# Analysis of Sequential Pretreatments to Enhance the Early-Stage Biorefinery Designs
## 2 Materials and Methods
### Heuristic Analysis  
#### 2.2.1 Indicators' Description  
Ten techno-economic indicators were considered for the heuristic assessment. Indicators (i)-(v) were calculated based on lignocellulosic removals or concentrations from the literature, while Indicators (vi)-(ix) were determined through computational tools for scaling up biomass pretreatment. The following section briefly describes the indicators, including calculation and relevance for scoring. (i) Total lignocellulosic removal (I\({}_{\text{R}}\)) associates the isolated or fractionated amount of biomass at the end of the sequence regarding the initial composition. For further valorization, I\({}_{\text{R}}\) should be maximum for hemicellulose and lignin, as well as the minimum for cellulose. Note that throughout the sequences, there are more than two pretreatment schemes; therefore, there are mass losses or partial lignocellulosic removals during each scheme. (ii) There needs to be accessibility to the product of interest (I\({}_{\text{A}}\)). Given the structure of the biomass and the operational strength of the pretreatment, the isolation is not selective toward one fraction. Therefore, the liquor and WIS will have small-to-medium unwanted fractions. The I\({}_{\text{A}}\) (see Equation (3) for cellulose, Equation (4) for hemicellulose and Equation (5)) was calculated considering the composition of unwanted lignocellulosic compounds (UF) either in the liquors or in the final WIS of the sequence. In valorization schemes toward reactions or bioconversions, the I\({}_{\text{A}}\) should be highly reflected as the fraction purity. (iii) The next indicator is cellulose recovery (I\({}_{\text{CR}}\)). Most biotechnological processes seek to maximize sugars for biofuel production. The I\({}_{\text{CR}}\) relates the cellulose composition in the final WIS. High I\({}_{\text{CR}}\) values are mandatory to increase overall yields and process profits as a viable platform product for obtaining high-value-added products. (iv) The operational strength of pretreatment is directly related to severity (I\({}_{\text{S}}\)). High severity results in a higher process energy demand and equipment resistance to operational stress, thus increasing overall costs. Therefore, the severity should be as low as possible. The I\({}_{\text{S}}\) was calculated by considering the severity factors (Log (R\({}_{\text{O}}\))) of each pretreatment scheme in the sequential scheme, as shown in Equation (6), where R\({}_{\text{O}}\) was already reported elsewhere [16]. (v) The next indicator is the valorization potential of sub-streams (I\({}_{\text{V}}\)). Biorefinery designs are framed toward the integral valorization of biomass. Therefore, it is not feasible to consider the fractionation or isolation of a lignocellulosic fraction. I\({}_{\text{V}}\) refers to the possibility of recovering the sub-streams of the sequential scheme, either hydrolyzed products such as five-carbon sugars, soluble lignin, or solid cellulose. The I\({}_{\text{V}}\) multiplies the composition to be recovered (VF) by its accessibility at pretreatment \(i\), as shown in Equation (7) for cellulose, Equation (8) for hemicellulose and Equation (9) for lignin. For example, in a sequential dilute acid (DA) and kraft scheme for cellulose isolation, the first pretreatment (\(i=1\)) will hydrolyze much of the hemicellulose (VF\({}_{\text{Hemi}}\)), whereas in the second pretreatment (\(i=2\)), the lignin will be solubilized (VF\({}_{\text{lig}}\)). Likewise, I\({}_{\text{V}}\) describes that sequential schemes based on hemicellulose valorization should consider the composition of lignin in each obtained liquor and the cellulose in the WIS, while in lignin schemes, the composition of hydrolyzed five-sugars should be included. (vi) The mass yield (I\({}_{\text{Y}}\)) relates the amount of platform product possible to be valorized post-sequencing, correlating cellulose in the WIS, soluble lignin, and the five-carbon oligomers and monomers hydrolyzed from hemicellulose (see Equation (10)).