Bioresource Technology 173 (2014) 168–176
Contents lists available at ScienceDirect
Bioresource Technology journal homepage: www.elsevier.com/locate/biortech
Predicting the methane yield of lignocellulosic biomass in mesophilic solid-state anaerobic digestion based on feedstock characteristics and process parameters Fuqing Xu a,c, Zhi-Wu Wang b, Yebo Li a,⇑ a Department of Food, Agricultural and Biological Engineering, The Ohio State University/Ohio Agricultural Research and Development Center, 1680 Madison Ave., Wooster, OH 44691, USA b The Ohio State University ATI, 1328 Dover Rd, Wooster, OH 44691, USA c Environmental Science Graduate Program, The Ohio State University, USA
h i g h l i g h t s Methane yields in solid-state anaerobic digestion of plant biomass was predicted. Artificial neural network and multiple linear regression models were applied. Inoculation size, extractives, cellulose and lignin contents were essential factors. Interaction between lignin content and inoculation size was a significant factor. Higher prediction accuracy was obtained with the ANN model.
a r t i c l e
i n f o
Article history: Received 21 July 2014 Received in revised form 16 September 2014 Accepted 17 September 2014 Available online 28 September 2014 Keywords: Lignocellulosic biomass Methane Model Artificial neural network Multiple linear regression
a b s t r a c t In this study, multiple linear regression (MLR) and artificial neural network (ANN) models were explored and validated to predict the methane yield of lignocellulosic biomass in mesophilic solid-state anaerobic digestion (SS-AD) based on the feedstock characteristics and process parameters. Out of the eleven factors analyzed in this study, the inoculation size (F/E ratio), and the contents of lignin, cellulose, and extractives in the feedstock were found to be essential in accurately determining the 30-day cumulative methane yield. The interaction between F/E ratio and lignin content was also found to be significant. MLR and ANN models were calibrated and validated with different sets of data from literature, and both methods were able to satisfactorily predict methane yields of SS-AD, with the lowest standard error for prediction obtained by an ANN model. The models developed in this study can provide guidance for future feedstock evaluation and process optimization in SS-AD. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Lignocellulosic biomass such as crop residuals, switchgrass, miscanthus, yard trimmings, and forestry wastes offers an abundant organic carbon resource for bioenergy production (U.S. Department of Energy, 2011). Its organic components, such as cellulose, hemicellulose, protein, and lipids, can be metabolized by microbes into various types of biofuel, such as ethanol, butanol, and biogas (Zheng et al., 2014). The bioenergy produced from lignocellulosic biomass is considered to be renewable, locally available, and ‘‘carbon neutral’’ (Karthikeyan and Visvanathan, 2013; Weiland, 2010).
⇑ Corresponding author. E-mail address: [email protected] (Y. Li). http://dx.doi.org/10.1016/j.biortech.2014.09.090 0960-8524/Ó 2014 Elsevier Ltd. All rights reserved.
Solid-state anaerobic digestion (SS-AD), namely an anaerobic digestion (AD) system that operates at a total solids (TS) content higher than 15%, is a promising technology for converting lignocellulosic biomass to renewable energy in the form of biogas (about 50–75% CH4 and 25–50% CO2) (Verma, 2002; Weiland, 2010). SS-AD is considered to be more suitable for treating lignocellulosic biomass than traditional liquid AD (L-AD) due to the reduced floating and stratification problems associated with fibrous materials (Karthikeyan and Visvanathan, 2013; Li et al., 2011a). The lower water content in SS-AD also results in smaller reactor volume and less heating energy (Forster-Carneiro et al., 2007; Li et al., 2011a). Besides, the volumetric methane productivities (volume of CH4 produced per digester volume) of several types of lignocellulosic biomass were found to be 2–7 times higher in SS-AD than in
169
F. Xu et al. / Bioresource Technology 173 (2014) 168–176
L-AD (Brown et al., 2012). The end product of SS-AD is a stackable material that can be used as soil amendment (Li et al., 2011a). Due to increasing interest in renewable energy production via SS-AD of lignocellulosic biomass, many experimental studies have been conducted to determine the biochemical methane potential (BMP) of various feedstocks (Angelidaki et al., 2009; Gunaseelan, 2004; Raposo et al., 2012). Statistical analysis has shown that the BMP of a feedstock is predictable based on its characteristics, such as volatile solids (VS) content and the content of cellulose, hemicellulose, and lignin. Among these, lignin content has been regarded as one of the essential factors that have restricted BMP (Brown et al., 2012; Buffiere et al., 2006; Liew et al., 2012; Tong, 1990). Besides these feedstock characteristics, methane yield is also dependent on the actual AD operating conditions. This is especially true in SS-AD, where operating parameters are significantly different from those in BMP tests (Angelidaki et al., 2009; Li et al., 2011a). For example, one important parameter was the inoculation size, which can be expressed as the feedstock-to-inoculum (F/I) ratio, substrate-to-microbe (S/I) ratio, or feedstock-to-effluent (F/E) ratio used in this study. Reactors with lower F/E ratios have been found to start up faster and obtain higher methane yields (Forster-Carneiro et al., 2008; Xu et al., 2013). Other key factors that have been found to affect the performance of SS-AD include temperature, TS content, carbon-to-nitrogen (C/N) ratio, particle size of the feedstock, concentration of inhibitors (e.g. ammonia), and alkalinity of the system (Karthikeyan and Visvanathan, 2013; Li et al., 2011a; Shi et al., 2014). To date, there is still a lack of practical models that are able to predicate the methane yield in SS-AD. All conventional methods, which rely on lab experiments, are usually time consuming and labor intensive (Triolo et al., 2011). Besides, the results obtained between different research labs are usually not comparable due to discrepancies in materials and experimental procedures (Angelidaki et al., 2009; Raposo, 2011). Using data-driven models such as statistical and artificial neural network (ANN) methods may help predict SS-AD performance without extensive lab experiments (Triolo et al., 2011). Multiple linear regression (MLR) is a statistical method that has been widely used for the prediction of BMP of feedstocks (Gunaseelan, 2009; Raposo, 2011). MLR can help identify the significant variables in AD performance and achieve the needed monitoring and prediction accuracy with reduced laboratory analyses (Gunaseelan, 2009; Schievano et al., 2008). Therefore, MLR holds potential for SS-AD performance prediction. ANN is another potential mathematical method that is capable of using data
patterns to predicate the performance of complex systems like AD, where the input and output variables might be non-linear, highly redundant, and interact with each other (Ozkaya et al., 2007). ANN models have been previously applied to several wastewater digestion systems and successfully predicted methane production and system performance under various process conditions (Ozkaya et al., 2007; Sinha et al., 2002). However, to our knowledge, no application of ANN models has been found for AD of lignocellulosic biomass. The objective of this research was to develop practical data-driven models to predict the methane yields of SS-AD with different lignocellulosic feedstocks and process parameters. Both MLR and ANN methods were employed to analyze and quantify the contribution of feedstock, inoculum characteristics, AD process parameters, as well as the interactions between these factors to the methane yield. Although the accurate prediction of methane yield could be difficult due to the complexity of the SS-AD process, in which microbiological, biochemical, and physicochemical factors are closely linked and interact (Angelidaki et al., 2009), the outcome may help reduce experimental workload in optimizing the SS-AD process and identify those key parameters that govern SS-AD performance. 2. Methods 2.1. Data collection and structure Data utilized in this study consisted of 50 data points that were collected from ten publications. In order to prepare these literature data for statistical analysis, the explanatory variables were categorized into: (i) feedstock characteristics (VS, cellulose, xylan, lignin, and extractives contents and digestibility and sugar yield) (Table 1), (ii) inoculum characteristics (alkalinity and ammonia concentration), and (iii) SS-AD process parameters (F/E ratio, TS, C/N ratio, and particle size) (Table 2). The response variable was defined as the 30-day methane yield (Table 2). Data from Li et al. (2011b) were recalculated to convert the 40-day biogas yields to 30-day methane yields. Because some feedstocks have been used in several publications, their characteristics were summarized as ranges (Tables 1 and 2). The sugar yields and digestibility in Table 1 were obtained from enzyme hydrolysis of the feedstocks as defined in studies by Cui et al. (2011) and Liew et al. (2012). The extractives in Table 1 were defined as the combination of water and ethanol soluble materials in feedstocks, such as free sugars, oligomers, and organic acids, that can be quickly and easily converted to methane (Liew et al., 2012). To minimize the interference of other
Table 1 Data range of feedstock characteristics. Feedstock
VS
Extractives
Lignin
Cellulose
Xylan
Digestibility
Sugar yield
6.5–9.9 13.4–17.0 11.9 34.7–43.0 14.7–17.8 9.6–17.0 5.1 14.2
15.2–18.6 15.2–17.4 17.8 22.7–23.1 22.1–26 27.1–32.9 22.0 28.3
33.7–41.3 32.3–37.9 32.3 11.1–12.2 21.7–27.4 23.3–30.8 36.5 26.0
15.3–22.6 15.2–21.8 16.7 4.2–11.5 9.0–14.2 11.5–15.9 9.2 4.4
14.4–17.0 13.6–15.8 6.4 12.5–14.3 6.5–10.4 15.3 10.2 15.3
7.9–9.0 7.5–10.3 3.14 2.3–2.9 2.4–3.7 4.7–5.3 4.7 4.7
g/100 g dry biomass Corn stover1 Wheat straw2 Switchgrass3 Leaves4 Yard trimming5 Tree trimming6 Maple wood7 Pine wood8 1 2 3 4 5 6 7 8
81.9–96.0 83.4–94.7 89.9 86.9–93.0 91.7–96.5 98.9–99.6 92.2 90.5
Brown et al. (2012), Li et al. (2011b), Liew et al. (2012), Shi et al. (2013), Xu et al. (2013), Xu and Li (2012), Zhu et al. (2010). Brown et al. (2012), Cui et al. (2011), Liew et al. (2012). Brown et al. (2012). Brown et al. (2012), Liew et al. (2011). Yard waste in Brown et al. (2012), Liew et al. (2012). Yard trimming in Cherosky (2012), Zhao et al. (2014). Brown et al. (2012). Brown et al. (2012).
170
F. Xu et al. / Bioresource Technology 173 (2014) 168–176
Table 2 Methane yields of selected lignocellulosic biomass at various process conditions. Feedstock
Inoculum characteristics
F/E ratio
Particle size (mm)
C/N ratio
TS (%)
CH4 yield (L/kgVSfeed)
TAN (gN/kg)
Alkalinity (gCaCO3/kg)
Corn stover1
2.9–4.2
13.2–19.9
2–3 4 5–7
5–13 9–13 5–13
15.1–39.0 22.9–26.9 21.4–29
18.5–27 22 22
80.0–157.3 53–101 5–8.3
Wheat straw2
3.3–4.2
13.2–18.3
2–3 4 6
5–9 5–9 5
19.1–36 19.1–36 30.3
18.5–22 22 22
66–130 63–95 8
Switchgrass3
3.3
13.2
3
5
43
18.5
125
Leaves
3.3–4.2
8.9–18.3
2–3 4 5–8
5–9 9 9
18.3–21.5 18–24.1 22–26.1
18.5–22 20–22 20–26
47–75 26–65 1–13
Yard trimming5
3.3–4.2
13.2–18.3
2–4 5
5–9 9
20.3–31.5 31.8
18.5–22 22
32–50 8
Tree trimming6
2–2.9
14.5–16.5
2 4
5–13 5–13
17.8 27–34.9
13.9 13.9–20
10.5–15.5 9.5–18
Maple wood7
3.3
13.2
3
5
50.3
18.5
45
Pine wood8
3.3
13.2
3
5
64.2
18.5
20
4
1
F/E = 2–3: Li et al. (2011b), Liew et al. (2012), Shi et al. (2013), Xu et al. (2013), Xu and Li (2012), Brown et al. (2012); F/E = 4: Liew et al. (2012), Xu and Li (2012); F/E = 5– 7: Liew et al. (2012), Xu et al. (2013), Xu and Li (2012), Li et al. (2011b). 2 F/E = 2–3: Brown et al. (2012), Liew et al. (2012); F/E = 4: Cui et al. (2011), Liew et al. (2012). F/E = 6: Cui et al. (2011). 3 Brown et al. (2012). 4 F/E = 2–3: Brown et al. (2012), Liew et al. (2011); F/E = 4: Liew et al. (2011, 2012); F/E = 5–8: Liew et al. (2011). 5 Yard waste in the original references. F/E = 2–4: Brown et al. (2012) and Liew et al. (2012); F/E = 5: Liew et al. (2011, 2012). 6 Yard trimming in the original references. F/E = 2: Cherosky (2012); F/E = 4: Cherosky (2012), Zhao et al. (2014). 7 Brown et al. (2012). 8 Brown et al. (2012).
factors that are not listed in Tables 1 and 2 in this study, we excluded those data that were obtained with feedstock pretreatment, chemical addition, or co-digestion. Due to limited data availability in literature, factors such as inoculum source, digester operating temperature, and TS were not considered in this study, and only data from mesophilic digesters using sewage sludge digester effluent as inoculum were collected. Therefore, this study only focused on mesophilic AD systems with digested sewage sludge as inoculum, un-pretreated lignocellulosic biomass as the sole substrate, and a TS content around 20%. 2.2. Statistical analysis Two-sample t-test with a threshold p-value of 0.05 was applied to analyze the compositional difference between different types of lignocellulosic biomass using R-project software 3.0.2. Principal component analysis (PCA) was conducted to analyze the correlations between explanatory variables and methane yield based on their correlation matrix, with values standardized by the maximum value of each variable. The PCA was carried out using PC-ORD version 5 (MjM Software, Gleneden Beach, OR, USA). Multiple linear regression (MLR) is a statistical technique that uses several explanatory variables to predict the outcome of a response variable. The goal of MLR is to model the relationship between the explanatory and response variables. In this study, MLR models were developed using R-project software 3.0.2. based on the key variables screened by PCA and a two-way interaction plot to predict the methane yield of SS-AD. The artificial neural network (ANN) is a computational method capable of machine learning as well as pattern recognition. In this study, three ANN models were developed to predict methane yield with different combinations of input variables using software RapidMiner Studio 5 (RapidMiner, Cambridge, MA, USA). The first model, namely ANN_full model, was developed using all input variables without selection. The second model, namely ANN_significant model, only adopted significant variables identified from MLR. The third model, namely ANN_simple model, adopted
variables that are easily measured or controlled, including F/E ratio, VS and particle size of the feedstock, and the TS and C/N ratio of the digester contents. Feed-forward neural network models were trained by a back propagation algorithm, with a training cycle of 500 and learning rate of 0.3. Different numbers of hidden layers (0–3) and numbers of nodes (0–6) in each layer were tested for model calibration, and the model with the best prediction was chosen. Although in many other ANN models more than one layer was required to accurately model the experimental data, in this research, the best model was obtained when the number of hidden layers was zero. Twenty percent of the 50 data points were used for model validation, which were from three independent studies (Liew et al., 2011; Xu and Li, 2012; Xu et al., 2013). Forty data points from other published literature summarized in Tables 1 and 2 were used for model calibration of MLR, ANN, and PCA analysis. Out of the 10 validation data points, one was removed because its F/E ratio (8.2) was out of the calibration range. The intercept of MLR models was set to go through zero because methane yield should be zero when all input variables are zero. Standard error for prediction (SEP) was calculated using the following equation to check prediction accuracy:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n uX b i Y i Þ2 SEP ¼ t ð Y
ð1Þ
i¼1
b i is the ith model predicted value and Yi is ith corresponding where Y measured value. Theoretically, a smaller SEP value indicates better prediction accuracy. 3. Results and discussion 3.1. Statistical analysis of the composition of lignocellulosic biomass Although all feedstock summarized in Table 1 belong to the family of lignocellulosic biomass, they can be classified into
F. Xu et al. / Bioresource Technology 173 (2014) 168–176
herbaceous biomass (corn stover, wheat straw, and switchgrass) and woody biomass (leaves, yard waste, yard trimmings, maple wood and pine wood) (Tong, 1990). As can be seen in Table 1, herbaceous biomass generally had cellulose contents higher than 32%, xylan contents higher than 16%, lignin contents lower than 19%, and extractives contents less than 17%. In contrast, woody biomass generally had cellulose contents less than 30%, xylan contents less than16%, lignin contents of more than 22%, and extractives contents of more than 10%. A t-Test of the two types of lignocellulosic biomass showed that the average cellulose and xylan contents, and the sugar yields of herbaceous biomass were significantly higher than those of woody biomass (p < 0.05), (5%) and the average lignin and extractives contents of herbaceous biomass were significantly lower than those of woody biomass (p < 0.05). However, no significant difference was found in VS between the two types of lignocellulosic biomass as indicated by p > 0.05, with the average VS contents of both types of biomass around 92.5%. It should be pointed out that the composition of maple wood in Table 1 is close to herbaceous biomass in terms of cellulose content (36%) and extractives contents (5%). Its major difference from herbaceous biomass lies in its high lignin content (22%). Thus, lignin content appears to be the best indicator for differentiating the two types of lignocellulosic biomass. As a result, eight types of biomass were classified into a low lignin (herbaceous biomass) or a high lignin (woody biomass) group for further analysis as discussed in Section 3.3. 3.2. Principal component analysis (PCA) of explanatory variables Principal component analysis (PCA) was used to analyze the correlation among explanatory variables and their correlations with methane yield. As the PCA biplot shows in Fig. 1, each vector represents an individual variable, and the correlation between any two variables is determined by the cosine value of the angle between the two vectors, which ranges between 1 and 1. Simply speaking, two vectors pointing toward similar directions are highly positively correlated (cosine ? 1); two vectors pointing toward opposite directions are highly inversely correlated (cosine ? 1); while two vectors with an angle close to 90° are highly independent (cosine ? 0) (Appels et al., 2011; Gabriel, 1971). The length of a variable vector represents its weight on each axis (principal
Fig. 1. Analysis of explanatory variables by PCA. PC1 is the first principal component and PC2 is the second principal component.
171
component) and indicates the relative importance of each principal component. Based on the principles above, Fig. 1 suggests that feedstock characteristics such as cellulose content were very positively correlated with methane yield; extractives and lignin were very inversely correlated with methane yield (Fig. 1). The xylan content, on the other hand, was loosely correlated with methane yield. The feedstock VS appears to be in a low and inverse correlation with methane yield, which might be attributed to the fact that several woody feedstocks containing very high VS content gave low methane yields as shown in Tables 1 and 2. For SS-AD inoculum properties and process parameters in Fig. 2, only the F/E ratio had a strong and inverse correlation with methane yield. This result is in agreement with previous studies that reported increasing the F/E ratio significantly reduced methane yield in SS-AD, which is probably due to the reduced microbial population and alkalinity at high F/E ratios (Shi et al., 2014). Fig. 1 shows the particle size was in an inverse correlation with methane yield. This is understandable in view of small particle size providing high specific surface area favorable for SS-AD of lignocellulosic biomass (Cherosky, 2012; Li et al., 2011b). Although in some literature, small particle size can cause excessive hydrolysis, leading to quick volatile fatty acids (VFA) accumulation (Motte et al., 2013; Zheng et al., 2014), or result in slurry consistency of the digestate and limit gas transfer (Abbassi-Guendouz et al., 2012), the reduction of particle size in this study (from 13 to 5 mm) did not cause inverse effects. For the other process parameters such as C/N ratio, TS of the digestate, and the alkalinity and ammonia content of inoculum, their vectors were almost orthogonal to the methane yield vector,
Fig. 2. Interaction of F/E ratio with (a) feedstock type and (b) lignin level on methane yields.
172
F. Xu et al. / Bioresource Technology 173 (2014) 168–176
indicating very little correlation (Fig. 1). The narrow range of data collected in this study, as mentioned in Section 2.1, might lead to this low correlation. For example, the collected C/N ratios mostly ranged from 18 to 30, which were regarded as suitable for SS-AD (Li et al., 2011a). The low correlation between C/N ratio and methane yield in Fig. 1 suggested that, as long as the C/N ratio fell within this suitable range, the exact value of the C/N ratio might not strongly affect methane yield. A similar explanation also applies to alkalinity and ammonia content in Fig. 2. In SS-AD of lignocellulosic biomass, ammonia and alkalinity contribute to nitrogen supplementation and reactor pH stabilization (Shi et al., 2014; Wang et al., 2013). Therefore, since their values were all within the acceptable range, they may not have significant influence on methane yield. Based on this PCA analysis, some less correlated explanatory variables, such as the ammonia concentration and alkalinity in inoculum, and the TS and C/N ratio of the digestate, can be ignored in further analysis.
methane yield in PCA, including F/E ratio, particle size, and VS, lignin, cellulose, xylan, and extractives contents in feedstock. Interactions between F/E ratio and feedstock characteristics, including lignin, cellulose, and extractives contents were also included. As the correlation between F/E ratio and methane yield might not be linear (Fig. 2a), models with quadratic and cubic terms of F/E ratio were also developed and tested. During the multiple regression analysis, insignificant variables as indicated by a p value higher than 0.1 were removed, including VS of feedstock, xylan content except for Eq. (3), particle size, and interactions of F/E ratio with cellulose and extractives. Finally three MLR models were obtained as shown in Eqs. 2–4:
3.3. Two-way interaction plot of explanatory variables
Y ¼ 3:83X cel þ 3:04X ext 12:16X lig þ 3:11FE3 41:85FE2 þ 98:32FE
Two-way interaction plots of explanatory variables were created in order to check for any interactive effect on methane yield. Yard and tree trimmings, maple wood, and pine wood were combined as trimmings, because of the limited range of F/E ratio for each type of feedstock. Similarly, switchgrass was not shown on the figure as only one F/E ratio was available. In the two-way interaction plot, if two factors do not have interactive effect on methane yield, the plotted lines for average methane yield will be parallel. However, as shown in Fig. 2a, feedstock type and F/E ratio have strong interaction in their effects on methane yield. For example, at F/E ratios between 2 and 4, corn stover gave the highest methane yield, followed by wheat straw, leaves, and trimmings. At high F/E ratios, e.g., F/E ratios greater than 5, feedstock type did not have much effect on methane yield (Fig. 2a). Further analysis revealed that the interaction shown in Fig. 2a actually can be explained by the interaction between lignin content and F/E ratios observed in Fig. 2b. Fig. 2b shows that the F/E ratio had a higher influence on methane yield when the lignin content of the feedstock was low, and vice versa when the lignin content was high, which was in line with the observation in Fig. 2a. Thus, Fig. 2 suggested that it is necessary to consider the interactions between F/E ratio and lignin content in the latter MLR analysis. Similar interactions were also found between cellulose/extractives content and F/E ratio (Figures not shown). 3.4. Model calibration and validation 3.4.1. Multiple linear regression (MLR) MLR models were developed to predict methane yield based on variables which were found to be more correlated with the
Y ¼ 6:91X cel þ 5:40X ext 8:02X lig 64:21FE þ 2:22FE X lig
ð2Þ
Y ¼ 5:28X cel þ 3:74X ext 6:52X lig 2:17X xy 4:79FE2 þ 1:04FE X lig ð3Þ
þ 2:66FE X lig
ð4Þ
where, the response variable (Y) is 30-day methane yield, L/kgVSfeed; Xcel is cellulose content, %; Xxy is xylan content, %; Xlig is lignin content, %; Xext is extractives content, %; FE is F/E ratio, and FE Xlig represents the interaction between F/E ratio and lignin content. Some previous studies have reported that the lignin contents of feedstocks were linearly associated with methane yields or BMP (Brown et al., 2012; Liew et al., 2012; Tong, 1990), while other research indicated that BMP cannot be predicted by a single parameter, and a combination of two or more variables should be used to provide a better fit (Gunaseelan, 2007, 2009). In this study, lignin content was also found to be the most significant factor among all feedstock characteristics (Table 3); however, MLR analysis showed that lignin alone could not result in satisfactory model fit (R2 = 0.33 and SEP = 38.63 L/kgVSfeed). Nevertheless, none of the individual parameter in Table 3 provided satisfactory fit. In contrast, a combination of multiple feedstock characteristics and F/E ratios offered better regression results (Table 3). The regression coefficient in Eqs. 2–4 of each explanatory variable suggested its correlation with methane yield, i.e., variables with positive coefficients, such as cellulose and extractives contents, may positively contribute to methane yield, while negative coefficients such as lignin and F/E suggested negative correlation. A positive effect of the interaction between F/E ratio and lignin content on methane yield was obtained in MLR, which was in line with the results shown in Fig. 2b. As described earlier, Eqs. 2–4, which were calibrated using data from 40 data points, were further verified using another
Table 3 Regression of methane yields using explanatory variables. Explanatory variables
p-Value
R2
Adjusted R2
SEP
Simple linear regression Lignin (lig) Cellulose (cel) FeedVS FE Extractives (ext) Particle size Xylan (xy)
9.515e–05 7.557e–04 1.207e–03 3.453e–03 5.409e–02 0.1164 0.1242
0.334 0.261 0.2437 0.204 0.094 0.064 0.061
0.316 0.242 0.224 0.183 0.070 0.039 0.036
38.63 40.68 41.16 42.23 45.04 45.80 45.86
Multiple linear regression cel, ext, lignin, FE, FE lig cel, ext, lig, FE2 , FE lig cel, ext, lignin, FE3, FE2, FE, FE lig
Contents lists available at ScienceDirect
Bioresource Technology journal homepage: www.elsevier.com/locate/biortech
Predicting the methane yield of lignocellulosic biomass in mesophilic solid-state anaerobic digestion based on feedstock characteristics and process parameters Fuqing Xu a,c, Zhi-Wu Wang b, Yebo Li a,⇑ a Department of Food, Agricultural and Biological Engineering, The Ohio State University/Ohio Agricultural Research and Development Center, 1680 Madison Ave., Wooster, OH 44691, USA b The Ohio State University ATI, 1328 Dover Rd, Wooster, OH 44691, USA c Environmental Science Graduate Program, The Ohio State University, USA
h i g h l i g h t s Methane yields in solid-state anaerobic digestion of plant biomass was predicted. Artificial neural network and multiple linear regression models were applied. Inoculation size, extractives, cellulose and lignin contents were essential factors. Interaction between lignin content and inoculation size was a significant factor. Higher prediction accuracy was obtained with the ANN model.
a r t i c l e
i n f o
Article history: Received 21 July 2014 Received in revised form 16 September 2014 Accepted 17 September 2014 Available online 28 September 2014 Keywords: Lignocellulosic biomass Methane Model Artificial neural network Multiple linear regression
a b s t r a c t In this study, multiple linear regression (MLR) and artificial neural network (ANN) models were explored and validated to predict the methane yield of lignocellulosic biomass in mesophilic solid-state anaerobic digestion (SS-AD) based on the feedstock characteristics and process parameters. Out of the eleven factors analyzed in this study, the inoculation size (F/E ratio), and the contents of lignin, cellulose, and extractives in the feedstock were found to be essential in accurately determining the 30-day cumulative methane yield. The interaction between F/E ratio and lignin content was also found to be significant. MLR and ANN models were calibrated and validated with different sets of data from literature, and both methods were able to satisfactorily predict methane yields of SS-AD, with the lowest standard error for prediction obtained by an ANN model. The models developed in this study can provide guidance for future feedstock evaluation and process optimization in SS-AD. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Lignocellulosic biomass such as crop residuals, switchgrass, miscanthus, yard trimmings, and forestry wastes offers an abundant organic carbon resource for bioenergy production (U.S. Department of Energy, 2011). Its organic components, such as cellulose, hemicellulose, protein, and lipids, can be metabolized by microbes into various types of biofuel, such as ethanol, butanol, and biogas (Zheng et al., 2014). The bioenergy produced from lignocellulosic biomass is considered to be renewable, locally available, and ‘‘carbon neutral’’ (Karthikeyan and Visvanathan, 2013; Weiland, 2010).
⇑ Corresponding author. E-mail address: [email protected] (Y. Li). http://dx.doi.org/10.1016/j.biortech.2014.09.090 0960-8524/Ó 2014 Elsevier Ltd. All rights reserved.
Solid-state anaerobic digestion (SS-AD), namely an anaerobic digestion (AD) system that operates at a total solids (TS) content higher than 15%, is a promising technology for converting lignocellulosic biomass to renewable energy in the form of biogas (about 50–75% CH4 and 25–50% CO2) (Verma, 2002; Weiland, 2010). SS-AD is considered to be more suitable for treating lignocellulosic biomass than traditional liquid AD (L-AD) due to the reduced floating and stratification problems associated with fibrous materials (Karthikeyan and Visvanathan, 2013; Li et al., 2011a). The lower water content in SS-AD also results in smaller reactor volume and less heating energy (Forster-Carneiro et al., 2007; Li et al., 2011a). Besides, the volumetric methane productivities (volume of CH4 produced per digester volume) of several types of lignocellulosic biomass were found to be 2–7 times higher in SS-AD than in
169
F. Xu et al. / Bioresource Technology 173 (2014) 168–176
L-AD (Brown et al., 2012). The end product of SS-AD is a stackable material that can be used as soil amendment (Li et al., 2011a). Due to increasing interest in renewable energy production via SS-AD of lignocellulosic biomass, many experimental studies have been conducted to determine the biochemical methane potential (BMP) of various feedstocks (Angelidaki et al., 2009; Gunaseelan, 2004; Raposo et al., 2012). Statistical analysis has shown that the BMP of a feedstock is predictable based on its characteristics, such as volatile solids (VS) content and the content of cellulose, hemicellulose, and lignin. Among these, lignin content has been regarded as one of the essential factors that have restricted BMP (Brown et al., 2012; Buffiere et al., 2006; Liew et al., 2012; Tong, 1990). Besides these feedstock characteristics, methane yield is also dependent on the actual AD operating conditions. This is especially true in SS-AD, where operating parameters are significantly different from those in BMP tests (Angelidaki et al., 2009; Li et al., 2011a). For example, one important parameter was the inoculation size, which can be expressed as the feedstock-to-inoculum (F/I) ratio, substrate-to-microbe (S/I) ratio, or feedstock-to-effluent (F/E) ratio used in this study. Reactors with lower F/E ratios have been found to start up faster and obtain higher methane yields (Forster-Carneiro et al., 2008; Xu et al., 2013). Other key factors that have been found to affect the performance of SS-AD include temperature, TS content, carbon-to-nitrogen (C/N) ratio, particle size of the feedstock, concentration of inhibitors (e.g. ammonia), and alkalinity of the system (Karthikeyan and Visvanathan, 2013; Li et al., 2011a; Shi et al., 2014). To date, there is still a lack of practical models that are able to predicate the methane yield in SS-AD. All conventional methods, which rely on lab experiments, are usually time consuming and labor intensive (Triolo et al., 2011). Besides, the results obtained between different research labs are usually not comparable due to discrepancies in materials and experimental procedures (Angelidaki et al., 2009; Raposo, 2011). Using data-driven models such as statistical and artificial neural network (ANN) methods may help predict SS-AD performance without extensive lab experiments (Triolo et al., 2011). Multiple linear regression (MLR) is a statistical method that has been widely used for the prediction of BMP of feedstocks (Gunaseelan, 2009; Raposo, 2011). MLR can help identify the significant variables in AD performance and achieve the needed monitoring and prediction accuracy with reduced laboratory analyses (Gunaseelan, 2009; Schievano et al., 2008). Therefore, MLR holds potential for SS-AD performance prediction. ANN is another potential mathematical method that is capable of using data
patterns to predicate the performance of complex systems like AD, where the input and output variables might be non-linear, highly redundant, and interact with each other (Ozkaya et al., 2007). ANN models have been previously applied to several wastewater digestion systems and successfully predicted methane production and system performance under various process conditions (Ozkaya et al., 2007; Sinha et al., 2002). However, to our knowledge, no application of ANN models has been found for AD of lignocellulosic biomass. The objective of this research was to develop practical data-driven models to predict the methane yields of SS-AD with different lignocellulosic feedstocks and process parameters. Both MLR and ANN methods were employed to analyze and quantify the contribution of feedstock, inoculum characteristics, AD process parameters, as well as the interactions between these factors to the methane yield. Although the accurate prediction of methane yield could be difficult due to the complexity of the SS-AD process, in which microbiological, biochemical, and physicochemical factors are closely linked and interact (Angelidaki et al., 2009), the outcome may help reduce experimental workload in optimizing the SS-AD process and identify those key parameters that govern SS-AD performance. 2. Methods 2.1. Data collection and structure Data utilized in this study consisted of 50 data points that were collected from ten publications. In order to prepare these literature data for statistical analysis, the explanatory variables were categorized into: (i) feedstock characteristics (VS, cellulose, xylan, lignin, and extractives contents and digestibility and sugar yield) (Table 1), (ii) inoculum characteristics (alkalinity and ammonia concentration), and (iii) SS-AD process parameters (F/E ratio, TS, C/N ratio, and particle size) (Table 2). The response variable was defined as the 30-day methane yield (Table 2). Data from Li et al. (2011b) were recalculated to convert the 40-day biogas yields to 30-day methane yields. Because some feedstocks have been used in several publications, their characteristics were summarized as ranges (Tables 1 and 2). The sugar yields and digestibility in Table 1 were obtained from enzyme hydrolysis of the feedstocks as defined in studies by Cui et al. (2011) and Liew et al. (2012). The extractives in Table 1 were defined as the combination of water and ethanol soluble materials in feedstocks, such as free sugars, oligomers, and organic acids, that can be quickly and easily converted to methane (Liew et al., 2012). To minimize the interference of other
Table 1 Data range of feedstock characteristics. Feedstock
VS
Extractives
Lignin
Cellulose
Xylan
Digestibility
Sugar yield
6.5–9.9 13.4–17.0 11.9 34.7–43.0 14.7–17.8 9.6–17.0 5.1 14.2
15.2–18.6 15.2–17.4 17.8 22.7–23.1 22.1–26 27.1–32.9 22.0 28.3
33.7–41.3 32.3–37.9 32.3 11.1–12.2 21.7–27.4 23.3–30.8 36.5 26.0
15.3–22.6 15.2–21.8 16.7 4.2–11.5 9.0–14.2 11.5–15.9 9.2 4.4
14.4–17.0 13.6–15.8 6.4 12.5–14.3 6.5–10.4 15.3 10.2 15.3
7.9–9.0 7.5–10.3 3.14 2.3–2.9 2.4–3.7 4.7–5.3 4.7 4.7
g/100 g dry biomass Corn stover1 Wheat straw2 Switchgrass3 Leaves4 Yard trimming5 Tree trimming6 Maple wood7 Pine wood8 1 2 3 4 5 6 7 8
81.9–96.0 83.4–94.7 89.9 86.9–93.0 91.7–96.5 98.9–99.6 92.2 90.5
Brown et al. (2012), Li et al. (2011b), Liew et al. (2012), Shi et al. (2013), Xu et al. (2013), Xu and Li (2012), Zhu et al. (2010). Brown et al. (2012), Cui et al. (2011), Liew et al. (2012). Brown et al. (2012). Brown et al. (2012), Liew et al. (2011). Yard waste in Brown et al. (2012), Liew et al. (2012). Yard trimming in Cherosky (2012), Zhao et al. (2014). Brown et al. (2012). Brown et al. (2012).
170
F. Xu et al. / Bioresource Technology 173 (2014) 168–176
Table 2 Methane yields of selected lignocellulosic biomass at various process conditions. Feedstock
Inoculum characteristics
F/E ratio
Particle size (mm)
C/N ratio
TS (%)
CH4 yield (L/kgVSfeed)
TAN (gN/kg)
Alkalinity (gCaCO3/kg)
Corn stover1
2.9–4.2
13.2–19.9
2–3 4 5–7
5–13 9–13 5–13
15.1–39.0 22.9–26.9 21.4–29
18.5–27 22 22
80.0–157.3 53–101 5–8.3
Wheat straw2
3.3–4.2
13.2–18.3
2–3 4 6
5–9 5–9 5
19.1–36 19.1–36 30.3
18.5–22 22 22
66–130 63–95 8
Switchgrass3
3.3
13.2
3
5
43
18.5
125
Leaves
3.3–4.2
8.9–18.3
2–3 4 5–8
5–9 9 9
18.3–21.5 18–24.1 22–26.1
18.5–22 20–22 20–26
47–75 26–65 1–13
Yard trimming5
3.3–4.2
13.2–18.3
2–4 5
5–9 9
20.3–31.5 31.8
18.5–22 22
32–50 8
Tree trimming6
2–2.9
14.5–16.5
2 4
5–13 5–13
17.8 27–34.9
13.9 13.9–20
10.5–15.5 9.5–18
Maple wood7
3.3
13.2
3
5
50.3
18.5
45
Pine wood8
3.3
13.2
3
5
64.2
18.5
20
4
1
F/E = 2–3: Li et al. (2011b), Liew et al. (2012), Shi et al. (2013), Xu et al. (2013), Xu and Li (2012), Brown et al. (2012); F/E = 4: Liew et al. (2012), Xu and Li (2012); F/E = 5– 7: Liew et al. (2012), Xu et al. (2013), Xu and Li (2012), Li et al. (2011b). 2 F/E = 2–3: Brown et al. (2012), Liew et al. (2012); F/E = 4: Cui et al. (2011), Liew et al. (2012). F/E = 6: Cui et al. (2011). 3 Brown et al. (2012). 4 F/E = 2–3: Brown et al. (2012), Liew et al. (2011); F/E = 4: Liew et al. (2011, 2012); F/E = 5–8: Liew et al. (2011). 5 Yard waste in the original references. F/E = 2–4: Brown et al. (2012) and Liew et al. (2012); F/E = 5: Liew et al. (2011, 2012). 6 Yard trimming in the original references. F/E = 2: Cherosky (2012); F/E = 4: Cherosky (2012), Zhao et al. (2014). 7 Brown et al. (2012). 8 Brown et al. (2012).
factors that are not listed in Tables 1 and 2 in this study, we excluded those data that were obtained with feedstock pretreatment, chemical addition, or co-digestion. Due to limited data availability in literature, factors such as inoculum source, digester operating temperature, and TS were not considered in this study, and only data from mesophilic digesters using sewage sludge digester effluent as inoculum were collected. Therefore, this study only focused on mesophilic AD systems with digested sewage sludge as inoculum, un-pretreated lignocellulosic biomass as the sole substrate, and a TS content around 20%. 2.2. Statistical analysis Two-sample t-test with a threshold p-value of 0.05 was applied to analyze the compositional difference between different types of lignocellulosic biomass using R-project software 3.0.2. Principal component analysis (PCA) was conducted to analyze the correlations between explanatory variables and methane yield based on their correlation matrix, with values standardized by the maximum value of each variable. The PCA was carried out using PC-ORD version 5 (MjM Software, Gleneden Beach, OR, USA). Multiple linear regression (MLR) is a statistical technique that uses several explanatory variables to predict the outcome of a response variable. The goal of MLR is to model the relationship between the explanatory and response variables. In this study, MLR models were developed using R-project software 3.0.2. based on the key variables screened by PCA and a two-way interaction plot to predict the methane yield of SS-AD. The artificial neural network (ANN) is a computational method capable of machine learning as well as pattern recognition. In this study, three ANN models were developed to predict methane yield with different combinations of input variables using software RapidMiner Studio 5 (RapidMiner, Cambridge, MA, USA). The first model, namely ANN_full model, was developed using all input variables without selection. The second model, namely ANN_significant model, only adopted significant variables identified from MLR. The third model, namely ANN_simple model, adopted
variables that are easily measured or controlled, including F/E ratio, VS and particle size of the feedstock, and the TS and C/N ratio of the digester contents. Feed-forward neural network models were trained by a back propagation algorithm, with a training cycle of 500 and learning rate of 0.3. Different numbers of hidden layers (0–3) and numbers of nodes (0–6) in each layer were tested for model calibration, and the model with the best prediction was chosen. Although in many other ANN models more than one layer was required to accurately model the experimental data, in this research, the best model was obtained when the number of hidden layers was zero. Twenty percent of the 50 data points were used for model validation, which were from three independent studies (Liew et al., 2011; Xu and Li, 2012; Xu et al., 2013). Forty data points from other published literature summarized in Tables 1 and 2 were used for model calibration of MLR, ANN, and PCA analysis. Out of the 10 validation data points, one was removed because its F/E ratio (8.2) was out of the calibration range. The intercept of MLR models was set to go through zero because methane yield should be zero when all input variables are zero. Standard error for prediction (SEP) was calculated using the following equation to check prediction accuracy:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n uX b i Y i Þ2 SEP ¼ t ð Y
ð1Þ
i¼1
b i is the ith model predicted value and Yi is ith corresponding where Y measured value. Theoretically, a smaller SEP value indicates better prediction accuracy. 3. Results and discussion 3.1. Statistical analysis of the composition of lignocellulosic biomass Although all feedstock summarized in Table 1 belong to the family of lignocellulosic biomass, they can be classified into
F. Xu et al. / Bioresource Technology 173 (2014) 168–176
herbaceous biomass (corn stover, wheat straw, and switchgrass) and woody biomass (leaves, yard waste, yard trimmings, maple wood and pine wood) (Tong, 1990). As can be seen in Table 1, herbaceous biomass generally had cellulose contents higher than 32%, xylan contents higher than 16%, lignin contents lower than 19%, and extractives contents less than 17%. In contrast, woody biomass generally had cellulose contents less than 30%, xylan contents less than16%, lignin contents of more than 22%, and extractives contents of more than 10%. A t-Test of the two types of lignocellulosic biomass showed that the average cellulose and xylan contents, and the sugar yields of herbaceous biomass were significantly higher than those of woody biomass (p < 0.05), (5%) and the average lignin and extractives contents of herbaceous biomass were significantly lower than those of woody biomass (p < 0.05). However, no significant difference was found in VS between the two types of lignocellulosic biomass as indicated by p > 0.05, with the average VS contents of both types of biomass around 92.5%. It should be pointed out that the composition of maple wood in Table 1 is close to herbaceous biomass in terms of cellulose content (36%) and extractives contents (5%). Its major difference from herbaceous biomass lies in its high lignin content (22%). Thus, lignin content appears to be the best indicator for differentiating the two types of lignocellulosic biomass. As a result, eight types of biomass were classified into a low lignin (herbaceous biomass) or a high lignin (woody biomass) group for further analysis as discussed in Section 3.3. 3.2. Principal component analysis (PCA) of explanatory variables Principal component analysis (PCA) was used to analyze the correlation among explanatory variables and their correlations with methane yield. As the PCA biplot shows in Fig. 1, each vector represents an individual variable, and the correlation between any two variables is determined by the cosine value of the angle between the two vectors, which ranges between 1 and 1. Simply speaking, two vectors pointing toward similar directions are highly positively correlated (cosine ? 1); two vectors pointing toward opposite directions are highly inversely correlated (cosine ? 1); while two vectors with an angle close to 90° are highly independent (cosine ? 0) (Appels et al., 2011; Gabriel, 1971). The length of a variable vector represents its weight on each axis (principal
Fig. 1. Analysis of explanatory variables by PCA. PC1 is the first principal component and PC2 is the second principal component.
171
component) and indicates the relative importance of each principal component. Based on the principles above, Fig. 1 suggests that feedstock characteristics such as cellulose content were very positively correlated with methane yield; extractives and lignin were very inversely correlated with methane yield (Fig. 1). The xylan content, on the other hand, was loosely correlated with methane yield. The feedstock VS appears to be in a low and inverse correlation with methane yield, which might be attributed to the fact that several woody feedstocks containing very high VS content gave low methane yields as shown in Tables 1 and 2. For SS-AD inoculum properties and process parameters in Fig. 2, only the F/E ratio had a strong and inverse correlation with methane yield. This result is in agreement with previous studies that reported increasing the F/E ratio significantly reduced methane yield in SS-AD, which is probably due to the reduced microbial population and alkalinity at high F/E ratios (Shi et al., 2014). Fig. 1 shows the particle size was in an inverse correlation with methane yield. This is understandable in view of small particle size providing high specific surface area favorable for SS-AD of lignocellulosic biomass (Cherosky, 2012; Li et al., 2011b). Although in some literature, small particle size can cause excessive hydrolysis, leading to quick volatile fatty acids (VFA) accumulation (Motte et al., 2013; Zheng et al., 2014), or result in slurry consistency of the digestate and limit gas transfer (Abbassi-Guendouz et al., 2012), the reduction of particle size in this study (from 13 to 5 mm) did not cause inverse effects. For the other process parameters such as C/N ratio, TS of the digestate, and the alkalinity and ammonia content of inoculum, their vectors were almost orthogonal to the methane yield vector,
Fig. 2. Interaction of F/E ratio with (a) feedstock type and (b) lignin level on methane yields.
172
F. Xu et al. / Bioresource Technology 173 (2014) 168–176
indicating very little correlation (Fig. 1). The narrow range of data collected in this study, as mentioned in Section 2.1, might lead to this low correlation. For example, the collected C/N ratios mostly ranged from 18 to 30, which were regarded as suitable for SS-AD (Li et al., 2011a). The low correlation between C/N ratio and methane yield in Fig. 1 suggested that, as long as the C/N ratio fell within this suitable range, the exact value of the C/N ratio might not strongly affect methane yield. A similar explanation also applies to alkalinity and ammonia content in Fig. 2. In SS-AD of lignocellulosic biomass, ammonia and alkalinity contribute to nitrogen supplementation and reactor pH stabilization (Shi et al., 2014; Wang et al., 2013). Therefore, since their values were all within the acceptable range, they may not have significant influence on methane yield. Based on this PCA analysis, some less correlated explanatory variables, such as the ammonia concentration and alkalinity in inoculum, and the TS and C/N ratio of the digestate, can be ignored in further analysis.
methane yield in PCA, including F/E ratio, particle size, and VS, lignin, cellulose, xylan, and extractives contents in feedstock. Interactions between F/E ratio and feedstock characteristics, including lignin, cellulose, and extractives contents were also included. As the correlation between F/E ratio and methane yield might not be linear (Fig. 2a), models with quadratic and cubic terms of F/E ratio were also developed and tested. During the multiple regression analysis, insignificant variables as indicated by a p value higher than 0.1 were removed, including VS of feedstock, xylan content except for Eq. (3), particle size, and interactions of F/E ratio with cellulose and extractives. Finally three MLR models were obtained as shown in Eqs. 2–4:
3.3. Two-way interaction plot of explanatory variables
Y ¼ 3:83X cel þ 3:04X ext 12:16X lig þ 3:11FE3 41:85FE2 þ 98:32FE
Two-way interaction plots of explanatory variables were created in order to check for any interactive effect on methane yield. Yard and tree trimmings, maple wood, and pine wood were combined as trimmings, because of the limited range of F/E ratio for each type of feedstock. Similarly, switchgrass was not shown on the figure as only one F/E ratio was available. In the two-way interaction plot, if two factors do not have interactive effect on methane yield, the plotted lines for average methane yield will be parallel. However, as shown in Fig. 2a, feedstock type and F/E ratio have strong interaction in their effects on methane yield. For example, at F/E ratios between 2 and 4, corn stover gave the highest methane yield, followed by wheat straw, leaves, and trimmings. At high F/E ratios, e.g., F/E ratios greater than 5, feedstock type did not have much effect on methane yield (Fig. 2a). Further analysis revealed that the interaction shown in Fig. 2a actually can be explained by the interaction between lignin content and F/E ratios observed in Fig. 2b. Fig. 2b shows that the F/E ratio had a higher influence on methane yield when the lignin content of the feedstock was low, and vice versa when the lignin content was high, which was in line with the observation in Fig. 2a. Thus, Fig. 2 suggested that it is necessary to consider the interactions between F/E ratio and lignin content in the latter MLR analysis. Similar interactions were also found between cellulose/extractives content and F/E ratio (Figures not shown). 3.4. Model calibration and validation 3.4.1. Multiple linear regression (MLR) MLR models were developed to predict methane yield based on variables which were found to be more correlated with the
Y ¼ 6:91X cel þ 5:40X ext 8:02X lig 64:21FE þ 2:22FE X lig
ð2Þ
Y ¼ 5:28X cel þ 3:74X ext 6:52X lig 2:17X xy 4:79FE2 þ 1:04FE X lig ð3Þ
þ 2:66FE X lig
ð4Þ
where, the response variable (Y) is 30-day methane yield, L/kgVSfeed; Xcel is cellulose content, %; Xxy is xylan content, %; Xlig is lignin content, %; Xext is extractives content, %; FE is F/E ratio, and FE Xlig represents the interaction between F/E ratio and lignin content. Some previous studies have reported that the lignin contents of feedstocks were linearly associated with methane yields or BMP (Brown et al., 2012; Liew et al., 2012; Tong, 1990), while other research indicated that BMP cannot be predicted by a single parameter, and a combination of two or more variables should be used to provide a better fit (Gunaseelan, 2007, 2009). In this study, lignin content was also found to be the most significant factor among all feedstock characteristics (Table 3); however, MLR analysis showed that lignin alone could not result in satisfactory model fit (R2 = 0.33 and SEP = 38.63 L/kgVSfeed). Nevertheless, none of the individual parameter in Table 3 provided satisfactory fit. In contrast, a combination of multiple feedstock characteristics and F/E ratios offered better regression results (Table 3). The regression coefficient in Eqs. 2–4 of each explanatory variable suggested its correlation with methane yield, i.e., variables with positive coefficients, such as cellulose and extractives contents, may positively contribute to methane yield, while negative coefficients such as lignin and F/E suggested negative correlation. A positive effect of the interaction between F/E ratio and lignin content on methane yield was obtained in MLR, which was in line with the results shown in Fig. 2b. As described earlier, Eqs. 2–4, which were calibrated using data from 40 data points, were further verified using another
Table 3 Regression of methane yields using explanatory variables. Explanatory variables
p-Value
R2
Adjusted R2
SEP
Simple linear regression Lignin (lig) Cellulose (cel) FeedVS FE Extractives (ext) Particle size Xylan (xy)
9.515e–05 7.557e–04 1.207e–03 3.453e–03 5.409e–02 0.1164 0.1242
0.334 0.261 0.2437 0.204 0.094 0.064 0.061
0.316 0.242 0.224 0.183 0.070 0.039 0.036
38.63 40.68 41.16 42.23 45.04 45.80 45.86
Multiple linear regression cel, ext, lignin, FE, FE lig cel, ext, lig, FE2 , FE lig cel, ext, lignin, FE3, FE2, FE, FE lig
