1 Introduction

Nowadays, conventional fossil fuels are replaced by renewable energy sources due to several drawbacks such as emissions that cause global warming, fuel depletion, and other severe environmental impacts. In response to the rise in global energy demand, Biogas Technology (BT) has widely attracted the attention of researchers abided by green energy sources. Lignocellulosic biomass mainly agricultural residues, energy crops, and other municipal wastes can be utilized as a substrate for the most significant energy conversion using anaerobic digestion process (Liew et al. 2011). Moreover, its renewability and ample availability in low cost account these wastes to be a potential raw material for the energy generation. In this context, an increase of 2.5% in the biomass supply for energy has been estimated yearly since 2010. According to the current studies, REN21 (Renewables 2017 global status report 2017) reported that India holds a biogas capacity of 300 MW and many industrial processes follow waste to the energy concept to produce biomethane to tackle waste disposal problems. The use of biomass energy was in two forms: (1) traditional uses and (2) modern uses. Burning of biomass on fire for heating and cooking belongs to traditional uses, whereas the production of bioethanol, biogas, and other biofuels from biomass belongs to the modern use.

Anaerobic digestion (AD) process is the breakdown of the organic matter to produce biogas with the aid of a diverse group of microorganisms. Biogas has a composition of methane, CO2, and traces of other gases. It is the microbial consortium that carries out different activity starting from the hydrolysis phase to methanogenesis phase during the biogas conversion. Anaerobic digestion completes in a series of four metabolic phases: (I) hydrolysis, (II) acidogenesis, (III) acetogenesis, and (IV) methanogenesis. In phase I, the complex organic matter disintegrates into simpler monomers by hydrolysis and microorganism starts their microbial activity after this stage. In phase II, volatile fatty acids (VFA) were formed from the monomer units by fermentative bacteria and called acidogenesis stage. Later, in phase III of acetogenesis, VFAs are converted to acetic acid, H2, and CO2 by acetogens. Finally, in phase IV of the methanogenesis stage, conversion to methane and CO2 takes place through the action of methanogens. This method scores the best option out of all other methods for the environmental balance (Vasco-correa et al. 2018).

1.1 Lignocellulosic biomass: a substrate for biogas production

Plant biomass residues obtained as a by-product from agricultural and industrial processes serve as a sustainable carbon pool for bioenergy production. Plant biomass mainly consists of polymers such as cellulose (40–50%), hemicellulose (20–30%), lignin (10–25%), and traces of extractives (Kim and Dale 2004). Cellulose forms the inner core, and hemicellulose and lignin act as the encrusting material (Anwar et al. 2014; Saini et al. 2015). After hydrolysis, the sugar components such as cellulose and hemicellulose are easily fermentable, which makes them a better feedstock for the biogas production. Cellulose is a polysaccharide polymer of glucose disaccharides, strongly linked with β-1, 4 glycosidic bond and attached with hydroxyl groups forming a linear structure. Within the structure, they differ their orientation leading to different crystallinity levels. At high crystallinity level, the degradation rate of the cellulose reduces (Dulermo et al. 2016). Hemicellulose is a branched and amorphous kind of substance which is readily susceptible to thermal, chemical, and biological hydrolyses. Lignin is the most complex, hydrophobic, aromatic, and amorphous heteropolymers found in biomass. It is made up of sinapyl and coniferyl alcohols forming a firm 3-D structure of cell wall (Guo et al. 2014; Zheng et al. 2014). The lignin hinders the hydrolysis process accounting for the rate-limiting step in the anaerobic digestion process. This hindrance necessitates the application of pretreatment for the lignocellulosic biomass before the AD. The pretreatment causes the lignin degradation and uncovers the hemicellulose and cellulose for the microbial attack to increase the biogas yield. Softwood contains higher lignin content than hardwood and agricultural residues. So, the softwood resists the bioenergy conversion even after pretreatment (Olusola and Omojola 2013).

1.2 Pretreatment methods of lignocellulosic biomass

The application of pretreatment such as physical, chemical, biological, enzymatic, thermal, and their combination on various lignocellulosic biomass helps them to overcome the recalcitrance through structural and chemical changes during hydrolysis.

Physical pretreatment comprises of mechanical (milling and grinding), hydrothermal (liquid or gaseous), irradiation, and extrusion processes (Amin et al. 2017). The hydrothermal treatment (liquid hot water) of sugar beet pulp at 160 °C yielded four times more free glucose than at 120 °C. This glucose yield entailed an increase in the methane yield by 76% when compared with the raw sugar beet pulp (Zieminski et al. 2014). Chemical pretreatment method is a promising and effective method of degrading complex organic substrates using different chemicals with different nature. They can be roughly grouped into alkaline, dilute acid, organosolv (Mancini et al. 2018), oxidizing agents, etc. The reagents involved are sodium hydroxide (NaOH), sodium carbonate (Na2CO3), sodium bicarbonate (NaHCO3), calcium hydroxide, sulphuric acid (H2SO4), acetic acid, citric acid, hydrogen peroxide (H2O2), acetone, ethanol, ammonia, etc. Other inorganic salts such as sodium chloride (NaCl), and calcium chloride (CaCl2). are also used in chemical pretreatments of lignocellulosic biomass (Achkar et al. 2018; Kaur and Phutela 2016a; Pellera and Gidarakos 2017).

Biological pretreatment includes the bacterial and fungal action to rupture the rigid lignocellulosic cell wall. This method accounts to be low cost, inhibition free and environmental friendly with no chemical input, only if an appropriate selection of the microbes (bacterial strain) is done. The only drawback is that it consumes time when compared to other treatment methods (Barua et al. 2018). The recent introduction of the advanced oxidation process in the pretreatment of biomass along with the aid of UV irradiation has glorified the new chances for its combined applications. The studies have revealed that the oxidative fractionation of lignin takes place during the pretreatment and the by-products formed do not cause any inhibitions to the anaerobic digestion process (Alvarado-Morales et al. 2016). Researchers are now more interested in the combination of various pretreatments, i.e., physicochemical, thermochemical, etc. (Alexandropoulou et al. 2016; Ethaib et al. 2018; Kaur and Phutela 2016a). An extensive study on the enhancement of digestibility by enzymatic, ultrasounds, and their combinations by Pérez-Rodríguez, García-Bernet, and Domínguez (2016) have shown some impressive results. They found that ultrasound pretreatment showed a detrimental effect on methane production, whereas the enzymatic hydrolysis showed a beneficial rise in methane production. The relocation of lignin forms a shield over the substrate thereby blocking the biodegradability, which was the prime reason for their detrimental effect. The prior application of ultrasound to the enzymatic hydrolysis did not have much rise in methane generation potential.

1.3 Efficacy of pretreatment method and its issues

The effective pretreatment of biomass involve many key features. The pretreatment option adopted should be a low cost both in capital as well as operational aspects. It should be applicable in wide range and have to be effective in the recovery of most of the biomass components in an amenable form. It should not produce any inhibitory compounds that inhibit the fermentative microorganism growth or the hydrolytic enzymes action and should be energy efficient (Hendriks and Zeeman 2009). The efficacy of pretreatment also depends on the feedstock characteristics (e.g., Lignocellulosic biomass) and in addition to that lignocellulosic biomass in a bulk quantity requires a severe pretreatment (alkali, acidic, thermal, and thermochemical) method (Amin et al. 2017; Costa et al. 2014; Ward-Doria et al. 2016). However, improper implementations of these pretreatments can show negative influence on anaerobic digestion. Nowadays, combined bioethanol–biogas production process is gaining attraction as they contribute to energy-intensive bio refinery platform in near future. Various pretreatment methods have both advantages and disadvantages but process cost and consumption of energy plays a crucial role in selection for process upscaling application. Thus, economic feasibility with the derived benefits in form of waste minimization, biogas production, and digestate as bio fertilizers should be the watchword for the selection of pretreatment method (Noonari et al. 2017). Research on the pretreatment methods are still going on and these parameters considered should balance against the entire cost involved and steps in the down streaming process. It is complicated to evaluate and compare various pretreatment methods as they include total processing (upstream and downstream) cost, initial investment, recycle of chemicals, and treatment systems for wastes. This calls the need for a decision-making in the pretreatment method selection for the given feedstock from the various methods available so that methane yield can be maximized.

1.4 Preliminaries

Multi-attribute decision-making (MADM) is one among the divisions of multi-criteria decision-making (MCDM). MADM helps in making the best possible decisions for various alternatives based on attributes which can be quantitative or qualitative in nature. Several methods were employed in this decision-making model which are outranking, priority, distance, and mixed methods. The methods adopted can be of fuzzy, deterministic, or stochastic in nature or even a combination of the above. Each method differed in its characteristics and systematized into a single decision-making method or a grouped one. In the MADM model, the alternatives were customized from a particular pool of objective functions rather than taking it explicitly. These alternatives were assessed against the set of attributes, and the best from the various alternatives were chosen with respect to the attributes (Pohekar and Ramachandran 2004).

The primary available techniques in MADM modelling is simple additive weight (SAW) method, weighted product method (WPM), compromise and goal programming (CP and GP), technique for order preference by similarity to ideal solution (TOPSIS), Analytical Hierarchical Process (AHP), Elimination and Choice Translation Reality (ELECTRE), Preference Ranking Organisation Method for Enrichment evaluation (PROMETHEE) (Ameri et al. 2018; Dhanisetty et al. 2017; Mousavi-nasab and Sotoudeh-Anvari 2018; Zaman et al. 2018), and Multiple Attribute Utility Theory (MAUT) (Pohekar and Ramachandran 2004). Among the different approaches, TOPSIS and AHP were extensively used for logical decision-making. MADM model has found applications in every field of science and technology for the selection of the best choice from many alternatives. This modelling makes the subtle task of selection to more easier and simpler (Ashby 2000). Rao and Davim (2008) assessed the selection of material by evaluating and ranking the various materials using TOPSIS and AHP techniques of MADM model.

TOPSIS approach is based on the selection of alternatives which has least Euclidean distance from an ideal solution. In the given database, the ideal solution can be hypothetically best or hypothetically worst from the attribute value, assimilating maximum and minimum values, respectively. The choice of alternatives was close enough to hypothetical best and far enough to hypothetical worst. In a decision-making process, tangible and intangible attributes were considered by prioritizing those attributes by comparing one by one. Now, AHP plays a crucial role in the comparison by reducing the difficulty level and making the decision process flexible and helps in forming the relative importance of each parameter (Tan et al. 2013). Expert’s choice of weights played a significant role in the decision-making process and the weights can be given by a single expert or a group of experts. In the real-time application of MADM, uniqueness in the expert's preferences makes them reluctant to assign the specific numerical values for the relative importance matrix. In this regard, the results from MADM techniques were meant to be sensitive to this relative importance (dominance weights) of each attribute. Hence, it is necessary to ascertain a set of unique weights which is very important to make the decision-making process accurate.

The primary intent of this research is to predetermine the best pretreatment method for biogas generation prior to the anaerobic digestion. The study includes the integration of Design of Experiments (DoE) with the TOPSIS approach to tackle the difficulty in assigning weights during the selection process. A comparison in the ranks between integrated DoE–TOPSIS and TOPSIS was accomplished along with this research. According to the previous studies, the DoE–TOPSIS features a set of weights which makes them less sensitive to frame the relative importance or dominance of weights (Sabaghi et al. 2015; Tansel 2012; Yusuf 2014; Wang et al. 2013). The selection of the best pretreatment method was done based on the prioritization results from both the techniques. The direct selection of the pretreatment method can be employed without performing the actual set of AD experiments. Thus, limiting the digesters count to one single digester without compromising the maximum biogas yield.

2 Materials and methods

2.1 Attributes involved in pretreatment and AD process

The varied and complex chemical structure of biomass resists the degradation process. The optimization of the pretreatment method depends on the type of lignocellulosic material. The compositional and structural properties include lignin content, hemicellulose content, silica content, crystallinity index, surface area, the degree of acetylation, and degree of polymerization of cellulose (Zheng et al. 2014). The attributes can be classified as general, physical, and chemical attributes. The physical attributes include Colour, odour, temperature, moisture content, total solids, and volatile solids. Similarly, chemical attributes include pH, alkalinity, volatile fatty acids (VFA), carbon/nitrogen ratio (C/N), chemical oxygen demand, biochemical oxygen demand, sulphates, phosphates, lignin content, silica content, dissolved carbohydrates, lignin/cellulose ratio, uronic acids, heavy metals, inhibitory by-products (such as hydroxymethylfurfural (HMF), furfural, etc.), Ammonia, etc. Other general attributes comprise of the nature of the feedstock, its source, price, seasonal availability and production rate, the age of feedstock, biogas productivity, methane composition, and mode of transport. In the attributes as mentioned earlier, most of them are interdependent. Any variation in one attribute affects the other (Cioabla et al. 2012). These attributes are critical in the case of pretreated lignocellulosic materials for the anaerobic digestion.

The attributes can be mentioned in two ways, i.e., either quantitative or qualitative. Quantitative measurements of attributes are value based, whereas the qualitative measurements are some characteristics such as very poor, poor, average, good, excellent. The conversion of these qualities into some values was done by using a set of scales ranging from 1 to 9 (Rao and Baral 2011).

2.2 TOPSIS approach

TOPSIS method is a widely accepted technique known for its simplicity and user friendly approach for ranking the alternatives according to the ranking score obtained. It is also well known for its easy computational practice, and they can be grouped with other MADM approaches solving the complex problems in structured and easy manner. The advantage of TOPSIS over other methods is that interpreted data can be given directly as input by not considering the past mathematical calculations (Tansel and Ergun 2011; Yusuf 2014). In this study, the methodology was used for the evaluation and ranking of the pretreatment method for the lignocellulosic biomass with due emphasis on attributes. The methodology is as follows: (1) selection of pertinent attribute, (2) TOPSIS analysis, and (3) selection from the priority list (Bhangale et al. 2004; Kumar and Agrawal 2009).

2.2.1 Phase 1: Selection of pertinent attribute

The application-specific attributes were selected from the pool of attributes considered for the pretreated substrate anaerobic digestion. The irrelevant attributes were eliminated.

2.2.2 Phase 2: TOPSIS analysis

The analysis using TOPSIS was done as explained below in steps 1–8.

Step 1: Decision matrix (DM) development:

The decision matrix contains the attribute values corresponding to the alternatives. The attributes were arranged in a column, whereas the alternatives were arranged along the row to form a matrix as given in Eq. 1:

$$D = \left[ {x_{{ij}} } \right]_{{m \times n}},$$
(1)

where, i = 1, 2, 3… m and j = 1, 2, 3… n; m is the number of attributes, n is the number of alternatives.

Step 2: normalized decision matrix (NDM) development.

The computationally efficient and symmetric vector normalization of the decision matrix values brings all attribute values to the same dimensionality (Vafaei et al. 2015; Yang et al. 2017). This transformation process helps in comparing the input data in a common scale and are done using Eq. 2:

$${{r}}_{ij} = \frac{{X}_{ij}}{\sqrt{{\sum }_{u=1}^{m}{{X}{{uj}}}^{2}}},$$
(2)

The rij matrix denotes the normalized decision matrix.

Step 3: relative importance matrix (RIM) development.

The field experts frame the RIM by judging the importance of one attribute to another attribute concerning the problem statement. The scale of judgment was based on the Analytical Hierarchical Process (AHP) by Saaty (2008).

Step 4: formation of Eigenvalues.

The Eigenvalues calculation and the weights associated with each attribute were obtained using MATLAB code. The procedure to find the weights for each criterion was developed by Saaty (2008)and represented as a matrix wij. The determination of consistency index (CI) and consistency ratio (CR) were checked inorder to check the consistency of the judgement. If the CR value is lesser or equal to 0.1, the considered judgemental matrix is consistent in nature (Alonso and Lamata 2006; Kolios et al. 2016).

Step 5: development of a weighted normalized matrix (WNM).

These weights were incorporated into the normalized decision matrix to obtain the weighted normalized matrix. Thus, the values attained for each attribute can be structured to a comparable form and denoted as given in Eq. 3:

$${\text{WNM}},a_{{ij}} = {\text{ }}w_{{ij}} \times r_{{ij}},$$
(3)

Step 6: estimation of ideal best and ideal worst solution.

Let I+ and I− be the ideal best and ideal worst solution for the given attributes. The ideal best and the ideal worst solutions were found by considering maximum and minimum values from the alternatives for each attribute. If the jth attribute is a beneficial factor, it follows as mentioned in Eqs. 4 and 5:

$$I^{ + } = \max \left\{ {a_{{ij}}, i = 1,2,3 \ldots, m} \right\},$$
(4)
$$I^{ - } = \min \left\{ {a_{{ij}} , i = 1,2,3 \ldots, m} \right\},$$
(5)

If the attribute is non-beneficial, consider Eqs. 6 and 7:

$$I^{ + } = \min \left\{ {a_{{ij}} , i = 1,2,3 \ldots, m} \right\},$$
(6)
$$I^{ - } = \max \left\{ {a_{{ij}}, i = 1,2,3 \ldots, m} \right\},$$
(7)

Step 7: calculation of separation measures.

The distance between each attribute and its corresponding ideal positive solution (I+) is called a positive separation measures (PSM). Similarly, the distance between the attributes and the ideal negative solution (I−) is called a negative separation measure (NSM). The PSM and NSM calculations for each alternative are given as mentioned below:

$$S^{{i + }} = \sqrt {\left( {a_{{i1}} - I^{ + } _{1} } \right) + \left( {a_{{i2}} - I^{ + } _{2} } \right) + \cdots + (a_{{in}} - I^{ + } _{n} )}$$
(8)
$$S^{{i - }} = \sqrt {\left( {a_{{i1}} - I^{ - } _{1} } \right) + \left( {a_{{i2}} - I^{ - } _{2} } \right) + \cdots + (a_{{in}} - I^{ - } _{n} )}$$
(9)

Step 8: calculation of TOPSIS score or relative closeness of a particular alternative.

The TOPSIS score or relative closeness of each alternative to its ideal solution is found using Eq. 10:

$${\text{TOPSIS scores}} = \frac{{{\text{S}}^{ - } }}{{{\text{S}}^{ + } + {\text{S}}^{ - } }}$$
(10)

2.2.3 Phase 3: Selection from the priority list

According to the decreasing order of the TOPSIS scores, a ranking list of the alternatives was provided. The alternatives having the same TOPSIS scores have assigned the same rank. The first rank alternative was selected as the best alternative or the best pretreatment method.

2.3 Integrated TOPSIS-DOE approach

Design of experiments (DoE) is a statistical method applied to evaluate the effect of various factors simultaneously. The changes in the input variables (independent variables) are made intentionally to determine their effects on the output variable (dependent variables). In this study, full factorial design (2k) is used to illustrate the variation in the TOPSIS scores with the attributes. The ‘k’ denotes the number of attributes considered in the model. The upper and lower levels of attributes selected for the factorial design is the maximum and minimum values that an attribute can accept. Generally, in the DoE, the critical attributes are determined by fitting the data related to the problem statement to a polynomial in a multiple linear regression analysis (Yusuf 2014). In this design, we try to examine the linear effects of attributes on TOPSIS scores. Figure 1 shows the steps in the integrated TOPSIS–DoE approach.

Fig. 1
figure 1

Application steps of the integrated TOPSIS–DoE approach

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3 Results and discussion

The data for the analysis of model and to select the best pretreatment method to yield maximum biogas (Song et al. 2014) can be referred from Table 1 along with their notations. They have examined the effect of seven pretreatment methods in biogas production under batch mode and on the mesophilic condition. The pretreatments applied were H2SO4 (2%), HCl (2%), CH3COOH (4%), H2O2 (3%), NaOH (8%), Ca(OH)2 (8%), and NH3.H2O (10%).

Table 1 Data considered for modelling (Song et al. 2014)
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3.1 TOPSIS model

3.1.1 Phase 1: Selection of pertinent attribute.

As the main aim of the present decision-making is to maximize the biogas generation, attributes that are highly influencing the methane generation can be considered. Pretreatment option mainly facilitate the reduction in recalcitrance and enhances the methane production. The pretreatment helps in reduction of lignin content can increase the accessibility to cellulose and hemicellulose. From the various attributes considered for pretreatment options, some are interdependent in nature. For example, any reduction in the cellulose, hemicellulose, and lignin content forms the degradation compounds which are inhibitory in nature. Moreover, lignin content shows a negative correlation with the methane production as studied by Monlau et al. (2012). So, cellulose hemicellulose and lignin content can be considered as an important attribute responsible for methane production. The analysis of total carbon and C/N ratio affirmed that on pretreatment the TC decreases and C/N ratio drops down to a range of 20–30 which is crucial for an efficient anaerobic digester performance (Song et al. 2014). Hence, the selected pertinent attributes for the present study was cellulose, hemicellulose, lignin content, total carbon (TC), and C/N ratio. The database for the study was obtained from the batch mode digestion study done by (Song et al. 2014) on corn stalks. The importance is given for the selection of attributes as beneficial and non-beneficial attributes (Bhangale et al. 2004). In this research, the attribute values were considered after pretreatment with cellulose, hemicellulose, total carbon, and C/N ratio as the beneficial attributes and lignin content as the non-beneficial attribute. The selection of the pertinent attributes from the list of attributes primarily depends on the designer's choice by considering economic feasibility, technical difficulty, field conditions, and viability (Rao and Baral 2011).

3.1.2 Phase 2: TOPSIS analysis.

The explanation for the analysis of TOPSIS is given below.

Step 1: decision matrix (DM) development:

The matrix contains the attribute values (column-wise) corresponding to the alternatives (row-wise). The attributes were denoted as ‘A’ and alternatives as ‘P’. In this illustrative example, it forms a 7 × 5 decision matrix and the decision matrix (D) is shown in Eq. 11:

$$D = \left[ {\begin{array}{*{20}c} {{\text{Cellulose}}} & {{\text{Hemicellulos}}e} & {{\text{Lignin}}} & {{\text{TC}}} & {{\text{C/N}}} \\ {41.3} & {22.5} & {7.3} & {30.6} & {38.7} \\ {40.4} & {22.2} & {7.2} & {32.4} & {39.5} \\ {30.4} & {15.1} & {6.7} & {26.4} & {32.2} \\ {30.8} & {14.3} & {5.7} & {25.1} & {30.6} \\ {46.7} & {16.2} & {4.6} & {33.7} & {42.1} \\ {46.3} & {16.4} & {5.4} & {29.4} & {38.7} \\ {45.1} & {17.8} & {5.5} & {30.7} & {37.4} \\ \end{array} } \right]$$
(11)

Step 2: normalized decision matrix (NDM) development.

Vector normalization was done and have made into single dimensionality with values less than 1. The NDM was developed as shown in Eq. 12:

$$NDM = \left[ {\begin{array}{*{20}c} {0.3839} & {0.4712} & {0.4501} & {0.3869} & {0.3929} \\ {0.3756} & {0.4649} & {0.4439} & {0.4096} & {0.4010} \\ {0.2826} & {0.3162} & {0.4131} & {0.3338} & {0.3269} \\ {0.2863} & {0.2995} & {0.3514} & {0.3173} & {0.3107} \\ {0.4304} & {0.3435} & {0.3329} & {0.3717} & {0.3929} \\ {0.4342} & {0.3393} & {0.2836} & {0.4261} & {0.4275} \\ {0.4193} & {0.3727} & {0.3391} & {0.3881} & {0.3797} \\ \end{array} } \right]$$
(12)

Step 3: relative importance matrix development.

The group of experts decides the relative importance matrix (RIM) by scaling the judgment from 1 to 9 (Saaty 2008) and is depicted as shown in Eq. 13:

$$RIM = \left[ {\begin{array}{*{20}c} {1.0000} & {5.0000} & {7.0000} & {0.2000} & {0.1100} \\ {0.2000} & {1.0000} & {3.0000} & {4.0000} & {7.0000} \\ {0.1400} & {0.3300} & {1.0000} & {0.2000} & {0.1100} \\ {5.0000} & {0.2500} & {5.0000} & {1.0000} & {0.1400} \\ {9.0000} & {0.1400} & {9.0000} & {7.0000} & {1.0000} \\ \end{array} } \right]$$
(13)

Step 4: determination of weights.

The Eigenvalues for the weight determination was calculated from the Eigenvectors of relative importance matrix Eigenvalues using MATLAB code. The procedure to find the weights for each criterion was developed by Saaty (2008). The weights for each attribute is shown as given in Eq. 14. The CI and CR values for the judgement set was calculated as 0.077 and 0.068, respectively, which is less than 0.1 shows a better consistency and reliability.

$$\begin{array}{ccccc}\mathrm{w}\hspace{0.17em}=[0.1902& 0.1311& 0.4132& 0.1491& 0.1164\end{array}]$$
(14)

Step 5: development of a weighted normalized matrix (WNM).

The normalized decision matrix multiplied to the attribute weight matrix gives a weighted normalized matrix as detailed in Eq. 15:

$$WNM = \left[ {\begin{array}{*{20}c} {0.0730} & {0.0618} & {0.1860} & {0.0577} & {0.0457} \\ {0.0715} & {0.0609} & {0.1834} & {0.0611} & {0.0467} \\ {0.0538} & {0.0414} & {0.1707} & {0.0498} & {0.0380} \\ {0.0545} & {0.0392} & {0.1452} & {0.0473} & {0.0361} \\ {0.0819} & {0.0450} & {0.1376} & {0.0554} & {0.0457} \\ {0.0826} & {0.0445} & {0.1172} & {0.0635} & {0.0497} \\ {0.0798} & {0.0489} & {0.1401} & {0.0579} & {0.0442} \\ \end{array} } \right]$$
(15)

Step 6: estimation of ideal best and ideal worst solution.

The maximum and minimum values of attributes account for the ideal best and the ideal worst solution. The ideal best and worst solution for cellulose, hemicellulose, lignin content, total carbon (TC), and C/N ratio are tabulated in Table 2.

Table 2 Ideal best and ideal worst solutions for the attributes
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Step 7: Separation measure determinations.

The Euclidean distance between the alternative and its particular ideal solution gives the separation measure for each alternative. The positive separation measure and negative separation measure for each alternative are shown in Table 3.

Table 3 Positive and negative separation measures, TOPSIS scores, and ranking of alternatives
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Step 8: calculation of TOPSIS score or relative closeness of a particular alternative.

The TOPSIS scores calculated as per Eq. 10 are given in Table 3.

3.1.3 Phase 3: Selection from the priority list.

The ranking of alternatives was in accordance with the decrease in the suitability index value. The alternative with the highest TOPSIS score has chosen as the best pretreatment method. The ranking for each alternative is shown in Table 3 along with separation measures and TOPSIS scores.

3.2 Integrated TOPSIS-DoE method

Step 1: factor level determination.

As per Table 1, cellulose (A1) with maximum level of 49.3 and minimum level of 30.4, hemicellulose (A2) with maximum level of 28.8 and minimum level of 14.3, lignin (A3) with maximum level of 7.5 and a minimum level of 4.6, TC (A4) with maximum level of 42.3 and a minimum level of 25.1, and C/N ratio (A5) with maximum level of 51.4 and a minimum level of 30.6 were determined as the levels of factors affecting the selection of best pretreatment method.

Step 2: decision matrix development.

The independent attribute variables (A1, A2, A3, A4, and A5) along with their factor levels were used as an input to obtain the TOPSIS scores which forms the dependent output variables in the TOPSIS model. A 25 full factorial design with 32 combinations were studied. Only minimum and maximum levels of each attribute were considered to perform the data collection using TOPSIS models.

Step 3: TOPSIS model replications.

The replications were carried out by taking random weight sets which follows independency for the set of combinations. In this study, 3 replications performed accounts for 32 combinations using 3 sets of independent random attribute weights. The weights were determined using the 9 point scale (Sen and Yang 1998) and incorporated into the decision matrix. The 25 full factorial design was based on five attributes, two levels, and three replications as given in Table 4.

Table 4 A 25 full factorial design results
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Step 4: regression model determination.

The evaluation of experimental results can be done using ANOVA table which summarizes the main effects and the interactions. The ANOVA (Analysis of Variance) with a five-factor interaction (5FI) effect helps to analyse the DoE layout using the Design expert 10 software. The ANOVA results are shown in Table 5. The Fischer (F value) of 4.33 for the model shows that the model was significant. The terms corresponding to p value < 0.05 indicates their significance with 95% of confidence. The significance of the attributes and their interactions can be studied using ANOVA.

Table 5 ANOVA results for the model
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From Table 5, it is clear that lignin content and C/N ratio interactions were significant model terms (p value < 0.05), whereas their two-factor, three-factor, four-factor, and five-factor interactions were non-significant terms (p value > 0.05). So, the regression equation has only statistically significant terms as coded factors.

The TOPSIS score obtained for the above model is represented as follows:

$${\text{TOPSIS score}} = { 36}.{599}0{4 } + \, \left( {\left( {{\text{C}}/{\text{N ratio }} \times { 1}.{2}0{851}} \right) - \left( {{5}.{27}0{28 } \times {\text{ lignin content}}} \right)} \right)$$
(16)

Equation 16 represents the linear regression relation between C/N ratio, lignin content, and the TOPSIS scores since no any significant interactions among the attributes. The positive coefficient term indicates direct proportional whereas, negative coefficient indicates inversely proportion to the response. Thus, we can confirm the negative correlation of the lignin and a positive correlation of C/N ratio with the considered response. The coefficient of determination (R2) value of 0.95 shows that the significant factors model the response well.

Step 5: Prioritizing of alternatives.

Now, the regression can be used to find the TOPSIS scores for various alternatives. The decision makers were able to rank the alternatives according to the decreasing TOPSIS scores. Table 6 shows the ranking of the alternatives obtained.

Table 6 Comparison of ranking by TOPSIS and integrated TOPSIS–DoE method
Full size table

The selection of the best pretreatment method has been made by analysing the attributes using TOPSIS and integrated TOPSIS–DoE approaches. Seven pretreatment methods were taken into consideration in this study. The decreasing value of TOPSIS score portrays the ranking of each alternative as given in Table 6. From the above studies, it was observed that alkaline pretreatment have a higher rank than the acidic pretreatment. As per the experimental study was done by Song et al. (2014), the highest methane yield was obtained for Ca(OH)2 and H2O2 pretreatment followed by NaOH pretreatment. With due consideration with the cost, alkaline pretreatment was found to be efficient for the biogas production. As per our statistical study, the results obtained matches well with the results of an experimental study done by Song et al. (2014). The results from TOPSIS and TOPSIS–DoE analysis have a close resemblance and can be adopted for decision-making in terms of selection of the best pretreatment method for biogas production.

Anaerobic digestion process is complex in view with the operational conditions, its maintenance, biogas quality and quantity, feedstock characteristics and its pretreatment, performance time, and digestate quality which is evident from Tables 7, 8, and 9 in appendix. So, the evaluation and selection of pretreatment method for a particular feedstock is a must in order to ease the further down streaming process. Thus, direct selection of the pretreatment can be done without actually performing the anaerobic digestion experiment for the entire digestion period which in turn saves time and energy. The proposed methodology helps the biogas unit operators to select the best pretreatment option for the particular feedstock based on the cellulose, hemicellulose, and lignin content in order to maximize energy yield. This makes the process economically feasible.

4 Conclusion

The selection of the best pretreatment method for enhanced biogas production from the lignocellulosic substrate is always a chaotic task. Pretreatment is essential in the case of lignocellulosic substrates as the lignin content cause hindrance to the anaerobic digestion. The prioritization of the pretreatment method was done using MADM technique to figure out the best out of all.

There were many attributes concerned with the pretreatment aided anaerobic digestion. The selection of pertinent attributes can minimize the time taken for decision-making. However, the increase in the number of pertinent attributes can raise the accuracy of the TOPSIS scores. The relative importance matrix varies with respect to the attributes and problem statement. The ideal best and worst solutions were calculated based on the attribute data for various alternatives. The ranking done for each alternative from the suitability index value gives the priority list. The weight sets reduce the sensitivity of the weights, and the regression equation was obtained using DoE. Further, the calculated TOPSIS scores from the regression equation were used for the ranking.

The best option obtained was the alkaline pretreatment both in terms of efficiency and economy. Similarly, the worst option was acidic pretreatment methods. The confirmation of the best pretreatment method obtained from the two techniques can be done using the experimental findings by the source. It was clear that alkaline pretreatment aided a rise in methane potential and it can be concluded that the model works well in prioritizing the pretreatment method for the sustainable conversion of lignocellulosic biomass to biogas.