**2. Methodology**

*2.1. Measurement of Thermal Conductivity*

Thermal conductivity is one of the main characteristics of thermal insulators. According to standards such as TS 825, ISO 9164:1989 and DIN 4108, materials with thermal conductivities of less than 0.07 W/m·K can be considered thermal insulators [41]; other studies consider materials to be thermal insulators if the conductivity is less than 0.1 W/m·K [14]. One of the most widely used methods to measure this property is the protected hot plate method, which consists of taking the sample to a stationary state with two different and known temperatures so that Fourier's law of heat conduction in its one-dimensional form is applicable; this can be expressed as follows:

.

.

$$k = \frac{QL}{A\Delta T} \tag{1}$$

where *k* is the thermal conductivity of the material, *Q* is the heat transfer rate, *L* is the thickness of the sample, *A* is the heat transfer area, and Δ*T* is the temperature difference. For this purpose, the sample is located between two plates that act as a heat source and a heat sink, in order that, from their temperatures, the power required by the device, its geometry, and the material's ability to conduct heat can be calculated.

In the present study, the protected hot plate method was used to measure the conductivity of nonwoven fique samples at different densities, for which the equipment shown in Figure 1 was built, which was designed according to ASTM C 177-13 [42] with a doublesided configuration to ensure a stable and constant transmission of energy by conduction perpendicular to the surfaces of the samples. This device consists of four main parts, namely: a measurement and control system, a support system, a heating system, and a cooling system, which are presented in Figure 1.

**Figure 1.** Thermal conductivity measuring bench in accordance with ASTM C 177-13. (1) Measuring and control system, (2) support system, (3) heating system, and (4) cooling system.

#### 2.1.1. Measurement and Control System

The measurement and control system allows real-time temperature measurement by means of eight K-type thermocouples, four located on the hot plate (Figure 2b) and four on the cold plates (two on the upper plate and two on the inner plate). The system also supplies the electrical power required by the two flat plate heaters, which are controlled by two electronic PID microcontrollers (Autonics TCN4).

**Figure 2.** Heating system: (**a**) aluminum plates and electrical resistors and (**b**) thermocouples for temperature measurement in the system.

#### 2.1.2. Support System

The support system supports the other systems and is mounted on a hydraulic unit, which ensures constant pressure on the specimens by means of a hydraulic actuator, thus ensuring the reproducibility of the measurements.

#### 2.1.3. Heating System (Guarded-Hot-Plate)

The heating system consists of two aluminum plates, measuring 300 mm × 300 mm × 10 mm, in the middle of which there are two independent flat coplanar resistors, as shown in Figure 2; one corresponding to the area of the protected hot plate with a power value of 225 W (150 mm × 150 mm) and another resistor corresponding to the area of the primary guard, which supplies an electrical power of 360 W. Four temperature sensors (T1, T2, T3, T4) are located on the plate to measure the temperature values and to ensure that there is no lateral flow, i.e., that there is only unidirectional flow.

#### 2.1.4. Cooling System

The cooling system consists of two aluminum plates (cold surfaces), measuring 300 mm × 300 mm × 20 mm, through which seven 12 -inch copper tubes pass on each plate, as shown in Figure 3. Two K-type thermocouples (T5–T8) are placed on each cold plate to obtain temperature data during the test.

**Figure 3.** Cooling system assembly with two heat exchangers.

#### *2.2. Kinetic Modelling*

Kinetics, represented by the kinetic triplet, is an important property for the study of the thermal decomposition of biomass, as it allows the complete simulation of the conversion vs. time curve, as well as the control and optimization of the process parameters. The most common method to determine it is the analysis of thermogravimetric (TG) data [43,44], as it is the most effective, least expensive, and simplest way to observe fuel combustion and pyrolysis profiles [45]. The thermogravimetric (TG) tests were carried out in a TGA Q500-TA instruments analyzer, using a nitrogen atmosphere with a constant flow rate of 15 mL/min and a heating rate of 5 ◦C/min, taking the sample from 27 ◦C to 480 ◦C.

The rate at which the thermal decomposition process of solid samples occurs is usually expressed by Equation (2):

$$\frac{d\alpha}{dt} = f(\alpha) \ A \exp\left(-\frac{E\_a}{R\_\text{H}T}\right) \tag{2}$$

where *f*(*α*) is known as the decomposition function or reaction model, *A* is the preexponential factor, *Ea* the activation energy, Ru the universal pass constant, and *T* the absolute temperature. This equation has no analytical solution, so several methods have been developed to determine the factors *f*(*α*), *Ea*, and *A* (known as the kinetic triplet), which can be classified into fitting and isoconversional models. In the former, a predefined form of *f*(*α*) is assumed, while, in the latter, data with the same value as the degree of conversion *α* are selected, so that *f*(*α*) is constant, and *A* and *Ea* are independent of its form, allowing the Arrhenius equation to be evaluated without choosing the order of the reaction. Fitting methods have been widely used in solid-state reactions due to their ability to directly determine the kinetic parameters from TG data at a single heating rate, one of the most important of which is the Coats–Redfern integral method [46], which has been successfully used in the kinetic modelling of plant biomass, as can be seen in the work of Alvarez et al. [47] According to this method, Equation (2) has the following solution:

$$\ln\left(\frac{g(a)}{T^2}\right) = \ln\left[\frac{AR\_{\rm H}}{\beta E\_a}\left(1 - \frac{2R\_{\rm u}T}{E\_a}\right)\right] - \frac{E\_a}{R\_{\rm u}T} \tag{3}$$

where *g*(*α*) is the integral form of the reaction model and *β* is the reaction rate. The 2*RuT*/*Ea* term is very small, so it is usually neglected, leading to:

$$\ln\left(\frac{\mathcal{g}\left(a\right)}{T^2}\right) = \ln\left[\frac{AR\_u}{\beta E\_a}\right] - \frac{E\_a}{R\_u T} \tag{4}$$

Thus, the graph ln *g*(*α*) *T*<sup>2</sup> vs. 1*T* is a straight line with slope −*Ea*/*Ru* and ordinate at the origin equal to ln *ARu βEa* , which allows us to clear the values of *Ea* and *A*. To determine the reaction model, the "master plots" graphs were used, which is the method recommended by the International Confederation for Thermal Analysis and Calorimetry (ICTAC) [48,49]. For this purpose, the reaction models presented in Table 2 were plotted first, and then the experimental curve *g*(*α*)/*g*(0.5) vs. *α* was plotted and the theoretical curve that best fit according to equality was chosen:

$$\frac{g(a)}{g(0.5)} = \frac{\frac{E\_a A}{\beta R} p(x)}{\frac{E\_b A}{\beta R} p(x\_{0.5})} = \frac{p(x)}{p(x\_{0.5})} \tag{5}$$

where *x* = *Ea*/*RT*, *p*(*x*) is calculated according to the approximation of Pérez-Maqueda and Criado [50]:

$$p(\mathbf{x}) = \left(\frac{e^{-\mathbf{x}}}{\mathbf{x}}\right) \left(\frac{\mathbf{x}^7 + 70\mathbf{x}^6 + 1886\mathbf{x}^5 + 24, 920\mathbf{x}^4 + 170, 136\mathbf{x}^3 + 577, 584\mathbf{x}^2 + 844, 560\mathbf{x} + 35, 120}{}^3\mathbf{x}\right) \tag{6}$$

$$p(\mathbf{x}) = \left(\frac{e^{-\mathbf{x}}}{\mathbf{x}}\right) \left(\frac{\mathbf{x}^8 + 72\mathbf{x}^7 + 2024\mathbf{x}^6 + 28, 560\mathbf{x}^5 + 216, 720\mathbf{x}^4 + 880, 320\mathbf{x}^3 + 1794, 240\mathbf{x}^2 + 1, 572, 480\mathbf{x} + 403, 200\right) \tag{7}$$

The experimental conversion data were compared with the respective theoretical ones obtained from kinetic modelling, and the quality of their fit was evaluated by means of the average percentage deviation (AVP) proposed by Orfao et al. [51]:

$$AVP = 100\sqrt{\frac{SS}{N}}\tag{7}$$

$$SS = \sum\_{i=0}^{N} \left[ \left( a \right)\_{i, \text{exp}} - \left( a \right)\_{i, \text{to}} \right]^2 \tag{8}$$

where *αexp* is the experimental conversion and *αteo* is the theoretical conversion, determined from Equation (2) and the kinetic triplet calculated from the reaction models, and *N* is the number of experimental TG data.

**Table 2.** Integral a and differential b form of various reaction models for solid phase kinetics. Information taken from Rueda-Ordoñez [52].



**Table 2.** *Cont.*

#### **3. Results and Discussion**

*3.1. Thermal Conduction*

Figure 4 shows the influence of the density of the fique samples on their thermal conductivity. Density was one of the manufacturing parameters controlled during the elaboration of the samples, obtaining three levels of density: 50 kg/m3, 65 kg/m3, and 80 kg/m3. As can be seen, there is a small decrease in thermal conductivity with increasing density in the 50 to 80 kg/m<sup>3</sup> range, where the maximum average value is 0.06 W/m·K at a density of 50 kg/m3, while the minimum average value is 0.055 W/m·K at 80 kg/m3. It seems reasonable to expect an increase in thermal conductivity with the increasing density of the nonwovens, as the solid fraction increases. However, the sample of fique nonwovens with the highest density has the lowest thermal conductivity value. This indicates that voids are also a parameter to be considered, as the results sugges<sup>t</sup> that the higher the packing density, the smaller the size of the voids and the higher the thermal resistance.

**Figure 4.** Results of thermal conductivity measurements at different densities.

#### *3.2. Thermal Decomposition*

Figure 5 shows the TG–DTG profile of the analyzed sample. As can be seen, there are five stages: a first stage of weight loss due to drying, a stable phase with no weight loss, two stages of high loss due to the decomposition process, and a final stage of degradation and combustion. It has been observed that hemicellulose, cellulose, and lignin decompose from 197 to 327 ◦C, 277 to 427 ◦C, and 277 to 527 ◦C, respectively [53]; therefore, the third stage can be attributed to the decomposition of hemicellulose and cellulose, while the fourth stage can be attributed to the decomposition of cellulose and lignin.

**Figure 5.** TG–DTG diagram of the fique samples.

Applying the Coats–Redfern method to the data obtained from the thermogravimetric tests, we obtained the straight line ln *g*(*α*) *T*<sup>2</sup> vs. 1*T* presented in Figure 6a. The correlation coefficient (R2) of this plot is 0.9903, which speaks well for the efficiency of the method. The values of the activation energy and pre-exponential factor obtained from this graph were 120.12 kJ/mol and 2.62 × 107. On the other hand, by applying the "Master Plots" method, it was found that the reaction model that best fit the analyzed biomass was the "Power law-P4", as presented in Figure 6b.

**Figure 6.** *Cont.*

**Figure 6.** Determination of the kinetic triplet: (**a**) activation energy and pre-exponential factor by the Coats–Redfern method and (**b**) reaction model by means of the "Master Plots" method.

The results obtained show that, as expected, fique fibers decompose much faster than common insulators, so it is necessary to apply treatments or mix them with other materials to improve their resistance to high temperatures. The evaluation of the results by comparing the theoretical and experimental conversion curves is presented in Figure 7. As can be seen at the beginning and end of the process, there is a small underestimation of the results when using the model; however, the difference is very small, so a good fit is observed. To evaluate this adjustment, the average deviation percentage (AVP) was calculated, which gave a result of 3.7%, indicating that the results obtained can be used successfully in the simulation of the thermal decomposition of fique fibers.

**Figure 7.** Theoretical and experimental conversion curves.

## **4. Conclusions**

Equipment for measuring thermal conductivity was built, based on the ASTM C 177-13 standard, with which samples of nonwoven fique fibers of densities between 50 and 80 kg/m<sup>3</sup> were tested. The conductivity of the samples was found to be between 0.055 and 0.06 W/m·K, which is a value close to that of the common insulators found on the market. This indicates that, from a heat transfer point of view, the material can be a good thermal insulator for buildings.

Thermogravimetric tests were also carried out in an inert atmosphere at 10 ◦C/min on the fique samples. It was observed that the thermal decomposition process consists of five stages: drying, heating without loss of mass, two stages of decomposition, and final degradation. These were carried out in the temperature ranges: 27–100 ◦C, 100–250 ◦C, 250–320 ◦C, 320–378 ◦C, and 378–480 ◦C, respectively.

From the TG data, the kinetic modelling of the biomass was carried out by means of the Coats–Redfern method, using the master plot curves for the determination of the reaction models, thus obtaining the kinetic triplet that allows us to model its thermal decomposition process. The results obtained were evaluated by comparing the theoretical and experimental conversion curves, obtaining average deviation percentages (AVP) of less than 4%, which leads us to the conclusion that the value of the kinetic triplet obtained is adequate for modelling the thermal decomposition process.

Very few studies evaluate the environmental impacts "cradle to grave" in a rigorous way, using, for instance, the life cycle assessment approach (LCA) of nonwoven fique samples. This lack of data is mainly caused by the state of the research on these materials that is still at an early stage. Further analyses should also be performed to evaluate other important properties for thermal insulators such as fire classification, resistance to water vapor diffusion, acoustic absorption, degradation due to moisture, bacteria, mildew, and fungi. In conclusion, issues remain to be solved before the widespread use of the fique nonwoven materials as thermal insulators.

**Author Contributions:** Conceptualization, G.F.G.S. and R.E.G.L.; methodology, G.F.G.S. and R.E.G.L.; validation, G.F.G.S., R.E.G.L. and R.A.G.-L.; resources, G.F.G.S., R.E.G.L. and R.A.G.-L.; review and editing G.F.G.S., R.E.G.L. and R.A.G.-L. All authors have read and agreed to the published version of the manuscript.

**Funding:** The authors wish to thank CEU San Pablo University Foundation for the funds dedicated to the Project Ref. USP CEU-CP20V12 provided by CEU San Pablo University.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** Funding from Minciencias, Ministry of National Education, Ministry of Industry, Commerce and Tourism and ICETEX, Scientific Ecosystem—Colombia Científica, Fund Francisco José de Caldas, through Contract RC-FP44842-212-2018, is gratefully acknowledged and the Universidad Pontificia Bolivariana under gran<sup>t</sup> No. 028-0717-2600.

**Conflicts of Interest:** The authors declare no conflict of interest.
