2.2.3. Statistical Analyses

Results of CSF production and proximate analysis were subjected to regression analyses to provide empirical equations. These equations are used to describe the following properties of CSF: MY, EDr, EY, VM, AC, FC, VS, CP, and HHV depending on process temperature and time. The regression was performed according to previous work [19]. In brief, experimental data were subjected to four regression models: (I) linear equation, (II) second-order polynomial equation, (III) factorial regression equation, and (IV) response surface regression equation. Then, determination coefficient (R2) and Akaike value (AIC) were calculated for each model. Next, models with the greatest R<sup>2</sup> and the lowest AIC value were chosen as the best fit to experimental data; the other models were rejected. In the case chosen model had some insignificant regression coefficients (an), they were removed, and regression analysis was performed again.

To check if process conditions have an impact on fuel properties, ANOVA was performed, with a post hoc Tukey test to test the pairwise significance (*p* < 0.05).

## 2.2.4. Thermal Analysis

The dry samples were subjected to TG/DTG/DSC thermal analysis using a simultaneous thermal analyzer (Netzsch, 449 F1 Jupiter, Selb, Germany). Term TG/DTG/DSC stands for thermogravimetry/difference thermogravimetry/differential scanning calorimetry. TG/DTG results present how material decomposes in the function of temperature, while the DSC results show transformations and reactions occurring at a particular temperature.

The sample was placed into a corundum crucible. The mixture of nitrogen and argon 4:1 was used as an inert gas. The sample was heated 10 ◦C·min−<sup>1</sup> from 30–800 ◦C. As a reference, an empty crucible was used. TGA/DTG/DSC analyzer automatically recalculated DSC data to mW·mg−<sup>1</sup> and determined DTG from TG.

The TG data was used to determine kinetic parameters according to the Coats–Redfern (CR) method. The CR's kinetic triplet is activation energy (Ea), pre-exponential factor (A), and order of reaction (n). The methodology of CR determination was presented elsewhere [24].

2.2.5. Theoretical Mass and Energy Balance of the Torrefaction Process

Using part of the data from analyses that have been mentioned in the earlier paragraphs, theoretical energy balance for the torrefaction of PLA and paper waste was calculated. The calculations refer to the production of 1 g of CSF and include the determination of the:


For calculations, data of MY, HHV, and DSC results were used. The scheme of energy balance determination is shown in Figure 1. The green squares represent the order of calculations, the grey squares represent experimental/calculated data used for energy balance determination, and the blue squares stand for input and output data results.

**Figure 1.** Scheme of mass and energy balance determination.

In step I, the mass yield of CSF production was used to determine the mass of substrate to produce 1 g of CSF by Equation (4), which allowed us to calculate the energy contained in the substrate used to produce 1 g of CSF by Equation (5).

$$M\_{\\$} = \frac{M r\_{\rm CSF}}{M Y\_{\rm CSF}} \tag{4}$$

where: *Ms*—mass of substrate used to produce the required amount of CSF, (here 1 g), g; *MrCSF*—required mass of CSF, (here 1 g), g; and *MYCSF*—mass yield of CSF production, % (Equation (1)).

$$E\_s = M\_s \cdot HHV\_s \tag{5}$$

where: *Es*—energy contained in the substrate used to produce CSF, J; *Ms*—mass of substrate used to produce CSF, g; and *HHVs*—high heating value of substrate, J·g<sup>−</sup>1.

For step II, the results from DSC were used as input in the form of a power flow by the sample during heating. The DSC was converted from mW·mg−<sup>1</sup> to J mg−<sup>1</sup> by the multiplication by time in seconds, providing information about the energy in J used to increase the temperature for 1 g of substrate. The energy demand to heat to setpoint temperature and mass of substrate demand produce CSF per g were used to calculate the demand of external energy to produce 1 g of CSF.

For step III, it is assumed, that the energy contained in 1 g of CSF equals the HHV, which was determined by the experiment.

In step IV, the energy contained in the gas was calculated indirectly. The energy in the gas is assumed to be a sum of external energy from step II, and the difference between energy contained in substrate and energy contained in CSF obtained from torrefaction, following Equation (6).

$$E\_{\rm gas} = E\_{\rm external} + E\_{\rm substrate} - E\_{\rm CSF} \tag{6}$$

where: *Egas*—energy contained in the gas, J; *Eexternal*—external energy provided to thereactor to heat the substrate to setup temperature, J; *Esubstrate*—energy contained in the substrate used to produce CSF, J; and *ECSF*—energy contained in produced CSF, J.

To keep calculations as simple as possible, the calculations were performed following assumptions:

