Moisture Measurement in Paper Pulp Using Fringing Field Dielectrometry

Transcription

1 Moisture Measurement in Paper Pulp Using Fringing Field Dielectrometry Project Report 2003-F-1 K. Sundararajan, L. Byrd II, C. Wai-Mak, N. Semenyuk, and A.V. Mamishev Sensors, Energy, and Automation Laboratory Department of Electrical Engineering University of Washington

2 Abstract Moisture control of paper pulp is a key step in paper manufacturing. To ensure control efficiency, a fast and accurate moisture sensor is desired. Currently existing technologies can accurately measure moisture content of the pulp with fiber content in excess of 20%; yet for cases with lower paper percentages, challenges still remain. Significant market potential exists for an inexpensive and reliable feed-forward moisture control technique. Existing techniques do not yet perform adequately in the field, although laboratory studies claim high measurement accuracy and reliability. In this report, fringing electric field dielectric spectroscopy is used to estimate the fiber content of laboratory-made paper pulp. The fiber content and the titanium dioxide concentration in the paper pulp samples are varied from 100% to 3%, and 0% to 7% respectively. The resulting dielectric measurements show a near-linear dependency on the fiber content. The moisture content in the pulp is estimated using a self-adapting algorithm. The algorithm automatically selects different parameters and equations for the estimation process based on the data sets used to train it. The fiber content was estimated, using a linear self-learning model.

3 Table of Contents List of Figures...iii Chapter 1. Introduction... 1 Chapter 2. State of the Art Microwave Techniques Reflection Based Techniques... 5 Chapter 3. Interdigital Fringing Field Dielectrometry Interdigital Fringing Field Sensor Dielectric Spectroscopy Debye Model Chapter 4. Experimental Setup Chapter 5. Experiments with High Fiber Concentration Pulp (100% to 10%) Experimental Procedure Experimental Results Data Analysis Chapter 6. Experiments with Low Fiber Concentration Pulp (10% to 3%) Experimental Procedure Experimental Results Data Analysis Chapter 7. Experiments with Titanium Dioxide Experimental Procedure Experimental Results Data Analysis Chapter 8. Experiments with Clay Experimental Procedure Experimental Results Data Analysis i

4 Chapter 9. Experiments with Calcium Carbonate Experimental Procedure Experimental Results Data Analysis Chapter 10. Parameter Selection Algorithm Chapter 11. Repeatability Tests Chapter 12. Reproducibility Tests Chapter 13. Validation of Estimation Algorithms Chapter 14. Pass line Sensitivity Experimental Results Data Analysis Chapter 15. Disturbance factors Chapter 16. Variation with Pulp Chapter 17. Temperature Variations Experimental Procedure Experimental Results Chapter 18. Future Work High Frequency Measurements: Temperature Variation Improvements in Estimation Algorithms Pass line Sensitivity Chapter 19. Conclusions References Appendix ii

5 List of Figures Figure 1.1. Photograph of a paper machine Figure 3.1. A fringing field dielectrometry sensor can be visualized as a parallel plate capacitor whose electrodes open up to provide a one-sided access to material under test [29]... 8 Figure 3.2. The term interdigital refers to the pattern of fingers or digits that is resembled by the shape and relative position of the electrodes [31] Figure 3.3. A generic interdigital sensor with a periodicity λ [34,35] Figure 3.4. A conceptual view of multiple penetration depth sensor Figure 3.5. Mechanisms influencing the loss factor of a moist material over a wide range of frequencies f (Hz). (A) DC conductivity, (B) Maxwell-Wagner polarization, (C) dipolar polarization of water bound to the matrix of the material, (D) dipolar polarization of free water [36] Figure 3.6. Debye model for time dependent polarization [39] Figure 3.7. Real and imaginary parts of complex susceptibility as a function of frequency. [40] Figure 4.1. Photograph of experimental setup Figure 4.2. The top-down view of the interdigital sensor tray with the spatial periodicity of 40 mm, finger length of 160 mm and an approximate penetration depth of 13 mm Figure 5.1. Measurements of paper pulp samples with 0% to 90% moisture concentration at frequencies from 200 Hz to 100 khz Figure 5.2. Fiber content as a function of the conductance of the paper pulp samples with 0% to 90% moisture concentration at various frequencies from 200 Hz to 100 khz Figure 5.3. Fiber content as a function of the capacitance of the paper pulp samples with 0% to 90% fiber concentration at various frequencies from 200 Hz to 100 khz Figure 6.1. Measurements of paper pulp samples with 90% to 97% moisture concentration at frequencies from 200 Hz to 100 khz Figure 6.2. The capacitance measured at 5 khz shows separation between measurements to be much greater than twice the standard deviation. This indicates towards the possibility of achieving higher resolution using the sensor Figure 6.3. Cole-Cole plots from measurements of paper pulp samples with 3% to 10% paper concentration at frequencies from 50 Hz to 100 khz iii

6 Figure 6.4. Conductance plots from measurements of paper pulp samples with 90% to 96% moisture concentration at frequencies from 200 Hz to 100 khz Figure 6.5. Capacitance plots from measurements of paper pulp samples with 90% to 96% moisture concentration at frequencies from 200 Hz to 100 khz Figure 6.6. Variation of the slope, m, in (6.1) depicting the plot between percentage of moisture content and capacitance with respect to frequency of excitation Figure 6.7. Variation of the offset, k, in (6.1) depicting the plot between percentage of moisture content and capacitance with respect to frequency of excitation Figure 6.8. The data obtained experimentally at 5 khz is in agreement with the curve formulated in (6.1) Figure 6.9. Standard deviation of the capacitance measurements at various moisture levels is two orders of magnitude smaller than the capacitance (10-11 vs ). 32 Figure 7.1. Measurements of paper pulp samples with 0% to 7% titanium dioxide concentration at frequencies from 200 Hz to 100 khz Figure 7.2. Cole-Cole plots from measurements of paper pulp samples with 0% to 7% titanium dioxide concentration at frequencies from 200 Hz to 100 khz Figure 7.3. Conductance plots from measurements of pulp samples with 0% to 7% titanium dioxide concentration at frequencies from 200 Hz to 100 khz Figure 7.4. Capacitance plots from measurements of pulp samples with 0% to 7% titanium dioxide concentration at frequencies from 200 Hz to 100 khz Figure 7.5. Comparison of the estimated concentration of fiber in the pulp to the actual concentration Figure 7.6. Comparison of the estimated concentration of titanium dioxide in the pulp to the actual concentration Figure 7.7. Comparison of the estimated concentration of moisture in the pulp to the actual concentration Figure 8.1. Measurements of paper pulp samples with 10% to 5% fiber concentration and 0% to 5% clay at frequencies from 200 Hz to 100 khz Figure 8.2. Cole-Cole plots from measurements of paper pulp samples with 10% to 5% paper concentration and 0% to 5% clay at frequencies from 200 Hz to 100 khz.43 Figure 8.3. Conductance plots from measurements of pulp samples with 0% to 5% clay concentration at frequencies from 200 Hz to 100 khz Figure 8.4. Capacitance plots from measurements of pulp samples with 0% to 5% clay concentration at frequencies from 200 Hz to 100 khz Figure 8.5. Comparison of the estimated concentration of fiber in the pulp to the actual concentration iv

7 Figure 8.6. Comparison of the estimated concentration of clay in the pulp to the actual concentration Figure 8.7. Comparison of the estimated concentration of moisture in the pulp to the actual concentration Figure 9.1. Measurements of paper pulp samples with 10% to 7.5% fiber concentration and 0% to 2.5% calcium carbonate at frequencies from 200 Hz to 100 khz Figure 9.2. Cole-Cole plots from measurements of paper pulp samples with 10% to 7.5% paper concentration and 0% to 2.5% calcium carbonate at frequencies from 200 Hz to 100 khz Figure 9.3. Conductance plots from measurements of pulp samples with 0% to 2.5% calcium carbonate concentration at frequencies from 200 Hz to 100 khz Figure 9.4. Capacitance plots from measurements of pulp samples with 0% to 2.5% calcium carbonate concentration at frequencies from 200 Hz to 100 khz Figure 9.5. Comparison of the estimated concentration of fiber in the pulp to the actual concentration Figure 9.6. Comparison of the estimated concentration of calcium carbonate in the pulp to the actual concentration Figure 9.7. Comparison of the estimated concentration of moisture in the pulp to the actual concentration Figure Flow chart of the training algorithm Figure Flow chart for evaluation algorithm Figure Plot of the estimated fiber content in pulp consisting of fibers and water. The estimates are based on the parameter selected by the algorithm Figure Repeatability test for measurements made using pulp containing just fiber and water Figure Repeatability test for measurements made using pulp containing fiber, calcium carbonate, and water Figure Reproducibility test for measurements made using pulp containing just fiber and water Figure Reproducibility test for measurements made using pulp containing fiber, calcium carbonate, and water Figure Validation of estimation process using equation (6.1) Figure Validation of estimation process described in Section Figure Validation of estimation process described in Section Figure Validation of estimation process described in Section v

8 Figure Measurements of paper pulp samples with 90% to 92% moisture concentration at frequencies from 200 Hz to 100 khz, for an air gap of 2.5 mm. 69 Figure Measurements of paper pulp samples with 90% to 92% moisture concentration at frequencies from 200 Hz to 100 khz, for an air gap of 4.2 mm. 70 Figure Cole-Cole plots from measurements of paper pulp samples with 90% to 92% moisture concentration at frequencies from 200 Hz to 100 khz, for an air gap of 2.5 mm Figure Cole-Cole plots from measurements of paper pulp samples with 90% to 92% moisture concentration at frequencies from 200 Hz to 100 khz, for an air gap of 4.2 mm Figure Normalized Capacitances measured at 7.9 khz for an air gap of 2.5 mm, and 4.2 mm Figure Pass line sensitivity of the sensor at 7.9 khz Figure Photograph of the controlled environment chamber Figure Phase measurements of 3 different types of paper pulp samples with 96% to 90% moisture concentration from 200 Hz to 100 khz Figure Capacitance measurements of 3 different types of paper pulp samples with 96% to 90% moisture concentration from 200 Hz to 100 khz Figure Conductance measurements of 3 different types of paper pulp samples with 96% to 90% moisture concentration from 200 Hz to 100 khz Figure Measurements of 3 different types of paper pulp samples with 96% to 90% moisture concentration at 600 Hz Figure Normalized measurements showing the effect of temperature variation on various electrical parameters of a paper pulp with 95% moisture from 1kHz to 100 khz Figure Normalized measurements showing the effect of temperature variation on various electrical parameters of a paper pulp with 95% moisture at 7.9 khz Figure Cole-Cole plots from measurements of paper pulp samples with 0% to 90% moisture concentration at frequencies from 200 Hz to 100 khz Figure Example Cole-Cole plots Figure A1.1. Plot of RMS voltage between the sensing electrodes and ground at various water depths and frequencies Figure A1.2. Near linear relationship was observed between the measured voltage and water depth vi

9 1 Chapter 1. Introduction One of the amazingly inconspicuous, yet indispensable articles used in everyday life is paper. Thousands of mills worldwide churn out 312 million tons of paper annually. Interestingly, papermaking process is still more of an art than science. More often than not, not all of the paper rolled out of a paper machine is perfect. To ensure quality output, it is critical to monitor and control various properties of paper such as its caliper, thickness, opacity and, importantly, its moisture content. Currently, all the properties of the paper are measured only at the dry end of the paper machine; at the very end of the process cycle. Thus, the quality control is primarily a feedback control loop [1,2]. While this control architecture offers stability, it is highly reactive in nature. That is, the system parameters are altered only after output deviations are registered. Hence, there is a considerable delay from the moment there is a deviation in the output, to the moment the parameter changes are reflected in the output. This delay is critical in the case of paper machines. A delay of even ten seconds in the control system of a paper machine, operating at a nominal speed of 2000 m/min, will result in more than 0.2 miles of paper of unacceptable quality. Even though this paper can be recycled to produce lower quality paper, there is considerable monetary loss that is incurred on counts of energy usage, machine time, and utilization of human resources. The obvious solution to this problem is to incorporate additional feed forward control architecture. In such architecture, the properties of the paper are measured at wet end of the paper machine (the initial stages), and the process parameters down the process line are modified to correct the deviations in the paper properties. Figure 1.1 shows the wire section (wet end) of the paper machine. A major hurdle in the practical implementation of feed forward control in paper machines is the availability of sensing technologies for the wet end. The paper pulp at the wet end contains numerous chemical additives, and is primarily an aqueous suspension. These additives alter the response of the paper pulp for various sensing techniques. The changes in the response cannot be calibrated into the existing measurement techniques

10 2 based on microwave attenuation or infrared absorption, as the composition of the additives change on a daily basis depending on the type of paper being produced. Thus, it is very difficult to estimate the fiber content of the pulp accurately and reliably. Figure 1.1. Photograph of a paper machine. Paper manufacturers are looking for non-invasive, non-contact sensing technologies that can accurately measure the fiber content of paper pulp at the wet end of the paper machine. The moisture content of the paper pulp at the wet end ranges from 99% to 80%. This low concentration of fiber in the pulp makes it hard to detect concentration fluctuations with adequate resolution. Fringing field dielectric spectroscopy is a potential sensing technology that could be used to estimate the moisture content of the paper pulp at the wet end of a paper machine. In this technique, fringing electric field penetrates through the paper pulp. The phase and the magnitude of these field lines change depending on the dielectric properties of the paper pulp. These changes in the fields are studied over a frequency range of 200 Hz to 100 khz. Based on these changes, the fiber content of the paper pulp is estimated.

11 3 Chapter 2. State of the Art The methods currently being used to measure moisture in paper pulp are mostly intrusive [3-5], or require certain special operating conditions such as double-sided contact measurements [3-5]. Several patents [6-21] have proposed using an electromagnetic field perturbation sensor for measuring the water concentration in the wet end of the paper machine. In these patents it is assumed that all the water in the pulp is held by paper fibers and that all of electrical conductivity is due to water molecules alone. The concentration of paper fibers in the pulp is indirectly determined by measuring the conductivity of the pulp. The first assumption limits the measurements to high concentrations of fiber content. At higher moisture levels, the fiber is in suspension in water and hence the assumption is no longer valid. The conductivity of the pulp is altered by the presence of additives such as titanium dioxide, alkalis, and clay. Hence, this method cannot be adapted for measuring moisture content in the pulp under realistic operating conditions Microwave Techniques Microwave techniques have been used to study the subsurface moisture since 1970s [3,22,23]. When the propagating electromagnetic wave has a frequency that is equal to the resonance frequency of the medium of propagation, stationary waves are created. Every medium has its own characteristic resonance frequency. Hence, in a multicomponent system, the system s resonance frequency is a function of the resonance frequency of the individual components and their mole fractions. This characteristic can be used to determine the composition of materials [3,22]. Attenuation based microwave techniques have been used to estimate the moisture content of paper pulp [3]. The attenuation factor of the signal at resonance and the frequency shift are used to estimate the moisture content. Fiber concentration as low as

12 4 0.6% has been measured, with a standard deviation of 0.03% [3]. However, this method cannot be used for on-line monitoring of fiber concentration, as it requires a closed cavity resonator. Moreover, the method is sensitive only to fiber concentrations from 0.06% to 1%. In a paper machine, such concentrations of pulp can be found only at the headstock, where the presence of metallic stirrers and the high entropy of the pulp can affect the accuracy of the method. The methods suggested in [23,24] require measuring attenuation of the material, which is difficult to obtain [25]. The difficulty is more pronounced with low attenuation materials as the attenuation measurements are easily influenced by multiple reflections [25]. Most microwave techniques need at least two different types of measurements, such as attenuation and phase [24], or attenuation and density of sample [25]. If these techniques were to be realized, they would require at least two instruments [25] to obtain two different parameters. This would increase the measurement complexity and the cost of the measurement system [25]. Electromagnetic interference from other sources of radiation can affect the accuracy of microwave techniques. The resonance frequency of pulp is around 2.6 GHz [3], which is close to the commonly used 2.4 GHz communication channels. As the communication signals at 2.4 GHz are random in nature, their effect on the measurements cannot be effectively compensated. Hence, all the microwave systems have to be electromagnetically shielded, thus rendering the open cavity measurement models [22] impractical. The sensor reported here uses a single-sided guard plane. The proximity of the guard plane to the sensing electrodes ensures the immunity of the sensor to stray low frequency electromagnetic fields. The stray fields penetrate the pulp sheet and the wire to influence the sensor output. However, the process of penetration weakens the stray fields sufficiently, and the effect of these fields on the sensor output is negligible. The penetration depth of the electromagnetic waves cannot be controlled. Hence, it is not possible to study the moisture distribution in the pulp along the axis perpendicular to the surface of the pulp sheets.

13 2.2. Reflection Based Techniques 5 When an electromagnetic wave encounters a discontinuity in the medium of propagation, a part of the wave is reflected back into the incident media. The ratio of the amplitudes of the electric field of the reflected wave to that of the incident wave is called the reflection coefficient. The operational efficiency of reflection based microwave techniques can be analyzed using the basic laws of electromagnetism [26-28]. Let the discontinuity in the medium of propagation be at Z = 0. Let the wave propagate from a media with dielectric constant ε 1 and magnetic permeability µ 1, into a different media with dielectric constant ε 2 and magnetic permeability µ 2. Let the angle of incidence be i and that of refraction be r. By Fresnel s law, if the electric field vector of the incident wave is along the X- axis, the reflection coefficient, R, is defined as, E µ sin( i)cos( i) µ sin( r)cos( r) sin( )cos( ) sin( )cos( r) y1 1 2 R = = E y2 µ 1 i i + µ 2 r (2.1.) where E y1 is the amplitude of the incident electric field, and E y2 is the amplitude of the incident electric field. If the electric field vector of the incident wave is along the Y-axis, we have, Ey1 µ 1tan( i) µ 2 tan( r) R = = E µ tan( i ) + µ tan( r) y2 1 2 (2.2) Since the choice of axis is arbitrary, we can choose either of the equations. Let us assume that the electric field vector of the incident wave is along the X-axis, and hence (2.1) is valid. By Snell s law, sin( i) sin( r) n n 2 = (2.3) where n 1 and n 2 are the refractive indices of the two media. Assuming non-absorbent mediums, the refractive indices are given by, 1 n1 ε 1 µ 1 = (2.4)

14 6 From (2.3), (2.4), and (2.5), n2 ε 2 µ 2 = (2.5) r ε µ = sin sin( i) ε 2µ 2 (2.6) Let the original medium of propagation be air, and the reflecting medium be predominantly water. We have, µ 1 = µ 2 = µ 0 (2.7) ε1 1 (2.8) To minimize the interference between the incident and the reflected waves, let, From (2.6), (2.7), (2.8), and (2.9), R = i = cos sin 2 2ε 2 2ε cos sin 2 2ε 2 2ε 2 (2.9) (2.10) If we consider the dielectric constant of the reflecting media to be close to that of water, From (2.10) and (2.11), ε 2 80 (2.11) R = (2.12) Considering a 10% change in the dielectric constant of the reflecting media, i.e. ε 2 = 72, we have, R = (2.13) From (2.12) and (2.13), we can estimate the sensitivity, S, of the method, i.e. the percentage change in the reflection coefficient for a unit change in the dielectric constant of the reflecting medium, to be S = (2.14) As seen from (2.14), the change in reflection coefficient for a unit change in dielectric constant is very small. Hence, this method requires a setup that can measure the

15 7 reflection coefficient very accurately. This can be achieved by using a high power, high amplitude incident wave. However, a high power incident wave will cause polarization in the reflecting media. Another important factor to be considered is the variation in the refractive indices of the media. According to Clausius - Mosotti relation, the refractive index of a medium vary inversely with its density. n 1 1 = k (2.15) n + 2 ρ where ρ is the density of the medium, and k is a constant. Hence, a non-uniform distribution of constituents of the reflecting media will adversely affect the accuracy of the method.

16 8 Chapter 3. Interdigital Fringing Field Dielectrometry 3.1. Interdigital Fringing Field Sensor The interdigital fringing field sensor operates in a way that is very similar to a conventional parallel plate capacitor. Figure 3.1 shows the transition from a parallel plate capacitor to a fringing field sensor. It can be seen from Figure 3.1 that the electric field lines always penetrate the bulk of the material under test, irrespective of the position of the electrodes. Hence, in addition to the electrode geometry, the capacitance between the electrodes also depends on the material s dielectric properties and geometry. Figure 3.1. A fringing field dielectrometry sensor can be visualized as a parallel plate capacitor whose electrodes open up to provide a one-sided access to material under test [29]. As seen from Figure 3.1(c), the electrodes of a fringing field sensor are coplanar. Hence, the signal-to-noise ratio of measured capacitance will be considerably low. To strengthen the measured signal, the electrode pattern can be repeated several times. The resulting structure of the sensor is known as an interdigital structure. The term interdigital refers to a digit-like or finger-like periodic pattern of parallel in-plane electrodes used to build up the capacitance associated with the electric fields that penetrate into a material sample [30]. This pattern is illustrated in Figure 3.2.

17 9 Figure 3.2. The term interdigital refers to the pattern of fingers or digits that is resembled by the shape and relative position of the electrodes [31]. Figure 3.3 shows a generic interdigital sensor. The wavelength of the sensor is defined as the distance between the centers of two adjacent electrodes of same type. For a semi-infinite homogeneous medium placed on the surface of the sensor, the periodic variation of the electric potential along the X-axis, creates an exponentially decaying electric field along the Z-axis, which penetrates the medium. The possible variation in the properties of the material under test along the Z-axis, and hence is complex dielectric permittivity, ε * (ω), is schematically represented in Figure 3.3 by the variation in shading. The model for analyzing such multi-layered systems is discussed in detail in [32]. There exist many definitions for penetration depth. The penetration depth of a fringing field sensor is usually defined as the position at which the measured value varies from the asymptotic value by 3% [33]. As the penetration depth of a sensor depends on the position, size, and shape of the electrodes, there exists no simple mathematical expression to compute the penetration depth. The penetration depth is often estimated to be equal to one-third the wavelength of the sensor. Exact penetration depth of a sensor can be estimated by using finite element analysis software. Figure 3.4 shows the cross section of a multiple penetration depth sensor.

18 10 Figure 3.3. A generic interdigital sensor with a periodicity λ [34,35]. Figure 3.4. A conceptual view of multiple penetration depth sensor.

19 3.2. Dielectric Spectroscopy 11 All dielectric materials consist of polarized dipoles. When subjected to an external electric field, these dipoles re-align so as to neutralize the effect of the external field. This re-alignment of dipoles occurs to a varying extent for different materials. Thus, the dielectric response of each dielectric material across the frequency spectrum is different, and in most cases unique. The study of this response variation is known as dielectric spectroscopy. The dielectric response of a material is generally quantified in terms of its complex dielectric permittivity. The complex dielectric permittivity ε * ( ω) is usually represented as, ε * ( ω) = ε ( ω) + jε ( ω) (3.1) where ε ( ω) is the real part of permittivity and ε ( ω) is the loss factor. For all materials the loss factor is a function of the excitation frequency. The loss factor mechanisms are schematically shown in Figure 3.5. For a few low-loss materials, and non-polar materials, the variation in the loss factor with frequency is predominantly due to distortion in the electron clouds. Hence, the magnitude of variation of loss factor is negligibly small. The polarization of molecules arising from their reorientation with the imposed electric field is the most important phenomenon contributing to the loss factor in the radio and microwave frequencies (10 7 to 3x10 10 Hz). This includes the dipolar polarization due to bound and free water relaxation. At infrared and visible light frequencies, the loss mechanisms due to atomic and electronic polarization (collectively known as distortion polarization) are the dominating loss mechanisms [36]. The description for the process for pure polar materials was developed by Debye in 1929 [37]. The Debye model is explained in detail in Section 3.3.

20 12 Figure 3.5. Mechanisms influencing the loss factor of a moist material over a wide range of frequencies f (Hz). (A) DC conductivity, (B) Maxwell-Wagner polarization, (C) dipolar polarization of water bound to the matrix of the material, (D) dipolar polarization of free water [36] Debye Model The Debye dielectric relaxation model [37] is the simplest way to analyze polarization in purely polar materials. The model assumes that the relaxation process is governed by first order dynamics, and hence can be characterized with a single time constant. The model can be derived using basic laws of polarization and conduction [38] as shown in the following arguments. When a dielectric is subjected to an electric field, it interacts in two principal ways, re-orientation of the defects in the dielectrics with a dipole moment, and the translative motion of the charge carriers. The resulting current in the dielectric can be written as, D J = σ E+ (3.2) t

21 where 13 J is the current density, E is the electric field, and D is the electric displacement. The electric displacement is defined as the total charge density on the electrodes and is mathematically defined by, D= ε E+ P 0 (3.3) where ε 0 is the permittivity of free space and P is the polarization vector. The Debye model deals with the displacement current represented by the second term in (3.2). When a dielectric is subjected to an electric field E, the resulting polarization P comprises of two parts based on the time constant of the response. One part of the polarization P is the instantaneous polarization due to the displacement of electrons with respect to the nuclei (distortion of the electron cloud). The high frequency dielectric constant ε is thus defined by, P ε 1 = (3.4) ε 0E The second part of the polarization P is the time-dependent polarization P () t due to the orientation of the dipoles in the electric field. If we let the field remain in place infinitely long, the resulting total polarization P s defines the static dielectric constant ε s as, Ps ε s 1 = (3.5) ε E Thus we have, 0 P P = P + P ( t = ) s (3.6) Let us assume that the time dependent polarization is governed by first order kinetics with a relaxation time of τ, such that the rate at which P approaches P s is proportional to the difference between them. That is, dp () t Ps P = dt τ When a unit step voltage u 0 (t) is applied, we have, (3.7)

22 P = P u () t + P() t o (3.8) Taking Laplace transforms of (3.7) and (3.8), and solving for the Laplace transform of polarization { P }, we get, P s P { P} = p+ τ p p+ τ τ (3.9) where p is the complex frequency variable. Taking Inverse Laplace transform of (3.9) and simplifying, we obtain, Ps + jωτ P P = jωτ + 1 (3.10) Assuming a conductivity of zero and a sinusoidal steady state fields of the form, ˆ jωt J =R Je (3.11) ˆ jωt E =R Ee From (3.2), (3.7), (3.10) and (3.11), we get, ( s ) 2 ( ωτ ) ( s ) ( ωτ ) * ε ε ωτ ε ε ε ε = j (3.12) The real and imaginary parts of (3.12) are known as the Debye dispersion relations, and have remained the basic model of dielectric relaxation since their inception. The frequency response of the Debye model corresponds exactly to the response of the simple lumped circuit element shown if Figure 3.6 (a), for a parallel plate electrode geometry with area A and gap d. 14

23 15 Figure 3.6. Debye model for time dependent polarization [39]. The similarity between the Debye model and the lumped circuit element is given by (3.13), (3.14) and (3.15). C s C p ε 0ε A = (3.13) d ( ) ε0 εs ε A = (3.14) d τ = R C (3.15) Even when the conductivity of a material is zero, its complex dielectric permittivity can still have a non-zero imaginary part. The energy dissipation process due to dipole re-orientation in the material, and energy dissipation due to translatory motion of charge carriers introduces the imaginary part of the complex dielectric permittivity. Equations (3.2) and (3.12) can be combined to include ohmic conductivity and Debye polarization as, ε = ε + ε dipole (3.16) ε σ ω s s o = + ε dipole (3.17) dipole ( ε s ε ) 1 ( ωτ ) 2 ε = (3.18) + ε = dipole ( s ) 1+ ( ωτ ) 2 ε ε ωτ (3.19)

24 Equations (3.16) (3.19) can be presented as Cole-Cole plots shown in Figure 3.6 (b). The Cole-Cole plots plot ε vs. ε with frequency ω as an independent parameter and is an exact semicircle. Another way of studying equations (3.16) (3.19) is shown in Figure 3.7. Dielectric Susceptibility, χ * ( ω ), is related to permittivity, and can be expressed in terms of its real and imaginary components. χ * ( ω) = χ ( ω) jχ ( c) (3.20) The difference between the susceptibility and permittivity is that the term ε * ( ω) refers to the sum of all permittivities between infinity and the frequency of interest, while χ * ( ω) refers to the permittivity at that specific frequency [40]. 16 Figure 3.7. Real and imaginary parts of complex susceptibility as a function of frequency. [40]

25 17 Chapter 4. Experimental Setup The experiments reported in this report emulate the operational conditions in a paper machine. The pulp in the wet end of the paper machine is primarily a suspension. This pulp suspension is spread on to a semi-permeable membrane made of nylon or similar polymer, and is hence unavailable for contact measurements. To emulate this setup in the laboratory, the pulp is blended to a consistency of a suspension and is placed on a tray. The tray wall prevents contact with the pulp, and hence is equivalent to the wire on the paper machine. The sensor used for these measurements is an interdigital sensor tray with a spatial periodicity of 40 mm, finger length of 160 mm, and penetration depth of 7 mm. The sensor electrodes are not in direct contact with paper pulp. Instead, the sensor is attached to the outer side of the base of an acrylic tray with a wall thickness of 5 mm. Figure 4.1 shows a photograph of the experimental setup. A guard plane is placed underneath the sensor electrodes to provide shielding from external electric fields. The geometry of the sensor is shown in Figure 4.2. Figure 4.1. Photograph of experimental setup.

26 18 Measurements reported here were taken using the Fluke manufactured RCL meter (model PM 6304). It generates a one-volt sinusoidal AC voltage in the frequency range from 50 Hz to 100 khz. A custom designed circuit is also available for making measurements. The circuit is capable of making measurements from three sensors simultaneously. A data acquisition system for the circuit has been written using LabVIEW. Advanced data analysis can be potentially integrated into the software. However, as the measurements reported in this report require only single channel measurements, the custom designed circuit was not used. The interdigital sensor tray filled with paper pulp is connected to the two channels of the RCL meter. The effective impedance between the two channels is calculated by computing the magnitude attenuation and phase shift between the input voltage and loop current. Drive 4 cm 16 cm Guard Sense Figure 4.2. The top-down view of the interdigital sensor tray with the spatial periodicity of 40 mm, finger length of 160 mm and an approximate penetration depth of 13 mm. The measurements are made at frequencies in the range of 200 Hz to 100 khz. The measurements made at the lower end of the frequency spectrum (below 200 Hz) have noise due to the AC power supply. The instrumentation limits the highest viable frequency to 100 khz. Ten sets of measurements were taken at each frequency, and then

27 19 averaged to reduce the noise. It is assumed that all sources of noise have zero mean distribution. Initial contact with the Forestry Department of UW, and subsequent lab tours to the paper machines at the Forestry Department of UW and at Port Townsend paper mill, confirmed feasibility of installing these sensors on paper machines. The sensors can potentially be installed in two positions on the paper machine depending on the need. The sensor can be embedded in the mounts for hydrofoils in the wire section. This would be preferable if the sensor is to be used to measure moisture in the range of 97% to 80%. Alternatively, the sensor could also be installed just after the wire but before the press section. Currently, the setup is very simple. Although the equipment is suitable for portable measurements, it is too early in the project to install the sensors on a running paper machine.

28 Chapter 5. Experiments with High Fiber Concentration Pulp (100% to 10%) 20 Experiments were conducted to characterize the response of the sensor to the variation of moisture level in pulp with very high fiber content. The moisture content of the pulp was varied from 0% to 90%, and measurements were made using the setup described in Chapter Experimental Procedure When the required moisture content is relatively low, it is not possible to prepare minced pulp in the laboratory using the currently available devices. Hence sheets of dried pulp are used for the measurements. Sheets of dried paper pulp are cut into the size of the sensor tray and subsequently stacked in it. The pulp sheets have to be absolutely flat, failing which air pockets are formed between the pulp sheets. These air pockets affect the measurements adversely. Calculated amount of water is sprinkled on to the sheets. The pulp sheets, being relatively dry, absorb the water quickly. The key to the successful measurement in this range is uniform distribution of water. The interdigital sensor tray filled with paper pulp is then connected to the two channels of the RCL meter and measurements are made Experimental Results Figure 5.1(c) shows the dependence of capacitance on the moisture content and excitation frequency. It can be seen that the capacitance initially increases with the moisture content and then starts to decrease after moisture level of 85%.

29 21 Figure 5.1(b) shows the dependence of phase on the moisture content and excitation frequency. The magnitude of the phase change is small. Hence, even a small noise in the phase measurement leads to cross-overs at various frequencies and moisture levels. Figure 5.1. Measurements of paper pulp samples with 0% to 90% moisture concentration at frequencies from 200 Hz to 100 khz.

30 5.3. Data Analysis 22 Figure 5.2 and Figure 5.3 show respectively conductance and capacitance as a function of moisture concentration of the pulp as measured. It can be observed that the capacitance starts to decrease with increase in moisture after 85% moisture concentration. This trend continues into lower fiber concentration region as will be shown in Chapter 6. It can be seen from Figure 5.2 that the rate of change of moisture concentration with conductance is very high. Hence, if conductance is used as a parameter to estimate the paper moisture concentration, then any small error in conductance measurement will be amplified and hence the resulting the error in the moisture concentration estimate will be unacceptably high. Figure 5.2. Fiber content as a function of the conductance of the paper pulp samples with 0% to 90% moisture concentration at various frequencies from 200 Hz to 100 khz. As shown in Figure 5.3, the rate of change of moisture concentration with capacitance is low, so amplification of the error in measurement of capacitance will be

31 marginal. Hence capacitance can be used as a parameter to estimate the moisture concentration in the pulp. 23 Figure 5.3. Fiber content as a function of the capacitance of the paper pulp samples with 0% to 90% fiber concentration at various frequencies from 200 Hz to 100 khz.

32 Chapter 6. Experiments with Low Fiber Concentration Pulp (10% to 3%) 24 Experiments were conducted to characterize the response of the sensor to the variation of moisture level in pulp with very low fiber content. The mositure content of the pulp was varied from 90% to 97% in steps of 1% and measurements were made using the setup described in Chapter Experimental Procedure Known quantities of paper and water are mixed in a commercial blender to obtain the paper pulp. The pulp is then cooled to ambient temperature of 25 C. The moisture loss due to evaporation can be neglected, as the loss is small compared to the total water content in the pulp. The prepared pulp is then deposited in the sensor tray. The homogeneity of spatial distribution of the pulp and reduction in the number of air pockets in the bulk of the pulp are achieved by manually rearranging the pulp in the tray. The interdigital sensor tray filled with paper pulp is then connected to the two channels of the RCL meter and measurements are made Experimental Results Figure 6.1(c) shows the dependence of capacitance on the moisture content and excitation frequency. It can be seen that the variation is monotonous and strictly decreasing with frequency and moisture content. As seen from Figure 6.2, the obtained curves were found to be displaced by at least twice the standard deviation. Hence inaccuracies in measurement introduce relatively smaller errors in the concentration estimates.

33 25 Figure 6.1. Measurements of paper pulp samples with 90% to 97% moisture concentration at frequencies from 200 Hz to 100 khz. Figure 6.1(d) shows the dependence of conductance on the moisture content and excitation frequency. The spatial separation of the curves is not adequate to mitigate the effect of any small inaccuracies in the measurement of conductance. This may explain the high error percentages reported in [5,41,42]. Figure 6.1(b) shows the dependence of phase on the moisture content and frequency. There are cross-overs in the phase plots at various frequencies and moisture levels. This is partly due to instrumentation errors and also due to the fact that the phase is highly sensitive to noise. Hence the phase shifts at two frequencies cannot be used with

34 the frequency range under consideration to estimate the moisture content of the pulp as suggested in [25]. 26 Figure 6.2. The capacitance measured at 5 khz shows separation between measurements to be much greater than twice the standard deviation. This indicates towards the possibility of achieving higher resolution using the sensor. Figure 6.3 shows the Cole-Cole Plots for the measurements made. The admittance plot shows adequate resolution at higher frequencies to differentiate between the different moisture content levels of the paper pulp.

35 27 Figure 6.3. Cole-Cole plots from measurements of paper pulp samples with 3% to 10% paper concentration at frequencies from 50 Hz to 100 khz Data Analysis Figure 6.1(c) and Figure 6.1(d) show that the measured capacitance and conductance decrease with increasing excitation frequency till 20 khz and then increase. This can be attributed to presence of multiple relaxation processes in the paper pulp. If

36 only one relaxation process was present, the trend in capacitance and conductance would be monotonous, and strictly decreasing with frequency. The rate at which the capacitance or conductance decreases is unique to the relaxation processes of the fiber and water molecules. This can be exploited to estimate the moisture content in the pulp in the presence of other fillers, which too can influence the electrical parameters. However, it has to be first established that no other constituent of the pulp undergoes the same relaxation processes. Figure 6.4 shows the moisture content as a function of conductance at different frequencies. It can be seen that the rate of change of conductance with moisture content is small. Hence, it is not advisable to estimate the moisture content based on the conductance and the excitation frequency. This may be the main reason the methods suggested in [5,20,21,41] did not perform adequately for lower fiber concentrations. The slopes of the curves are better defined at higher concentrations of paper fiber, and hence the foresaid methods can be used to estimate the moisture content in those regions. Figure 6.5 shows the moisture concentration as a function of capacitance at different frequencies. It can be seen that slopes of the curves are higher than those of the conductance plots in Figure 6.4. Hence we estimate the moisture content of the pulp based on the measured capacitance measured and the frequency used. The curves in Figure 6.5 can be linearized and the relationship between moisture concentration, P and the capacitance, C can be expressed as: P= m C+ k (6.1) where m is the slope of the line and k is the offset constant. It can be seen that both m and k are related to the frequency of excitation. 28

37 29 Figure 6.4. Conductance plots from measurements of paper pulp samples with 90% to 96% moisture concentration at frequencies from 200 Hz to 100 khz. Figure 6.5. Capacitance plots from measurements of paper pulp samples with 90% to 96% moisture concentration at frequencies from 200 Hz to 100 khz. Figure 6.6 and Figure 6.7 respectively show the variation m and k with excitation frequency. It can be observed that the resolution of this method is noticeably higher at lower frequencies and hence these frequencies offer smaller error margins.

38 30 Figure 6.6. Variation of the slope, m, in (6.1) depicting the plot between percentage of moisture content and capacitance with respect to frequency of excitation. Figure 6.7. Variation of the offset, k, in (6.1) depicting the plot between percentage of moisture content and capacitance with respect to frequency of excitation. To determine the moisture content in the pulp given the capacitance of the pulp and the frequency of excitation used, we first determine the corresponding values of m and k from Figure 6.6 and Figure 6.7. Once these values have been determined, they are

39 31 substituted in (6.1) along with the measured capacitance and the moisture concentration is estimated. Figure 6.8 shows the conformity of the curve formulated in (6.1) to the data obtained experimentally. The curve formulated in (6.1) will be always valid for estimation of moisture content for all similar pulp samples if adequate reproducibility is ensured. The reproducibility and repeatability of the measurements are discussed in Chapter 11. Figure 6.8. The data obtained experimentally at 5 khz is in agreement with the curve formulated in (6.1).

40 32 Figure 6.9. Standard deviation of the capacitance measurements at various moisture levels is two orders of magnitude smaller than the capacitance (10-11 vs ). The accuracy of this method relies on the ability to measure capacitance accurately and the sensitivity of the method. Figure 6.9 shows the standard deviation of the measured capacitance at 5 khz for various moisture concentration levels. It can be seen from Figure 6.6 and Figure 6.9 that the maximum standard deviation of the estimated moisture content would be approximately %.

41 33 Chapter 7. Experiments with Titanium Dioxide Experiments were conducted to characterize the response of the sensor to the variation of moisture level in pulp with low fiber and titanium dioxide content. The concentration of the fiber was initially 6% with 94% moisture. The titanium dioxide concentration was varied from 0% to 7% in steps of 1%. The measurements were made using the setup described in Chapter Experimental Procedure Known quantities of paper, titanium dioxide and water are mixed in a commercial blender to obtain the paper pulp. The pulp is then cooled to ambient temperature of 25 C. The moisture loss due to evaporation can be neglected as the loss is small compared to the total water content in the pulp. The prepared pulp is then deposited in the sensor tray. The homogeneity of spatial distribution of the pulp and reduction in the number of air pockets in the bulk of the pulp are achieved by manually rearranging the pulp in the tray. The interdigital sensor tray filled with paper pulp is then connected to the two channels of the RCL meter and measurements are made Experimental Results Figure 7.1(c) shows the dependence of capacitance on the titanium dioxide content and excitation frequency. It can be seen that the variation is monotonous and strictly decreasing with titanium dioxide content. The capacitance measured at 6% fiber concentration, 94% moisture and 0% titanium dioxide is not the same as that measured for a similar configuration in Section 6.2, as shown in Figure 6.1. This could be because different types of pulp sheets were used to prepare the pulp for these experiments. The

42 34 fibers in each of the pulp sheet types are different and have unique dielectric properties. If desired, this property can be exploited to determine the type and the quality of the fiber in the pulp. Figure 7.1. Measurements of paper pulp samples with 0% to 7% titanium dioxide concentration at frequencies from 200 Hz to 100 khz. Figure 7.1(b) and Figure 7.1(d) shows the dependence of phase and conductance on the titanium dioxide content and excitation frequency. There is a change in the trend of the parameters between the 20 khz and 100 khz. This is due to the combination of the different dielectric relaxation process of titanium dioxide, the paper fibers, and water. The frequency that exhibits the minimum conduction will also depend on the composition

43 35 of the pulp. This frequency can potentially be used as a handle to eliminate the effects due to additives. Figure 7.2 shows the Cole-Cole plots for the measurements made. Figure 7.2. Cole-Cole plots from measurements of paper pulp samples with 0% to 7% titanium dioxide concentration at frequencies from 200 Hz to 100 khz. Figure 7.3 and Figure 7.4 respectively show the conductance and the capacitance measured at different frequencies from 200 Hz to 100 khz.

44 36 Figure 7.3. Conductance plots from measurements of pulp samples with 0% to 7% titanium dioxide concentration at frequencies from 200 Hz to 100 khz. Figure 7.4. Capacitance plots from measurements of pulp samples with 0% to 7% titanium dioxide concentration at frequencies from 200 Hz to 100 khz.

45 7.3. Data Analysis 37 The variations in capacitance, conductance and other electrical parameters are influenced by all the three components of the pulp, namely, paper fiber, titanium dioxide, and moisture. Since two independent variables are involved here, it is not possible to estimate the fiber concentration using a single parameter. So we solve the inverse problem, by estimating any three of the electrical parameters as X m11 m12 m13 p C1 Y = m m m t + C (7.1) Z m31 m32 m 33 w C 3 where X, Y and Z are the electrical parameters estimated using fiber concentration p, titanium dioxide concentration t, moisture content w, and constants m 11, m 12, m 13 m 33 and C 1, C 2, and C 3. Once the constants are determined, the parameters X, Y and Z can be used to estimate the concentrations of fiber, titanium dioxide and water in the pulp using (7.2), (7.3), (7.4), and (7.5). e( α d) a( β g) w = eb af t = f ( α d) b( β g) af be (7.2) (7.3) p = 100 ( t+ w) (7.4)

46 38 where, ( ) a= m m m m b= ( m m m m ) d = ( m c m c ) e= ( m m m m ) f = ( m m m m ) g = ( m c m c ) α = ( m X m Y) β = ( m Y m Z) (7.5) The key to the success of the estimation is in the choice of the parameters X, Y and Z, and the constants m 11, m 12, m 13 m 33 and C 1, C 2, and C 3. Figure 7.5. Comparison of the estimated concentration of fiber in the pulp to the actual concentration.

47 39 Figure 7.6. Comparison of the estimated concentration of titanium dioxide in the pulp to the actual concentration. Figure 7.7. Comparison of the estimated concentration of moisture in the pulp to the actual concentration. Figure 7.5, Figure 7.6 and Figure 7.7 respectively compare the concentrations of fiber, titanium dioxide, and moisture as obtained using the method described above. The

48 40 estimates were based on the measured phase, capacitance and conductance. These parameters were chosen manually. The algorithm that is introduced in Chapter 10 can be potentially used for choosing these parameters. Currently, we are attempting to devise a method to determine the constants and the parameters that would reduce the error.

49 41 Chapter 8. Experiments with Clay Experiments were conducted to characterize the response of the sensor to the variation of fiber concentration the in the presence of clay and water. The concentration of the fiber was varied from 10% to 5% and that of clay from 0% to 5% in steps of 1%. The moisture content was maintained a constant at 90%. The measurements were made using the setup described in the Chapter Experimental Procedure Known quantities of paper and water are mixed in a commercial blender to obtain the paper pulp. The pulp is then cooled to ambient temperature of 25 C. The moisture loss due to evaporation can be neglected, as the loss is small compared to the total water content in the pulp. The required amount of clay is dissolved in known quantity of water. The clay solution is then added to the prepared pulp, and the mixture is thoroughly mixed. The prepared pulp is then deposited in the sensor tray. The homogeneity of spatial distribution of the pulp and reduction in the number of air pockets in the bulk of the pulp are achieved by manually rearranging the pulp in the tray. The interdigital sensor tray filled with paper pulp is then connected to the two channels of the RCL meter and measurements are made Experimental Results Figure 9.1c shows the variation of capacitance with clay content and frequency. The change in capacitance with clay content is negligibly small. This indicates that the reactance of the clay molecules is very close to that of the paper fiber. Hence, the

50 42 additional reactance due to clay compensates for the reduction in the reactance due to the reduction in the percentage composition of the fiber molecules. Figure 9.1b and Figure 9.1d respectively show the variation in phase and conductance with the clay content and frequency. The conductance increases with the clay content. This is due to the presence of free carrier molecules in clay, which increase the conduction of the pulp. The increase in conduction, with the capacitance remaining nearly the same is reflected in the change in phase. Figure 8.1. Measurements of paper pulp samples with 10% to 5% fiber concentration and 0% to 5% clay at frequencies from 200 Hz to 100 khz.

51 Figure 8.2 shows the Cole-Cole plots for the measurements made. 43 Figure 8.2. Cole-Cole plots from measurements of paper pulp samples with 10% to 5% paper concentration and 0% to 5% clay at frequencies from 200 Hz to 100 khz. Figure 9.3 and Figure 9.4 respectively show the conductance and the capacitance measured at different frequencies from 200 Hz to 100 khz.

52 44 Figure 8.3. Conductance plots from measurements of pulp samples with 0% to 5% clay concentration at frequencies from 200 Hz to 100 khz. Figure 8.4. Capacitance plots from measurements of pulp samples with 0% to 5% clay concentration at frequencies from 200 Hz to 100 khz.

53 8.3. Data Analysis 45 The pulp with clay in it is again a three-component system similar to the one with titanium dioxide. Hence the same estimation algorithm as used for titanium dioxide can be used for estimating the concentrations of clay, fiber and moisture in the pulp. The key to the success of the estimation is in the choice of the parameters X, Y and Z, and the constants m 11, m 12, m 13 m 33 and C 1, C 2, and C 3. Figure 9.5, Figure 9.6, and Figure 10.3 respectively show the estimated concentrations of fiber, clay and moisture against the respective actual concentrations. These estimates were based on the conductance and phase measurements at 5 khz. Figure 8.5. Comparison of the estimated concentration of fiber in the pulp to the actual concentration.

54 46 Figure 8.6. Comparison of the estimated concentration of clay in the pulp to the actual concentration. Figure 8.7. Comparison of the estimated concentration of moisture in the pulp to the actual concentration.

55 47 Chapter 9. Experiments with Calcium Carbonate Experiments were conducted to characterize the response of the sensor to the variation of fiber concentration the in the presence of calcium carbonate and water. The concentration of the fiber was varied from 10% to 7.5% and that of calcium carbonate from 0% to 2.5% in steps of 0.5%. The moisture content was maintained a constant at 90%. The measurements were made using the setup described in Chapter Experimental Procedure Known quantities of paper and water are mixed in a commercial blender to obtain the paper pulp. The pulp is then cooled to ambient temperature of 25 C. The moisture loss due to evaporation can be neglected, as the loss is small compared to the total water content in the pulp. The required amount of calcium carbonate is dissolved in known quantity of water. The calcium carbonate solution is then added to the prepared pulp, and the mixture is thoroughly mixed. The prepared pulp is then deposited in the sensor tray. The homogeneity of spatial distribution of the pulp and reduction in the number of air pockets in the bulk of the pulp are achieved by manually rearranging the pulp in the tray. The interdigital sensor tray filled with paper pulp is then connected to the two channels of the RCL meter and measurements are made Experimental Results Figure 9.1c shows the variation of capacitance with calcium carbonate content and frequency. The change in capacitance with calcium carbonate content is negligibly small. This indicates that the reactance of the pulp is dominated by moisture concentration.

56 48 Figure 9.1b and Figure 9.1d respectively show the variation in phase and conductance with the calcium carbonate content and frequency. The conductance increases with the calcium carbonate content. This is due to the presence of free carrier ions in calcium carbonate, which increase the conduction of the pulp. The increase in conduction, with the capacitance remaining nearly the same is reflected in the change in phase. Figure 9.1. Measurements of paper pulp samples with 10% to 7.5% fiber concentration and 0% to 2.5% calcium carbonate at frequencies from 200 Hz to 100 khz. Figure 9.2 shows the Cole-Cole plots for the measurements made.

57 49 Figure 9.2. Cole-Cole plots from measurements of paper pulp samples with 10% to 7.5% paper concentration and 0% to 2.5% calcium carbonate at frequencies from 200 Hz to 100 khz. Figure 9.3 and Figure 9.4 respectively show the conductance and the capacitance measured at different frequencies from 200 Hz to 100 khz.

58 50 Figure 9.3. Conductance plots from measurements of pulp samples with 0% to 2.5% calcium carbonate concentration at frequencies from 200 Hz to 100 khz. Figure 9.4. Capacitance plots from measurements of pulp samples with 0% to 2.5% calcium carbonate concentration at frequencies from 200 Hz to 100 khz.

59 9.3. Data Analysis 51 The pulp with calcium carbonate in it is again a three-component system similar to the one with titanium dioxide. Hence the same estimation algorithm as used for titanium dioxide can be used for estimating the concentrations of calcium carbonate, fiber, and moisture in the pulp. The key to the success of the estimation is in the choice of the parameters X, Y and Z, and the constants m 11, m 12, m 13 m 33 and C 1, C 2, and C 3. Figure 9.5, Figure 9.6, and Figure 10.3 respectively show the estimated concentrations of fiber, calcium carbonate, and moisture against the respective actual concentrations. These estimates were based on the conductance and phase measurements at 5 khz. Figure 9.5. Comparison of the estimated concentration of fiber in the pulp to the actual concentration.

60 52 Figure 9.6. Comparison of the estimated concentration of calcium carbonate in the pulp to the actual concentration. Figure 9.7. Comparison of the estimated concentration of moisture in the pulp to the actual concentration.

61 53 Chapter 10. Parameter Selection Algorithm Figure 5.1, Figure 6.1, and Figure 7.1 illustrate that all the electrical parameters measured are dependent on the moisture content of the paper pulp. Hence, there is a choice of parameters that can be used to estimate the moisture content. We propose an algorithm to choose these parameters. Figure 10.1 shows the flowchart for the training process. There are 12 basic electrical parameters that are measured or calculated over a frequency range of 500 Hz to 100 khz for each of the paper pulp samples. These form the base parameters for the estimation process. Derived parameters are then obtained from a linear combination of any two of the base parameters. To exploit the spectral data in these parameters, parameters are further derived from a linear combination of the value of a parameter at two distinct frequencies. Each of the base and the derived parameters are used to derive a linear estimation model similar to that shown in (6.1). Least square fitting technique is used to obtain these models. Based on the model obtained, the fiber concentration of the paper pulp is estimated for numerous training data sets. The mean estimation error is then calculated for all of the parameters for each of the data sets. The parameters are then ranked according to their accuracy for each individual data set. The sum total of the ranks for the parameters is then calculated. The methods with the 10 highest total ranks are then compared with each other based on the product of their sensitivities and the accuracies to which they can be measured. The standard deviation of the parameters in the given training data set is used as a measure of measurement accuracy. This product is a measure of the inherent unbiased error component of the estimated fiber content. Figure 10.2 shows the flowchart for the estimation process. The parameter and the model selected during the training are used to estimate the moisture content of the given pulp sample. At the end of measurement, the data set collected during the estimation process is added to the database of the training set and the system is re-trained. This improves the accuracy of the method over time.

62 54 Figure 10.3 shows the estimated fiber content based on the parameter selected using the proposed algorithm on three unique training data sets. The sample pulp consisted of only fibers and water. The parameter used in for estimation is the ratio of the phase to the magnitude of the current flowing through the sensor at 20 khz. The estimates have a mean normalized error of 3.096%.

63 Figure Flow chart of the training algorithm. 55

64 Figure Flow chart for evaluation algorithm. 56

65 57 Figure Plot of the estimated fiber content in pulp consisting of fibers and water. The estimates are based on the parameter selected by the algorithm.

66 58 Chapter 11. Repeatability Tests The ability of the sensor to repeat measurements is critical for estimation process. The prepared pulp sample was placed in the sensor and measurements were made. The measurements are repeated approximately every 3.24 seconds. During this process, neither the sensor, nor the pulp, is disturbed. The repeatability test was performed on two types of pulp samples. The first sample had 90% moisture content with 10% fiber. Six sets of measurements were made. Figure 11.1 shows the results of the repeatability test for capacitance measured at 7.9 khz. The mean capacitance measured was pf. The standard deviation was found to be pf. The estimated moisture concentration showed a peak-to-peak variation of %. The second sample had 90% moisture content, 7.5% fiber and 2.5% calcium carbonate. Twenty sets of measurements were made. Figure 11.2 shows the results of the repeatability test for capacitance measured at 7.9 khz. The mean capacitance measured was pf. The standard deviation was found to be pf. The estimated moisture concentration showed a peak-to-peak variation of e-013%.

67 59 Figure Repeatability test for measurements made using pulp containing just fiber and water.

68 60 Figure Repeatability test for measurements made using pulp containing fiber, calcium carbonate, and water.

69 61 Chapter 12. Reproducibility Tests The ability of the sensor to reproduce the measurements for similar pulp sample is established by the reproducibility test. The prepared pulp sample was placed in the sensor and measurements were made. The pulp sample is then removed from the sensor. The sensor surface is cleaned and then the same pulp sample is deposited back into the sensor tray. The reproducibility tests were performed on two types of pulp samples. The first sample had 90% moisture content with 10% fiber. Five sets of measurements were made. Figure 12.1 shows the results of the reproducibility test for the estimated moisture content, based on capacitance measured at 4 khz. The mean capacitance measured was pf. The standard deviation was found to be e-14 F. The peak-to-peak variation in the estimated moisture content was found to be %. The second sample had 90% moisture content, 7.5% fiber and 2.5% calcium carbonate. Twenty sets of measurements were made. Figure 12.2 shows the result of the reproducibility test for the measured capacitance at 4 khz. The mean capacitance measured was pf. The standard deviation was found to be e-14 F. The peak-to-peak variation in the estimated moisture content was found to be %.

70 62 Figure Reproducibility test for measurements made using pulp containing just fiber and water.

71 63 Figure Reproducibility test for measurements made using pulp containing fiber, calcium carbonate, and water.

72 64 Chapter 13. Validation of Estimation Algorithms To validate the estimation algorithms presented in so far, blind data tests were conducted. The algorithms were trained using the data from a single experiment. One of the data points obtained was omitted in the training data set. Hence, for the purpose of evaluation, the omitted data point serves as a blind data point. The entire data from the experiment is then provided to the estimation algorithms, and the estimated moisture content is compared to the actual moisture content. Figure 13.1, Figure 13.2, Figure 13.3, and Figure 13.4 respectively show the result of the validation tests performed on equation (6.1), estimation algorithms in presence of titanium dioxide, clay and calcium carbonate. Figure Validation of estimation process using equation (6.1).

73 Figure Validation of estimation process described in Section

74 Figure Validation of estimation process described in Section

75 Figure Validation of estimation process described in Section

76 68 Chapter 14. Pass line Sensitivity Pass line sensitivity of the sensor is an important measure of the practical applicability of the sensor. Pass line sensitivity can be defined as the ability of the sensor to detect variation in the moisture content of the paper pulp in the presence of an air gap between the sensor surface and the paper pulp. The following experiments was conducted to demonstrate the pass line sensitivity of the fringing electric field sensor. A sensor with a spatial periodicity of 4.3 cm, finger length of 7.9 cm, and an approximate penetration depth of 1.43 cm is fabricated on a 5 mm thick Plexiglas substrate. A grounded metal plate placed beneath the sensor substrate acts as a guard plane. The paper pulp is placed in a tray of wall thickness 5 mm. The base of the tray is elevated from the surface of the sensor electrodes by use of spacers. Two set of experiments were conducted, one with an air gap of 2.5 mm, and other with 4.2 mm. The pulp preparation, and measurement techniques are the same as described in Section 6.1. The moisture content of the pulp was varied from 90% to 92% in steps of 1% Experimental Results Figure 14.1(a) shows the variation in magnitude of admittance with moisture content, and excitation frequency, for an air gap separation of 2.5 mm. A monotonous decrease in admittance with increasing moisture content is noticed. Figure 14.1(b) shows the variation in phase with moisture content, and excitation frequency, for an air gap separation of 2.5 mm. The lower frequency phase measurements are very noisy. Figure 14.1(c) shows the variation in capacitance with moisture content, and excitation frequency, for an air gap separation of 2.5 mm. A monotonous decrease in admittance with increasing moisture content is noticed.

77 69 Figure 14.1(d) shows the variation in conductance with moisture content, and excitation frequency, for an air gap separation of 2.5 mm. The measured conductance is erroneous for most of the frequencies, and hence cannot used for parameter estimation purposes. Figure Measurements of paper pulp samples with 90% to 92% moisture concentration at frequencies from 200 Hz to 100 khz, for an air gap of 2.5 mm. Figure 14.2(a) shows the variation in magnitude of admittance with moisture content, and excitation frequency, for an air gap separation of 4.2 mm. A monotonous decrease in admittance with increasing moisture content is noticed.

78 70 Figure 14.2(b) shows the variation in phase with moisture content, and excitation frequency, for an air gap separation of 4.2 mm. The lower frequency phase measurements are very noisy. Figure 14.2(c) shows the variation in capacitance with moisture content, and excitation frequency, for an air gap separation of 4.2 mm. A monotonous decrease in admittance with increasing moisture content is noticed. Figure 14.2(d) shows the variation in conductance with moisture content, and excitation frequency, for an air gap separation of 4.2 mm. The measured conductance is erroneous for most of the frequencies, and hence cannot used for parameter estimation purposes. Figure Measurements of paper pulp samples with 90% to 92% moisture concentration at frequencies from 200 Hz to 100 khz, for an air gap of 4.2 mm.

79 14.2. Data Analysis 71 Figure 14.3, and Figure 14.4 show the Cole-Cole plots obtained from the measured data. It is clearly evident from the figures that the real part of the impedance and admittance was incorrectly measured. This is also reflected in Figure 14.1(b), and Figure 14.2(b). The high frequency points in the Cole-Cole plots show very good resolution with respect to moisture variation. This can be used for data extraction in the future stages of data analysis. As observed in Figure 14.1, and Figure 14.2, there is an offset in the absolute values of the measured electrical parameters. This is due to the exponential decay in the electric field intensity along the axis normal to the plane of the electrodes. The presence of a strong dielectric, the base of the Plexiglas tray, enhances this offset variation. As a first step towards minimizing this offset, we consider the ratio of the measured capacitance in the presence of the tray and pulp, to that measured in the presence of only the tray and air. Figure 14.5 shows the normalized capacitances measured at 7.9 khz for the two air gaps. There is still a considerable variation with the change in air gap. Development of advanced algorithms is needed to reduce this variation. Figure 14.6 shows the pass line sensitivity of the sensor at 7.9 khz. The pass line sensitivity was calculated using (14.1). C P = d d1 Cd2 (14.1) d 1 2 where C d1,and C d2 are the normalized capacitances for air gaps d 1 and d 2. It can be observed from Figure 14.5 that the rate of change of normalized capacitance is about for unit change in moisture concentration. It can be seen from Figure 14.6 that the change in normalized capacitance with change in distance is about per millimeter. Hence, the pass line sensitivity is approximately 3.29% of moisture per mm.

80 72 Figure Cole-Cole plots from measurements of paper pulp samples with 90% to 92% moisture concentration at frequencies from 200 Hz to 100 khz, for an air gap of 2.5 mm.

81 73 Figure Cole-Cole plots from measurements of paper pulp samples with 90% to 92% moisture concentration at frequencies from 200 Hz to 100 khz, for an air gap of 4.2 mm.

82 74 Figure Normalized Capacitances measured at 7.9 khz for an air gap of 2.5 mm, and 4.2 mm. Figure Pass line sensitivity of the sensor at 7.9 khz.

83 75 Chapter 15. Disturbance factors The dielectric properties of most materials vary with temperature, which results in a difference in the measured impedance. The experiments conducted in this paper were performed in an air-conditioned lab with room temperature maintained around 25 C. The paper pulp was made by mixing minced paper with water in a blender. The blending process raises the temperature of the paper pulp. To accommodate this variation, all the paper samples were cooled to room temperature before the experiments were conducted. Figure 15.1 shows the controlled environmental chamber that is currently being built. The temperature and the humidity of chamber can be digitally controlled using the same computer that is used for data acquisition. Figure Photograph of the controlled environment chamber. Paper fibers in the pulp tend to coagulate. This leads to non-homogeneous spatial distribution. Special attention needs to taken to ensure that the distribution is as homogeneous as possible. Uneven distribution can lead to variations in the results. The water used to prepare the pulp samples could contain varying degrees of metal ion concentration. This can lead to erroneous results. It is preferable to use distilled water