted signal is much stronger than the reflected signalfor low-loss samples.

4.1. Normalization

Figure 4 shows the permittivity of carbon tetrachloridecalculated by using the normalization technique ofequation (9), with three different reference fluids. Thecalculated permittivity corresponds to the reference values,but the uncertainty depends on the permittivity of thereference fluid. The uncertainty is low when the differencein permittivity between the reference fluid and the sampleis low. The reason for this is that the effects of themismatches in the measurements of the fluids are about thesame, and the normalization of equation (9) compensatesfor the mismatches in addition to the phase-shift andloss. The permittivity of carbon tetrachloride is constantin the measured frequency range, and consequently theaverage value of the permittivity and the standard deviationof the measurements give a measure of the precision inthe calculations. Table 2 shows that the permittivity iscalculated with the desired high precision only when thepermittivity of the reference fluid is very close to that ofthe sample.

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Figure 4. The permittivity of carbon tetrachloride calculated with the normalization technique (equation (9)) from transmissionmeasurements: (a) the real part and (b) the imaginary part.

It is important to use the correct sample length,l, whensolving equation (2). If too low a value ofl is used, thepermittivity is overestimated when the reference fluid haslower permittivity than the sample and vice versa. If toohigh a value ofl is used, the permittivity is underestimatedwhen the reference fluid has lower permittivity than thesample and vice versa. The correct value ofl is of courseknown from the mechanical specifications of the cell, butsmall errors in the length can give rather large errors inthe calculated permittivity. The correct length can befound from measurements of another fluid with knownpermittivity.

4.2. Bilinear S-parameter transformation

Figure 5 shows the permittivity of carbon tetrachloridecalculated with the bilinear S-parameter transformationmethod (equation (10)) with one narrow and one broadcalibration range. At high frequencies the model doesnot estimate the permittivity correctly due to resonanceeffects. The high-frequency limit can be extended to

higher frequencies by using reference and calibrationfluids that have permittivities close to that of the sample.The average value of the permittivity and the standarddeviation of the measurements show that the permittivityis calculated with the desired high precision when thenarrow calibration range is used (table 3). It is also seenthat this procedure gives higher precision than does thenormalization technique (equation (9)) for all cases exceptwhen p-xylene is the reference fluid. Correct samplelength is not as crucial in BST as in the normalizationmethod, because the calibration coefficientsA21, B21 andC21 compensates for small errors inl.

4.3. The bilinear calibration routine

Figure 6 shows the permittivity of carbon tetrachloridecalculated with the bilinear calibration procedure (equa-tion (13)) with one narrow and one broad calibration range.At low frequencies the BCP gives the same results as theBST, but the high-frequency limit is lower. The reason forthis is that the bilinear approximation of the transmission

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Bilinear calibration of coaxial cells

Figure 5. The permittivity of carbon tetrachloride calculated with the bilinear S-parameter transformation technique(equation (10)) from transmission measurements: (a) the real part and (b) the imaginary part.

Table 4. Average values and standard deviations in thecalculated permittivity of carbon tetrachloride using thebilinear calibration procedure (equation (13)). The valuesare calculated from 201 measurement points in thefrequency range 10 MHz to 6 GHz. n-Decane, p-xyleneand toluene are used in the narrow calibration, whereasn-pentane, n-heptane and toluene are used in the broadcalibration.

Calibration 〈ε ′〉 〈ε ′′〉 σ(ε ′) σ (ε ′′)

Broad 2.2269 −0.0102 0.0308 0.0206Narrow 2.2388 0.0012 0.0045 0.0049

coefficient (equation (12)) is not valid at high frequencies.Table 4 gives the average value of the permittivity and thestandard deviation of the measurements.

4.4. Reflection measurements

At frequencies below 100 MHz the phase-shift of the signaltransmitted through the cell is too small to give high-precision measurements of the permittivity. This could be

improved by measuring the reflection coefficient insteadof the transmission coefficient, but the reflected signal isweak and the error in the measured phase and amplitude istherefore large. However, measurements indicate that thiserror is mainly systematic and can therefore be reducedby proper calibration. Both the BST and the BCP methodremove systematic errors, and the permittivity is calculatedwith high precision in the lowest decade (see figure 7and table 5). Figure 7 shows that normalization doesnot remove the systematic errors and therefore cannot beused with reflection measurements of low-loss fluids. Theresonance problems when using reflection measurementsare also seen in figure 7. The problems are reduced by thebilinear calibraton, but are nonetheless more severe than intransmission measurements.

4.5. Crude oils

The permittivities of three North Sea crude oils (figure 8)were measured to confirm that the bilinear S-parametertransformation works for low-loss liquids as well as forthe lossless liquids studied earlier. The permittivity was

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Figure 6. The permittivity of carbon tetrachloride calculated with the bilinear calibration procedure (equation (13)) fromtransmission measurements: (a) the real part and (b) the imaginary part.

Table 5. Average values and standard deviations in thecalculated permittivity of carbon tetrachloride using thebilinear S-parameter transformation (equation (10)).n-Decane, p-xylene and toluene are used as calibrationfluids. The values are calculated from 73 measurementpoints in the frequency range 10 MHz to 100 MHz.

Measuredparameter 〈ε ′〉 〈ε ′′〉 σ(ε ′) σ (ε ′′)

S11 2.238 0.0003 0.001 0.002S21 2.237 0.004 0.007 0.007

determined from impedance measurements using a coaxialcell as described in [1] at frequencies below 10 MHz,whereas transmission measurements were used at higherfrequencies. The BST withn-decane, p-xylene andtoluene as calibration fluids was used to calculate thepermittivity from the measured transmission coefficient.Ideally, the calibration liquids should have permittivities(both ε′ and ε′′) that correspond to the permittivities ofthe oils. Such calibration fluids are difficult to obtain, formost low-permittivity liquids either are lossless or have

relaxation times much shorter than those of crude oils. Wehave found (through experiments) that the most importantfactor in obtaining high-precision measurements is that thecalibration fluids haveε′ very close to that of the unknownsample. Thus, lossless liquids with lowε′ are prefered tolow-loss liquids with higherε′.

The measured permittivity spectra of the oils were fittedto the Cole–Cole model [19]:

ε∗ = ε∞ + εS − ε∞1 + (jωτ)1−α

− jσ

ωε0(14)

whereεS is the static permittivity,ε∞ is the high-frequencypermittivity, τ is the relaxation time,α is the distributionfactor, σ is the conductivity andε0 = 8.854 pF m−1

is the permittivity of vacuum. The resulting Cole–Coleparameters are shown in table 6.

Figure 8 confirms that the measurement system has thenecessary sensitivity to measure the small differences inpermittivity between different crude oils. The differencesin ε′ are significant whereasε′′ of the three oils differvery little at frequencies above 10 MHz. The fitting tothe Cole–Cole model corresponds to the precision which

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Bilinear calibration of coaxial cells

Figure 7. The real part of the permittivity of carbon tetrachloride: (�), calculated with the normalization technique fromreflection measurements; ( ), calculated with the bilinear S-parameter transformation technique from reflectionmeasurements; (– – –), calculated with the billinear S-parameter transformation technique from transmission measurements;and (——), literature values.

Figure 8. The measured permittivity of crude oils from three North Sea oil fields: (a) the real part and (b) the imaginary part;(�), oil 1; (◦), oil 2; and (M), oil 3. The lines represent the Cole–Cole fitting of the measured permittivity spectra.

was found for carbon tetrachloride (figure 5) except foran increaced oscillation at frequencies above 1 GHz. Thislarger oscillation may occur because the oils do not have

permittivities as close to that of the calibration liquidp-xylene as carbon tetrachloride does.

Information about the physical properties of the oils

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Table 6. Estimated Cole–Cole parameters of three NorthSea crude oils.

Crude oil εS ε∞ τ (ns) α σ (nS m−1)

Oil 1 2.295 2.169 3.35 0.54 42.9Oil 2 2.324 2.198 11.3 0.52 2.0Oil 3 2.248 2.151 2.40 0.50 11.4

can be revealed from the permittivity spectra. The high-frequency permittivity ε∞ is correlated with the oil’sdensity [2] and the static permittivityεS and the dielectricincrement (εS − ε∞) is dependent on the amount ofheavy polar components in the oil. Information about themicroscopic viscosity can be found from the relaxationtime τ and the distribution factorα is related to the sizedistribution of the molecules [20].

It is known [21] that asphaltenes, which areconcentrated in heavy crude oils, are among the mosttroublesome fractions for efficient petroleum cracking andrefining. North Sea crude oils have a relatively smallamount of asphaltenes [22] and are known to be oils ofhigh quality that are easy to process. This is consistent withthe low values ofεS (and(εS − ε∞)) (table 6) compared tovalues as high asεS = 3.4 for crude oils with high amountsof asphaltenes [26].

5. Conclusions

In this paper a bilinear calibration technique for calcu-lating the reference plane S-parameters of a transmis-sion/reflection cell from the measured S-parameters is pre-sented. The de-embedding procedure consists of determin-ing three calibration coefficients by measuring three sam-ples with known permittivities. The permittivity of an un-known sample is then calculated with high sensitivity fromthe S-parameters of the reference planes. Measurementson carbon tetrachloride and three crude oils confirmed theperformance of the technique.

The bilinear calibration technique was compared toa normalization technique and it was found that thenormalization method requires a reference fluid withpermittivity very close to that of the sample to give high-precision measurements, whereas the bilinear techniquegives high precision for a broader permittivity range.Another advantage of the bilinear technique is thatreflection measurements can be used even for low-permittivity samples and in that way give high-precisionmeasurements at frequencies below 100 MHz for the cellused in this work. The normalization technique has theadvantages that only one calibration measurement is neededand that the model works at higher frequencies than does thebilinear technique when a calibration fluid with permittivityclose to that of the sample is used.

The bilinear S-parameter transformation can besimplified to give an explicit bilinear expression for thepermittivity from the measured S-parameters. However,this expression has a lower upper frequency limit than doesthe BST.

Measurements on North Sea crude oils showed thatthe measurement method is sensitive enough to revealsignificant differences in the permittivity spectra. Thedielectric parameters of the oils can be correlated tophysical properties that influence the petroleum crackingand refining process. Dielectric spectroscopy is thereforeconsidered to be a relevant method for quality monitoringof the feedstock for refineries.

Acknowledgments

This work was performed at Christian Michelsen ResearchAS, Fantoftvegen 38, N-5036 Fantoft, Norway within theStrategic Technology Programme for On-line Monitoring ofOil and Gas Processes (TOP) supported by the NorwegianResearch Council (NRC), Statoil and Norsk Hydro.

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