Sustainable biopolymer synthesis via superstructure and multi-objective optimisation

Ehecatl Antonio del Rio-Chanona1,2, Dongda Zhang1,*, Nilay Shah1

1: Centre for Process Systems Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK

2: Department of Chemical Engineering and Biotechnology, University of Cambridge, Pembroke Street, Cambridge CB2 3RA, UK.

Abstract

Sustainable polymers derived from biomass have great potential to replace petrochemical based polymers and fulfil the ever-increasing market demand. To facilitate their industrialisation, in this research, a comprehensive superstructure reaction network comprising a large number of reaction pathways from biomass to both commercialised and newly proposed polymers is constructed. To consider economic performance and environmental impact simultaneously, both process profit and green chemistry metrics are embedded into the multi-objective optimisation framework, and MINLP is employed to enable the effective selection of promising biopolymer candidates. Through this proposed approach, the current study identifies the best biopolymer candidates and their most profitable and environmentally-friendly synthesis routes under different scenarios. Moreover, the stability of optimisation results regarding the price of raw materials and polymers and the effect of process scale on the investment cost are discussed in detail. These results, therefore, pave the way for future research on the production of sustainable biopolymers.

Keywords: sustainable biopolymer, superstructure optimisation, multiobjective optimisation, green chemistry metrics, MINLP

Introduction

Biomass generated through photosynthesis by utilising solar energy and atmospheric CO2 has been widely recognised as a promising sustainable feedstock to replace the non-renewable and dwindling fossil resources and fulfil the ever-increasing demand of fuels, chemicals and energy in the future 1,2. For example, carbohydrates (i.e. cellulose and hemicellulose) obtained from biomass have been predominately used to generate different biofuels including both transportation fuels such as biodiesel and bio-ethanol 3–5 and biogas e.g. syngas and biohydrogen 6,7. Lignin separated from lignocellulosic biomass has been mainly used to synthesise a number of value-added chemicals including solvents 8, resins 9, aromatic chemicals 10 and surfactants 11. What is more, biomass-derived catalysts have also been recently developed to catalyse various reactions for the synthesis of formamides and biofuels 12–14.

In particular, amongst these applications, bio-based sustainable polymers have been given significant attention during the last decade due to their extensive use in both daily life and industry 15–17. It was estimated that the global polymer market exceeded 290 million tonnes per year in 2009 and would reach an annual production of 870 million tonnes by 2015 16. However, at present almost all the commercialised polymers are generated from the petroleum and natural gas industries 15,18, thus in order to guarantee a stable feedstock supply for the rapid growth of polymer global market, it is necessary to identify primary biomass resources and develop promising biomass-derived synthesis pathways for future environmentally friendly polymers production.

So far, a variety of biomass candidates including agricultural residues 19,20, forestry and citrus wastes 21,22, and microorganisms such as microalgae 23,24 have been found to be able to synthesise monomers and polymers via different reaction routes. What is more, to save investment costs and simplify process complexity, polymers synthesised from monomers or precursors that can be easily obtained from biomass wastes through direct extraction or simple separation methods are particularly investigated. These monomers include limonene extracted from citrus waste 15,22, isoprene excreted by microalgae and cyanobacteria 23, and 1,4-cyclohexadiene synthesised from plant oil 25. Because of their outstanding advantages, intensive research has been conducted to synthesise a diverse range of polymers from these monomers, and important properties (e.g. glass transition temperature) of their derived new polymers (e.g. polylimonene carbonate, polycyclohexadiene) have been studied in detail 21,26,27.

Despite the above achievements, severe challenges still prevent the industrialisation of biomass-based sustainable polymers. For instance, one of the current challenges is the large number of potential reaction pathways from biomass to biopolymers, since there are a number of biomass resources that can be used to produce different categories of polymers e.g. polyester, polyether and polyolefin 21,28,29. Most of these pathways, however, have not been studied in depth and their economic feasibility is still unknown. As a result, efficient simulation methodologies must be constructed to narrow down the possible synthesis routes and identify the promising polymer candidates. Meanwhile, another challenge currently arising is the low biomass utilisation efficiency of newly proposed polymers, since their monomers only take into account a very low percentage of biomass weight (e.g. limonene content in citrus waste is less than 4 wt%) 30,31. Thus, the disposal of large amounts of biomass residues may cause a heavy economic and environmental burden. Hence, advanced technologies have to be developed to effectively convert biomass into numerous monomers for polymer production, so that both feedstock utilisation efficiency and process profitability can be improved.

Therefore, to resolve the aforementioned challenges, in a recent study, a biomass – syngas – polymer synthesis route based superstructure reaction network was proposed that utilises up to 73.6% of carbon from biomass for polymer production 32. This is significantly higher than that of the direct extraction route (rarely higher than 5%) 30,31. Furthermore, as biomass gasification technologies have been extensively researched and industrialised 33, the optimal synthesis route identified from this superstructure results in a potential production prototype for future sustainable polymers.

However, to identify the most profitable and environmentally friendly routes for biopolymer production, economic and green chemistry criteria should be embedded into the superstructure. Moreover, multi-objective optimisation should be conducted to balance the trade-off between these criteria so that the most promising biopolymers as well as their optimal processing sequences can be determined. These constitute the aims and contributions of the current study. The current work is organised as follows: in the Methodology section, a brief introduction to both recently constructed and currently extended superstructures are presented, followed by the detailed process screening and optimisation methodologies. The original findings including the best biopolymer candidates and their optimal synthesis routes as well as process scale-up potential are discussed in detail in the Results and discussion section.

Methodology

Biopolymer superstructure construction

The original superstructure reaction network which contains a variety of reaction pathways from biomass wastes to biopolymers through biomass gasification was presented in our recent study 32. In the current study, this superstructure is extended with the aim of investigating more potentially sustainable polymer candidates. The modified superstructure includes a total of 24 polymers categorised into three groups which are polyester, polyether and polyolefin; 72 chemicals all of which can be derived from biomass (additional supply of hydrogen and/or hydrogen peroxide may be added if necessary); and 76 reactions collected from an extensive literature review. All the reaction conditions are chosen to be close to the current existing industrial processes. To determine the potential of commercialising bio-based polymers in the near and long-term future, this modified superstructure reaction network includes both traditionally commercialised polymers such as polyethylene (PE), polybutylene terephthalate (PBT), and polypropylene carbonate (PPC), and currently intensively investigated limonene and 1,4-cyclohexadiene based biopolymers e.g. polylimonene carbonate (PLC), polycyclohexadiene (PCE) and polycyclohexadiene oxide (PCEDO) 21,26,27.

In specific, the reaction network is constructed following a structured procedure. Initially, both newly proposed biopolymers (in particular limonene based and 1,4-cyclohexadiene based polymers) and traditionally commercialised polymer candidates were identified from open publications. Then, a comprehensive literature review was performed to construct the reaction pathways for polymer synthesis. In particular, pathways presented in the reaction network were chosen based on three criteria: (1) reaction conditions and synthesis methods are close to current industrial polymer production process operating conditions; (2) pathways with the highest conversion efficiency and selectivity are selected when there exist different industrial methods for polymer or precursor production; (3) all the intermediates included in the network are allocated to several reactions so that they can be eventually converted to biopolymers instead of being sold as by-products or wastes.

These criteria are adopted because the current research aims to identify a number of feasible reaction routes for the industrial scale production of sustainable polymer in near future (criterion 1, as close as possible to current industrial operating conditions), and meanwhile maximise both raw material and energy utilisation efficiency (criteria 2 and 3, approaching zero waste). As a result, although there are reactions reported to exhibit higher selectivity or conversion efficiency under other circumstances (e.g. new technologies developed recently in laboratory scale research), they are not considered here.

It is notable that this study aims to identify the most promising polymers which can be purely synthesised from biomass (only containing carbon, hydrogen and oxygen; additional hydrogen may be provided from water electrolysis if necessary), therefore other polymers which contain significant amounts of elements that cannot be provided from biomass are not considered. For example, although polyamides have also been researched in previous studies 34, due to their much higher nitrogen content (over 10 wt%) than that of biomass (0.1~2.5%) 34,35, additional nitrogen sources and their environmental impact have to be searched and quantified. Therefore, these polymers are excluded from the superstructure. The detailed superstructure is presented in Fig. 1, and the full names of the 24 polymers are listed in Table S1 (supplementary).

Reaction network flux analysis

Reaction network flux analysis (RNFA) was developed from flux balance analysis in 2011 to evaluate reaction pathways for biorenewables processing, in particular microalgae and biomass wastes based biofuels 36–38. Its mathematical framework is listed in Eq. 1(a) to Eq. 1(c). The RNFA objective function can be either an economic or energy criterion and is defined case by case 36. The constraints include both material mass balance and specifications of individual fluxes (e.g. fluxes cannot be negative). RNFA in general results in a linear program (LP), and thus shows high efficiency when screening a comprehensive reaction network containing hundreds of synthesis pathways 37,38. A detailed introduction and literature review of RNFA can be found in previous work 32,36. The essential reaction network information including reaction conversion efficiency, heat of reaction, selectivity etc. in the current study is summarised in Table S2.

subject to:

where is the reaction molar flux, is the objective function coefficient vector, is the stoichiometric matrix and is the product vector. Specific to the current study, by embedding reaction conversion efficiency and selectivity, Eq. 1(b) is finally formulated as Eq. 1(d), where , , , and represent stoichiometric parameter, molar flux, conversion efficiency and selectivity of reactant ( is the set of reactants); and , are stoichiometric parameter and molar flux of product ( is the set of products).

Selection of objective functions

Three criteria are included in this study to screen the reaction network and determine the optimal biopolymer production routes. The first criterion is process profit, representing the economic criteria 37. The second and third criteria are atom economy and carbon efficiency, respectively, both of which come from green chemistry metrics and take the process environmental impact into account 39. This is because the current research aims to identify profitable and environmentally friendly routes for sustainable biopolymer production.

Process profit () is estimated in Eq. 2, where the first term on the right hand side denotes the annualised investment cost for a period of years and an interest rate of , and the second and third terms denote the annual raw material cost and annual product revenue, respectively 36,37. In the current study, the process is assumed to operate for 10 years with an annual operation time of 8500 hours and an interest rate of 8% 37. The annual feedstock supply for polymer production is assumed to be 100,000 ton initially, since the global market of different polymers ranges from 15,000 ton/year to 80 million ton/year 17,32. Then, the change of process annual cost with respect to the process production scale will be analysed in the Results and discussion section.

where (Million $) is the total investment cost estimated based on Eq. 2(b), and are molecular weight (g/mol) and price ($/kg) of raw material , where is the set of raw materials. and are molecular weight (g/mol) and price ($/kg) of the polymer , where is the set of polymers (those final products form which profit can be obtained), (MJ/mol) is the heat of reaction to generate chemical , where is the set of chemicals in the reaction pathway, and is the annual operation time.

The previous study 40 declared that used in Eq. 2(b) refers to the energy loss of a process, in specific, the difference between the enthalpy of combustion of raw materials and that of products. Based on the principle of energy balance, this energy loss is equivalent to the sum of enthalpy of reactions on each reaction step from feedstock conversion to final product synthesis, since in the current study energy integration (i.e. use of reaction heat for streams heating or cooling) is not included at the early stage of process design. Thus, attention should be focused on modifying the process energy loss in future study when a detailed process design for biopolymer production is carried out.

In this superstructure, the price of commercialised polymers and raw materials (biomass wastes, water, hydrogen, and hydrogen peroxide) can be found from manufacturer data, whilst that of newly proposed biopolymers (i.e. limonene and cyclohexadiene derived polymers) cannot be directly obtained since they are mainly studied under laboratory scale research and their potential market is unclear. Therefore, the group contribution method is applied in the current study to estimate their price 17,41,42. The principle of this method is to decompose a molecule into several functional groups, and then approximate the molecule’s price based on the quantity and estimated price of its constituent groups. A detailed introduction to group contribution and a price inventory of commonly used functional groups can be found in the recent study 17. Because the inventory was developed originally to estimate the price of monomers, by comparing the price of currently commercialised polymers and their approximated price based on group contribution, a scalar (2.648) is calculated to further refine the predicted price of the newly proposed biopolymers. The prices of raw materials and products are listed in Table S3.

Two green chemistry metrics, atom economy (AE) and carbon efficiency (CE) are used in this work. AE is one of the most widely used indices to indicate the greenness of a process, as it estimates how much of the reactants can be converted into final product 39. Specific to the current study, its definition is shown in Eq. 3(a). In addition, as the currently investigated biopolymers are directly derived from biomass which comes from atmospheric CO2, it is worthy of understanding how efficient the current reaction network can convert CO2 into useful commodities. Thus, CE is also used in this study and it is estimated by Eq. 3(b) 32.

where is carbon content (wt%) of polymer , , , and are the molar flux, molecular weight, and carbon content of biomass wastes.

Mixed integer nonlinear programming (MINLP)

One of the novelties of the current research distinguished from previous studies is to incorporate MINLP into RNFA, which enables the identification of the most promising synthesis pathways to produce a single bioproduct. Despite the wide application of RNFA for biorenewables production and reaction network screening, a severe challenge of RNFA is its limitation on pinpointing a single product instead of a combination of multiple products. In a recent study 32, it was demonstrated that although producing multiple products may result in a higher feedstock utilisation efficiency for high-level process design, this process could become economically unviable once detailed economic criteria are considered, since it will include more reaction and separation units compared to a single product synthesis route.

The first solution that could come to mind to obtain a single product is to solve 24 NLPs (each one producing only a single product). Once the optimal alternative for each product is determined, their answers will be compared, and then the best one among all alternatives will be chosen. This could be thought of as the brute force approach, where an exhaustive search is performed on all possible solutions. A more efficient strategy is to formulate a MINLP, which following a Branch and Bound algorithm 43 explores and prunes the solution space as needed to obtain the overall optimal solution with much higher efficiency. This turns out to be particularly beneficial when on top of the MINLP there is a multi-objective optimisation framework. Therefore, by embedding a MINLP into this study, the best single biopolymer candidate as well as its optimal synthesis route can be accurately identified from RNFA based high-level process design framework.

To ascertain that a single production route is obtained when solving the optimisation problem, the objective functions are reformulated as follows: for the economic objective in Eq. 2(a), the third term (profitability term) is modified to include binary variables ’s:

for AE, Eq. 3(a) is modified to:

for CE, Eq. 3(b) becomes:

and the following constraint is enforced:

Furthermore, to avoid bilinear terms in the problem formulation, this term is replaced by a new variable and the following constraints are added:

where and are upper and lower bounds, respectively, of variable .

Note that the above linearisation is possible because the product is either 0 (if ) or (if ). It should also be noted that although this linearisation can guarantee a mixed integer linear programming (MILP) formulation for the CE case, it will not do so for the AE or process profitability cases. Nonetheless, this transformation will ameliorate the nonlinearities in such problems and ease the solution process.

The MILP problem for the CE case is solved by a Branch and Cut algorithm, where relaxed LPs are solved by the solver GLPK (GNU Linear Programming Kit) 44. The MINLP problems are solved by a Branch and Bound procedure that includes multi-run (10 runs in this implementation) at every node as well as at the root, and an admissible gap before fathoming a node, as heuristics to address the nonconvexity of the problem 45. The relaxed NLPs are solved using IPOPT, the state-of-the-art interior point nonlinear optimisation solver 46. Implementations are programmed in the Python optimisation environment Pyomo 47, and computed in a Fedora Linux operating system with an Intel Core i7, 16 GB RAM 2.4 GHz computer.

By embedding the current optimisation framework into an MINLP formulation, the original economic and green chemistry objective functions are eventually written to be Eq. 4 and Eq. 5, respectively. Furthermore, three more constraints, Eq. 6(a) to Eq. 6(c), particularly for binary variables are added into the original RNFA framework (Eq. 1).

where is the binary variable of polymer , and if chemical is not a final product.

Multi-objective optimisation

As the current research aims to identify the most profitable and environmentally friendly biopolymer and its optimal synthesis route for future industrial sustainable polymer production, multi-objective optimisation is implemented. The multi-objective function is either maximising process profit and AE, or maximising process profit and CE. Presently, there are different approaches to solve multi-objective optimisation problems. Specific to superstructure optimisation, commonly used frameworks include the weighted sum method, ε-constraint method and fuzzy optimisation 48–50. In the current study the ε-constraint method is chosen to generate the Pareto-frontier under different cases and identify the compromise solution as it can guarantee Pareto-optimal solutions, as well as find any Pareto-optimal point even in the nonconvex case 51. When solving the problem of maximising process profit and AE, the optimisation problem can be formulated as below, and maximising process profit and CE is formulated in an equivalent fashion:

subject to:

where is the constraint index of atom economy.

Sensitivity analysis

Sensitivity analysis was developed to estimate the change of a system’s performance (, e.g. process profit) with respect to the change of a model parameter (, e.g. reaction selectivity), and has been widely used to identify the most influential parameters 52. The definition of sensitivity used in this study is presented in Eq. 8. It calculates the proportional change of a model performance with respect to the proportional change of a model parameter, thus reflecting the importance of the model parameter on the model simulation result. The sensitivity of polymer production and CE with respect to reaction selectivity has been explored in our recent study 32. This research, therefore, mainly focuses on the potential effect of price change of raw materials and polymers on process profitability. In specific, due to the significant amount of additional hydrogen gas supply and its more expensive price compared to other raw materials, its effect on the system’s performance (i.e. polymer ranking and profitability) is examined in detail. The best polymer candidates identified with respect to different objectives are chosen, and the impact of their price on the system’s performance is also explored. This analysis was conducted in Mathematica® 11.0 in a Windows 7 operating system in an Intel Core i7, 8.0 GB RAM 2.6 GHz computer. The sensitivity is calculated as follows:

where is the system’s performance, and is the model parameter. In this study, is defined as 10% (one -at-a-time analysis).

Results and discussion

Optimisation results of single objectives

Initially, biopolymer rankings with respect to the three individual objective functions are identified. In addition, as this superstructure includes a number of currently intensively studied sustainable biopolymers (14 limonene and cyclohexadiene based polymers), it is desirable to investigate their industrialisation potential against the economic and environmental criteria. As a result, two case studies, Case 1 focusing on all the polymers involved in the superstructure and Case 2 only focusing on limonene and cyclohexadiene based polymers, are included in this work, and Table 1 lists the biopolymer ranking.

From the table, it is found that when including all polymers, polymethyl methacrylate (PMMA) is always one of the top three polymers regardless of economic or environmental criteria, due to its high reaction selectivity, low reaction steps (thus low reaction and separation unit cost), and high price (profit is up to 61.8% of revenue). In addition, it is found that the second and the third best candidates w.r.t. the economic criterion are two different routes for polycyclohexadiene (PCE) production, with almost the same process profit. This is because PCE can be synthesised through either 1,4-cyclohexadiene or 1,3-cyclohexadiene in the reaction network, and the conversion between these two monomers happens under mild operating conditions (368 K and = 4.18 kJ/mol) with negligible operation costs. Such a conclusion means that PCE synthesis route is sensitive and unstable in the current superstructure, and at a high-level process design stage the two routes are indistinguishable. Therefore, more detailed process design must be carried out in the future to identify the optimal PCE production pathway. Furthermore, when considering green chemistry metrics, the two promising polymers identified in the recent study 32, polyethylene (PE) and polypropylene carbonate (PPC), also find their positions in the current rank because of their advantageous reaction selectivities over other polymers.

More importantly, a trade-off between the environmental objectives (AE and CE) and the economic objective (profit) is found to determine whether to use additional hydrogen supply for polymer production (H2 is assumed to generate by water electrolysis so that biopolymers can be as much “green” as possible). This can be clearly observed in Table 1 under both Case 1 and Case 2. In this study, hydrogen plays the important role to remove the oxygen from biomass and tune the composition of polymers. Without hydrogen supply, a significant amount of oxygen from biomass has to be released by utilising biomass carbon and forming CO2. Thus, both CE and AE will be remarkably decreased. However, because of the high price of hydrogen (2.7 $/kg to 4.0 $/kg depending on different resources, higher than the price of most polymers from 1.0 $/kg to 3.0 $/kg) 37, its intensive use results in an economic burden to the process profitability, and thus it is not favoured by the economic objective. This, therefore, decidedly emphasises the importance of conducting multi-objective optimisation for environmentally friendly biopolymer production and optimal synthesis route design.

In terms of the newly investigated polymers, it is found that similar to PMMA, polycyclohexadiene carbonate (PCHDC) is one of the best candidates for all the three criteria crossing economy to green chemistry, attributed to its superiority in both reaction selectivity and price. It is also observed that cyclohexadiene based polymers are more promising than limonene based polymers no matter what criterion is chosen. Based on a thorough comparison, it is concluded that both the number of reaction steps for limonene based polymers synthesis and their estimated prices are similar to those of cyclohexadiene based polymers, whilst their reaction selectivities (e.g. r7 and r28) are only around 50%. Thus, it is understandable why their production and green chemistry metrics are lower than cyclohexadiene based polymers. Therefore, more attention should be paid to identify the optimal reaction conditions and explore alternative reaction pathways for limonene derived polymers in future research.

Optimal synthesis routes with respect to multiple objectives

In order to identify the most profitable and environmentally friendly routes for biowaste derived sustainable polymer synthesis, multi-objective optimisation is conducted in this study and Pareto-frontiers are generated to determine the utopia point (ideal point where both objectives are optimised) and compromise point (feasible point that is closest to the utopia point). Moreover, as most of the newly proposed biopolymers share the same monomer (either limonene or cyclohexadiene) and their synthesis from monomer to polymer undergoes relatively short reaction steps, it is possible that multiple biopolymers can be produced simultaneously to improve both process profitability and raw material utilisation efficiency. As a result, the constraint that only one polymer can be produced from the system is released in Case 2 (exploring the optimal reaction pathways for the production of newly proposed polymers). Thus, MILP and MINLP are used when aiming to screen the entire superstructure and identify the best polymer amongst all the involved polymers (Case 1), and LP (linear programming) and NLP (nonlinear programming) are implemented for Case 2. In addition, two scenarios, profit vs. CE and profit vs. AE, are researched.

Scenario 1: Economic objective vs. CE. The Pareto-frontier of Case 1 and Case 2 are presented in Fig. 2, and their respective compromise point is summarised in Table 2. The detailed optimal synthesis routes corresponding to the compromise points are shown in Fig. 3.

From Table 1, it is concluded that the two extreme points in Fig. 2(a) represent PMMA production without hydrogen supply (highest profit) and PE production with hydrogen supply (highest CE), respectively. From Fig. 2(a), it is seen that when the frontier moves towards the environmental extreme point, the process becomes economically unviable (), indicating that the region close to the environmental optimum is unlikely to be implemented. This is probably due to the lower price of PE compared to PMMA and higher hydrogen demand for PE production. In order to balance the trade-off between process profit and CE, the water-gas shift reaction is activated to generate H2 which is much cheaper than directly purchasing hydrogen (Fig. 3(a)). At the compromise point listed in Table 2, the ratio of hydrogen supplied between direct purchase and self-generation (water-gas shift reaction, excluding H2 generated from biomass gasification) is 6.09:1, suggesting that most of the carbon is converted into polymer rather than generating H2 (thus converted into CO2). Because of the heavy hydrogen load, the overall gross process profit is less than half of the process revenue.

On the contrary, in Case 2 the two extreme points correspond to PCE production without hydrogen supply (highest profit) and PCHDC production with hydrogen supply (highest CE), and the entire frontier is feasible. The compromise point refers to the production of both PCE and PCHDC, because they are derived from the same monomer and thus the investment and operation cost to produce a second product is affordable. It is found that hydrogen is completely provided from direct purchase, probably due to the highest price of PCE amongst all the currently investigated polymers. Hence, the water-gas shift reaction is not recommended since it will reduce CE and process productivity. The process profit, however, is still lower than half of the revenue, which might be attributed to the longer reaction steps. It is also important to remember that since the cost of the two synthesis routes for PCE production (via 1,4-cyclohexadiene or 1,3-cyclohexadiene) are indistinguishable in the current study, both are included in Fig. 3(b) to represent the optimal synthesis routes identified in this work.

Scenario 2: Economic objective vs. AE. The Pareto-frontier of Case 1 and Case 2 are presented in Fig. 4, and their respective compromise point is summarised in Table 2. The optimal synthesis routes of the compromise points are same as those presented in Fig. 3.

From Fig. 4(a), it can be seen that in contrast to Scenario 1, the whole frontier in this scenario is feasible. This is because the environmental extreme point is now switched to producing PMMA (higher price than PE) with hydrogen supply. When comparing the results in Table 2, it is concluded that despite the fact that in Scenario 2 the compromise point also corresponds to single PMMA production, much less additional hydrogen is required in this scenario and the process profit is slightly enhanced. It indicates that the current optimal synthesis route is relatively stable with respect to different green chemistry metrics, and the only change is the amount of directly purchased hydrogen. Because PMMA is a commercialised polymer, the currently identified optimal synthesis route therefore has great potential to be industrialised in the future to produce sustainable and environmentally friendly PMMA.

Similarly, the same products are found for newly proposed polymer production in the two scenarios. It is also observed that when the environmental objective is to maximise AE, the ratio between PCHDC and PCE is significantly increased. This is because compared to PCE, PCHDC can utilise more oxygen from biomass, and as a consequence a higher percentage of raw materials can be utilised for polymer production. Furthermore, the same additional hydrogen load in the two scenarios indicates that the total amount of cyclohexadiene (monomer) synthesised from biomass is the same, and only the distribution towards the two polymers is affected by the change of the environmental objective. However, because of the lower price of PCHDC compared to PCE, in this scenario, process profit is reduced by over 8%. Similarly, the synthesis route shown in Fig. 3(b) is also found to be stable when changing green chemistry metrics, thus this pathway should be further refined for detailed process design.

Sensitivity analysis

To explore the stability of the above identified optimal biopolymer synthesis routes, sensitivity analysis is conducted. In Case 1 (all polymers) and Case 2 (newly proposed polymers) the best candidates with respect to different objectives are PMMA, PE, PCE and PCHDC. Hence, their prices are changed by 10% to explore the superstructure stability. Meanwhile, because of the higher price of hydrogen compared to other raw materials and its intensive use in these processes, its price is also included in the sensitivity analysis.

Sensitivity analysis of Case 1. In this case, the change in price of hydrogen, PMMA and PE is included. Through sensitivity analysis, it is found that changing the price of H2 and PE does not affect the reaction network results. However, when the price of PMMA is decreased by 10%, the best polymer candidate w.r.t. the economic criterion is shifted to PCE. This switch between PCE and PMMA occurs when the price of PMMA is reduced by 4%, meaning that the current system is sensitive to the price of PMMA and PCE. Because the economic extreme point is changed to PCE, it is necessary to re-estimate the compromise point so that both the best polymer and its optimal synthesis route can be identified. What is more, to better understand the performance of the reaction network when it becomes sensitive, the constraint that only one polymer can be produced is completely relaxed in this section. Table 3 lists the re-estimated compromise point.

By comparing Table 2 and Table 3, it is found that when the objective is maximising process profit and CE, the optimal synthesis route and polymer candidate are still the same and not affected by the price change of PMMA, even if neither of the extreme points correspond to the production of PMMA. It means that in order to balance trade-offs between different criteria, it is not necessary for the compromise point to choose either of the best polymers subject to an individual criterion (i.e. PE or PCE) or a mixture of them. Instead, a third candidate (e.g. PMMA) may be chosen, as shown in this case. However, if the objective is to maximise profit and AE, the best polymer indeed becomes a mixture of the two polymers synthesised at the extreme points, and the optimal synthesis route is also changed and shown in Fig. 3(c). Overall, this result shows that the current system is sensitive when the price of PMMA varies and the objective function is to maximise process profit and AE.

Sensitivity analysis of Case 2. In Case 2, the prices of PCE, PCHDC and hydrogen are investigated. Based on sensitivity analysis, it is found that the system’s performance is not sensitive to the price change in hydrogen and PCHDC. However, when the price of PCE is changed, the optimal synthesis route for PCE production is switched from the 1,3-cyclohexadiene pathway to the 1,4-cyclohexadiene pathway. As mentioned before, these two pathways are not distinguishable in this work. Therefore, this switch is probably introduced by the numerical precision. The optimal biopolymer candidates (PCE and PCHDC) are not affected, and only their ratio is changed due to the price change (shown in Table 3). It is also found that the total amount of cyclohexadiene synthesised from biomass is constant, as the volume of additional hydrogen supply is the same. This means that distinct from Case 1, the current superstructure is stable when aiming to produce newly proposed polymers. Furthermore, producing multiple polymers from one monomer also offers the process a higher flexibility, since the process can easily mediate the production of different polymers when the objective is changed or the price of polymers fluctuates frequently.

Effects of process scale

Finally, the effect of process scale on process cost is studied. In particular, the three promising polymers identified in this study, PMMA, PCHDC and PCE, are selected as the representatives. The process cost of these polymers with respect to the annual feedstock supply (ranging from 10,000 tonnes to 3000,000 tonnes) is shown in Fig. 5.

From Fig. 5, it is seen that for all the three polymers, their process cost decreases rapidly with the increasing process scale until the annual consumption of biomass feedstock reaches 500,000 tonnes, beyond which the decreasing trend of process cost slows down and becomes steady. This suggests that in order to improve and stabilise the process profitability for the industrial scale production of sustainable biopolymers, the annual production of PMMA and cyclohexadiene based polymers (sum of PCHDC and PCE) should be above 210,000 tonnes and 135,000 tonnes (cyclohexadiene basis), respectively, calculated based on the mass balance of their optimal synthesis route identified in this study.

At present, because cyclohexadiene based polymers are predominantly researched under laboratory scale experiments, their potential global market is still unclear and it is difficult to estimate their future demand. However, PMMA is a commercial polymer and its global market is estimated to exceed 4.8 Million tonnes/year by 2020 with an annual growth rate of 8.1% 53,54. Since its demand is higher than 210,000 tonnes/year which is the minimum required production for biomass derived PMMA synthesis process, it is concluded that PMMA has the great potential to be produced from biomass wastes in near future, and more attention should be paid to facilitate the industrialisation of this process.

Selection of biomass for sustainable biopolymers production

Finally, from the manufacturer’s perspective, it is useful to particularly address two questions: (1) for each polymer what is the best starting biomass feedstock, and (2) for a given biomass feedstock what would be the most suitable polymer to be produced. Therefore, three types of commonly used solar energy derived biomass feedstock, forestry wastes 55 (e.g. wood waste, (CH1.52O0.67)n), agricultural wastes 55 (e.g. wheat straw, (CH1.36O0.57)n), and microalgae biomass wastes 56 (e.g. Nannochloropsis sp., (CH1.66O0.43)n), are selected in this study, and the three most promising polymers, PMMA (CH1.6O0.4)n, PCHDC (CH0.86O0.29)n, and PCE (CH1.67)n identified in this research are chosen as the polymer representatives for this discussion.

Furthermore, as additional hydrogen supply is found to be a critical issue affecting both the environmental impact and process profitability for sustainable biopolymer production, the amount of extra hydrogen supply is considered as the criterion for the matching of biomass feedstock and biopolymers. As a result, Table 4 lists the amount of extra hydrogen that has to be provided so that one molecule of biomass is fully converted to one molecule of polymer without carbon emission. Table 5 lists the ranking of all the three feedstock and polymers.

From Table 4, it is found that compared to the three types of biomass feedstock, microalgae biomass is clearly a better choice over other biowastes for sustainable biopolymer production due to its highest hydrogen content and lowest oxygen content. In particular, hydrogen can be considered as a by-product when using microalgae for PCHDC production, and no additional hydrogen has to be supplied when this type of biomass is used for PMMA production. This conclusion strongly suggests the great potential of using solar energy and CO2 to cultivate microalgae biomass for future sustainable biopolymer production. Moreover, due to the similar composition of forestry and agricultural wastes, from the atom economy point of view, there is no much difference when using any of them for polymer synthesis.

In addition, from Table 5, it is seen that regardless of the type of biomass or biopolymer, microalgae biomass and PCHDC are always ranked as the most promising feedstock and sustainable biopolymer, respectively. Such a conclusion clearly indicates that although the synthesis of PCHDC is still predominantly conducted under laboratory scale research, it already exhibits significant advantages over other newly proposed sustainable biopolymers for future commercialisation. Thus, more attention should be focused on its future development and scale-up analysis. On the contrary, however, for the production of PCE, it seems that other types of biomass which have less oxygen content (or different feedstock pre-processing methods such as anaerobic digestion which is used for methane and hydrogen production) should be employed as a better option for its industrial production; otherwise a large amount of hydrogen has to be provided externally which will inevitably lower the process profitability.

Conclusion

In the current study, a superstructure reaction network including 72 chemicals, 76 reactions and 24 newly proposed and traditionally commercialised polymers is constructed to efficiently convert biomass feedstock into sustainable biopolymers. Meanwhile, MILP and MINLP are incorporated into reaction network flux analysis to conduct for the first time a high-level process selection and design of single polymer production. Furthermore, to effectively balance the trade-off between economic criteria and environmental impact, multi-objective optimisation is implemented to identify the best biopolymer candidates and their associated optimal reaction pathways with respect to both process profit and green chemistry metrics (i.e. carbon efficiency and atom economy).

Based on the current research, it is found that polymethyl methacrylate and cyclohexadiene based polymers, in particular polycyclohexadiene and polycyclohexadiene carbonate, are the most promising existing (drop-in) and newly proposed polymers, respectively, which can be produced from biomass in near future. In addition, through sensitivity analysis, it is found that their ranking and optimal synthesis routes are relatively stable when their prices as well as those of raw materials change within a mild range. This further improves their chances for industrialisation. More important, the current research concludes that when considering environmental impact, a large amount of additional hydrogen has to be supplied into the system, and the process profitability can be significantly decreased. This conclusion suggests that in order to facilitate the commercialisation of biomass based polymers, it is essential to develop more cost effective technologies for sustainable hydrogen production. Finally, in terms of future work, the fate of side products (e.g. sold directly or co-producing other products) should also be thoroughly investigated and compared when conducting detailed process design, so that both process profitability and material utilisation efficiency can be improved.

Acknowledgement

This research is supported by the EPSRC project under grant EP/L017393/1, “Sustainable Polymers”.

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Figure 1: Superstructure reaction network for biopolymer synthesis

Figure 2: Pareto-frontier with respect to process profit (minimising ) and CE (minimising ). Pentagram: utopia point, filled circle: compromise point. (a): optimal results of all polymers; (b): optimal results of newly proposed polymers.

Figure 3: Optimal biopolymer synthesis route. (a): optimal synthesis route of Case 1 in Scenario 1; (b): optimal synthesis route of Case 2 in Scenario 1. Thick line: synthesis route for the best polymer. Dashed line: another potential PCE synthesis route. (c): optimal synthesis route of Case 1 when the price of PMMA is decreased by 10%.

Figure 4: Pareto-frontier with respect to process profit (minimising ) and AE (minimising ). Pentagram: utopia point, filled circle: compromise point. (a): optimisation results of all polymers; (b): optimisation results of newly proposed polymers.

Figure 5: Process cost of polymers at different production scale. (a): PMMA production; (b): PCHDC production; (c): PCE production.

Table 1: Biopolymer ranking with respect to different objectives

Case1: All polymers

Case 2: Newly studied polymers

Process profit

(Million $/year)

1st: PMMA (no H2 supply), 38.21

1st: PCE (no H2 supply), 36.11

2nd: PCE (no H2 supply), 36.11

2nd: PCE (no H2 supply), 36.10

3rd: PCE (no H2 supply), 36.10

3rd: PCHDC (no H2 supply), 22.03

CE

(wt%)

1st: PE (H2 supply), 73.77

1st: PCHDC (H2 supply), 50.66

2nd: PMMA (H2 supply), 64.08

2nd: PCHC/PCHDC (H2), 48.82

3rd: PPC (H2 supply), 52.48

3rd: PCHC (H2 supply), 47.11

AE

(wt%)

1st: PMMA (H2 supply), 54.12

1st: PCHDC (H2 supply), 39.23

2nd: PPC (H2 supply), 53.71

2nd: PCHC/PCHDC (H2), 37.97

3rd: PE (H2 supply), 41.91

3rd: PCHC (H2 supply), 36.80

Table 2: Compromise points under different scenarios

Scenario 1: Economic objective vs. CE

Case1: All polymers

Case 2: Newly studied polymers

Biopolymer

PMMA

PCE (42.85% carbon), PCHDC (0.71% carbon)

Process profit

35.97 Million $/year

32.81 Million $/year

CE

64.2%

43.56%

Additional H2

0.043 kg/kg biomass

0.047 kg/kg biomass

Profit / Revenue

0.46

0.42

Scenario 2: Economic objective vs. CE

Case1: All polymers

Case 2: Newly studied polymers

Biopolymer

PMMA

PCE (29.3% carbon), PCHDC (16.5% carbon)

Process profit

37.97 Million $/year

27.21 Million $/year

AE

48.2%

29.8%

Additional H2

0.0066 kg/kg biomass

0.047 kg/kg biomass

Profit / Revenue

0.41

0.37

Table 3: Compromise points when the prices of polymers are changed

Case 1: When the price of PMMA is reduced by 10%

Profit vs. CE

Profit vs. AE

Biopolymer

PMMA

PCE (10.5% carbon),

PMMA (32.3% carbon)

Process profit

27.9 Million $/year

33.45 Million $/year

Environmental objective

64.2%

41.7%

Additional H2

0.043 kg/kg biomass

0.0 kg/kg biomass

Case 2: When the price of PCE is reduced by 10%

Profit vs. CE

Profit vs. AE

Biopolymer

PCE (30.6% carbon),

PCHDC (13.0% carbon)

PCE (29.3% carbon),

PCHDC (16.5% carbon)

Process profit

32.8 Million $/year

27.2 Million $/year

Environmental objective

43.6%

29.8%

Additional H2

0.047 kg/kg biomass

0.047 kg/kg biomass

Table 4: Amount of extra hydrogen supplied (mol/mol) for biopolymer production

Algae biomass

Forestry biomass

Agricultural biomass

PMMA

0.0

0.31

0.29

PCHDC

-0.26

0.05

0.03

PCE

0.44

0.75

0.73

Table 5: Ranking of different types of biomass and biopolymers

PMMA

PCHDC

PCE

Algae

Forestry

Agricultural

1st

Algae

Algae

Algae

PCHDC

PCHDC

PCHDC

2nd

Forestry

Forestry

Forestry

PMMA

PMMA

PMMA

3rd

Agricultural

Agricultural

Agricultural

PCE

PCE

PCE

1