Experimental Dielectric Properties and Temperature Measurement Analysis to Assess the Thermal Distribution of a Multimode Microwave-Assisted Susceptor Fixed-Bed Reactor

Abstract

In this study, the integration of microwave-assisted technology into fixed-bed configuration processes is explored aiming to characterize and address its challenges with a customized multimodal microwave cavity. This research focuses on evaluating the uncertainty in contactless temperature measurement methods as spectral thermographic cameras and infrared pyrometers, microwave heating performance, and the thermal homogeneity within fixed beds containing microwave–susceptor materials, including the temperature-dependent dielectric characterization of such materials, having different geometry and size (from 120 to 5000 microns). The thermal inhomogeneities along different bed configurations were quantified, assessing the most appropriate fixed-bed arrangement and size limitation at the employed irradiation frequency (2.45 GHz) to tackle microwave-assisted gas–solid chemical conversions. An increased temperature heterogeneity along the axial profile was found for finer susceptor particles, while the higher microwave susceptibility of coarser grades led to increased temperature gradients, ΔT > 300 °C. Moreover, results evidenced that the temperature measurement on the fixed-bed quartz reactor surface by a punctual infrared pyrometer entails a major error regarding the real temperature on the microwave susceptor surface within the tubular quartz reactor (up to 230% deviation). The experimental findings pave the way to assess the characteristics that microwave susceptors and fixed beds must perform to minimize thermal inhomogeneities and optimize the microwave-assisted coupling with solid–gas-phase reactor design and process upscaling using such multimode cavities.

1. Introduction

Fixed-bed gas–solid reactors are fundamental in numerous industrial processes, encompassing fields as diverse as chemical synthesis, environmental remediation, and energy production [1,2]. Their design enables interactions between a gaseous phase and solid materials, facilitating key chemical reactions such as catalysis [3], adsorption [4], and pyrolysis [5,6,7], underscoring their importance and widespread application. The fixed-bed configuration is particularly valued for its operational simplicity, robustness, and capacity to manage large material volumes, positioning it as a cornerstone in processes like gas purification and waste management [8,9]. Despite their broad application, fixed-bed gas–solid reactors face significant challenges, particularly related to energy efficiency and heat transfer limitations. One of the primary issues in these systems is the high energy consumption driven by conventional heating methods. Traditional techniques—such as convective or conductive heating—often require the entire reactor system to be heated to achieve the necessary reaction temperatures [10,11]. This inefficiency not only escalates operational costs but also complicates scalability from laboratory to industrial levels, highlighting the need for innovative approaches that can reduce energy demands and enable more effective scale-up. In response to these limitations, microwave technology has emerged as a promising alternative, offering a pathway to meet the high energy requirements typical of conventional gas–solid processes. By utilizing electromagnetic radiation, microwaves enable selective and volumetric heating, being particularly beneficial for materials acting as susceptors that can efficiently absorb microwave energy. This selective heating approach allows for faster temperature increases within the reactor, enhancing overall energy efficiency, potentially reducing environmental impact, and improving control over the process parameters [12,13,14]. Furthermore, microwave heating offers several advantages in fixed-bed applications. It allows for rapid and uniform heating, which has been associated with enhanced reaction kinetics, potentially leading to higher product yields and improved quality [15,16]. Applications of microwave-assisted fixed-bed reactors have been explored in fields such as biomass pyrolysis, where the microwave energy contributes to faster heating rates and more efficient conversion compared to traditional methods [17,18,19]. Additionally, in catalytic reactions, microwave-assisted reactors have shown promise in accelerating the synthesis of fine chemicals and pharmaceuticals, as microwaves can selectively heat catalytic sites, thereby optimizing reaction rates [20,21].

However, the design and implementation of microwave-assisted reactors pose significant technical challenges that must be addressed to realize their full potential. Among these challenges, it underlies the need for a comprehensive understanding of the complex interactions between microwave radiation and materials, including material dielectric properties and heating mechanisms. Achieving homogenous heating within microwave-assisted reactors remains the most critical concern in the optimization of these processes [22], as non-uniform electromagnetic fields and temperature distribution lead to the formation of hot spots and local temperature runaways [23]. Overcoming these challenges requires innovative reactor designs and sophisticated control strategies to warrant the efficacious coupling of microwave energy and the efficient absorption capacity of the susceptor, resulting in suitable heating rates for operating process conditions and ensuring optimal process performance and product quality. Techniques such as the use of mode stirrers and carefully designed applicators have been employed to homogenize the electromagnetic field within microwave cavities, thereby mitigating the formation of hot spots and promoting more uniform heating throughout the reactor [24,25]. Ultimately, accurate temperature measurement within microwave-assisted reactors presents a significant hurdle [26,27,28], as conventional temperature probes may not provide reliable readings in high-intensity microwave fields. Similarly, the precise measurement of the dielectric properties under dynamic heating of particulate mixtures for the estimation of thermal distribution and heating rates is challenging due to the relatively heterogeneous distribution of particle sizes and the anisotropy of the medium [29].

The ongoing decarbonization and electrification trends of chemical industry processes emphasize the potential of microwave heating as a sustainable and energy-efficient technology for fixed-bed applications. Given the lack of detailed prior studies, this paper aims to assess a comprehensive approach to address such microwave-assisted fixed-bed reactor applications: a deep assessment of microwave susceptor dielectric properties and its impact on effective process control, an evaluation of non-contact (optical) methods, their advantages and limitations regarding measurement accuracy, and the validation of experimental microwave heating runs of characterized dielectric properties microwave susceptors with obtained thermal distribution inside the process reactor. This research seeks to elucidate the potential of coupling microwave-assisted technology with fixed-bed reactors to address the shortcomings of traditional gas–solid chemical processes, emphasizing the potential of microwave heating as a sustainable and energy-efficient technology for fixed-bed applications.

2. Materials and Methods

2.1. Microwave Cavity Configuration

Microwave-assisted heating was carried out using a customized BP-211 microwave multimode cavity developed by Microwave Research and Applications, Inc., IL, USA [30]. The system is equipped with four independent 800 W magnetrons, allowing for a total microwave power output of 3.2 kW at a frequency band centered in 2.45 GHz. Furthermore, mode stirrers are placed at the end of each BJ26 waveguide (86 mm × 43 mm) to optimize the distribution of the electromagnetic field over the course of the microwave heating. Microwave power input can be adjusted through an electric power variator, which can be operated manually or automatically. In the automatic mode, a temperature PID control loop is employed to regulate the heating process by setting the desired heating ramp or target temperature to be reached. Microwave susceptor samples were employed to prepare fixed beds of certain lengths, ranging from 105 to 220 mm, inside a microwave-transparent tubular quartz reactor (600 mm length, 28 mm internal diameter). The quartz reactor, hosting the fixed bed of susceptor particles, was vertically positioned within the microwave cavity. An illustrated scheme of the microwave cavity and its different elements is depicted in Figure 1.

2.2. Non-Contact Temperature Measurement Devices

The sample temperature inside the quartz reactor was monitored using contactless thermometers, i.e., an IR pyrometer and thermal camera. The pyrometer was arranged beyond the lateral cavity wall, pointing to the sample through a perforation herein (Figure 1). The thermal camera was placed in front of the microwave oven door, which is featured by a quartz window and a Faraday cage.

Two complementary pyrometers were employed during the experiments, namely Optris CT LT and CT 3MH (Measurex, Malaga, Spain. The first had an infrared spectral range of 8–14 mm and a temperature range of −50–975 °C (±1% accuracy), while the second had a short wavelength spectral range of 2.3 mm and a temperature range of 100–600 °C (±0.3% accuracy). The LT sensor is able to monitor the temperature of a 12 mm surface spot on the quartz reactor wall in contact with the heated material at a distance of ca. 200 mm. The proper characterization of the sample temperature requires establishing a correlation between the monitored and real sample temperature inside the quartz reactor. To circumvent this, the CT 3M features an infrared transparency to quartz thanks to its specific IR spectral band. Throughout the entire temperature measurement range, a standard quartz emissivity coefficient was set manually at ε_quartz = 0.93 for all the temperature measurement devices. As a result, the temperature of the surface of the heated sample in contact with the inner reactor wall can be directly characterized, without needing any further correlation, at a defined material surface emissivity, although there may exist a systematic error induced from the variation of such emissivity coefficient at increasing temperatures.

Moreover, two different thermographic spectral cameras were used for the temperature distribution characterization of the particle fixed bed. The first, a FLIR Bcam (Measurex), allows for the measurement of external quartz reactor surface temperature featuring a temperature range of 0–360 °C (<1% accuracy), while the second, an Optris PI 1M (Measurex) features a spectral and temperature range of 1 mm and 450–1800 °C (±1% accuracy), respectively, thus allowing for measurement of the real temperature on the surface of the heated sample in contact with the inner reactor wall. Due to these characteristics, the latter camera can monitor the operando sample temperature through both the door window and quartz tube whenever it exceeds 450 °C.

2.3. Dielectric Properties Characterization

Microwave heating is a physical phenomenon. It is radically different from convection processes and is governed by materials specific physical properties that dictate their energy absorption capacity within the microwave radiation spectrum. These properties are intrinsically linked to the dielectric characteristics of materials [31,32]. Consequently, each material’s unique dielectric complex permittivity (Equations (1) and (2)) plays a key role in determining its susceptibility to microwave-induced heating. This becomes crucial for the comprehension and optimization of microwave-assisted heating processes. Complex effective permittivity (ε_eff*) comprises a real component, dielectric constant (ε′), and an imaginary part, the loss factor (ε″). The measurement of these properties facilitates an understanding of a material’s ability to polarize and accumulate radiation energy under the influence of the oscillating electromagnetic field generated by microwaves, leading to the absorption of electromagnetic energy (ε′) and subsequent dissipation as heat (ε″), respectively. Ultimately, the trade-off between the susceptibility of silicon carbide samples to interact with the shifting electric field of microwaves and their ability to transform that energy into heat is expressed by the tangent loss (tan δ). The values of these magnitudes are expressed by Equations (1) and (2).

$${\epsilon }_{ eff*}={\epsilon }^{\prime } – j{\epsilon }^{″}$$

(1)

$$tan \delta ={\displaystyle \frac{{\epsilon }^{″}}{{\epsilon }^{\prime }}}$$

(2)

For the empirical characterization of granulated materials, an integrated vectorial network analyzer (VNA), Dielectric Kit, developed by the Microwave Division of the institute ITACA, was used to determine the effective complex permittivity of the particulate microwave susceptors around the ISM frequency of 2.45 GHz [33]. The dielectric properties of the materials are calculated by the measurement of resonant frequency and quality factor, in conjunction with a full-wave mode-matching analysis of the microwave cavity. A quartz vial with a susceptor fixed bed with a minimum 15 mm height is placed inside an electric heater to set the material at a defined temperature. Then, the quartz tube is placed inside a microwave resonator that is able to calculate the complex permittivity from the shift of the probe response (resonant frequency and quality factor).

2.4. Microwave Susceptor Heating Curves and Thermal Homogeneity Characterization

Three samples of silicon carbide (SiC) from various providers and with different particle size ranges were tested: (1) a green powdered fine α,β mixed-silicon carbide average particle size (120 microns) purchased from Sigma Aldrich, Spain, (from now on, SA); (2) black medium β-silicon carbide size particles (500–600 microns) provided by Superior Graphite Inc., IL, USA. (SG), and (3) gray large β-silicon carbide particle size beads (1000–5000 microns) provided by SiCat Catalyst, Willstätt, Germany, (SC). Both the green powder and the black granular SiC susceptor showed a rough texture with sharp edges, while coarser gray beads were completely spherical. An analysis of the volumetric heating profile of the various silicon carbide susceptor samples has been carried out to elucidate which of them exhibits the most optimal dielectric properties and susceptor particle size for the installed fixed-bed reactor configuration. For these, three different susceptor fixed beds with identical dimensions of 10.5 cm in height and 2.8 cm in diameter were prepared (Figure 2a).

The different bulk densities and packing degrees calculated for the silicon carbide susceptor materials are listed in

Table 1. Fixed-bed physical dimensions and properties for the different susceptor silicon carbide materials.

Property	SA	SG	SC
SiC density (g/cm3)	3.21	3.21	3.21
Bed weight (g)	146	120	70
Bed volume (cm3)	64.6	64.6	64.6
Bulk density (g/cm3)	2.26	1.86	1.08
Fixed-bed void fraction (%)	30%	42%	66%

.

Experimental runs for heating curve characterization were carried out for the various SiC microwave susceptors under variable applied microwave power. It was deemed crucial to establish a comparison between those runs conducted in the presence and absence of a nitrogen carrier gas flow passing through the microwave susceptor beds. This approach aimed to simulate the performance that an analogous fixed-bed reactor shall exhibit in similar gas–solid phase chemical processes (e.g., thermochemical processes, catalysis, waste valorization). The heating curve characterization proceeded as follows: (1) a variable volumetric flow of nitrogen carrier gas was set through for the three different susceptor fixed beds; (2) a PID-controlled heating to 100 °C was carried out to remove water from the particulate bed material; and (3) after cooling to room temperature, a variable microwave power was applied for 80 s whilst temperatures measured by the pyrometer were registered for each 5-second interval. The temperature evolution on the quartz reactor wall during the susceptor heating curve characterizations was measured by the non-contact optical IR temperature measurement pyrometer Optris CT LT. Tested conditions are listed in

Table 2. Tested heating test variables for the different susceptor fixed beds and experimental runs.

Gas Flow (L/min)	Sample	Susceptor Mass (g)	Power (W)
0	SA	146	565
			1903
			3200
	SG	120	565
			1903
			3200
	SC	70	565
			1903
			3200
2	SA	146	1903
			3200
	SG	120	1903
			3200
	SC	70	1903
			3200

.

The volumetric temperature distribution along the external sample surface was determined in analogous studies via thermal images captured by two different portable infrared thermographic cameras. For these assessments, the microwave-assisted heating was PID-controlled by the non-contact optical IR temperature measurement pyrometer Optris CT 3MH. First, a portable FLIR Bcam infrared camera was employed to determine such volumetric temperature distributions along the external quartz reactor surface after switching off the microwave power and with the cavity door opened. Subsequently, the thermal image’s post-treatment was conducted via home-developed image processing code using the Image Processing Toolbox of Matlab R2021b to define the axial and radial temperature profiles. For deeper thermographic studies, a more precise Optris PI 1M camera, which features IR spectral band transparency to quartz, was used upon heating to assess a direct average temperature area measurement through the closed oven door for the characterization of susceptor fixed-bed axial/radial temperature profiles.

An additional study was conducted to investigate the effect of fixed-bed length and feedstock loads on the resulting temperature distribution within the system. The application of fixed-bed microwave susceptors in solid–gas phase chemical processes is particularly relevant for materials that are transparent to microwaves, as requiring its intimate mixing with the susceptor bed to reach the necessary processing temperatures [34]. Plastic waste residues are currently of great interest in the literature as potential candidates for microwave-assisted processing [13,14], showing a negligible microwave irradiation susceptibility. Therefore, a granulated LDPE waste material was selected as feedstock for this study and provided by a plastic waste sorting industrial partner. The maximum processing capacity of LDPE feedstock, when intimately mixed with the optimal susceptor (SG) in the current vertical fixed-bed configuration, has been evaluated to determine the optimal feedstock process capacity that maximizes the thermal homogeneity of the fixed-bed quartz reactor, thereby minimizing the temperature gradients observed along the axial axis of the bed (Figure 2b).

Table 3. LDPE:SiC fixed bed.

Fixed Bend Length (cm)	Waste LDPE Feedstock Chips (g)	SiC (g)	Ratio Susceptor: SiC	T ªset (°C)
12	28	140	5:1	100 °C
22	116	168	1.5:1	100 °C

summarizes the characteristics of two prepared fixed beds consisting of susceptor particles mixed in its specific SiC-to-feedstock ratio. These beds have been subjected to PID-loop-controlled heating up to a set temperature of 100 °C. The temperature measurements were recorded using an infrared thermographic camera that registered the thermal distribution on the quartz reactor wall surface.

3. Results

The role of microwave-assisted heating on the transient heating rate and temperature distribution within fixed beds filled with SiC particles having different geometries is discussed below. The experimental results presented along the following subsections report the critical impact that the various effective susceptor dielectric properties and their different packing degrees have on the heating efficiency and temperature distribution homogeneity of a fixed microwave-susceptor bed, highlighting the thoroughly required evaluation of these properties to optimize their application in microwave-assisted solid–gas phase chemical processes.

3.1. Dielectric Properties Measurement

The dielectric properties of the different SiC samples were studied within a range of temperatures from 20 °C to 220 °C to understand their temperature-dependent microwave susceptibility. Figure 3 depicts the evolution of dielectric constant, dielectric loss, and loss tangent of packed beds of SA, SG, and SC with temperature.

As can be observed in Figure 3, an increasing trend with temperature is reported for the SiC dielectric constant (ε′). A significantly steeper slope is observed for the temperature-dependent dielectric constant of SA compared to SG and SC. This behavior is correlated with the measured bulk density of the samples and thus the porosity of the susceptor fixed beds.

For SC, the higher porosity of the particle bed, and thus larger interstitial void volume, interferes with the resonant frequency and quality factor measurements of complex effective permittivity obtained via the VNA, as it considers both the susceptor material and the interstitial air. This interference dampens the effective measurement of the changes in the microwave susceptor’s physical properties as temperature increases, thereby reducing the sensitivity of ε′ to temperature variations in this material and exhibiting the lowest ε′ values. This hypothesis is supported by the results obtained for SA. Given that SA exhibits the highest packing density and lowest porosity, the VNA measurement of the ε′ demonstrates a more direct correlation with the changes in the physical properties of the material.

Consequently, SA is the susceptor that exhibits the steepest growth slope for ε′, further confirming the effective increase in its microwave susceptibility. The intermediate particle-sized SG susceptor has shown the highest ε′ values at room temperature (RT), ε′_SG,RT = 17.8, ca. 1.4 times higher than those exhibited by SA SiC susceptor, ε′_SC = 12.6, and 2.5 times higher than those of SA, ε′_SG = 7. Inversely, SG susceptor has exhibited the lowest capacity of converting electromagnetic energy into heat (ε″_SG,RT = 0.31), in contrast to SC (ε″_SC,RT = 1.32). ε″ showed different behaviors for the three SiC samples. A decreasing trend with temperature has been exhibited by ε″_SA. The opposite behavior stands for SC particles, while it remains nearly constant for SG particles within the evaluated temperature range. Typically, the dielectric loss (tan δ = ε″/ε′) tends to increase with temperature as a result of the enhanced mobility of charge carriers, which increases the polarization in the material. As such, the charge accumulation at grain boundaries is typically deemed responsible for the dielectric loss increase with temperature [35]. Taking into account the characteristics of the analyzed particles, SC beads present discrete contact points among consecutive spheres, which may easily lead to charge accumulation. Therefore, ε″ (and, consequently, tan δ) increase with temperature in this case. Contrarily, the intimate and larger surface contact in SA and SG smaller particle beds may result in relatively lower charge accumulation at the particle boundaries, thus leading to a negligible increase in tan δ with temperature. Possibly, a higher moisture content in those susceptor samples with a greater surface contact may also play an interfering role in the measurement of dielectric properties, as water molecules can competitively interact for the absorption of the applied microwave field in the vectorial network analyzer at the initial room temperatures before their vaporization.

Besides its evolution with temperature, the tangent loss of the coarse SC particles at a given temperature is significantly higher than those measured for the other samples: tan δ_SC = 0.18, tan δ_SA = 0.062, and tan δ_SG = 0.02 at room temperature. The above discussion also explains this trend, which is mostly based on the SC superior capacity of converting electromagnetic energy into heat, i.e., ε″_SG. In any case, all three values fall within the range of dielectric properties described in the literature for silicon carbide subjected to a 2.45 GHz irradiation frequency [36,37].

For the sake of temperature homogeneity inside a microwave-assisted heated fixed-bed reactor, it is considered that a notable change in the dielectric properties of the susceptor during the heating process is undesirable. Consequently, the increasing susceptibility of SC susceptor particles with temperature may lead to process’ temperature control issues, eventually causing significant thermal inertia within the medium and hot spot formation. The great accumulation of electromagnetic fields and microwave energy at tangential points of large susceptor beads may lead to severe hot spot formation inside the reactor fixed-bed body. These phenomena may have immediate practical consequences towards temperature distribution in fixed beds caused by inconsistent and inhomogeneous microwave-assisted heating leading to potential further detrimental effects over process reaction control, degradation of products, the buildup of pressure, thermal runaway risks, and ultimately process operation safety issues [23,38,39,40].

Similarly, the smaller size of SA particles, higher density, and its increasing dielectric constant with temperature could lead to an over-measured dissipation of electromagnetic energy, the generation of hot spots, and pre-sintering (agglomeration) of the fine silicon carbide powder. In this sense, SG susceptor has shown the highest susceptibility to interact with the microwave electromagnetic field, ε′ = 18, and superior homogeneity of its effective complex permittivity during the temperature increase in the studied range, even though it shows the lowest tan δ values.

3.2. Susceptor’s Heating Rate Characterization

To validate the previously discussed dielectric characterization findings, tested susceptor materials were subjected to microwave heating using the MW input power and gas flows indicated in Table 1. The main objective of the described heating experiments is to assess the performance of a fixed bed of particulate susceptors approaching microwave-assisted thermochemical process conditions, such as gas–phase catalytic conversions or solid waste valorization processes. Therefore, the chosen strategy aimed to evaluate the influence of the applied power output on the representative bed temperature and thermal homogeneity for each susceptor bed type. Figure 4 depicts the transient sample heating results for the three susceptor beds at different power inputs, with and without flowing cool inert gas (2 L_N/min N₂). The reported temperatures were measured by a pyrometer pointing to the external quartz reactor wall at mid-bed height and do not correspond to the average temperature of the bed or any other similar averaged magnitudes.

As was expected, results reveal that lower applied microwave powers of approximately 565 W fail to achieve higher fixed-bed temperatures than 50 °C during the applied 80-second heating time for any of the susceptor types. It is considered that such applied power may not be sufficient to induce effective heating of SiC beds with masses ranging from 70 to 144 g during the monitored time on stream. As concluded in the previous section, SC has proven to be the susceptor type with the highest capability to convert microwave electromagnetic energy into thermal energy, proven by its superior ε″ values, as evidenced experimentally by the distinct heating curves, in which it reaches the highest temperatures in the evaluated time frame. On the other hand, SA susceptor dielectric loss (ε″) showed a declining trend with temperature, meaning a loss of efficiency in transforming applied power into thermal energy at higher temperatures. While this explains the diminishing heating rate over time observed in Figure 4 represented graphically by the gradual decrease in the slope of the heating curve, it is insufficient to account for the lower apparent temperatures reached by SA in comparison to the SG bed, whose tan δ value is higher than that reported for the latter. This fact is grounded in further physical properties of the susceptor particles that outweigh its specific microscopic dielectric properties.

Apparently, susceptor particle size has empirically evidenced a stronger impact on the heating rate than the specific susceptibility values of each silicon carbide type. This suggests that the microwave-assisted heating rate for the current fixed-bed reactor configuration may be inversely proportional to the susceptor fixed-bed packing degree (or, analogously, bulk density). All tested SiC samples feature a similar particle density of ca. 3.21 g/cm³, whilst the specific bulk bed density relies on the arrangement and packing of the particles/beads and, thus, on the interparticle void fraction. Since the atmosphere surrounding the particles does not absorb microwave irradiation, the larger the void fraction (i.e., the lower apparent bed density, see Table 1), the higher the available microwave power per sample unit (SiC volume or mass) at a given constant forwarded microwave power, and so is the heating rate. The susceptor particle size and shape determine the bed packing degree of the different prepared susceptor beds, thus impacting their heat capacity being subjected to the same forward power. Further from the specific microscopic susceptibility of an individual SiC particle, macroscopically, the less densely packed bed would obtain the highest power per sample unit, leading to comparatively higher heating rates.

Moreover, all curves showed lower heating rates in the presence of a gas flow through the reactor fixed bed. The inert carrier gas flow diffuses the generated heat while flowing upwards, thus removing it from the irradiated sample environment.

3.3. Fixed-Bed Thermal Distribution Homogeneity

3.3.1. Impact of Susceptor Material Nature on the Temperature Distribution

The resulting thermal distribution and homogeneity for each susceptor fixed bed were studied by thermographic analysis. Thermal images were captured immediately after the 80 s heating tests were conducted at a maximum microwave power (3.2 kW) under non-gas flowing conditions. The sample temperature distributions are presented in Figure 5a.

It can be observed that the SA susceptor presents the lowest overall temperature and the highest axial thermal homogeneity. A lower overall temperature can be explained by the SA susceptor bed properties, which have the highest bulk density among the tested samples (see employed susceptor masses in Table 2), resulting in the lowest normalized irradiation power per susceptor mass unit (3.2 kW/146 g). However, the more homogeneous thermal profile has to do with the dielectric properties of the bulk material. As presented in Figure 3, the susceptibility of this material slightly decays with temperature. Generally, the propagation of microwave energy within dielectric mediums involves a complex formulation, but it is considered that there exists an exponential decay of microwave energy absorption inside the material [41,42]. Equation (3) describes the penetration depth (Z) of a microwave electric field as the distance from the surface of a dielectric material where the incident power is decreased to 1/e (37%) of the incident power based on its dielectric properties:

$$Z={\displaystyle \frac{\lambda }{2\pi }}{\left[{\displaystyle \frac{2}{{{\epsilon }^{\prime }}_T\left(\sqrt{1+{{tan}^2\delta }_T}-1\right)}}\right]}^{1/2}={\displaystyle \frac{\lambda }{2\pi }}{\left[{\displaystyle \frac{2}{{{\epsilon }^{\prime }}_T\left(\sqrt{1+{{\left(\frac{{\epsilon }^{″}}{{\epsilon }^{\prime }}\right)}_T}^2}-1\right)}}\right]}^{1/2}$$

(3)

where λ is the microwave wavelength at the chosen 2450 or 915 MHz frequency; tan δ_T is the experimentally measured tangent loss at a defined temperature, formulated as the ε″_T (dielectric loss) and ε′_T (dielectric constant) ratio.

From this expression it is inferred that the lower the loss factor (ε″), the greater the penetration depth through the material, thus easing a more averaged absorption of microwave energy within the bulk material. In this sense, the decreasing trend of ε″_SA with temperature shall explain the reported higher SA susceptor bed thermal homogeneity, whilst the lower achieved temperature is further hindered by the high bulk density of SA particles, which receive lower irradiation power per susceptor mass unit.

Contrarily, SG and SC show a thermal distribution behavior featured by two regions at comparatively higher temperatures than the sample core located at both bed ends. This trend is, again, ascribed to the different dielectric properties of the materials and the higher porosity of susceptor beds. First, since both the dielectric loss tangent curves of SC and SG increase with temperature, the power dissipation at the overheated fixed-bed regions increases with the temperature, causing the formation of hot spots. The fact that the hottest regions appear at both bed ends has to do with the effect of fixed-bed packing degree and bed porosity. Previous literature has proven that microwave electric field density concentrates at the void-to-susceptor interphase, whereas the microwave power density is highly dissipated at those vicinal contact points between particles, proving the formation of hot spots at those susceptor particle beds with a greater void volume, i.e., porosity [43,44,45]. Among the samples, SC shows the highest maximum temperature, in agreement with its superior dielectric loss tangent (tan δ), as shown in Figure 3. Moreover, it is remarkable that the maximum local temperature for SG, as shown in Figure 5, exceeds that of SA, although Figure 4 appeared to suggest the opposite. The reason is that the operando temperatures presented in Figure 4 were obtained from a pyrometer pointing to the center of the bed, and, at this region, the temperature of SG is slightly lower than that at the SA bed center, as it can be observed in Figure 5.

Figure 5b quantifies the degree of thermal homogeneity along the axial position in the bed, showing normalized temperature profiles with respect to the average bed temperatures for all three cases. The resulting temperature variation coefficients, i.e., standard deviation around the mean temperature value along the axial dimension (denoted as σi, being i the material type), are σSA = 0.061, σSC = 0.085, and σSG = 0.083, respectively. As above-mentioned, the higher thermal homogeneity of SA was favored by its dielectric properties’ evolution with temperature and, thus, its temperature-dependent penetration depth. As a counterpart, its comparatively greater fixed-bed packing degree became a limiting factor on the lower heating rates. On the other hand, the highest complex permittivity of the loosely packed SC susceptor bed led to greater absolute temperature gradients but the most heterogeneous thermal distribution. Aiming to find a susceptor configuration that presents a tradeoff between heatability and thermal homogeneity, the SG sample was selected as the most suitable material among those evaluated.

3.3.2. Assessment of Temperature Measurement in Microwave Reactor

The choice of temperature measurement methodology exerts a profound impact on the accuracy of the temperature distribution characterization within microwave susceptor particle beds. For the heating rate curves characterized in Section 3.2, a contactless optical IR pyrometer (8–14 μm spectral band) was used, which displayed the temperature at the external surface of the quartz reactor wall. Unfortunately, on-surface or near-surface measurements are often ill-suited to fully capture these intricate temperature profiles, leading to substantial discrepancies between measured and actual real internal temperatures inside the fixed bed. It is considered that the discrepancy between surface-measured temperatures and the actual conditions within the core of the susceptor bed underscores a critical gap in the understanding and monitoring of microwave heating dynamics and ultimately hinders the assessment of the optimization and scale-up of microwave-assisted solid–gas phase chemical processes.

For instance, some SA SiC susceptor fixed-bed regions glowed during microwave-assisted heating tests (red glowing typically indicates temperatures beyond 650 °C), although the monitored temperature at the external reactor wall surface did not exceed 300 °C in any case. As a result of glowing, the SA bed particles at this region became compacted, quasi-sintered, thus partially clogging the bed and leading to gas flow channeling and mass and heat transfer limitations. This makes this bed configuration unsuitable for gas–phase thermochemical processes. However, this malfunction could not be detected either by the contactless pyrometer pointing at the external reactor wall or by the thermal camera with spectral band 8–14 μm.

Hence, there exists a severe inconsistency between the temperature measurements taken at the surface of the quartz reactor and the actual temperatures reached within the bed inside the reactor. Consequently, it becomes evident that implementing efficient temperature measurement strategies is crucial for conducting thermochemical processes under controlled thermal conditions.

To assess the real sample temperature and quantify the transient deviation of standard (8–14 μm) contactless IR measurements upon microwave-assisted heating, these measurements were compared to those attained using a quartz-transparent IR spectral band camera (Optris PI 1M), thus able to measure the temperature on the susceptor bed surface through the quartz reactor wall thickness. Figure 6 provides a visual representation of the temperature distribution on the surface of the silicon carbide bed for SG and SC samples at the maximum temperature achieved during heating tests, i.e., after 80 s irradiation time, together with the axial and radial profiles calculated for the bed using image processing methods integrated on the optical software. On one hand, the spatial temperature distribution results are aligned with the analysis conducted in the previous Section 3.3.1. On the other hand, the observed maximum temperatures and thermal gradients are significantly higher than those results obtained from temperature measurements on the quartz surface. In the case of the SG susceptor particle bed (Figure 6a), the maximum temperature recorded on the quartz surface was approximately T_{max SG} = 340 °C, while the actual temperature displayed for the silicon carbide particles exceeded 700 °C. The radial temperature gradient exhibits a less pronounced thermal gradient, ΔT = 40 °C, whereas the temperature gradient for the axial dimension exceeds ΔT = 120 °C. The discrepancy between the temperature measurements reported by the two infrared pyrometers can be attributed to the thermal gradient across both sides of the quartz reactor wall, which can be described by Fourier’s Law, based on the temperature between the inner and outer quartz wall surfaces and the quartz material’s intrinsic thermal conductivity. Given the low conductivity of ceramic materials, i.e., quartz wall, the temperature gradient across the wall is significant. This leads to a large discrepancy between the two temperature readings throughout the heating process, as the heat transfer across the quartz does not achieve an immediate equilibrium.

A similar, albeit more exaggerated, outcome is observed for the bed consisting of larger SC particles. The spectral range of the IR camera allows for the visualization of the temperature distribution of the coarse silicon carbide beads, as it can penetrate through the quartz. The thermal gradient in the radial dimension presented in Figure 6b, is as high as ΔT = 200 °C. Furthermore, the thermal gradient in the axial dimension is even larger, ΔT > 350 °C. These measurements evidence the fact that the temperature reached inside the susceptor fixed bed is vastly greater than those measured at the external wall in the transient sample heating phase, starting from room temperature. Existing literature suggests that the highest accumulation of temperature and local microwave electromagnetic field in beds of coarse susceptor beads occurs at the tangency points of susceptor beads, leading to arcing and plasma generation [17]. These experimental findings align with such an explanation and provide further support for the very high temperatures observed within the fixed bed (Figure 6b).

Given these very significant local thermal gradients in fixed beds, the implementation of microwave-assisted heating technology for solid–gas chemistry applications under homogeneous and controlled temperature may require the adoption of further strategies such as bed fluidization and/or the introduction of reactor rotation or mixing methods. However, from a different point of view, certain gas–solid chemical processes could potentially benefit from the high temperature gradients induced by microwave radiation. These gradients might locally promote specific chemical reactions over others in different regions of the bed, providing a unique avenue for reaction selectivity and enhancing the overall efficiency of the process under certain conditions, e.g., boosting surface-catalytic processes and suppressing to some extent unwanted secondary gas–phase reactions taking place in a comparatively colder environment [44,45,46,47,48,49].

To assess and quantify the deviation of the different contactless thermal measurements, Figure 7 depicts the relationship between three simultaneous temperature measurements: (a) average fixed-bed mean temperature (A1) captured via quartz transparent thermographic camera; (b) average mean temperature on the setpoint control measurement zone of MW cavity, captured via quartz transparent thermographic camera (A2); and (c) MW cavity temperature control on quartz reactor wall surface via infrared pyrometer; all of them at a set emissivity value of 0.95. Figure 7a presents the thermal distribution map of the SG bed after 80 s of sample irradiation, while Figure 7b showcases the temperature evolution of the three compared thermal measurements monitored along the heating (0–80 s) and cooling (80–560 s) times, reporting the thermal gradient across the quartz wall. It is evidenced that the quartz reactor thickness and its resistance to heat transfer induce a temperature reading discrepancy between the temperature measured on the external surface of the quartz wall during heating (a punctual temperature reading using an infrared laser) and the thermal reading on the A2 susceptor bed surface (average temperature value measured by thermographic camera through the quartz wall). This analysis suggests that the real temperature on the susceptor particles doubles that monitored by the infrared pyrometer pointing at the external reactor wall (T_cam = 2.32 × T_pyr). This discrepancy between temperature readings is crucial for understanding the importance of a proper assessment of implemented non-contact temperature measurement methods. It is proved that such temperature measurement approaches are advocated to a significant error in the view of the actual thermal conditions of a fixed-bed chemical process, thus not being suitable for such microwave-assisted process optimization.

With all these, it can be deduced that the fixed-bed configuration of the installed microwave cavity leads to certain deviations in the control of the setpoint process temperature, which is inevitably due to the nature of microwave heating, and which value tends to increase with heating time, at a given constant microwave input power, as the fixed-bed temperature inequalities are magnified. However, it is noteworthy to highlight that obtained results suggest a 120 g SG fixed-bed temperature increase from 100 °C to 600 °C in less than 80 s, or, analogously, a microwave-assisted heating temperature ramp of approximately 375 °C/min, 4.17 °C/g, or 0.16 °C/W. This time- and energy-efficient heating constitutes one of the most remarkable advantages of microwave heating.

3.3.3. Impact of Fixed-Bed Length and Feedstock Load on Temperature Distribution

Aiming at assessing the role of susceptor-to-feedstock mixing and bed size on the thermal homogeneity for a thermochemical process of interest, i.e., microwave-assisted LDPE waste pyrolysis, Figure 8a illustrates the temperature distribution on the quartz reactor wall surface for two fixed beds consisting of (a) 22 cm long 1.5:1 SiC:LDPE (top) and (b) 12 cm long 5:1 SiC:LDPE (bottom). As can be observed, the longer fixed bed led to higher temperatures at the same irradiation time, with the highest temperature regions located at both fixed-bed ends. Interestingly, the 12 cm bed presents a fairly homogeneous axial temperature distribution with a maximum temperature region located at the bed center. The completely different thermal distribution between both samples may be attributed again to the relation between bed size length and microwave electric field density. In practice, the interaction between the microwave field and the material generates standing wave patterns or interference effects leading to localized areas of higher and lower energy absorption. Due to the poor susceptor-to-electric-field coupling effect at the interphase between air and high-loss materials [50], microwave electric fields tend to concentrate at the bed edges, leading to increased microwave power absorption and heating rates in these areas. Additionally, the overheating and subsequent enhancement of SiC dielectric properties with temperature contribute to a greater conversion of radiative energy into thermal energy at those regions exposed to a higher concentration of the microwave electric field, as hot spot generation.

Figure 8b shows the axial thermal profiles for both fixed beds. It can be observed that a 22 cm longer bed exhibits higher thermal gradients, ΔT = 96 °C. Consequently, this would lead to unsuitable low-temperature homogeneity and temperature process control inside the reactor. Contrarily, the profile in the case of the 12 cm bed is significantly more gradual and homogeneous, being the maximum thermal gradient ΔT = 55 °C. Based on these results, it seems that there exists a trade-off between the processing capacity of the current microwave susceptor fixed-bed reactor configuration and the thermal process control inside the reactor. Lower operating feedstock mass loads must be prioritized for this fixed-bed configuration for the sake of an acceptable reactor thermal homogeneity and process control. As above-mentioned, additional strategies such as fluidization may enhance this axial thermal homogeneity. Fluidized beds have already been reported in the literature for microwave-assisted coupled applications of plastics and biomass [51], being able to enhance mass and heat transfer properties within the bed. As a counterpart, the reduced gas–phase residence time in the reactor may pose process yield limitations for certain gas–solid chemical conversions of interest. Contrarily, the implementation of longer beds with hotter edges would be advisable instead if the purpose is to promote gas-phase conversions and quenching effects for its application in gas-to-solid chemical processes.

The following presents the summary of the previous findings: (a) achieving homogeneous microwave-assisted heating of fixed particulate beds is challenging; however, a proper balance of particle size, dielectric properties, and bed length can result in reasonably uniform heating; (b) microwave heating has proven to be extremely rapid, especially with the use of appropriate susceptors (e.g., ~400 °C/min for 120 g samples at 3.2 kW power); (c) the use of thermographic cameras with an appropriate spectral range provides a highly realistic representation of the temperature distribution at the particle level; and (d) the presence of high local temperature gradients and hot spots can be exploited to intensify processes or to promote specific thermochemical transformations of interest.

4. Conclusions

A customized 3.2 kW multimode microwave cavity was configured for the microwave heating assessment of three different silicon carbide (SiC) susceptor samples in a fixed-bed quartz reactor: (1) SA, 120 microns; (2) SG, 500–600 microns; (3) SC, 1000–5000 microns. SC exhibited the highest complex susceptibility, tan δ = 0.18, proving the highest dissipation of microwave energy as heat among the tested samples. Its comparatively higher microwave dielectric properties resulted in greater overall heating rates and maximum temperatures on the fixed-bed quartz (T_max > 360 °C, 4.5 °C/s) and a heterogeneous temperature distribution (variation coefficient, σ_SC = 0.085). Moreover, it was concluded that the macroscopical properties of the susceptor bed, such as bulk density and particle size, had a major critical impact on its microwave-assisted heating and temperature distribution. Greater porosities, such as those with lower fixed-bed bulk densities and larger susceptor particle sizes (i.e., SG and SC), lead to a more available microwave power per sample unit (SiC volume or mass), resulting in comparatively higher heating rates. However, a higher specific susceptor–void interphase has been found to induce poorer thermal homogeneities within the microwave susceptor fixed bed. The SG bed configuration was found to balance microwave susceptibility and thermal homogeneity, providing the most promising performance in terms of microwave effective heating and thermal homogeneity for its use in further applications. Moreover, microwave heating has demonstrated exceptional speed, achieving remarkably high heating rates, particularly when using appropriate solid susceptors. For instance, gas–solid phase process temperatures were proved to increase at an impressive rate of ca. 400 °C/min under 3.2 kW of power. This highlights the unparalleled efficiency of microwave heating in comparison to conventional methods for heating processes starting up, even though it presents further complex technical challenges, such as the induction of hot spots, thermal runaway, and uneven heating, or leading to glowing and particle compaction, as particularly observed for SC and SA susceptors.

A significant uncertainty is associated with the contactless temperature measurements used. The use of infrared cameras and pyrometers that are transparent to the reactor quartz wall was identified as crucial for a proper microwave heating evaluation. Pyrometers with spectral ranges opaque to quartz revealed transient temperature measurement discrepancies as high as 230% upon heating between the external reactor wall and the contained hot sample, thus preventing precise control of the internal temperature of the process. This discrepancy has been attributed to the thickness of the quartz reactor and the inherent low thermal conductivity of the material. As a result, the discrepancy between temperature readings is crucial for understanding the importance of a proper assessment of non-contact temperature measurement methods, with the goal of controlling the reactor process temperature in future applications. This finding outlines the most challenging limitation of microwave-assisted technologies’ application to chemical processes, as the correct control of temperature is deemed crucial for industrial implementation. In this sense, future research must investigate alternative temperature measurement and thermal homogenization strategies, such as optical fibers or the implementation of a stirred susceptor microwave susceptor reactor, to ease the development of microwave-assisted technologies into industrial processes. For these, computational studies on multimodal microwave cavities and susceptor particle heating will improve physical insights and scientific evidence of the experienced hot spot formation and the detected fixed-bed edges susceptor-to-void interphase overheating.

In conclusion, microwave susceptor dielectric properties must be properly assessed and selected for its implementation in fixed-bed reactor configurations, whereas there is a trade-off between its complex susceptibility, the control of thermal homogeneity within the reactor, and the potential microwave heating-induced quenching effects on solid–gas processes.