Dielectric Sensing of Mass Concentration and Moisture in Coal Powders

In powder processing industries, information about the mass concentration, and the moisture content of the material is often required for process monitoring and control. Capacitive sensors are widely applied for measurements of powder materials, as they are sensitive to variations in mass concentration and changes in moisture content. However, for processes where the mass concentration and the moisture content of the material can vary, it is not possible to distinguish between the two effects based on capacitive measurements alone. This letter shows how permittivity and conductivity measurements can be used to independently determine the mass concentration and the moisture content of a powder. The proposed method is demonstrated for an exemplary coal powder. A dielectric characterization based on impedance measurements of a coaxial probe is carried out. Based on these measurement experiments, a modeling approach is presented that allows the independent determination of the mass concentration and the moisture content of powders, which is of great interest for the development of measurement systems for powder processing industries.


I. INTRODUCTION
Various industrial applications involving the processing of powders require information about the mass concentration β s and the moisture content x of the material. Examples include flow metering of pneumatically conveyed solids [1], [2], [3] or monitoring fluidized bed reactors [4], [5]. For mass flow measurements in pneumatic conveyors, the mass concentration β s of the solid particles is a crucial parameter [6], [7], whereas information about the moisture content x of powder materials is needed for monitoring and controlling drying processes in fluidized bed reactors [8], [9].
Electrical measurement methods, such as capacitive sensors, are often used to monitor the processing of powder materials [10], [11], [12]. In capacitive sensing, the measurements are influenced by the dielectric properties of the materials, i.e., the relative permittivity ε r , which, in turn, depends on the mass concentration β s as well as on the moisture content x of the powders. The dependence of ε r on β s and on x is one of the major drawbacks of capacitive sensors for the application in processes where x and β s can vary [8], [13]. The determination of the mass concentration of pneumatically conveyed solids is, therefore, prone to error, as the moisture content of the powder varies and the monitoring of drying processes in fluidized bed reactors is affected by fluctuating mass concentrations of the materials [14], [15]. For this reason, a sensing approach capable of determining both the mass concentration and the moisture content of a powdered material is of great interest for the development of instrumentation for powder processing industries.
In this letter, the independent determination of the mass concentration β s and the moisture content x from permittivity ε r and conductivity σ measurements of powder materials is proposed. The dielectric properties of an exemplary coal powder are determined from impedance measurements of a coaxial probe at different mass concentrations and moisture contents. Based on these measurements, a modeling approach of the relationship between the permittivity ε r , the conductivity σ , the mass concentration β s , and the moisture content x of the powder material is presented. The developed model can be used to independently determine the mass concentration β s and the moisture content x from σ and ε r measurements.
The rest of this letter is organized as follows. In Section II, the measurement setup is discussed. Section III addresses the preparation of the powder samples to generate defined moisture contents. In Section IV, the measurement results are demonstrated and the modeling approach of the relation between σ , ε r , β s , and x is discussed. Finally, Section V concludes this letter.

II. MEASUREMENT SETUP
In this section, the measurement setup for the dielectric characterization of powder materials and the determination of the mass concentration is discussed.

A. Dielectric Measurements
The measurement procedure for determining the conductivity σ in S · m −1 and the dimensionless relative permittivity ε r is based on impedance measurements of a coaxial probe [16], [17]. Fig. 1  Powder materials can be filled between the outer and the inner conductors of the coaxial probe, affecting the probe impedance Z in ohms. For the acquisition of the probe impedance, a Rohde & Schwarz ZVL network analyzer is used in this letter. Given the probe impedance Z, a model-based estimation approach is used to determine σ and ε r . Details on the probe modeling and the determination of σ and ε r from the measured probe impedance Z can be found in [16] and [17].

B. Generation of Defined Mass Concentrations
To determine the mass concentration of a material sample in the coaxial probe, the mass of the probe filling m s is determined with a balance [17]. From the mass of the material sample, the mass concentration can be calculated by β s = m s /V , where V = (r 2 o − r 2 i )π h is the volume of the probe. Hereby, it is required that the material sample fills the entire probe volume. To control the mass concentration of the filling, a defined mass of powder m s is filled into the probe via a funnel, so that the filling height exceeds the height of the probe. Subsequently, the powder is compacted by vibrations, so that the filling height of the powder decreases to h + d. Closing the probe with the cover further compacts the powder to the height of the probe volume h. This ensures that the entire probe is filled with the powder material. Repeated measurements with constant mass concentrations show relative standard deviations in the range of 0.1% comparable to the results demonstrated in [17], indicating the repeatability of the measurements. In addition, the measurements were verified by the coaxial probe for fluidized powders, which was demonstrated in [16] and [17]. Hereby, the homogeneity of the material sample is ensured by a fluidization of the powder material by means of an axial gas stream. This approach, however, is limited to relatively dry powders as increased moisture contents disable the homogeneous fluidization of powders due to liquid bridge forces between particles [18]. For moisture contents up to x = 2%, the measurements for fluidized powders agree with measurements carried out for loosely to tightly packed beds of the powder material. Thus, the proposed measurement approach is used to determine σ and ε r at different mass concentrations β s [19], [20], [21].

III. PREPARATION OF SAMPLES
This section discusses the preparation of material samples to produce defined moisture contents. The relative moisture content x is defined by x = m water m dry + m water (1) where m dry is the mass of dry powder, and m water is the mass of water in the material sample. The total mass of a sample is m s = m dry + m water . The following procedure is performed to prepare the material samples.
1) The powder samples are filled within saleable containers.
2) Drying of the samples at 105 • C within a climate chamber (fan assisted convection heating) [22], [23], [24]. 3) Regularly weighting of the samples. The drying process is completed if m s = const. = m dry (approximately after 72 h). 4) After the drying process is completed, the samples are exposed to an air humidity of >95% at 60°C within the climate chamber. 5) The weight increase m is recorded, which corresponds to the mass of the water m = m water . 6) The containers are sealed, stored for a week, and turned regularly to obtain a homogeneous moisture distribution. 7) Final weighting of the samples. Moisture content x is calculated according to (1).

A. Measurement Results
Figs. 2 and 3 show the conductivity and the relative permittivity of the exemplary coal powder at different mass concentrations β s and moisture contents x, respectively. The powder has an average particle size of d 50 = 30 µm. The dielectric material properties σ and ε r are generally frequency dependent. The results shown in Figs. 2 and 3 depict the dielectric material properties at a frequency of f = 40 MHz, which corresponds to the operating frequency of a capacitive measurement system used by the authors for flow measurements of pneumatically conveyed solids [6], [10], [25], [26]. However, the results presented in this letter and the applicability of the proposed methods were verified in a frequency range reaching from f = 1 MHz to f = 100 MHz [16].
Both the conductivity σ and the relative permittivity ε r increase with increasing mass concentration as well as with increasing moisture content. This stems from the larger ε r and density values of the solid coal compared to the background material air. This behavior is consistent with the results shown in [17] and [20]. The increase in ε r and β s with increasing moisture content x is due to the conductive nature of water and the comparatively high relative permittivity value of ε r,water = 80.

B. Modeling of the Relationship Between σ , ε r , β s , and x
To describe the relationship between the dielectric properties of a powder material and the mass concentration, power law models have been successfully applied to a variety of materials [17], [20], [27]. Thus, the relationship between σ and β s and between ε r and β s can be described by In addition to the measurement results, Figs. 2 and 3 also show the power law models fitted to the data. Hereby, p σ = 2 and p ε = 3 resulted in the best fit between the models and the measurements. The values of p σ = 2 and p ε = 3 correspond to the complex refractive index (CRI) mixing equation [28], [29] and the Landau-Lifshitz-Looyenga (LLL) equation [30], [31], respectively [20]. In general, power law models are empirical equations. However, the CRI and LLL equations are physically motivated models that are also valid for

η(x) into (2) and (3) results in
To illustrate that (4) and (5) can be uniquely solved for β s and x, Fig. 4 depicts σ as a function of ε r . Hereby, (4) and (5) are evaluated at the mass concentration and moisture content values at which the measurement experiments were performed. This results in contour lines of constant moisture content x and constant mass concentration β s . Owing to the strictly monotonically increasing behavior of σ and ε r with respect β s and x, the contour lines do not overlap, and (4) and (5) can be uniquely solved for β s and x. The solution of (4) and (5) is illustrated in Fig. 5 showing the unique relationship between a measured σ and ε r pair and the moisture content x, as well as the mass concentration β s . For the demonstration of the proposed method, an exemplary coal powder is used. However, owing to the wide applicability of the LLL equation and the CRI model to various organic materials such as coal, limestone, flour, corn, bread, etc. [20], [26], [32], [33], [34], the applicability of the proposed measurement approach is not limited to the demonstrated material. The applicability of the affine approximations depicted in Figs. 2 and 3 to describe the relationship between the model parameters η and ζ and the moisture content x has been verified for coal powder for moisture contents up to x ≈ 5%. As the ability of organic powders to absorb moisture varies, the relationships η(x) and ζ (x) have to be individually analyzed for different organic powders and moisture content ranges by means of the proposed measurement approach.

V. CONCLUSION
This letter discussed the independent determination of the moisture content and the mass concentration of powder materials based on conductivity and relative permittivity measurements. The dielectric characterization of powders for defined moisture contents and mass concentrations was presented. Based on these measurements, a modeling approach for the relationship between the conductivity, the relative permittivity, the moisture content, and the mass concentration was presented. The derived model allowed the independent determination of the moisture content and the mass concentration of powder materials, making the proposed approach a valuable tool for developing measurement systems for various powder processing industries.