Energy Crops and Methane: Process Optimization of Ca(OH)2 Assisted Thermal Pretreatment and Modeling of Methane Production

Switchgrass earned its place globally as a significant energy crop by possessing essential properties such as being able to control erosion, low cost of production, biomass richness, and appeal for biofuel production. In this study, the impact of a Ca(OH)2-assisted thermal pretreatment process on the switchgrass variety Shawnee for methane fuel production was investigated. The Ca(OH)2-assisted thermal pretreatment process was optimized to enhance the methane production potential of switchgrass. Solid loading (3–7%), Ca(OH)2 concentration (0–2%), reaction temperature (50–100 °C), and reaction time (6–16 h) were selected as independent variables for the optimization. Methane production was obtained as 248.7 mL CH4 gVS−1 under the optimized pretreatment conditions. Specifically, a reaction temperature of 100 °C, a reaction time of 6 h, 0% Ca(OH)2, and 3% solid loading. Compared to raw switchgrass, methane production was enhanced by 14.5%. Additionally, the changes in surface properties and bond structure, along with the kinetic parameters from first order, cone, reaction curve, and modified Gompertz modeling revealed the importance of optimization.


Introduction
Electrified transportation is expected to increase in the future; however, implementing its use will not happen everywhere, in every industry, and all at once [1]. Therefore, it is predicted that liquid biofuels will be extremely necessary for the ensuing decades. Sustainable and renewable fuel technologies have been focused on lignocellulosic energy crops as a promising substrate for producing biofuels. Due to enormously increased energy security demands coupled with climate change mitigation, the world's biofuel production has also drastically expanded.
Energy crops, as a specific crop species, have been grown for advanced cellulosic biofuel production in recent decades. Switchgrass, one of these promising energy crops, belongs to the Poaceae family and is a native North American prairie grass species that can rapidly grow large amounts of carbohydrate-rich biomass. It is a species of C4-type plants (which utilize the Hatch-Slack cycle for carbon fixation), and as such, it can perform this process four times more productively than C3-type plants (which utilize the C3 pathway for carbon fixation). From an environmental point of view, switchgrass-based biofuels are carbon negative due to switchgrass's high carbon sequestration ability owing to its deep and complex root system. Moreover, switchgrass has the ability to clean soils and waters by removing excess nutrients (N, P) originating from fertilization. This plant is also a great growth and living habitat for wildfowl and mammals, especially in ecotone zones between forest and agricultural fields [2,3]. From the agricultural perspective, switchgrass is very easy to establish and maintain due to its low nutrient and water requirements, high adaptability to many climates, and high resistance to naturally occurring pests and

Characterization Analysis Results
Characterization of biomass for biofuel production is the first step for evaluation. A field-dried, milled, and homogenized variety of Shawnee as an energy crop was used to characterize biomass. The general composition of switchgrass Shawnee is presented in Table 1, and detailed analysis results can be found in Başar et al. [30]. The variety of Shawnee contained 93.8% dry matter, indicating a moisture content of approximately 6.2%. Volatile solids (VS) were measured as 82.4%, mostly formed of lignocellulose. The lignocellulose composition of switchgrass is quantified as 34.8% hemicellulose, 33.1% cellulose, 26.5% neutral detergent solubles, and 5.6% lignin. Lemusa et al. [33] found 32.6% hemicellulose, 36.8% cellulose, and 6.30% lignin in the switchgrass sample. The results from this study are very close to Lemusa et al.'s [33] findings. Niu et al. [34] and Imam and Capareda [35] have also reported similar results. The elemental composition of the field-dried variety of Shawnee was quantified as 40.13% C, 5.75% H, and 0.87% N, representing switchgrass as a convenient energy crop for biofuel production. Elemental analysis results are in line with the values measured for the switchgrass variety of Shawnee in literature [35][36][37][38]. Furthermore, structural carbohydrate (polymeric carbohydrates, namely cellulose and hemicellulose. Glucose, mannose, galactose, xylose, and arabinose are the monosaccharide component of the cellulose and hemicellulose) analysis resulted that switchgrass variety of Shawnee has 29.41% glucose and 17.36% xylose. The results of the structural carbohydrate analysis were also consistent with the literature [39,40].

Effect of Ca(OH) 2 Assisted Thermal Pretreatment Process on Switchgrass
Thomas et al. [41] indicated that alkaline pretreatments have a variety of effects, such as (i) delignification, which results in the unmasking of cellulose, (ii) the breakdown of hemicellulose and cellulose, and (iii) a reduction in crystalline cellulose. pH, sSugar, and BMP analyses were carried out on raw and pretreated Shawnee switchgrass to observe the pretreatment effect. pH, sSugar, and BMP results of Ca(OH) 2 -assisted thermal pretreatment experiments are shown in Figure 1a-c, respectively.
Since the Ca(OH) 2 is applied in the range of 0-2% in the pretreatment experiments, it is expected that changes in the pretreatment inlet and outlet pHs depend on the applied amount of Ca(OH) 2 . As can be seen in Figure 1a, the pH values of the variety of Shawnee switchgrass that were not pretreated with Ca(OH) 2 at the reaction temperatures of 50, 75, and 100 • C were measured close to each other before and after the pretreatment experiments. While initial pH values were measured as 6.5-6.7, pH values varied between 5.2 and 6.7 depending on solid loading and reaction time after the pretreatment. In the pretreatment experiments assisted with 2% Ca(OH) 2 , the initial pH values ranged from 10.3 to 10.9. At the end of the reactions, at low temperatures (50 • C), pH values changed in the range of 7.7-8.2 depending on the pretreatment reaction time, while at high temperatures (100 • C), it changed between 6.5 and 6.9 regardless of the reaction time. When 1% Ca(OH) 2 was applied in the pretreatments, the initial pH values were 9.5-9. 8  sSugar analysis found that raw switchgrass has 50 mg sSugar VS −1 . The amounts of sSugar were measured at 7% solid loading (SL), as DM is higher than 3% SL when 50 • C reaction temperature, 6 h and 16 h reaction times, and without Ca(OH) 2 conditions are applied in the pretreatments. It is normal that sugar's solubilization from high solid loading was higher than from low solid loading. On the other hand, under the pretreatment conditions of 50 • C reaction temperature, 6 h and 16 h reaction times, and 2% Ca(OH) 2 , the amount of sSugar at 7% solid loading was lower than 3% solid loading. Higher sSugar values were measured from the raw switchgrass samples at all conditions of 75 • C reaction temperature applied. Furthermore, at 100 • C reaction temperature conditions, the sSugar values measured at 7% SL were higher than those measured at 3% solid loading.
Raw Shawnee switchgrass produced 217.1 mL CH 4 gVS −1 . In the literature, the methane production potential of switchgrass was reported as 169-252 mL CH 4 gVS −1 by Masse et al. [18] and 104.0-153.5 mL gVS −1 by Frigon et al. [16] depending on different harvesting seasons. Furthermore, the methane potential of raw Kanlow was reported as 197.39 mL CH 4 gVS −1 by El-Mashad et al. [24], the raw Alamo variety was presented as 246 mL CH 4 gVS −1 by Grigatti et al. [42], raw Kanlow was found 215.5 mL CH 4 gVS −1 by Başar et al. [30], and raw Shawnee was quantified as 208.4 mL CH 4 gVS −1 by Başar and Perendeci [3]. Considering the results in previous studies, obtained results from this study are in the range of reported methane yields.
The maximum methane generation was achieved as 231.4 mL CH 4 gVS −1 , specifically under the pretreatment conditions of 100 • C reaction temperature, 16 h of reaction time, 0% Ca(OH) 2 , and 3% solid loading. Methane generation was enhanced by 6.6% compared to raw switchgrass. In contrast, the lowest methane production was observed as 62.4 mL CH 4 gVS −1 when the 75 • C reaction temperature, 11 h reaction time, 2% Ca(OH) 2 , and 5% solid loading pretreatment conditions.
As is seen in Figure 1c, an increase in solid loading from 3% to 7% led to a severe fall in BMP results under all conditions. Zheng et al. [21] observed a similar outcome that monodigestion of a high dose (>4% TS) of switchgrass led to volatile fatty acid accumulation and process failure, suggesting that a high solid loading might introduce excessive quantities of easily digestible material into digesters.
When 50 • C reaction temperature, 6 h and 16 h reaction times, and 3% solid loading conditions are applied in the pretreatments, an increase in Ca(OH) 2 from 0% to 2% resulted in high BMP values. A similar trend was observed at 100 • C reaction temperature, 6 h reaction time, and 3% solid loading conditions, but low BMP production was obtained when raising the reaction time from 6 h to 16 h. Furthermore, BMP values slightly rose or remained stable while the reaction temperature increased from 50 • C to 100 • C. When a reduction in methane production is observed, it should be kept in mind that process optimization is required for the amount of chemicals used in the pretreatment process, depending on the composition of lignocellulose. Gunerhan et al. [43] indicated that the ability to optimize the process within a significant design boundary and assess the positive and negative effects of independent variables and their ranges are compelling qualities in selecting a wide range of independent variables.

Modeling and Optimization of Ca(OH) 2 Assisted Thermal Pretreatment Process
BMP results from the experiments of 51 Ca(OH) 2 -assisted thermal pretreatment, containing duplicates of 25 varied pretreatment conditions and triplicate of the center point, were loaded into Design Expert software. The model for BMP was developed by RSM. The accuracy of the BMP model was evaluated by the highest determination of coefficient (R 2 ), adjusted-R 2 , and predicted-R 2 . In addition, modification (Backward) was applied to the quadratic BMP model to obtain high R 2 . Backward selection seeks to remove terms from a model that are detrimental to the criterion. p-value criterion was used in the backward selection. The BMP model equation was used to optimize the Ca(OH) 2 -assisted thermal pretreatment process for maximum methane production with an acceptable process cost. BMP Model equation, statistics, and information are presented in Table 2. A BMP model with R 2 of 0.8572, adjusted-R 2 of 0.8121, and predicted-R 2 of 0.7646 was developed. The coefficient of determination, expressed as R 2 , shows the model's predictive power in percent. The developed model could only explain 85.72% of the relation between BMP and independent variables. The quadratic modified BMP model presented a low probability result (p-value < 0.0001), indicating the model is in the confidence range of 99%. p-values less than 0.05 indicate that model terms are significant. According to the BMP model statistics, solid loading (B) and Ca(OH) 2 concentration (D) were found to be significant terms from the first-degree effect terms, whereas reaction time (C) and reaction temperature (A) were determined insignificant terms in the BMP model of Ca(OH) 2 -assisted thermal pretreatment process. Furthermore, solid loading * Ca(OH) 2 concentration (BD), square terms of solid loading (B 2 ), and reaction time (C 2 ) are effective independent variables in the BMP model. Since the first-degree effect of the reaction temperature (A) does not change BMP directly and to obtain a hierarchical model, insignificant terms from the quadratic BMP model were excluded by the application of backward modification.
The individual effects of independent variables of Ca(OH) 2 assisted thermal pretreatment process on BMP and desirability (0.977) are presented in Figure 2. The individual effect of each independent variable on the BMP model presents that 179-236 mL CH 4 gVS −1 should be produced by the application of 3% solid loading, 6 h reaction time, and 0% Ca(OH) 2 concentration conditions in the pretreatment process. As is seen in Figure 2, the BMP value is observed to be stable between the 50 and 100 • C reaction temperature. On the other hand, BMP values decrease from 231.4 to 81.6 mL CH 4 gVS −1 by increasing solid loading from 3% to 7%. Furthermore, increasing solid loading, reaction time, and Ca(OH) 2 concentration resulted in low desirability and BMP values.
3D response surface plots for the effects of independent variables on the BMP model are given in Figure 3a-d. In the interaction effect of solid loading and reaction temperature presented in Figure 3a, the maximum BMP value was reached only at the lowest solid loading of 3%. The graph also indicates that temperature change did not affect the BMP value where solid loading is kept constant, but the drops in solid loading value remarkably caused a rise in BMP values. effect of each independent variable on the BMP model presents that 179-236 mLCH4 gVS −1 should be produced by the application of 3% solid loading, 6 h reaction time, and 0% Ca(OH)2 concentration conditions in the pretreatment process. As is seen in Figure 2, the BMP value is observed to be stable between the 50 and 100 °C reaction temperature. On the other hand, BMP values decrease from 231.4 to 81.6 mLCH4 gVS −1 by increasing solid loading from 3% to 7%. Furthermore, increasing solid loading, reaction time, and Ca(OH)2 concentration resulted in low desirability and BMP values. 3D response surface plots for the effects of independent variables on the BMP model are given in Figure 3a-d. In the interaction effect of solid loading and reaction temperature presented in Figure 3a, the maximum BMP value was reached only at the lowest solid loading of 3%. The graph also indicates that temperature change did not affect the BMP value where solid loading is kept constant, but the drops in solid loading value remarkably caused a rise in BMP values. In Figure 3b, the maximum BMP value is also reached only at the lowest solid loading value of 3%. Furthermore, keeping the solid loading at a constant 7% and increasing the Ca(OH) 2 concentration positively impacted BMP values. Where solid loading is kept at a constant minimum of 3%, increasing the Ca(OH) 2 concentration did not show any significant impact on the methane yield. On the other hand, where Ca(OH) 2 concentration was kept at its constant, increasing the solid loading adversely affected the BMP values; specifically, at the maximum solid loading and 0% Ca(OH) 2 concentration, BMP resulted in the lowest value. Figure 3c revealed that, within this experimental design, the optimum reaction time is around 6 and/or 16 h to reach the highest methane yield. Between 6 and 16 h reaction time, methane production yield is observed to have a decreasing trend. Figure 3d shows that a change in reaction temperature and Ca(OH) 2 concentration in any direction did not affect the BMP values significantly. Conclusively, solid loading * Ca(OH) 2 concentration was the most effective interaction for the maximum methane yield.
Most of the work in the literature focused on the production of methane from switchgrass without pretreatment. Pretreatment conditions for switchgrass and results available in the literature are presented in Table 3. In Figure 3b, the maximum BMP value is also reached only at the lowest solid loading value of 3%. Furthermore, keeping the solid loading at a constant 7% and increasing the Ca(OH)2 concentration positively impacted BMP values. Where solid loading is kept at a constant minimum of 3%, increasing the Ca(OH)2 concentration did not show any significant impact on the methane yield. On the other hand, where Ca(OH)2 concentration was kept at its constant, increasing the solid loading adversely affected the BMP values; specifically, at the maximum solid loading and 0% Ca(OH)2 concentration, BMP resulted in the lowest value. Figure 3c revealed that, within this experimental design, the optimum reaction time is around 6 and/or 16 h to reach the highest methane yield. Between 6 and 16 h reaction time, methane production yield is observed to have a decreasing trend. Figure 3d shows that a change in reaction temperature and Ca(OH)2 concentration in any direction did not affect the BMP values significantly. Conclusively, solid loading * Ca(OH)2 concentration was the most effective interaction for the maximum methane yield.
Optimization of a Ca(OH)2-assisted thermal pretreatment process was implemented to generate the maximum specific methane yield using the BMP model. In the optimization solid loading (%) (+++++), reaction time (h) (+++++), Ca(OH)2 concentration (%) (+++++) It can be concluded from Table 3 that there is limited work focused on the pretreatment of switchgrass for methane production in the literature. Pretreatment work can be classified into two groups. Chemical pretreatment works are supported by the application of heat. Basic (Ca(OH) 2 , NaOH, KOH), acidic (HCl, H 2 SO 4 ), and oxidizing (H 2 O 2 ) chemical agents were preferred in pretreatment. As seen in Table 3, with the pretreatment application, the methane production was 12.2-325.9% enhanced compared to untreated switchgrass [3,4,24,27,31]. Thermal pretreatment as microwave and steam explosion also enriched methane production by 5.2-9.1% [25][26][27][28][29][30][31][32]. Results show that combined chemical and thermal pretreatment application seems to be more effective. The enhancement result obtained in this study is in line with the literature. On the other hand, this work is the first to focus on optimizing Ca(OH) 2 -assisted thermal pretreatment, considering all the process variables for methane enhancement. However, this result revealed that Ca(OH) 2 -assisted thermal pretreatment for switchgrass does not significantly affect methane enhancement.

Effects of Ca(OH) 2 -Assisted Thermal Pretreatment Process on Switchgrass Surface Modification and Molecular Bond Changes
SEM images and the FTIR analysis of the raw and pretreated switchgrass samples were performed to appraise the alterations in surface properties and the structural-chemical modifications that emerged during the Ca(OH) 2 -assisted thermal pretreatment process. SEM images of raw switchgrass sample (a), pretreated switchgrass samples at 3% SL, 50 • C, 0% Ca(OH) 2 , 6 h, (b), 3% SL, 100 • C, 2% Ca(OH) 2 , 16 h (c), and 3% SL 100 • C, 0% Ca(OH) 2 , 6 h (d) are presented in Figure 4.
In the SEM image of the raw switchgrass, the sample surface is smooth, compact, and rigid ( Figure 4a). Therefore, there is no deformation noticed naturally. On the other hand, the SEM image in Figure 4b reveals that the pretreatment achieves peeling off the outer crust as a function of reaction temperature and time. Additionally, sub-surface canals are observed to begin deterioration. The SEM image of the pretreated switchgrass sample at 3% SL, 2% Ca(OH) 2 , 16 h, and 100 • C conditions (Figure 4c) indicates how application caused the entire breakdown of the outer crust and sub-surface canals. As a result, the porosity of the material structure has increased, thus enhancing further hydrolysis. Notably, in these conditions, the fibril structure of the switchgrass was entirely altered, and structural unity was distorted. The SEM image of the switchgrass sample at the optimized pretreatment conditions (3% SL, 0% Ca(OH) 2 , 6 h, and 100 • C) (Figure 4d) shows that the outer crust broke down totally, and slight deterioration is observed on the sub-surface canals.

Effects of Ca(OH)2-Assisted Thermal Pretreatment Process on Switchgrass Surface Modification and Molecular Bond Changes
SEM images and the FTIR analysis of the raw and pretreated switchgrass samples were performed to appraise the alterations in surface properties and the structural-chemical modifications that emerged during the Ca(OH) 2-assisted thermal pretreatment process. SEM images of raw switchgrass sample (a), pretreated switchgrass samples at 3% SL, 50 °C, 0%Ca(OH)2, 6 h, (b), 3% SL, 100 °C, 2%Ca(OH)2, 16 h (c), and 3% SL 100 °C, 0%Ca(OH)2, 6 h (d) are presented in Figure 4. In the SEM image of the raw switchgrass, the sample surface is smooth, compact, and rigid ( Figure 4a). Therefore, there is no deformation noticed naturally. On the other hand, the SEM image in Figure 4b reveals that the pretreatment achieves peeling off the outer crust as a function of reaction temperature and time. Additionally, sub-surface canals are observed to begin deterioration. The SEM image of the pretreated switchgrass sample at 3% SL, 2% Ca(OH)2, 16 h, and 100 °C conditions (Figure 4c) indicates how application caused the entire breakdown of the outer crust and sub-surface canals. As a result, the porosity of the material structure has increased, thus enhancing further hydrolysis. Notably, in these conditions, the fibril structure of the switchgrass was entirely altered, and structural unity was distorted. The SEM image of the switchgrass sample at the optimized pretreatment conditions (3% SL, 0% Ca(OH)2, 6 h, and 100 °C) (Figure 4d) shows that the outer crust broke down totally, and slight deterioration is observed on the sub-surface canals.
FTIR spectra of raw switchgrass sample (a), pretreated switchgrass samples at 3% SL, 50 °C, 0% Ca(OH)2, 6 h, (b), 3% SL, 100 °C, 2% Ca(OH)2, 16 h (c), and 3% SL 100 °C, 0% Spectroscopic results obtained by FTIR analysis indicate that raw and pretreated switchgrass samples show similar binding properties at the wavelength between 400 and 1800 cm −1 . It is observed that the switchgrass sample pretreated at 3% SL, 100 • C, 2% Ca(OH) 2 , and 16 h conditions show sectional similarities with the switchgrass sample pretreated at 3% SL, 100 • C, 0% Ca(OH) 2 , and 6 h conditions. Nevertheless, upon careful examination, differences in chemical bonds were observed in both samples. Between the 400-1800 cm −1 wavelength, 470 cm −1 , 560 cm −1 , 620 cm −1 , 775 cm −1 , 895 cm −1 , 1050 cm −1 , 1180 cm −1 , 1245 cm −1 , 1440 cm −1 , 1465 cm −1 , 1580 cm −1 and 1735 cm −1 wavelengths in particular show remarkable differences. FTIR spectrum of raw switchgrass sample shows differences in Si-O-Si and (PO 4 ) 3 − bonds at 470 cm −1 wavelengths compared to pretreated switchgrass samples. Additionally, a notable resonance in Si-O-Si and (PO 4 ) 3 − bonds is observed for the switchgrass samples pretreated at 3% SL, 100 • C, 2% Ca(OH) 2 , and 16 h conditions compared to raw switchgrass, indicating a concentration increase of fragments containing these groups. However, the resonance in C-O and C=O bonds at 620 cm −1 wavelengths remained identical when high temperatures were applied to the switchgrass samples. Thus, this shows how temperature application makes a difference in C-O and C=O bonds. 775 cm −1 wavelength corresponds to resonance in NH 2 bonds. Switchgrass samples pretreated at 3% SL, 100 • C, 2% Ca(OH) 2 , and 16 h conditions have minimum absorbance value compared to raw switchgrass samples. This observation indicates how much deterioration occurred under the effects of Ca(OH) 2 -assisted temperature pretreatment. Moreover, 895 cm −1 wavelength states the resonance in β-glucosidic bonds directly related to cellulose. Switchgrass sample either pretreated at 3% SL, 50 • C, 0% Ca(OH) 2 , 6 h, or at 3% SL, 100 • C, 0% Ca(OH) 2 , 6 h conditions showed similar properties. However, the sample pretreated at 3% SL, 100 • C, 2% Ca(OH) 2 , and 16 h conditions had a low absorbance value. This is an indication of the deterioration of the β-glycosidic bonds. The 1050 cm −1 wavelength indicates C-O, C=C, C-OH, and C-O-C stretching vibrations in cellulose and hemicellulose compounds. FTIR spectrums of raw and pretreated switchgrass samples at 3% SL, 50 • C, 0% Ca(OH) 2 , 6 h, and 3% SL, 100 • C, 0% Ca(OH) 2 , 6 h conditions indicated similar absorbance values. However, a minimum absorbance value was obtained from the switchgrass sample pretreated at 3% SL, 100 • C, 2% Ca(OH) 2 , and 16 h conditions. This shows the tension in the C-O, C=C, C-OH, and C-O-C bonds of cellulose and hemicellulose. Alteration in the band position and intensity may represent a reduction in the content of the structural ingredients by the application of pretreatment [44]. The peaks at 1180 cm −1 and 1245 cm −1 wavelengths are related to the C-O-C asymmetrical bending vibration in cellulose and hemicellulose compounds and the C-O bonds of acetyl groups of hemicellulose, respectively. Switchgrass samples pretreated at 3% SL, 100 • C, 2% Ca(OH) 2 , and 16 h conditions resulted in lower absorbance values than others at these wavelengths. This is evidence of the disintegration of the acetyl groups of hemicellulose. In the fingerprint zone of the spectra, modifications in spectra, especially at 1440, 1465, and 1580 cm −1 wavelengths, can be observed from the pretreated switchgrass samples compared to raw switchgrass. Chemical bonds at 1140, 1465, and 1580 are related to lignin decomposition. Out of the fingerprint region, at 2900 and 3400 cm −1 wavelengths, modifications were monitored that indicate an alteration in C-H and O-H bonds. Ca(OH)2, 6 h (d) are presented in Figure 5. Bands in FTIR spectra available in the literature are also given in Table 4 for comparison.   [45,46] 620 Resonance in C-O, C=O bonds [47] 775 Resonance in NH 2 bonds [48] 895 Resonance in β-glucosidic bonds, Indicator for crystalline and amorphous cellulose rate [49][50][51] 1050 C-O, C=C, C-OH, and C-O-C tensions in cellulose and hemicellulose [52,53] 1180 Asymmetrical C-O-C tension in cellulose and hemicellulose [54] 1245 C-O adsorption of acetyl groups in hemicellulose [52] 1280 C-H warping in crystallized cellulose [55] 1440 O-H bond in linear warping of hemicellulose and lignin [54] 1465 C-H deformation in lignin [54] 1580 Resonance of aromatic rings in lignin [51] 1735 Resonance of bonds in ketone and ester carbonyl groups [55] 2900-3400 Resonance and tension of C-H and O-H bonds in cellulose [51,53,56]

Kinetic Modeling
The BMP test was finalized at 56 days. Since the biogas production reached a plateau after the first 28 days, this period was considered in the kinetic modeling. Predicted methane production and kinetic parameters from the first order, cone, modified Gompertz, and reaction curve modeling, along with the statistical indicators as R 2 and Adjusted-R 2 , are presented in Table 5. Simulated methane potential values were plotted against experimental data to visually compare, shown in Figure 6.
High compatibility (R 2 ) was achieved for all models. All four models were successfully applied to determine the biogas potential of the switchgrass. The hydrolysis rate constant (k) is an important parameter showing the methane production efficiency in the anaerobic degradation process. The k values estimated with the first order kinetic model for the different pretreatments applied to the switchgrass varied in the range of 0.115-0.159 d −1 . The k value varies between 0.136 and 0.210 d −1 from cone modeling. Parallel with the first order modeling, the minimum k value was estimated from the pretreated switchgrass at 3% SL, 50 • C, 0% Ca(OH) 2 , 6 h and was followed by the pretreated switchgrass at 3% SL, 100 • C, 0% Ca(OH) 2 , 6 h conditions and the raw sample. The estimated and experimental results show a variance between 2.55% and 6.41%. The high R 2 values and minor differences between model results and experimental results for methane production indicate that the cone model can be used successfully.
When examining the results of the reaction curve model, the Rm value was calculated as 26.33 mL CH 4 gVS −1 d −1 for pretreated switchgrass at 3% SL, 100 • C, 2% Ca(OH) 2 , 16 h conditions, as in the modified Gompertz model, followed by 22.70 mL CH 4 gVS −1 d −1 for raw, 20.33 mL CH 4 gVS −1 d −1 from pretreated switchgrass at 3% SL, 100 • C, 0% Ca(OH) 2 , 6 h, and 20.19 mL CH 4 gVS −1 d −1 from pretreated switchgrass at 3% SL, 50 • C, 0% Ca(OH) 2 , 6 h. In conclusion, in evaluating the success of each four models in this study, every model achieves applicable results, while first order, cone, and reaction curve methods proved to have a better prediction capacity than modified Gompertz. For the comparison, the effects of pretreatments on methane production kinetic parameters available in the literature are presented in Table 6.
Compared to the untreated raw switchgrass (λ: 3.1 d and µm: 1.9 mLSTP gVS −1 d −1 ), while λ decreased, the µm value increased by the pretreatment. In this study, parallel with the literature, the Rm value increased, and the λ value decreased obtained from the reaction curve and modified Gompertz models compared to raw by applying 3% SL, 100 • C, 2% Ca(OH) 2 , 16 h pretreatment condition.

Reaction Curve
Rm (mL CH4 gVS added d ) 26 In conclusion, in evaluating the success of each four models in this study, every model achieves applicable results, while first order, cone, and reaction curve methods proved to have a better prediction capacity than modified Gompertz. For the comparison, the effects of pretreatments on methane production kinetic parameters available in the literature are presented in Table 6. Obtained k values from this study are slightly higher than the literature values. However, it should be noted that k values were calculated for the first time for Ca(OH) 2 -assisted thermal pretreatment for switchgrass.
The cone model uses the kinetic parameters of the hydrolysis rate constant k and the shape factor n to predict methane production Unyay et al. [26] calculated the k and n values as 0.067-0.080 and 1.7-1.9, respectively, for the anaerobic digestion of raw switchgrass at different substrate-inoculum ratios. As a result of the Ca(OH) 2 -assisted thermal pretreatment in this study, k constants increased, and the n values decreased compared to the work of Unyay et al. [26].

Switchgrass
In this study, the switchgrass variety of Shawnee is utilized as biomass. Switchgrass was planted and dried on the field in Karapınar (Konya, Turkey). The size of the samples was reduced to 3 mm to achieve textural homogeneity and consistency [57][58][59][60]. Samples of Shawnee were kept in labware plastic bags at 20 • C temperature for further experimentation for one year.

Experimental Design and Analysis
The experimental design of Ca(OH) 2 -assisted thermal pretreatment on switchgrass was applied by Central Composite Design (CCD) and Response Surface Method (RSM). CCD with 3 levels of 4 independent variables as switchgrass solids loading (3-7%) as DM, reaction temperature (50-100 • C), Ca(OH) 2 concentration (0-2%), and reaction time (6-16 h) were designated for the process optimization. Biochemical methane potential (BMP) and sSugar results were selected as dependent variables. Design Expert 11 software (Stat-ease Inc., Minneapolis, MN, USA) was used for experimental design and statistical analysis.
Experimental results were modeled, and the obtained regression model was evaluated by the analysis of variance (ANOVA), regression coefficients, and the pand F-Values. Model quality was determined by the coefficient of determination (R 2 ) and an adjusted determination coefficient (adj-R 2 ). Optimization of Ca(OH) 2 -assisted thermal pretreatment was done by using maximization and minimization criteria for independent and dependent variables [64,65] by using obtained model equation. The optimization module investigated the merging of independent variable values that meet the demands placed on each of the dependent variables. The optimizations were performed for maximum methane production potential.

Ca(OH) 2 -Assisted Thermal Pretreatment
Ca(OH) 2 -assisted thermal pretreatment experiments were conducted in 1 L laboratoryscale glass reactors equipped with a reflux condenser immersed in a 2 L oil heating bath. To provide the desired temperature and mixing conditions, magnetic stirrers with heaters (IKA C-Mag HS-7, IKAWerke GmbH, Staufen, Germany) and oil baths were used. Glass reactors were closed with condensers, which were kept at constant temperature by a circulating water bath (Lauda Alpha RA-8, Lauda Dr. R. Wobser GmbH, Lauda-K€onigshofen, Germany) to avoid evaporation.
In the Ca(OH) 2 -assisted thermal pretreatment experiments, reactors were heated to predetermined temperatures after the addition of a calculated amount of switchgrass, Ca(OH) 2 , and deionized water. The reaction time was started, and the temperature was kept at the determined temperature during the pretreatment experiments. The reactor contents were continuously mixed with magnetic stirrers at 150 rpm. All pretreatment experiments were performed in duplicates. At the end of reaction time, the temperature of the reactor content was rapidly cooled down to room temperature. pH values of reactor content were measured before and after the pretreatment experiments. Reactor contents were centrifuged two times at 4400 rpm for 5 min and 14,500 rpm for 15 min to obtain the liquid phase for soluble sugar (sSugar) analysis. Soluble sugar (sSugar) analysis was performed by the Dinitro Salicylic Acid (DNS) method [66] to observe the pretreatment efficiency. Mixed solid and liquid samples for BMP tests were kept at −20 • C.

Biochemical Methane Potential Test (BMP)
The standard BMP test was applied to define the biochemical methane potentials of raw and pretreated switchgrass by Ca(OH) 2 -assisted thermal. The BMP experiment works on the basis of incubating a specific amount of switchgrass samples mixed with anaerobic sludge at 35 • C and detecting the gas composition and volume produced. The BMP test was conducted according to Perendeci et al. [67]. BMP experiments were performed in 500 mL glass reactors with a 400 mL working volume. pH was set to neutral, and reactors were flushed with N 2 /CO 2 (70%/30%) gas blend for the anaerobic condition after the addition of the switchgrass sample, seed sludge, required nutrients, buffer solution, and deionized water. The substrate-to-seed ratio was selected as 0.5 (gVS gVS −1 for solid samples). BMP reactors were incubated at 35 • C, and experiments were finalized at 56 days. The gas composition of N 2 , CH 4 , and CO 2 in headspaces of the BMP reactors was quantified by Varian CP-4900 Micro-Gas Chromatography (Varian Inc., Palo Alto, CA, USA). Details of the measurements of biogas volume and the analysis of gas composition can be found in Basar et al. [30].

Scanning Electron Microscopy (SEM) and Fourier Transform Infrared Spectroscopy (FTIR)
The surface structure of raw and pretreated switchgrass samples was evaluated by SEM to determine the changes caused by Ca(OH) 2 -assisted thermal pretreatment. Samples firstly were lyophilized and coated with gold-palladium for 120 s under 18 mA current (Polaron SC7620 Sputter Coater, Quorum Technologies, Lewes, UK). After coating, the samples were monitored at different magnifications, and images were kept with SEM (Zeiss Leo 1430, Zeiss Group, Oberkochen, Germany) at 15 kV voltage.
To determine the effects of Ca(OH) 2 -assisted thermal pretreatment on the molecular bond characteristics of the lignocellulosic structure, Fourier transforms infrared spec-troscopy (FTIR) analyzes were performed for both raw and pretreated samples. Samples were lyophilized, and measurements were performed by a Perkin Elmer, Spectrum Two in 400 cm −1 and 4000 cm −1 wavelength ranges.

Kinetic Modeling
To evaluate the effect of Ca(OH) 2 -assisted thermal pretreatment on the anaerobic digestion reaction kinetics, specific cumulative methane production was modeled by using modified Gompertz and reaction curve equations. Furthermore, first order and cone models were implemented for the determination of the hydrolysis rate. Detailed descriptions of the model equations can be found in the work of Yılmaz et al. [68]. All model simulations were done by AQUASIM 2.1 Trial version.

Conclusions
Energy crops have garnered considerable attention due to their significant potential as biofuel feedstock and agricultural benefits. Most switchgrass varieties are a powerful alternative to produce energy-efficient biofuel. In this study, Ca(OH) 2 -assisted thermal pretreatment was applied to energy crops to enhance biodegradability and biofuel yield and remove a significant handicap of lignocellulose by unmasking cellulose. Neat optimization revealed that solid loading as DM (3-7%) and Ca(OH) 2 concentration (0-2%) were found to be significant independent variables compared to reaction temperature (50-100 • C) and time (6-16 h) within range desing boundary. Essentially, increasing solid loading, reaction time, and Ca(OH) 2 concentration resulted in low desirability and methane production yield. A biochemical methane production model was built and validated specific methane yield with 14.5% increases compared to untreated switchgrass. Nevertheless, it is concluded that Ca(OH) 2 -assisted thermal pretreatment did not significantly affect methane enhancement compared to other pretreatment methods.