*2.3. Thermal Analyses*

A Setaram equipment, model SETSYS Evolution was used in this work. Non-isothermal combustion runs were carried out after calibration for baseline, weight, temperature, and heat flow. Throughout these runs, Thermogravimetry (TG) and Differential Scanning Calorimetry (DSC) signals were simultaneously registered during the temperature-programmed combustion of MB, BC, and their blend (MB-BC). In the blend, a 10% wt. of MB was used, since it has been shown that such a percentage is adequate for the practical implementation of co-combustion of coal with biomass in existing infrastructures, namely in thermal power plants [20]. Derivative TG (DTG) curves were also determined as the first derivation of TG results with respect to time. The runs were carried out up to 1200 K at four different heating rates (β = d*T*/d*t*): 0.1, 0.2, 0.4, and 0.5 K/s, in order to determine the corresponding TG-DSC curves. For each sample and β, three repetitive runs were carried out using 15 ± 1 mg of MB, BC, or MB-BC, after having verified that this mass ensured representativeness and avoided heat and/or mass transfer limitations. All the runs were done under a continuous air flow (100 cm<sup>3</sup>/min at 1 atm of gauge pressure).

The theoretical DTG curves (DTG(T)) and DSC curves (DSC(T)) were calculated for the blend MB-BC using Equations (1) and (2), respectively, as a weighted average of its composition in order to check interaction between MB and BC during their co-combustion:

$$DTG\_{\{T\}} = 0.1 \times DTG\_{MB} + 0.9 \times DTG\_{BC} \tag{1}$$

where DTGMB and DTGBC are the weight loss rate of MB and BC throughout their respective temperature-programmed combustions.

$$DSC\_{\{\Gamma\}} = 0.1 \times DSC\_{MB} + 0.9 \times DSC\_{BC} \tag{2}$$

where DSCMB and DSCBC are the differential scanning calorimetry results that correspond to the temperature-programmed combustion of MB and BC, respectively.

#### *2.4. Non-Isothermal Kinetic Analysis*

The rate of heterogeneous solid state reactions is generally described by the following equation:

$$\frac{d\alpha}{dt} = k(T)f(\alpha) \tag{3}$$

where α is the extent of reaction or fractional conversion, *t* is time, *T* is temperature, *k*(*T*) is the temperature-dependent constant, and *f*(α) is a function that describes the dependence of the reaction rate on α.

Usually, the decomposition from a solid state is mathematically described in terms of the kinetic triplet (apparent activation energy (*E*), pre-exponential factor (*A*), and an expression of the kinetics in terms of *f*(α)), which may be correlated to the obtained results by this rate expression:

$$\frac{d\alpha}{dt} = A\varepsilon^{-\mathcal{E}/\mathcal{R}T}f(\alpha)\tag{4}$$

The previous rate expression (Equation (4)) may be transformed into a non-isothermal one, which defines the reaction rate in function of *T* at a constant β:

$$\frac{\mathbf{d}\alpha}{\mathbf{d}T} = \frac{A}{\beta} A e^{-E/\mathbb{RT}} f(a) \tag{5}$$

When Equation (5) is integrated up to α, results in:

$$\int\_{0}^{a} \frac{\mathbf{d}\alpha}{f(a)} = \mathbf{g}(\alpha) = \frac{A}{\beta} \int\_{T\_0}^{T} e^{-E/\mathbb{RT}} \mathbf{d}T \tag{6}$$

where *g*(α) is the integral reaction model.

Several methods may be used in order to obtain a description of the combustion process in terms of *E* [48]. These methods can be classified depending on the experimental conditions and on the mathematical analysis that was carried out. As for the experimentation, the results may be obtained either under isothermal or non-isothermal conditions. Regarding mathematical analysis, either the model-fitting or the iso-conversional (model-free) approaches may be followed.

For non-isothermal kinetic analysis, different iso-conversional models that involve carrying out temperature-programmed runs at different β [48] have been developed to determine *E*. During the last decade, these methods have been frequently used to study the thermal decomposition kinetics of very different types of biofuels [20,21], including microalgae biomass [49].

In this sense, *E* may be estimated by applying the iso-conversional model developed by Flynn, Wall, and Ozawa [50,51], which is an integral method that uses the Doyle's approximation [52]:

$$\ln(\beta) = \ln\left[\frac{AE}{R\ g(\alpha)}\right] - 5.331 - 1.052\frac{E}{RT} \tag{7}$$

The utilization of the Flynn-Wall-Ozawa (FWO) method [50,51] requires the determination of the *T* corresponding to fixed values of α from runs carried out at different β. *E* is estimated by plotting ln(β) vs. 1/*T* for each α, which gives straight lines with slope—*E*/*R*.

*E* may be also determined on the basis of the Kissinger-Akahira-Sunose (KAS) kinetic model [53,54], as it is next described.

In Equation (5) *E*/2*RT* » 1, therefore, the integral can be approximated by:

$$\int\_{T\_0}^{T} e^{-E/RT} dT \approx \frac{R}{E} T^2 e^{-E/RT} \tag{8}$$

Substituting the temperature integral and taking the logarithm:

$$\ln \frac{\beta}{T^2} = \ln \left[ \frac{RA}{Eg(\alpha)} \right] - \frac{E}{R} \frac{1}{T} \tag{9}$$

For the application of the KAS model [53,54], it is necessary to carry out runs at different β, the respective conversion curves being evaluated from the measured TG curves. For each α, ln(β/*T*2) plotted versus 1/*T* gives a straight line with slope <sup>−</sup>*E*/*R*.

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

## *3.1. Materials Characterization*

The results from the proximate and elemental analyses of MB and BC are depicted in Table 2, together with the measured HHV for each material.

**Table 2.** Proximate analysis, elemental analysis, and calorific values for the microalgae biomass (MB) and the bituminous coal (BC) used in this work.


FC: fixed-carbon; HHV: high heating value; d.b.: dry basis; \* calculated by difference.

As may be seen in Table 2, the proximate and elemental analyses of MB and BC evidence that these fuels have very distinct properties due to their different origin and nature. Within the proximate analysis, moisture percentages for both materials are usual equilibrium values for storeroom conditions. With respect to the ash yield, it is quite smaller for MB (6.2%) than for BC (31.1%), which is a positive fact for the biofuel utilization of MB, since relatively high ash contents are undesirable in many combustion facilities. However, the amount of volatiles in MB (78.2%) is much larger than in BC (8.2%). The higher volatile matter content of biomass, as compared with coal, is known to improve the combustion of the latter, which results in a better burn out and lower unburned carbon in the ashes [21]. Still, adaptations of the combustor may be necessary for the co-processing of fuels with very different volatiles content. On the other hand, due to the higher volatile content of MB, it possesses a lower fixed-carbon (15.6%) than BC (60.7%), which is expected to be corroborated in their separate combustion DTG profiles.

Regarding the elemental analysis, BC has a higher C content (62.7%) than MB (52.0%). Contrarily, BC has much lower O content (1.7%) than MB (29.8%). Additionally, the H and N contents of BC (2.5 and 1.3%, respectively) are lower than those of MB (6.8 and 10.7%, respectively). Nonetheless, it has been demonstrated that NO emissions are not strongly dependent on the fuel nitrogen content [55]. Meanwhile, both BC and MB have a similar S content (0.7 and 0.6%, respectively), so their combustion may involve similar SO*x* emissions.

The results from proximate and elemental analyses of MB are very similar to those that were determined for *C. vulgaris* biomass by Gao et al. [56]. However, slightly different results have been obtained by other authors for *C. vulgaris* biomass [57], being especially relevant the comparatively higher volatiles content and lower percentage of ashes of MB. The differences are probably related to the specific strain and the way or stage of culturing. In fact, nitrogen supplementation [58] and the age of the culture [59] have already been shown to affect thermal properties of *C. sorokiniana*. Regarding BC, the results are comparable to previously published data for coal with the same rank and origin [23].

Finally, as regards the HHV, both MB and BC have very similar values (22.9 and 24.3 MJ/kg, respectively), which means that the combustion of their blend is not going to have remarkable energetic effects as compared with the combustion of BC. The HHV determined in this work for MB is within the range of values referred in the review by Chen et al. [4], namely 14 to 24 MJ/kg, while the HHV of BC is close to published data for coal with the same rank and origin [23].

As for the estimation of HHV, Figure 1 shows the values that were obtained by the correlations depicted in Table 1 for each MB and BC, together with the measured value and a deviation limit of ±10%. Some of the correlations satisfactorily estimate the HHV of MB and BC, mainly those that are based on elemental or on both elemental and proximate analyses. However, correlations that are only based on proximate analysis (No. 7–11 in Table 1) mostly underestimate the HHV, except for correlation No. 10 [43], which overestimates the HHV of MB, and correlations No. 8 [42] and 10 [43], which only give an acceptable HHV estimation for BC. Correlation No. 1, which is the well-known Dulong correlation [35] and is just based on the C, H, and O contents, correlation No. 4 [38], which also depends on the C, H and O contents, and correlation No. 14 [46], which stands on the elemental analysis and the ash content, are those that more closely estimate the HHV for both MB and BC. These correlations may be very useful for the quick estimation of the calorific potential of microalgae and coal when planning their co-processing.

**Figure 1.** Estimated High Heating Value (HHV) for microalgae biomass (MB) (**a**) and BC (**b**) by correlations No. 1 to No. 15 listed in Table 1. For each material, the estimated HHV values are represented by verticals bars, the measured value is represented by a continuous horizontal line, the upper limit (measured HHV + 10%) is represented by a dashed line, and the lower limit (measured HHV − 10%) is marked with a dotted line.

To the best of our knowledge, there are no published studies using correlations for the estimation of HHV in the specific case of microalgae biomass. Therefore, the applicability of the here considered correlations (Table 1) was tested in this work for available data in the literature on the calorific value of microalgae biomass from di fferent strains. In the case of those microalgae biomasses for which just the elemental analysis is available, the estimated HHV values are depicted in Table 3. For biomasses whose elemental and proximate analyses are available, the estimations of HHV are displayed in Table 4.


**Table 3.** Published results on the elemental and calorific analysis for different microalgae biomasses. For each case, the published High Heating Value (HHV) is shown together with the HHV estimated by correlations based on elemental analysis displayed in Table 1. Estimated HHVs that are within ± 10% the measured


*Energies* **2019**, *12*, 2962

As may be observed in Table 4, estimations that are just based on proximate analyses (correlations No. 7 to 11 in Table 1) are mostly inadequate, while those that are just based on the elemental analysis (Table 3) or elemental analysis together with proximate analysis (Table 4) give estimations that are more satisfactory. On the whole, and coincidently with the case of microalgae biomass that was obtained in this work, correlations No. 1, 4, and, especially, No. 14 were the most accurate for estimating the HHV of microalgae biomasses in the literature.
