Optimal Conversion of Organic Wastes to Value-Added Products: Toward a Sustainable Integrated Biorefinery in Denmark

Abstract

It is crucial to leave behind the traditional linear economy approach. Shifting the paradigm and adopting a circular (bio)economy seems to be the strategy to decouple economic growth from continuous resource extraction. To this end, producing bio-based products that aim to replace a part, if not all, of the fossil-based chemicals and fuels is a promising step. This can be achieved by using multi-product integrated biorefineries that convert organic wastes into chemicals, fuels, and bioenergy to optimize the use and close the materials and energy loops. To further address the development and implementation of organic waste integrated biorefineries, we proposed the open-source organic waste to value-added products (O2V) model and multi-objective optimization tool. O2V aims to provide a quick and straightforward holistic assessment, leading to identifying optimal or near-optimal design, planning, and operational decisions. This model not only prioritizes economic benefits but also takes on board the other pillars of sustainability. The proposed tool is built on a comprehensive superstructure of processing alternatives that include all stages concerning the conversion of organic waste to value-added products. Furthermore, it has been framed and formulated in a “plug-and-play” format, where, when required, the user only needs to add new process data to the structured information database. This database integrates data on (i) new processes (e.g., different conversion technologies), (ii) feedstocks (e.g., composition), and (iii) products (e.g., prices), among others. Due to Denmark’s high availability of organic waste, implementing a second-generation integrated biorefinery in Denmark has been chosen as a realistic showcase. The application of O2V efficiently led to the identification of trade-offs between the different sustainability angles. Thus, it made it possible to determine early-stage decisions regarding product portfolio, optimal production process, and related planning and operational decisions. Henceforth, it has been demonstrated that applying O2V aids in shifting the fossil to bio-based production, thereby contributing to the switch toward a circular bioeconomy.

1 Introduction

FIGURE 1

The remainder of the article is structured as follows. Section 2 describes the pathways for the conversion of organic waste into value-added products. It also provides details regarding data collection, superstructure generation, and the specifics concerning the implementation of an integrated biorefinery in Denmark. In Section 3, the O2V model is described and the mathematical formulation is defined. The results and discussion are presented in Section 4. Finally, conclusions and future perspectives are drawn in Section 5.

2 Organic Waste to Value-Added Products in Denmark: Toward a Realistic and Sustainable Integrated Biorefinery

The main objective of this work is to design a sustainable integrated biorefinery for the conversion of organic waste into value-added products. Denmark was selected as the location and thus the showcase. The data needed are collected (in a structured database) and presented in this section.

2.1 Availability of Organic Waste in Denmark

LCF availability in Denmark is expected to reach 4.5 million dry tons/year by 2030 (Panoutsou and Singh, 2020). Straw is the second biggest contributor to the total available LCF (1.367 million dry tons/year). Panoutsou and Singh (2020) presented that wheat straw and barley straw have the highest availability. In 2019, the annual production in Denmark was 2017 and 2580 million kg of barley and wheat straw, respectively (Denmark, 2020b). However, this total is not entirely available. Approximately 50% is not collected and the rest is mainly used to produce energy and feed (Nilsson et al., 2016). Pig manure is another significant source of organic waste in Denmark. A total of 12 million pigs were registered in Denmark (2020a). Considering an average of 4.1 kg of manure/swine per day (Losinger and Sampath, 2000), the total quantity of manure is approximately 18,000 million kilos per year. Therefore, wheat and barley straw are the LCF sources selected along with pig manure due to the aforementioned considerations. These are very promising feedstocks for the development and implementation of a sustainable integrated biorefinery in Denmark.

2.2 Value-Added Products From Organic Waste

2.2.1 Lignocellulosic Feedstock

Although the most common use of straw in Denmark is for energy production, its great potential for the production of chemicals and fuels is not explored. A certain set of steps are needed to convert the LCF into valuable products. The main step is to convert LCF into fermentable sugars: C₅ (e.g., xylose and arabinose) and C₆ (e.g., mainly glucose, mannose, galactose, and rhamnose) (Lee, 2015). These sugars can be converted through fermentation (biological) or chemical processing. An extensive analysis of fuels and platform chemicals that can be obtained from the conversion of LCF was presented by Isikgor and Becer (2015). It is necessary to reduce the portfolio of products to include in the superstructure of alternatives that will be analyzed in this study. Different criteria can be applied to choose the most promising product portfolio for the integrated biorefinery (Bozell and Petersen, 2010). To this end, some of the strategies are as follows: (i) to perform an extensive analysis of recent literature and reports (e.g., European Union, IEA tasks); (ii) to assess if the product has direct fossil-based counterparts (can be used as a direct substitute); (iii) to identify the product as a commodity (high volume) or specialty chemical/precursor/building block (high value); and (iv) to analyze the potential for commercialization and industrial scale-up (Bozell and Petersen, 2010). The primary motivation behind the choice of products is to design an integrated biorefinery capable of and effective in producing high-volume products (EtOH) and specialty high-value-added products (SA, LA). Lactic acid and succinic acid are bioplastic precursors with direct applications in pharmaceutics and cosmetics. Their production market demand has steadily increased over the years. Bio-based ethanol can directly replace fossil-based ethanol in most applications. Furthermore, it is worth noting that these chemicals have been thoroughly studied, and therefore the data available are trustworthy for further use in follow-up studies, such as this study. Hence, based on the mentioned criteria, realistic manure and LCF-based product portfolio were selected, and these products are ethanol (EtOH), lactic acid (LA), and succinic acid (SA). The main processing stages for the production of fermentation products from LCF are as follows: (i) preprocessing (Kumar et al., 2009; Aristizábal-Marulanda and Cardona Alzate, 2019); (ii) pretreatment (Kumar et al., 2009; Aristizábal-Marulanda and Cardona Alzate, 2019); (iii) detoxification (Aristizábal-Marulanda and Cardona Alzate, 2019; Vikash and Shastri, 2019); (iv) hydrolysis and fermentation (Gomez et al., 2008; Aristizábal-Marulanda and Cardona Alzate, 2019); and (v) purification and concentration (Komesu et al., 2017; Aristizábal-Marulanda and Cardona Alzate, 2019). More details are presented in Section 2.3.

2.2.2 Manure

There are two main processing avenues to convert manure into value-added products: (i) energy-oriented technologies, such as biogas production, gasification, and combustion, followed by hydrothermal liquefaction, and (ii) technologies that lead to other products such as composting, pyrolytic carbonization, or hydrothermal carbonization (Khoshnevisan et al., 2021). In Denmark, biogas production has quadrupled between 2012 and 2020, producing approximately 20 PJ/year Støckler et al. (2020), in which manure and organic waste are the two chief feedstocks. Therefore, this valorization pathway, manure to biogas, and biogas upgrading are options included in this study.

Of note is that the production of biogas and EtOH can be used in-house to cover part, if not all, of the facility’s energy needs and thus closing both energy and materials loops (zero-materials and zero-energy wastes).

2.3 Data Collection and Superstructure Generation

FIGURE 2

FIGURE 3

The hydrolysis leads to the formation of fermentable sugars through enzymatic activity (cellulases and hemicellulases). Typically, the available commercial enzymes for saccharification and hydrolysis consist of a combination of several enzymes (Gomez et al., 2008). The required enzyme load for the hydrolysis, which depends on the preceding pretreatment stage, is given in Supplementary Table S14. Various organisms, such as bacteria and yeast (natural or engineered), can convert fermentable sugars into LA, SA, and ethanol (Di Lorenzo and Androsch, 2018). The strains are usually defined by their attainable titer (g/L), yield (g/g), and productivity (g/L/h). Supplementary Table S4 reports the bioconversion yields of fermentable sugars into products. The following hydrolysis and fermentation methods are considered in this work and hence included in the superstructure of alternatives: (a) separate hydrolysis and fermentation (SHF); (b) simultaneous saccharification and fermentation (SSF); (c) separate hydrolysis and co-fermentation (SHCF); and (d) simultaneous saccharification and co-fermentation (SSCF). A schematic representation of the main differences among the techniques is presented in Figure 4. The hydrolysis conversion factors for SHF and SHCF and the factors pertaining to the conversion of xylose to ethanol in SSCF and SSF are reported in Supplementary Table S6. The main traits and distinctions between the mentioned technologies are as follows.

FIGURE 4

SHF: the solid stream containing cellulose and hemicellulose obtained from Step 2 goes through hydrolysis, leading to a mixture of glucose and xylose. This stream is then led to the fermentation reactor. The xylose in the liquid stream from the pretreatment section is fermented in a separated bioreactor.

SSF: both solid and liquid streams exiting the pretreatment section enter two different bioreactors. Both undergo simultaneous hydrolysis and fermentation (one bioreactor for each stream).

SSHF: this technique is reminiscent of SHF; however, the xylose-rich liquid stream from pretreatment is mixed with the fermentable sugars from the hydrolysis of the solid stream. Thus, all the sugars obtained from both streams are fermented in one reactor.

The outlet of Step 3 is composed of main products (moderate-to-low concentration), by-products, and other species (e.g., non-fermented sugars). The unwanted compounds are removed in the purification and concentration step to reach the desired concentration and purity. To this end, documented technologies are, for example, precipitation, liquid–liquid extraction, and reactive distillation. Their implementation depends on the main product, and it is usually a compromise between energy and solvent consumption as well as the technology’s TRL (technology readiness level). Details on the available technologies are explored by Komesu et al. (2017). In this work, the following technologies are included:

LA purification and concentration: (i) precipitation → esterification → distillation; and (ii) electrodialysis → esterification → distillation.

SA purification and concentration: (i) electrodialysis, (ii) direct crystallization, and (iii) reactive extraction.

Ethanol purification and concentration: (i) distillation → extractive distillation with ethyl alcohol; (ii) distillation → azeotropic distillation with cyclohexane; and (iii) distillation → adsorption. The primary products’ recovery factors regarding the different purification and concentration technologies are presented in Supplementary Table S7. Supplementary Table S7 also illustrates the compatibility between the main product and Step 4’s technologies. In addition, the utilities required for this step are reported in Supplementary Tables S15–S17 for SA, LA, and ethanol, respectively.

2.3.1 Lignin and Manure Conversion

In this study, two options for the conversion of lignin are included in the superstructure: conversion of lignin into electricity using BIGCC technology (González-García et al., 2012), or lignin is disposed of as waste. The bioconversion of manure into biogas is achieved by applying one of the following technologies: (A) fermentation and biogas upgrade by CO₂ removal and (B) fermentation and biogas methanation using H₂ (electrolysis). The recovery factors for the manure and lignin conversion are reported in Supplementary Table S8. The data regarding the utilities and chemicals used in both lignin and manure conversion processes are reported in Supplementary Tables 18, 19.

3 O2V Model and Optimization Tool: Organic Waste to Value-Added Products

3.1 Model Outline

As previously mentioned, organic waste is a by-product of agro-activities, with a market price that is virtually zero. Thus, in order to thrive toward a circular bio-based and zero-waste economy, the upgrading of these wastes must/should not be overlooked. This study aims to identify and systematically investigate the optimal integrated biorefinery design(s) for converting organic waste into value-added products to aid and enable this paradigm shift. Therefore, in this work, as presented in Figure 5, we propose a modeling and optimization tool that aims to be accurate but also easy to apply for screening alternatives at the very early stages of design and decision-making.

FIGURE 5

O2V was built upon integrating (i) upstream and downstream processing models (black box models) for the conversion of organic waste into value-added products; (ii) technology selection and operational strategies; (iii) economic, environmental, and social modeling criteria; and (iv) a multi-objective optimization scheme. The problem is formally stated as follows:

Goal: To maximize the operating profit and minimize the E-factor of the integrated biorefinery.

3.2 Mathematical Formulation

The O2V model is formulated as a generalized disjunctive programming (GDP) model for the optimization of the integrated biorefinery superstructure shown in Figures 2, 3. Constraints are defined according to the superstructure of connections to represent, for example, mass balances and capacity limitations. The comprehensive mathematical model formulation is detailed below (constraints and objective function). The complete list of indices, sets, parameters, and binary and continuous variables used is given in the Nomenclature Section.

3.2.1 Constraints

If the binary variable is active, then the set of Eq. (7) attribute the output particle size of a specific preprocessing option to the variable. The set of Eq. (7) guarantee that the maximum input particle size into a pretreatment option is equal to the preprocessing output particle size.The output of the pretreatment step is then divided into two flows: solid and liquid. The liquid stream is composed of the sugars obtained in the pretreatment process and by-products (Vikash and Shastri, 2019), whereas the solid stream contains no converted hemicellulose and cellulose. Lignin can be found in both solid and liquid streams, depending on the pretreatment technology. This is modeled by the following constraint:where α^Cel (b₁) is the content of cellulose in the LCF (b ∈ B₁). is the cellulose recovery factor obtained when using pretreatment alternative (d ∈ D). Finally, the variable stands for the amount of cellulose in the inflow of biomass/LCF (b₁ ∈ B₁) sent from the preprocessing (c ∈ C) to the pretreatment step (d ∈ D). Therefore, as explicit in Constraint (8), represents the total cellulose recovered in the output solid stream of the pretreatment step(s). Applying the same reasoning, all the other components’ recoveries in the pretreatment options are estimated. These are presented in the folloeing constraints:

Noteworthy is that some of the pretreatment technologies are not compatible with SSCF and SHCF. In addition, some data concerning the different fermentation types may be missing. Hence, some of these techniques might not be implemented. In order to accommodate and model these facts/arguments/details/information, a matrix is created. takes the value of 1 if the match between pretreatment technology d ∈ D and the fermentation section h ∈ H using the fermentation technology i ∈ I is considered feasible. Otherwise, it takes the value 0. The selection of a compatible combination is modeled in the following constraints:The flows of solid and liquid into the fermentation sections ( and , respectively) are only positive if the combination of technologies is possible.In order to avoid non-linearities, it is assumed that both solid and liquid streams obtained from feedstock b₁ ∈ B are sent to the same fermentation step.

SHF-related constraints:Additional constraints are modeled to account for limitations brought by the selection of SHF as the fermentation method. Given a feedstock b₁ and fermentation i, the total solid flow going through the fermentation section h is represented by . As the liquid fraction is fermented separately, water is added to the reactor to obtain the correct solid loading. Thus, if the solid loading is known, the water consumption in the fermentation section is given as follows:

The total output flow from the fermentation reactor is equivalent to the sum of solid and dilution water added to the reactor Constraint (23):

When a fermentation technique is chosen to convert the feedstock b₁ into product h, , all pretreatment’s liquid and solid output flows d (from feedstock b₁) is to be sent to fermentation technique i, that is, and . Else, and ; thus, no flow is sent. In case of SHF and SHCF, hemicellulose and cellulose are hydrolyzed into sugars prior to the fermentation reactor. The amount of fermentable sugars obtained in the hydrolysis step depends on the pretreatment technique previously implemented. This is modeled using the following factors: and . They stand for the portion of hemicellulose converted into fructose and the fraction of cellulose converted into glucose, respectively.

Granted that SHF is selected, the glucose available is given by the flow of cellulose recovered from the feedstock b₁ leaving pretreatment option d. This is represented by multiplying with the conversion factor . In contrast, if SHF is not favored, the glucose available for SHF must be equal to zero. The same reasoning applies to xylose and the amount of xylose that is available for fermentation . This flow, when SHF is picked, is obtained by multiplying the flow of hemicellulose, , with the conversion factor . Because the xylose in the liquid stream is obtained in the pretreatment section, the xylose in the liquid stream available for fermentation with SHF ( is the same as the flow of xylose leaving the pretreatment step . Therefore, if SHF is not chosen, these flows must be zero. These considerations and implications are mathematically expressed through the disjunction presentedas follows:As previously mentioned, in the SHF, the liquid and solid flows are fermented separately. Thus, two xylose fermentation strains have to be selected for this purpose. The selection of the xylose fermentation strains for the liquid stream is given in the following constraint:

Constraint (25) ensures that if SHF is selected only one fermentation strain is chosen, ; else and .

Similarly, the fermentation strain for xylose and glucose fermentation (obtained from hydrolysis) is modeled as follows:

The allocation of the glucose available to the different strains is modeled by Constraint (27). Likewise, the distribution of the total xylose (from hemicellulose?) stream to the different strains is given in Constraint (28):

For the xylose in the liquid fraction, its distribution to the different strains is modeled by the following constraint:

In Constraints (25) to (29), the set J encompasses all the strains included in the model. Of note is that (i) every strain is linked to only one main product (pure culture fermentation), and (ii) particular strains are only compatible with certain fermentation techniques. The matrix represents the compatibility among fermentation strains j, fermentation technology i, and main product h. It takes the value 1 if the technologies are compatible, 0 otherwise. Henceforth, the selection of compatible technologies is modeled in the following constraints:The rationale applied to the above constraints is equivalent to the one used in Constraints (20, 21).

Furthermore, Disjunction (33) represents the flow of the main product h obtained from the conversion of the xylose (liquid stream), . This flow is greater than zero if the fermentation strain j ∈ J is selected and 0 otherwise:

Likewise, the total quantity of the main product obtained from the conversion of glucose and xylose originating from the hydrolysis of hemicellulose and cellulose is modeled by the following disjunction:

SSF-related constraints:The following constraints are imposed if the fermentation technology SSF is selected. Analogous to the SHF case, the constraint that assures the reactor’s solid loading is modeled as follows:

If SSF is selected, cellulose and hemicellulose are sent to the same reactor for simultaneous saccharification and fermentation. Thus, the total inflow of cellulose, hemicellulose, and xylose into the SSF reactor is equal to the amounts obtained in the pretreatment stage. This is expressed through the following disjunction:

The constraints associated with the bioconversion of the pretreatment outflow liquid stream is equivalent to the ones described for SHF Constraints (25–34). Therefore, similar constraints are presented hereafter without further explanation:

Similarly, the strain selection for the glucose and xylose fermentation in the SSF reactor is modeled by the following constraint:

The distribution of cellulose and hemicellulose among the different strains is modeled in the following constraints:

The selection of compatible fermentation strains, sections, and techniques is modeled by the following constraints:

When a fermentation strain j ∈ J is selected to convert hemicellulose and cellulose into the main product h using SSF, the binary variable is active , the total product formed from cellulose and hemicellulose and is obtained by multiplying the respective and with the conversion factor of cellulose and hemicellulose into the product h using the strain j ( and , respectively). Otherwise, in case the strain is not selected, the flows are set to 0. These considerations are modeled by the following disjunction:

SHCF-related constraints:The following constraints are imposed if the fermentation technology SHCF is selected. In order to reach the required reactor’s solid loading and unlike SSF and SHF, the addition of water is not the single solution. The xylose in the liquid stream leaving the pretreatment step is fermented in the same reactor as the sugars in the solid stream. Thus, there is the possibility that there is an excess of liquid in the reactor, which has to be removed to maintain the desired solid loading. The excess flow removed is given by the variable. Henceforth, the two options, the addition of diluted water or the removal of excess liquid, are considered conflicting and thus modeled as in the following disjunction:

The total flow of liquid and solid streams into the fermentation section producing the main product h is modeled in the same way as in the SHF process. Moreover, the same holds true for the total amount of glucose and xylose available for fermentation into the main product. This is modeled by the following disjunction:

In contrast to SHF and SSF, only one fermentation strain j must be selected for SHCF. Xylose present in the liquid stream which leaves the pretreatment unit is mixed with the glucose and xylose formed by hydrolysis and then fermented. This is modeled as follows:

The allocation of glucose and xylose, among the different strains j ∈ J, alike SHF, is represented in the folloeing constraints:

To determine the main products h, total flows are modeled as in the SHF-related constraints. Despite that, and in contrast to SHF, the xylose from the liquid stream is fermented together with the sugars obtained through the hydrolysis of the solid stream. This is modeled by the following disjunction:

SSCF-related constraints: The following constraints are imposed if the fermentation technology SSCF is selected. In SSCF, as in SSF, hemicellulose and cellulose undergo hydrolysis and fermentation in one single reactor. The constraint regarding the reactor’s solid loading is given in Constraint (54). Because it follows the same rationale as in the previous fermentation techniques, no further explanation is provided here:

The solid and liquid flows are estimated with the same reasoning as in SSF. The same applies to the calculation of the cellulose, hemicellulose, and xylose amounts available to be converted into the main product h. Thus, a similar disjunction to the one for SSF is given as follows:Alike SHCF, only one fermentation strain can be chosen for SSCF. This is modeled in constraint (56), and no further explanation is provided. The distribution of cellulose, hemicellulose, and xylose present in the liquid stream is given by, as in SSF, Constraints (57, 59). The same holds for the identification of compatible fermentation strains, section, and techniques. This is given in constraints (60) to (62):

To determine total flow of the main products, the same rationale as in SSF is used. However, xylose fermentation is modeled differently since the xylose fermentation occurs together with the sugars from the saccharification step. These constraints are modeled in the following disjunction:

Constraint (65) that follows ensures that if a certain product is not obtained in the fermentation section , then that product is not sent to a purification and concentration technology k ∈ K ( and ). Otherwise, if product h ∈ H is produced then , but only one purification and concentration step can be chosen for each product h ∈ H. This is modeled in constraint (66):

An important consideration is the compatibility between the main product and the purification and concentration processes. Thus, to consider this, a compatibility matrix is defined , where if the purification and concentration processes k ∈ K are compatible with the main product (h ∈ H). By using this parametric matrix, the choice of compatible purification and fermentation operation is modeled by the following constraint:

The flow of the main product obtained after the purification and concentration processes is estimated where represents the recovery factor of the given process. When a given purification and concentration step is not selected, the outflow of the main product is 0. The following disjunction reflects the abovementioned implications:The total flow of the main product exiting all purification and concentration steps k ∈ K is given as follows:Lignin conversion:In this work, lignin is sent to the fermentation and after the purification and concentration steps, a lignin cake is recovered. The assumption is that all lignin in the solid stream exiting the pretreatment section is fully recovered, . The binary variable , if active, reflects the recovery of lignin. Then, when recovering lignin, two options for the subsequent step are included in the model: (i) disposed as waste or (ii) convert it into BIGCC for the production of electricity . The decision between both alternatives is modeled by the following disjunction:Manure conversion:The model developed in this work also accounts for the possibility to also convert manure into value-added products (Y^Manure). Furthermore, three alternatives are considered for the conversion of manure into biomethane based on anaerobic digestion and gasification (l ∈ L). This is modeled by the following constraint:

The following disjunction represents the selection (Y^Manure) and corresponding inlet flows of manure into the conversion step (F_Manure(l)):

3.2.2 Objective Functions

Two objective functions are defined reflecting economic and environmental/social optimization. These are given in Equations 73, 74, respectively.

OP stands for operating profit, where V^H, V^RM, and V^B correspond to the sales of the main products produced, the cost of the raw materials used in all stages, and the cost of the feedstock, respectively. E-factor, traditionally applied as a metric in green chemistry, is here used to minimize waste and thus waste disposal.

3.2.2.1 Multi-Objective Optimization

The multi-objective optimization leads to a Pareto front of solutions composed of the alternatives that represent the optimal trade-offs between the two targets. By minimizing waste, we aim to reduce environmental impact and health hazards associated with waste disposal, thus leading to benefits regarding both environmental and social aspects (e.g., soil acidification and the health and safety of local communities). In this work, these solutions are reached by applying the ϵ-constraint method, as defined in del Castillo-Romo et al. (2018).

3.3 Model Implementation and Solution

The above-described model has been implemented in Pyomo, an open-source software embedded in python. The GDP model was modified into an MINLP using a standard reformulation method provided by Pyomo. This is the most efficient strategy in terms of solving time. Another approach was tested where instead of reformulating the model into MINLP, the problem was solved straightforwardly with GDPopt. GDPopt is a logic-based nonlinear and open-source GDP solver for Pyomo (Chen et al., 2018a). The former strategy has been chosen because it indeed has the shortest computing time. Furthermore, although several solvers and their capabilities were investigated, Gurobi was the solver selected because most of the solvers were not compatible with the model developed. Some examples are IPOPT, GLPK, and CBaC. The former can solve nonlinear problems but cannot handle integer terms, and the latter two cannot solve nonlinear problems. Gurobi can deal with integer variables because it includes a bilinear solver (added in the Gurobi 9.0 version). As the model includes a nonlinear Equation (74), bilinear equality constraint, Gurobi was the most appropriate choice. The two most used approaches to reformulate a GDP model into an MINLP model are (i) the convex hull relaxation (HR) and (ii) the Big-M (Vecchietti et al., 2003; Chen and Grossmann, 2019b). The choice between these two strategies comes with a trade-off. Because Big-M requires a lower number of constraints and variables than HR, by using HR, one can reach a better continuous relaxation and thus stronger lower bounds (Chen and Grossmann, 2019b; Grossmann and Trespalacios, 2013). Testing both approaches is required if the solving time is a criterion to consider. Even though the better bounds gained with HR can lead to shorter solving times, the increased size of the reformulation might act in the opposite direction Grossmann and Trespalacios (2013). In this work, the Big-M reformulation performed better in terms of solving times and thus has been the strategy followed to convert the GDP model into MINLP.

4 Results and Discussion

The results regarding the application of the O2V model and multi-objective optimization tool to identify the potential optimal integrated biorefinery for converting organic waste into value-added products are presented in this section. The mathematical formulation corresponding to the O2V model was implemented in Pyomo and solved to global optimality with Gurobi 9.0. The model consists of 57,239 variables and 98,895 constraints.

4.1 Base Case Scenario

The scenario built in this work for producing SA, LA, EtOH, and biogas (RNG) is based on setting up target production capacities for the different products. A total of 1,218 GWh of biogas is generated by 154 plants in Denmark Kampman et al. (2017). This corresponds to 1,000 kWh/h per facility, and thus it has been chosen as the production target for the production of biogas from manure. The commercial scale for the production of SA and LA by DSM and Roquette Frères is set at 50 kton/year (6.25 ton/h) Vaswani (2010). Due to its commercial status, this represents a realistic production scale; thus, it has been chosen to be the production target of both SA and LA. The target capacity for EtOH production was set at approximately 15 ton/h, a scale that has been identified as optimal by Raftery and Karim (2014). Although one could have established other starting scenarios, this base case was chosen because (i) it leads to an optimal multi-product biorefinery as expected under the integrated biorefinery settings, where aiming at replacing fossil-refineries, high-value low volume and low-value high volume products are co-produced; and (ii) it enables the development of a credible integrated biorefinery by using realistic commercial production capacities. Thus, the estimated capital investment is also assumed to be reasonable and economically relevant for practical implementation.

4.2 Multi-Objective Optimization Results

A Pareto front of solutions is obtained by applying the ϵ-constraint method, as presented in Section 3.2.2. The Pareto front is depicted in Figure 6; the corresponding production networks and data points are given in Table 2. The codes describing the different superstructure steps are reported in Table 1. The circles show the impact that changing the purification and concentration technologies (Step 4) has on the objective functions. Besides, it is worth noting that the impact of manure conversion is negligible when compared to changes in Step 4.

FIGURE 6

From Table 2 and Figure 6, the main differences among the solutions forming the Pareto front are the choice of technologies in Step 4 and manure conversion. However, the choice of manure conversion technologies does not impact the OP and E-factor as much as the selection of Step 4 (purification and concentration) technologies. The selection of different technologies in Step 4 is linked to the energy consumption and/or addition of solvents/chemicals. The most striking similarities are that (i) wheat straw is always selected as the main feedstock; (ii) dilute acid is invariably chosen as the pretreatment step; (iii) the selected technologies for Step 3 are consistent among all solutions; and (iv) lignin is consistently converted into electricity. Furthermore, a quick analysis of the extreme solutions shown in the Pareto front in Figure 6 is performed. Solution A, presented in Figure 7, represents the optimal OP (maximizes OP), and Solution G, depicted in Figure 8, stands for the optimal E-factor (minimizes waste production). Because both solutions have the same production targets, the main difference is the operating costs (raw materials/chemicals and feedstock). Overall, the following observations can be made by comparing solutions A and G.

FIGURE 7

FIGURE 8

FIGURE 9

FIGURE 10

FIGURE 11

FIGURE 12

FIGURE 13

Furthermore, it is important to highlight that although the model developed in this work is extensive and comprehensive, it is based on available limited processing alternatives because research and implementation are ongoing. For example, Li et al. (2021) described the potential of using membrane technologies. Additionally, Step 3 was assumed to be pure culture fermentations; however, the review by Pinto et al. (2021) has documented that mixed cultures might bring some advantages. The superstructure does not include these alternatives due to the, so far, lack of maturity and data availability.

5 Conclusion and Future Perspectives

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