3.1 Establishment and analysis of methane yield regression model
In this experiment, methane yield (y) was taken as the response variable, TS% (\({\text{x}}_{1}\)), biochar (x2), and Fe3O4 (x3) were taken as factors to build a regression model. Design-expert 10.0 was used to conduct multivariate regression analysis on 23 groups of experimental data, and the multivariate regression Eq. (1) was obtained as follows:
$$\begin{gathered} {\text{y}}=230.44 - 48.82{x_1}+6.34{x_2} - 11.48{x_3}+0.86{x_1}{x_2} - 16.61{x_1}{x_3} - 7.24{x_2}{x_3} - 52.09x_{1}^{2} \hfill \\ - 12.07x_{2}^{2} - 6.88x_{3}^{2} - 8.07{x_1}{x_2}{x_3}+8.17x_{1}^{2}{x_2}+49.65{x_1}x_{2}^{2}+60.53x_{1}^{2}x_{2}^{2} \hfill \\ \end{gathered}$$
1
Table 4
Analysis results of regression model
Source Prob > F
|
Sum of Squares
|
df
|
Mean Square
|
F-Value
|
P-Value
|
Signature
|
Model
|
57461.93
|
13
|
4420.15
|
96.52
|
< 0.0001
|
significant
|
x1-TS%
|
13481.15
|
1
|
13481.15
|
294.37
|
< 0.0001
|
|
x2-Biochar
|
227.27
|
1
|
227.27
|
4.96
|
0.0529
|
|
x3-Fe3O4
|
1799.42
|
1
|
1799.42
|
39.29
|
0.0001
|
|
x1x2
|
5.85
|
1
|
5.85
|
0.13
|
0.7291
|
|
x1x3
|
2207.14
|
1
|
2207.14
|
48.19
|
< 0.0001
|
|
x2x3
|
419.34
|
1
|
419.34
|
9.16
|
0.0143
|
|
x12
|
35514.78
|
1
|
35514.78
|
775.48
|
< 0.0001
|
|
x22
|
1908.36
|
1
|
1908.36
|
41.67
|
0.0001
|
|
x32
|
619.68
|
1
|
619.68
|
13.53
|
0.0051
|
|
x1x2x3
|
520.35
|
1
|
520.35
|
11.36
|
0.0082
|
|
x12x2
|
221
|
1
|
221
|
4.83
|
0.0556
|
|
x1x22
|
8169.54
|
1
|
8169.54
|
178.39
|
< 0.0001
|
|
x12x22
|
11707.1
|
1
|
11707.1
|
255.63
|
< 0.0001
|
|
Residual
|
412.17
|
9
|
45.8
|
|
|
|
Lack of Fit
|
152.11
|
1
|
152.11
|
4.68
|
0.0625
|
Not significant
|
Pure Error
|
260.06
|
8
|
32.51
|
|
|
|
Cor Total
|
57874.1
|
22
|
|
|
|
|
The statistical analysis results of the multivariate regression model of the CCD experiment were shown in Table 4. It can be seen that the model was extremely significant (P < 0.0001) (Khodaei et al., 2016), and it greatly represents the relationship between predicted and observed value (Cheng et al., 2022). The lack of fit P-Value of the model was 0.0625 (P > 0.05), indicating that the regression model had a high degree of fit and could be used to predict the response value (Zhu et al., 2021). The P-Values of different factors were less than 0.05 except x2, x1x2, x12x2, showing that they performed a significant impact on methane yield. This experiment adopted dimensionless linear code, thus there was no correlation among all regression coefficients. The influence of various factors on methane yield can be ranked directly according to the absolute value of the first item regression coefficient (Mohtar et al, 2016; Deng et al., 2019), and the order was TS% > Fe3O4 > Biochar (48.82 > 11.48 > 6.34). The regression coefficient was independent, thus the simplified regression equation (2) can be obtained by directly deleting the insignificant items from the above model.
$$\begin{gathered} {\text{y}}=230.44 - 48.82{x_1} - 11.48{x_3} - 16.61{x_1}{x_3} - 7.24{x_2}{x_3} - 52.09x_{1}^{2} \hfill \\ - 12.07x_{2}^{2} - 6.88x_{3}^{2} - 8.07{x_1}{x_2}{x_3}+49.65{x_1}x_{2}^{2}+60.53x_{1}^{2}x_{2}^{2} \hfill \\ \end{gathered}$$
2
3.2 Effects of independent factor on coAD of AP and CS
3.2.1 Effect of TS% on methane yield
The effect of TS% on the coAD of AP and CS is shown in Fig. 1. Run 10 reached the maximum daily methane yield (DMY) (31.74 mL/gVS) on the 2nd day and was significantly higher than those of Run18 and Run9 (12.42 mL/gVS on the 21th day and 0.78 mL/gVS on 1st day) (Fig. 1a). This is attributed to the fact that a smaller TS% determines a larger IS ratio (ratio of inoculum to substrate) when the amount of inoculum was constant. During the start-up period, excessive organic loading rates lead to severe acid inhibition and even the cessation of AD (Deng et al., 2019). The biogas production of Run 18 was delayed until the 11th day, while Run 9 was terminated on the 3rd day. The reason for the delay or stop of biogas production might be that the AD process was inhibited due to the VFAs accumulation. The inhibition effect was more significant in Run 9, which caused the failure of the AD system (Abid et al., 2021). During AD, pH parameters can be used to estimate the degree of acidification in the reactor (Kunatsa and Xia, 2022), thus optimizing operating conditions. As shown in Fig. 1d, the pH value in the high TS% reactor dropped sharply in the initial stage. Run 9 was finally stabilized at around 5.0, which was far below the suitable pH (6.8 to 7.5) for the survival of methanogens (Mao et al., 2015). The acid accumulation severely inhibited the activity of methanogens and eventually led to the failure of the whole AD. In terms of cumulative methane yield (CMY), Run 18 and Run 10 obtained the highest yield of 209.03 mL/gVS and 165.22 mL/gVS, respectively, while Run 9 was only 1.02 mL/gVS under the influence of inhibition (Fig. 1b), suggesting that the CMY increased with the increase of the TS% within a certain range of TS%. However, a sharp decrease in CMY has occurred at excessively high TS%, which might be attributed to the higher organic loading, resulting in severe disruption of methanogenic pathways (Deng et al., 2019). The variation trend of methane content in each treatment was similar, ie., rose rapidly in the initial stage and remained in a stable state with the progress of anaerobic digestion (Fig. 1c). Run 10 obtained the highest percentage of 70.2%, indicating that the digester with a lower TS% can obtain a higher methane content.
3.2.2 Effect of biochar on methane yield
The effect of biochar on the coAD characteristics of AP and CS is shown in Fig. 2. As shown in Fig. 2a, the change trends of DMY in the three runs were similar. Run 18 obtained the highest CMY of 225.75 mL /gVS, followed by Run 11 of 206.95 mL /gVS, and Run 12 of 185.63ml /gVS (Fig. 2b). These results indicate that the appropriate addition of biochar can significantly promote methanogenesis, but high dose biochar would negatively affect methane yield. According to previous reports, the alkaline functional groups on the surface of biochar can improve the buffering capacity and stability of AD process (Qi et al., 2021b), effectively alleviate acid accumulation and provide a stable pH environment for methanogenic microorganisms. However, it is worth noting that AD requires a neutral environment, excessive biochar will cause the pH value of the digesting slurry increase, which will also inhibit the activity of anaerobic microorganisms (Cui al., 2021). Interestingly, the methane yield of Run 12 started 3 and 5 days earlier than those of Run 11 and Run 18, respectively. In terms of methane content (Fig. 2c), Run 12 was higher than these of Run 11 and Run 18. In fact, compared to Run 11 and Run 18, the pH of Run12 increased quickly after slight acidification. This provided a suitable environment forthe rapid growth of methanogenic microorganisms in Run12 and further improved methane content (Qi et al., 2021a).
3.2.3 Effect of Fe3O4 on methane yield
The effect of Fe3O4 on the AD characteristics of AP and CS is shown in Fig. 3. As shown in Fig. 3a, the maximum DMY of Run 14 was 16.46 mL /gVS on the 19th day, followed by 12.39 ml /gVS for Run 18 and 11.13 mL/gVS for Run 13. The CMY of Run 14 (223.61 mL/gVS) and Run 18 (225.75 mL/gVS) were close (Fig. 3b), both much larger than that of Run 13 (198.35 mL/gVS). With the Fe3O4 increased, the methane yield first increased and then decreased. Feng et al.(2014) and Zhao et al.(2018) reported that the addition of Fe3O4 could enhance the activities of major enzymes related to hydrolysis and acidification, and promote the possible direct interspecific electron transfer between bacteria and methanogenic archaea. However, the acceleration effect was at the low level, and high dose addition reduced methane yield, due to toxic effects on bacteria and methanogenic microorganisms (Kunatsa and Xia, 2022). The variation trend of methane content in these three runs was similar (Fig. 3c). Different from the CMY, The maximum methane content of 67.39% was obtained in Run 13 on the 25th day and obviously higher than those in Run 18 and 14. This indicates that a higher dose of Fe3O4 performed a a positive effect on methane content (Feng et al., 2014). Figure 3c shows that the variation trend of pH in these 3 Runs tended to be semblable, indicating that Fe3O4 had no significant effect on the pH of AD (p > 0.05).
3.3 Interaction effects of TS, biochar and Fe3O4 on AD characteristics of AP and CS
Interactions between different factors would affect methane yield, so regression models were employed to determine the interaction of different factors on methane yield (Hagos et al., 2017). Figure 4 shows the response surface and contour plot of the interaction effects of different factors on methane production. When the code value of Fe3O4 was 0 (12.5 g/kg), the response surface Eq. (3) was as follows:
$${\text{y}}=230.44 - 48.82{x_1} - 52.09x_{1}^{2} - 12.07x_{2}^{2}+49.65{x_1}x_{2}^{2}+60.53x_{1}^{2}x_{2}^{2}$$
3
Figure 4a and Fig. 4b show the response surface and contour of TS% and biochar. The response surface changed greatly, and the contour was irregularly circular, indicating that there was a significant effect between TS and biochar (Zhu et al., 2021). This might be due to the significant effect of high-order items in the regression model (p < 0.05). When the factors changed, high-order terms had a greater impact on the response value (methane yield). In the lower TS% range (< 10%), the methane yield first increased and then decreased with the addition of biochar. When large amounts of acidic intermediates accumulated, the alkaline properties of biochar began to neutralize acids, ensuring a suitable living environment for microorganisms (Zhao et al., 2020). However, the alkaline properties of biochar should to be rationally utilized. Too high addition might cause acid neutralization imbalance and form an alkaline environment, which is also not conducive to the survival of microorganisms. When biochar was maintained at a constant content, methane yield increased first and then decreases with the increase of TS%. Obviously, excessive organic loading rate led to serious acidification and inhibited the activity of methanogens (Indren et al., 2020). It can be seen from Fig. 4a that at a high level of TS%, methane yield dropped sharply at the larger code, and even stopped biogas production when the code is β, indicating that biochar could not completely alleviate acid accumulation when severe acid inhibition occurred in the AD system.
The increased biochar addition might decrease the mass transfer rate, and further lead to a decrease in methane yield, which was consistent with the results reported by Indren et al.(2020). It should be noted that in the regression model analysis in Table 4, the interaction between TS and biochar was not significant (p > 0.05), and the results obtained by the above two methods were contradictory, which might be because the P-value only indicates whether the experimental data is statistically significant or not, and cannot fully represent the significance in practical applications. The P-value needs to be considered in combination with practical issues (Yang et al., 2022).
Figure 4c and Fig. 4d show the response surface and contour plot of the interaction effects of TS% and Fe3O4. When the code value of biochar was 0 (5%), the response surface Eq. (4) was as follows:
$${\text{y}}=230.44 - 48.82{x_1} - 11.48{x_3} - 16.61{x_1}{x_3} - 52.09x_{1}^{2} - 6.88x_{3}^{2}$$
4
The contour in Fig. 4d was arc-shaped, indicating that there was a very significant interaction between TS% and Fe3O4 (P < 0.001). Figure 4c shows that when TS% was constant, the methane yield increased first and then decreased with the increase of Fe3O4. This might be because trace metals (such as iron, cobalt, and nickel) are cofactors and basic components of enzymes. Adding trace metals to the AD could stimulate and stabilize the performance of the biogas process, but the high content of trace elements could inhibit the biodegradation process (Abdelsalam et al., 2017). When Fe3O4 was fixed, the methane yield first increased and then decreased with the increase of TS%, showing a greater change range compared to that in the case of varying Fe3O4 with constant TS. According to the response equation, both the two factors had a primary term and a quadratic term, and the coefficient of TS% was larger than Fe3O4, so the change of methane yield with TS% was greater than Fe3O4.
Figure 4e and Fig. 4f show the response surface and contour plot of the interaction effects of biochar and Fe3O4. When the code value of TS% was 0 (12%), the response surface Eq. (5) was as follows:
$${\text{y}}=230.44 - 11.48{x_3} - 7.24{x_2}{x_3} - 12.07x_{2}^{2} - 6.88x_{3}^{2}$$
5
The contour in Fig. 4f was oval, showing that there was a significant interaction between biochar and Fe3O4 (P < 0.05). As can be seen from Fig. 4e, a great change was presented in methane yield. It might be attributed to the Fe3O4\(\)addition slowly dissolved into Fe2+and Fe3+ in the AD system, which could enhance the activity of methanogen microorganisms and promote direct interspecific electron transfer (Zhang et al., 2020a). When a small amount of Fe3O4 (< 12.5 g/kg) was added, the methane yield first increased and then decreased with the increase of biochar, indicating that the role of biochar in buffering acidification was effective, and the accumulation of acid was controlled within a certain range. Interestingly, the increase in methane yield still occurred in the case of the highest biochar and lower Fe3O4 additions, indicating that the negative effect of a high content of biochar was less than the positive stimulating effect of Fe3O4 on microorganisms. Judging from the regression equation, there were multiple \({\text{x}}_{3}\) in the model instead of x2, which further demonstrated that Fe3O4(\({\text{x}}_{3}\))had a greater impact on methane production than biochar (\({\text{x}}_{2}\)).
3.4 Optimisation of operational parameters
The methane yield can directly reflect the AD performance of raw materials (Cui al., 2021). Based on the experimental results and statistical analysis, the operation parameters were numerically optimized and the optimal level corresponding to the expected value was established.
Figure 5 presents the perturbation analysis of different parameters to the AD. x1, x2 and x3 represents TS%, biochar and Fe3O4, respectively, and the ordinate is methane yield. The gradient of the parabola could be used to determine the impact of these three factors on methane yield (Deng et al., 2019). As can be seen from Fig. 5a, the gradient of TS% was the largest, indicating that TS% had the most significant effect on the response value of methane yield (p < 0.0001). This was consistent with the results in Section 3.1 that the TS% was the most significant factor among the three factors. Figure 5 (b) (c) (d) are the univariate perturbation curves of TS%, biochar, and Fe3O4 on methane yield analyzed by Design expert 10.0. In Fig. 5b, the optimal TS % was 9.67% at the code value of -0.47. The methane yield first rose and then decreased with the increase of TS%. When TS% was greater than 9.67%, the methane yield decreased rapidly because of a higher organic loading rate, which inhibited the overall methanogenesis process. In Fig. 5c, the optimal value of biochar was 5.51% at the code value of 0.26. The methane yield also first increased and then decreased with the increase of biochar. When biochar was greater than 5.51%, the methane yield began to decrease, which may be caused by the alkaline properties of biochar. In Fig. 5d, the optimal value of Fe3O4 was 8.41 g at the coding value of -0.82. Methane yield increased slowly with the increase of Fe3O4, but when the amount of Fe3O4 was more than 8.41 g/kg, the methane yield decreased rapidly, and the high dose of Fe3O4 had negative effects on biogas production, showing the phenomenon of "low promotion but high inhibition" (Wang et al., 2021). Therefore, the optimal values of TS%, Fe3O4 and biochar were 9.67%, 8.41 g/kg and 5.51%, respectively.