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Optimum Batch-Reactor Operation for the Synthesis of BiomassDerived Renewable Polyesters Mónica Lomelí-Rodríguez,† Martín Rivera-Toledo,*,‡ and José A. López-Sánchez† †

Stephenson Institute for Renewable Energy, Department of Chemistry, University of Liverpool, Crown Street, Liverpool L69 7ZD, United Kingdom ‡ Departamento de Ingeniería y Ciencias Químicas, Universidad Iberoamericana, Prolongación Paseo de la Reforma 880, Ciudad de México, 01219 México S Supporting Information *

ABSTRACT: For the first time, we present the process simulation and multiobjective optimization of the batch-reactor polyesterification of a library of biomass-derived renewable polyesters: poly(1,5-pentylene 2,5-furandicarboxylate) (PTF), poly(1,5-pentylene succinate) (PTS), and poly(1,5-pentylene 2,5furandicarboxylate-co-1,5-pentylene succinate (PTFTS). The simulation environment was implemented in Aspen Plus, and the ε-constraint method was employed for the optimization problem, considering two objective functions that maximize the number-average degree of polymerization (DPN) and minimize the heat duty Q. The performance of the biobased polyesters was compared to that of poly(ethylene terephthalate) (PET). The kinetic rate expressions were defined following the functional-group approach, and the parameters were estimated by fitting a polyesterification model found in the literature to the experimental data. The present work provides comprehensive fundamental information toward a feasible process design and scale-up of the esterification of biomass-derived products.

1. INTRODUCTION In recent years, biorefinery products and lignocellulosic biomass sources have become increasingly important in efforts to decrease the dependence of the chemical industry on traditional petrochemical feedstocks. The biorefinery concept has emerged as a potential alternative for supplying a portfolio of products such as fuels, fine chemicals, and monomers for polymer production.1 As a result, the bioderived-polymer industry is steadily increasing, with estimations indicating that the worldwide production of bioderived plastics will reach approximately 6 million tonnes by 2016, which accounts for about 1% of the approximately 300 million tonnes of plastics produced annually.2,3 Among polymers, polyesters are an exciting field for the inclusion of biobuilding blocks because of their extended applications such as engineering resins, films, coatings, fibers, and plasticizers.4 In particular, our group has performed the synthesis and modeling of bioderived polyesters and copolyesters based on 2,5-furandicarboxylic acid (FDCA), succinic acid (SA), and either 1,3-propanediol (PDO)5 or 1,5pentanediol (PTO). As continuous research and progress have been pursued in the synthesis of novel renewable biomassderived polyesters and their potential applications, it is imperative to properly scale up the production processes so that these materials are feasible from both sustainability and economic perspectives and can eventually replace the petrochemical-based processes. Therefore, the implementation of a range of process engineering tools, such as modeling, sensitivity analysis, and optimization, would allow for the © XXXX American Chemical Society

determination of the best configurations and operating conditions for the production of these polymers. Proper modeling provides thorough information about the process, ensuring improved safety, cleanliness, profitable operations, and the smooth introduction of new products into markets.6 In the specific case of polymers, it is well-known that tackling the desired thermal and mechanical properties depends strongly on achieving a high molecular weight and a narrow molecular weight distribution (MWD), so optimal reactor operating conditions must be guaranteed.7 Along with the final quality of the synthesized polymers, the reduction of production costs needs to be considered when implementing the polymerization process. To achieve these goals, process optimization represents a powerful tool for effectively designing efficient industrial operations.8 Multiobjective optimization (MOO) techniques can be employed to deal with the simultaneous and opposing performance objectives commonly found in polymerization reactions. This methodology is based on finding a set of equally good solutions, known as Pareto optimal solutions. Along the Pareto frontier, no point is better than the other solutions with respect to all objective functions.9 Hence, there is no single global solution, which leads to the designation of a set of points that fit a definition of an optimum operating Received: August 25, 2016 Revised: October 29, 2016 Accepted: December 21, 2016

A

DOI: 10.1021/acs.iecr.6b03260 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research point.10 Several multiobjective optimization methods are commonly used in engineering fields, an excellent and comprehensive review of which was published by Marler and Arora.10 Within the field of multiobjective optimization of polymerization reactors, considerable work has been done on both the free-radical7−9,11 and step-growth12−17 mechanisms. As is wellknown, polyesterification kinetics falls into the latter category, as originally established by Flory18 and studied extensively by Kumar and Gupta.19,20 Regarding polyesterification process simulations, previous research has focused on different polyester systems such as the reaction of maleic anhydride with 1,2-propylene glycol,21 the reaction of glycerol and adipic acid,22 the production of poly(3hydroxybutyrate) by bacterial fermentation,23 and the evaluation of the process and greenhouse-gas balance of the production of poly(ethylene 2,5-furandicarboxylate) (PEF) from fructose.24 In the area of sustainability, a life-cycle assessment comparing the impacts of using ethylene glycol from biomass against petrochemical sources for the production of poly(ethylene terephthalate) (PET) showed reductions of 3.6−28% in greenhouse-gas emissions and a 16% reduction of fossil-fuel consumption for the use of biomass-derived ethanol.25 In the present work, we report an integrative process engineering study for the batch synthesis of the biomassderived polyesters poly(1,5-pentylene 2,5-furandicarboxylate) (PTF), poly(1,5-pentylene succinate) (PTS), and poly(1,5pentylene 2,5-furandicarboxylate-co-1,5-pentylene succinate) (PTFTS). First, we performed reaction modeling, including estimating kinetic parameters by fitting a predetermined polyesterification model to the experimental data. Next, the batch process simulation and multiobjective optimization were performed for all of the systems in Aspen Plus, concluding with the assessment of sustainability indicators for each case. The analysis of PET was included as a comparative petroleumderived polyester reference. We focused solely on the chemical reactor because it is considered to be the heart of any process; however, a complete chemical manufacturing process simulation would need to consider other stages such as separation and purification and, specifically for polymers, compounding, blending, and polymer reinforcement.26 The reader is encouraged to refer to the optimization work performed in other processing stages, for example, the separation stage using cyclone separators27 or batch distillation.28 Although the analysis of the full manufacturing process is beyond the scope of the present work, this study does set the cornerstone for future research in this area. Note that the sustainability indicators refer exclusively to the optimized reactor operating conditions and a similar assessment should be completed for the next production stages, as well as the production of monomers from carbohydrate sources, which will enable the performance of a complete life-cycle assessment (LCA). To the best of our knowledge, this is the first time that a comprehensive process modeling, simulation, and optimization work for a batch polymerization reactor has been presented for this library of biomass-derived renewable polyesters.

azeotropic distillation with a diol/diacid molar ratio of 1.3 at 210−230 °C. The reactor was fitted with an overhead stirrer, a thermocouple, a sampling port, a Raschig-ring-packed column, and a distillation condenser. Nitrogen was bubbled continuously through a gas inlet to ensure an inert system. The temperature at the condenser head remained in the range of 95−100 °C, and the reaction water was driven off and collected in the condenser. The esterification reaction was completed after all of the water had been removed and the head temperature returned to ambient temperature. The polycondensation reaction was continued by azeotropic distillation with a Dean−Stark trap and the addition of 3 wt % xylene as an azeotropic agent under atmospheric pressure. The actual experimental setup used is shown in Figures S1 and S2 of the Supporting Information. The complete experimental procedure and development can be found in our previous work.5 The structures of the polyesters, namely, PTS, PTF, and PTFTS, are shown in Figure 1, and the concentrations of the monomers are listed in Table 1. The synthetic procedure for the copolyesters PTFTS is shown in Figure 2.

Figure 1. Chemical structures of the biomass-derived polyesters.

Table 1. Compositions of the Synthesized Polyesters polyester PTS PTFTS PTFTS PTFTS PTFTS PTF

15/85 30/70 70/30 85/15

diol/diacid molar ratio

FDCA (mol %)

SA (mol %)

1.05 1.3 1.3 1.3 1.3 1.3

0 15 30 70 85 100

100 85 70 30 15 0

To perform an accurate simulation and allow for further optimization, a robust kinetic model must be implemented. We considered the functional-group approach, which is commonly used for step-growth polymerizations, as in the cases of the kinetics of PET29,30 and poly(propylene terephthalate)31 polymerizations. To develop our complete kinetic scheme, we followed the procedure reported by Seavey and Liu for the PET mechanism.29 First, the main species present were identified and the segments defined. We then proceeded with the definition of the reactions in the system and the species mass balance, to derive a particular reaction rate for each of the

2. DEVELOPMENT OF THE KINETIC MODEL The polyesters were synthesized from 2,5-furandicarboxylic acid, succinic acid, and 1,5-pentanediol in a four-neck roundbottom flask (250 mL) or a single-wall glass reactor (500 mL) by a two-step process comprising polyesterification and B


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Industrial & Engineering Chemistry Research

Figure 2. Synthesis of PTFTS copolyesters.

that were classified into the following five sets of rate constants (ki, i = 1, ..., 5): (1) Forward water formation considering 1,5-pentanediol (k1)

polyesterifications. The conventional species considered were water, 1,5-pentanediol, succinic acid, and FDCA. The diol and diacids polymerize to form the corresponding polyesters, which are composed of terminal (T-) and bound (B-) segments for both the diacids and the diol. Figure 3 shows the structures of

PTO + FDCA → H 2O + (T‐PTO) + (T‐FDCA)

(1)

PTO + (T‐FDCA) → H 2O + (T‐PTO) + (B‐FDCA) (2)

PTO + SA → H 2O + (T‐PTO) + (T‐SA)

(3)

PTO + (T‐SA) → H 2O + (T‐PTO) + (B‐SA)

(4)

(2) Forward water formation considering the diol terminal segment (T-PTO) (k2; k2 = k1) (T‐PTO) + FDCA → H 2O + (B‐PTO) + (T‐FDCA) (5)

(T‐PTO) + (T‐FDCA) → H 2O + (B‐PTO) + (B‐FDCA) (6)

(T‐PTO) + SA → H 2O + (B‐PTO) + (T‐SA)

(7)

(T‐PTO) + (T‐SA) → H 2O + (B‐PTO) + (B‐SA)

(8)

(3) Backward water formation (k1′ ; k1′ = 0)

Figure 3. Chemical structures of the repeat and terminal segments.

H 2O + (T‐PTO) + (T‐FDCA) → PTO + FDCA

(9)

H 2O + (T‐PTO) + (B‐FDCA) → PTO + (T‐FDCA)

the different segments involved in the mechanism. As in the case of PET, two main reactions were considered: esterification or water formation and ester interchange (transesterification). Side reactions such as degradation of the diester group or dehydration of the diol and its end segments, however, were not included in the kinetic model because experimental data are not available to validate the estimation of the kinetic parameters. The complete set of reaction stoichiometry and associated reaction rate equations and mass balances is available in the Supporting Information (Tables S1−S3). The following assumptions are also considered in the groupcontribution method: (1) The reactivity of the molecules is not a function of the size of the molecule (known as the equal reactivity hypothesis).20 (2) The rate coefficients ki of the conventional species are equal to those of the segments. (3) The reversible reactions do not govern the kinetics; they govern only the equilibrium and are disregarded. (4) No mass-transfer limitations are encountered. With the assumptions and species defined, Aspen Plus automatically29,32 generated a set of 12 reactions for the PTF and PTS homopolyesters and 24 for the PTFTS copolyesters

(10)

H 2O + (T‐PTO) + (T‐SA) → PTO + SA

(11)

H 2O + (T‐PTO) + (B‐SA) → PTO + (T‐SA)

(12)

H 2O + (B‐PTO) + (T‐FDCA) → (T‐PTO) + FDCA (13)

H 2O + (B‐PTO) + (B‐FDCA) → (T‐PTO) + (T‐FDCA) (14)

H 2O + (B‐PTO) + (T‐SA) → (T‐PTO) + SA

(15)

H 2O + (B‐PTO) + (B‐SA) → (T‐PTO) + (T‐SA) (16)

(4) Forward ester interchange (k3) PTO + (T‐FDCA) + (B‐PTO) → (T‐PTO) + (T‐PTO) + (T‐FDCA)

(17)

PTO + (B‐FDCA) + (B‐PTO) → (T‐PTO) + (T‐PTO) + (B‐FDCA) C

(18)


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Industrial & Engineering Chemistry Research dCCOOH = rCOOH dt

PTO + (T‐SA) + (B‐PTO) → (T‐PTO) + (T‐PTO) + (T‐SA)

(19)

dC H 2 O PTO + (B‐SA) + (B‐PTO) → (T‐PTO) + (T‐PTO) + (B‐SA)

dt (20)

dCOH = rOH , dt

(5) Reverse ester interchange (k′3; k′3 = 0)

rH2O = −rCOOH

(21)

(31)

rOH = rCOOH

dCCOOR = rCOOR , dt

(T‐PTO) + (T‐PTO) + (T‐FDCA) → PTO + (T‐FDCA) + (B‐PTO)

= rH2O ,

(30)

(32)

rCOOR = −rCOOH

(33)

The initial values at t = 0 are given by (T‐PTO) + (T‐PTO) + (B‐FDCA) → PTO + (B‐FDCA) + (B‐PTO)

(22)

(T‐PTO) + (T‐PTO) + (T‐SA) → PTO + (T‐SA) + (B‐PTO)

(23)

i=1

(35)

COH = CCOOH 0 + b0

(36) (37) −1

where k0 is the pre-exponential factor in kg·mol min ; Ea is the activation energy in J·mol−1; R is the universal gas constant in J·mol−1K−1; CCOOH, COH, CH2O, and CCOOR are the concentrations of carboxylic acid, hydroxyl, water, and ester, respectively, in mol·kg−1; K is the equilibrium constant, and b0 is the initial excess concentration of hydroxyl groups. Note that Aspen Plus defines ester interchange reactions as polymerization reactions. Thus, the overall rate equation considered is the one proposed by Fradet and Maréchal,33 which includes the water correction of Szabó-Réthy35 for a nonstoichiometric balance of reactants

(24)

Np

∑ (Ci − Ci(p))2

C H 2O = 0

−1

To estimate the reaction coefficients ki, the models proposed in the literature were fitted to the experimental carboxylic acid data.33,34 The predictions of the models were obtained on ordinary differential equations (ODEs) defined by the reaction rate equations implemented in the MATLAB interface. The experimental data were regressed using the weighted-sum-ofsquares method stated in eq 25 min Zp =

(34)

CCOOR = 0

(T‐PTO) + (T‐PTO) + (B‐SA) → PTO + (B‐SA) + (B‐PTO)

CCOOH = CCOOH 0

n ⎡ ⎛ 1 − 0.018C ⎞⎤ dCCOOH m⎢ COOH ⎟⎟⎥ = − kCCOOH CCOOH + b0⎜⎜ ⎢⎣ dt ⎝ 1 − 0.018CCOOH0 ⎠⎥⎦

(25)

with

(38)

Zp = Zp(t , y , yp , u)

(26)

y = [CCOOH],

(27)

i = PTS, PTFTS, PTF

yp = [k 0i , Eai , K i]

This general step-growth polymerization model reported by Fradet and Maréchal33 incorporates the deviation from stoichiometry of the diol/diacid molar ratio and the change in volume of the reaction mixture due to the loss of water and was proposed for uncatalyzed reactions. We selected this model because our reaction conditions fall within these specifications and also because it was validated against our experimental data throughout the entire reaction time as presented in the Supporting Information (section 3) and for 1,3-propanediolbased polyesters.5 The full description of the mathematical development of eq 38 is available in section 3 of the Supporting Information.

(28)

The objective function Zp is the sum over all Np data points of the squared difference between the model predictions Ci(p) and the measurements Ci; y refers to the state variables; u represents the gradient for the control variables (temperature and molar ratio of diacids FDCA/SA), and yp represents the estimated parameters. For the esterification reactions, we chose the model developed by Lehtonen et al.34 This polyesterification model considers not only the concentration of carboxylic acid groups but also the presence of more species in the reaction mixture, namely, water, ester groups, and hydroxyl groups, allowing for the modeling of the evolution of water during the first stage of the reaction (esterification). Their proposed mechanism can be found in Scheme S1 (Supporting Information). The rate equation r is thus defined as ⎛ CCOOR C H2O ⎞ r = k 0e−Ea / RT ⎜CCOOHCOH − ⎟ K ⎝ ⎠

3. OPTIMIZATION The general multiobjective optimization problem is defined as min Ψ(x , u) = [ψ1(x , u), ψ2(x , u), ..., ψk(x , u)]T x ,u

(39)

subject to the constraints

dx = f (x , u) dt

(40)

with the following initial conditions: t = t0, x = x0 (29)

which is considered for the weighted sums of squares (eqs 25−28) as follows D

h(x , u) = 0

(41)

g (x , u) ≤ 0

(42) DOI: 10.1021/acs.iecr.6b03260 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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xlb ≤ x ≤ x ub

polymer quality and the costs of production, as defined by the expressions

(43)

ulb ≤ u ≤ u ub

(44)

As stated elsewhere, x is the vector of decision variables x ∈ Rn; u corresponds to the vector of manipulated variables u ∈ Rm; and Ψ ∈ Ek is a vector of objective functions Ψi(x): Ψn → Ψ1, where n, m, and k refer to the numbers of states, manipulated variables, and objective functions, respectively. The equality and inequality constraints are given by h(x,u) and g(x,u), with their corresponding lower and upper bounds, denoted by the subscripts lb and ub, respectively. Because of the multiobjective nature of the optimization, there is no single solution to the problem, and a set of feasible points must be determined.10 This is accomplished through the Pareto solution. According to the definition of Pareto optimality, any feasible point x* is said to be Pareto optimal if and only if there exists no other feasible point x such that Ψk(x) ≤ Ψk(x*) and ψi(x) < ψi(x*) for at least one function. All of the Pareto points lie on a feasible performance space for the objective function, defined as the Pareto frontier. Another important definition is that of the utopia point, whose solution, xup i , is obtained from the minimization of Ψk(x) subject to h(x) = 0, g(x) ≤ 0, and their boundary conditions.9 The utopia point is unattainable because it lies outside the Pareto frontier, but it is used as a reference point. Within the Pareto frontier, the efficient or compromise solution xs of the objective function Ψn(xs) is defined as

max(DPN)

(50)

min(Q )

(51)

11

Ψn(x s) = min{ ∑ [ψk(x , u) − ψk(x up , u)]2 }1/2 x ,u

k ∈ Rn

where DPN is the number-average degree of polymerization and Q is the heat duty in kBTU·h−1. We considered the heat duty as an objective function because energy needs to be managed carefully and intelligently in every process. The heat duty is a direct consequence of the operating temperature, which is manipulated to ensure the required quality of the final polymer. Energy losses could occur by dissipation or leaks, and such losses might translate into higher residence times, which could lead to hot spots, gelation, degradation, or undesired side reactions. The total energy of the process can be defined by the simple equation QT = Q net + Q losses

In practice, this minimization of energy losses could be achieved through optimization strategies applied to the energy use, such as ensuring that the equipment is in good condition, that the pipes are correctly insulated, and that the return of condensates when using direct steam is efficient. The net heat of the process cannot be minimized, however, as it is the energy needed by the reaction to achieve completion. The objective function was not defined in terms of gross profit because of the lack of complete information regarding the costs of the biomass transformation processes for all of the biomonomers considered and of the current commercial production of these types of polyesters. Currently, only succinic acid is commercially produced from biomass, and its synthesis reduces greenhouse-gas emissions by 94% compared to those of petroleum-derived succinic acid.38 Although carbohydratebased FDCA is not yet produced industrially, plans for an FDCA production facility with an annual capacity of 50000 t/ year were recently announced.39 Even though sustainability indicators were not explicitly used in the objective functions, the parameters of these indicators, such as the CO2 emission rates, amount of polymer produced, and heat duty, are contained within the objective functions. These indicators were calculated during the simulations, enabling an initial evaluation of the degree of sustainability achieved by means of the synthesis stage while ensuring the fulfillment of the required product quality.

(45)

36

Recently, Dowling et al. proposed a variant of a multiobjective optimization problem by presenting a conditional-value-at-risk (CVaR) framework when dealing with multiple-stakeholder decision making. To assess the stakeholders’ satisfaction with a decision and how the stakeholders reflect the overall population’s opinions, the authors proposed a method that weighs each of the the stakeholder’s preferences and, from them, formulates dissatisfaction functions that account for the deviations from the ideal solution. Following this framework allows situations in which a single stakeholder dictates the solution to be avoided, enabling a solution to be obtained that complies with economic, sustainability, and safety targets. Such an approach would be very convenient when the multiobjective optimization of the full production process of biomass derivatives is undertaken. To solve our MOO problem, we used the ε-constraint method, an a posteriori MOO method in which one of the objective functions is optimized while the other is considered as a constraint.37 The problem is then defined as

min ψ1

4. RESULTS AND DISCUSSION 4.1. Kinetic Modeling. We developed a model for the design and simulation of an optimum and sustainable process to produce polyesters from biomass in Aspen Plus, considering a step-growth kinetic model. This model relies on the endgroup analysis presented in Section 2, providing information in terms of the number-average molecular weight, Mn, and the number-average degree of polymerization, DPN. Aspen Plus is unable to calculate weight-average molecular weight and, thus, the polydispersities of the studied systems. We considered a production rate of 40 t/day as the base case of the batch process. The monomers, namely, PTO, FDCA, and SA, were fed at 25 °C at the molar ratios listed in Table 1. Our initial estimates for the operating conditions were a processing temperature of 220 °C and a residence time of 8 h. For the estimation of the physical and thermodynamic properties, we used the polymer nonrandom two-liquid (PolyNRTL) activity-

(46)

x

subject to g ≤ 0,

h=0

ψ2 ≤ ε

(47) (48)

where ε defines the values along the Pareto frontier in the range min ψ2 ≤ ε ≤ min ψ2

(52)

(49)

The two objective functions considered for the biomassderived polyesterification in a batch process refer to both the E


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azeotropic distillation. Systems rich in FDCA were found to present the lowest initial rates, whereas SA-rich systems had the highest rates; however, all the polyesters reached a carboxylic acid conversion of 90% or above. This trend was also observed for similar polyesterifications with 1,3-propanediol.5 Representative simulated concentration profiles of water and diol using the model proposed by Lehtonen et al.34 are available in Figure S3 (Supporting Information). The kinetic fitting and estimated parameters of the nonstoichiometric model are available in Table S5 and Figure S4 (Supporting Information). 4.2. Simulation and Optimization. The batch simulations and ε-constraint optimizations performed in Aspen Plus for the different polyesters provided the optimum operating conditions and the results of the mass balances for each of the monomers, segment concentration profiles, energy balances, and polymer attributes such as number-average molecular weight Mn and DPN. These attributes were chosen because of the strong relationship between polymer structure and final polymer properties. Many of these properties increase with molecular weight, before reaching an asymptotic value. If the molecular weight and degree of polymerization were too low, the material would have oligomeric nature, and therefore, the final properties would probably not be suitable for the intended application. However, if the Mn and DPN values were above the upper limits, this would lead to a situation in which processability issues would be inevitable and the safety of the process would be put at risk.26 The intended application for the polyesters synthesized in this work is coil coatings. The molecular weights of most polyesters used in coatings range between 2 and 6 kDa.45,46 Table 2 summarizes the results of the optimization, indicating the efficient or compromise solutions. The Pareto frontiers for PTS, PTFTS 15/85, PTFTS 85/15, and PET are depicted in Figure 6. All of the optimum process temperatures of our polyesters were in the range of 190−225 °C, which corresponds to our previous experimental experience. The simulations suggest that the lowest processing temperature of 191 °C is sufficient for PTS, which is expected because SA does not lead to gelation or poor solubility as in the case of FDCA. All of the process temperatures for the furan polyesters were found to be above 210 °C, whereas PET was found to be processed well above that range, at 269 °C, which falls within the operating conditions found in the literature.29,30 The simulated final production of polymer in each case was between 1300 and 1430 kg·h−1, with Mn and DPN values of about 4 kDa and 40, respectively. The polymeric attributes for PET were lower, with a final Mn value of 3.6 kDa and a degree of polymerization of 38. In terms of heat duty, PET exhibited a slightly higher energy consumption (2.2 kBTU·h−1) than our biomass-derived polyesters (1.0−2.1 kBTU·h−1), which was further analyzed in terms of sustainability indicators, as reported in the next section. It is worth mentioning that multiplicity behavior could be found in the polymerization reactors, because of the high nonlinearity of the system. This is evident in the Pareto plot for PTFTS 15/85 in Figure 6c. The efficient solution was found to be a local solution because it fulfilled optimality requirements in a multisteady-state system. Further analysis of this matter would be required to establish the effects of the operating conditions in multiplicity regions, but such an analysis falls out the scope of the present work. Research on multiplicity regions has been carried out for a continuous reactor for the polymerization of methyl methacrylate.47

coefficient method because the system was operating at low pressure with varying copolymer compositions and sizes.40 This method was coupled with the van Krevelen41 and Joback42 group-contribution methods. The PolyNRTL model was also chosen over other thermodynamic methods because it has been satisfactorily implemented for the modeling of segment-based step-growth polymerizations.43,44 The Aspen Plus flowsheet for the batch reactor is shown in Figure 4. The estimation of the

Figure 4. Aspen Plus flowsheet for the batch polyesterification process, showing the batch reactor and heat exchanger (HX).

kinetic parameters was carried out using the standard methods embedded in MATLAB for esterification reactions using the model proposed by Lehtonen et al.,34 and the values obtained are summarized in Table S4 (Supporting Information). The sensitivity analysis for these parameters is included in the Supporting Information as well (section 6, Figure S13). In comparison, the reported values of k0 and Ea for the esterification of maleic acid and propylene glycol are 2.31 × 104 kg·mol−1·min−1 and 58.2 kJ·mol−1, respectively, which are similar to our own estimated parameters. As observed in Figure 5, the experimental conversion was satisfactorily fitted to the esterification model throughout the entire reaction time, with some outlier points between about 120 and 150 min possibly being due to the change in the configuration setup to

Figure 5. Conversion of COOH groups versus time for the PTFTS copolyesters, fitted to the polyesterification model. Symbols, experimental data; lines, model estimations. F


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Industrial & Engineering Chemistry Research Table 2. ε-Constraint Optimization Results for the Batch Syntheses of PTS, PTFTS, PTF, and PET polyester PTS PTFTS PTFTS PTFTS PTFTS PTF PET

15/85 30/70 70/30 85/15

temperature (°C)

Mn

DPN

polymer production rate (kg·h−1)

heat duty (kBTU·h−1)

191 213 217 216 217 210 269

4200 4100 4200 4500 4200 4700 3600

45 43 43 42 42 42 38

1401 1407 1414 1429 1401 1305 1276

2114 2082 1217 2098 2114 1012 2267

Figure 6. Pareto frontiers and utopia points of (a) PTS, (b) PTFTS 85/15, (c) PTFTS 15/85, and (d) PET. The objective functions are in dimensionless form (DPNA and QA).

The simulation provided the molar flows of the bound and end segments of the polymers. The profiles for each segment, Mn, and DPN for PTFTS 30/70 and 70/30 are shown in Figure 7. The concentrations of all oligomeric segments increased rapidly, but after 1 h, the concentration decreased for the terminal segments. This led to a considerably greater amount of bound segments and, therefore, chain growth, to finally reach a constant profile. Similar profiles were obtained for the segmentbased kinetic approach used in the polyesterification of succinic acid with propylene glycol.48 The higher concentrations of segments of both FDCA and SA align with the particular concentration of diacids in each copolyester, as expected. The complete set of Pareto curves and profiles of the segments of the remaining polyesters is available in the Supporting Information (section 4).

4.3. Sustainability Indicators. Today, process simulations must include a sustainability approach intended to minimize the mass and energy demands and environmental impacts.49 The simulations were thus assessed according to environmental, energy, and economic quantities in terms of common sustainability indicators for chemical processes.49 The four indicators considered for each batch polyesterifications are gathered in Table 3. The estimation of the sustainability indicators after the optimization was done considering natural gas and lignite coal as base fuels under U.S. Environmental Protection Agency (EPA) rule E9-5711. The results are summarized in Table 4, including the normalized results. The results suggest that the productions of PTF and PTFTS 30/70 release less CO2, as their GWPs are 0.05 and 0.06 kgCO2·kgpolymer−1, respectively, as G


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Figure 7. Segment flow, DPN, and Mn profiles for (a) PTFTS 30/70 and (b) PTFTS 70/30.

Table 3. Sustainability Indicators Considered for the Batch Polyesterification Process49 indicator

formula

global warming potential50,51 (GWP) specific energy intensity50,51 (RSEI)

GWP = (total mass of CO2 equivalents)/(mass of product)

kg·kg

R SEI = (net energy used as primary fuel equivalents)/(mass of product)

reaction mass efficiency52 (RME)

RME =

mass intensity50,51 (MI)

MI =

best target

units

mass of product total mass of reagents

total mass input mass of product

−1

worst case

0

all GWP is released

kBTU·kg−1

0

1.847 × 103 kBTU·kg−1

kg·kg−1

1

0

kg·kg−1

1

4053

Table 4. Sustainability Indicators Estimated for the Different Polyesters normalized results polyester PTS PTFTS 15/85 PTFTS 30/70 PTFTS 70/30 PTFTS 85/15 PTF PET

GWPnatural gas (kg·kg−1)

GWPcoal (kg·kg−1)

RSEI (kBTU·kg−1)

RME (kg·kg−1)

MI (kg·kg−1)

RSEI

RME

MI

0.10 0.09

0.19 0.20

1.51 1.48

0.84 0.84

1.19 1.18

0.73 0.48

0.19 0.21

0.73 0.70

0 0.16

1.00 0.84

0.06

0.11

0.86

0.85

1.18

0.08

0.02

0.08

0.32

0.67

0.10

0.56

1.47

0.86

1.17

0.69

1.00

0.69

0.72

0.27

0.09

0.18

1.45

0.86

1.16

0.68

0.18

0.68

0.86

0.13

0.05 0.12

0.09 0.22

0.78 1.78

0.86 0.84

1.16 1.18

0 1.007

0 0.27

0 1.00

1.00 0.14

0 0.85

well as lower specific energy intensities (0.78 and 0.86 kBTU· kg−1). The value of the GWP indicator for PTF represents a

GWPnatural gas GWPcoal

reduction of 60% with respect to PET. Also, the efficiency of the polyesterification processes, evaluated in terms of the RME H


Article


and PTFTS, provides an insightful and useful resource for further polymerization process design and implementation stages. Multiobjective optimizations of the different production stages, including separation, purification, and compounding, are required to develop a full optimization of the manufacturing process of biomass polyesters. We will also evaluate different reactor configurations and biomass-derived polyesterification systems in the future.

and MI indicators, was found to be satisfactory, because the relationship between the raw materials and the amount of polymer produced was close to the best target of 1 for all of the systems. In comparison, the continuous production of the common ester ethyl acetate was reported to have MI and RSEI values of 1.58 kginput·kgpolymer−1 and 2.17 kJ·kgpolymer−1, respectively.54 The production of PET presented the highest energy consumption and CO2 release among all of the polymers studied, suggesting that our polyesters would provide sustainable and efficient alternatives to conventional PET for the intended applications. Also, comparing the two fossil fuels, there is a considerable difference between natural gas and coal in terms of CO2 equivalents, especially in the syntheses of PTFTS 15/85 and 70/30. Because the present comparison refers to production only, a complete life-cycle analysis (LCA) should be performed to obtain a complete cradle-to-grave assessment of the polymerizations.55 However, the results provide interesting insight into a potential opportunity for these biomass-derived polyesters to be used at the industrial scale. In general, all of the polyesterifications hit the best target of each indicator. The combination of such indicators provides an initial evaluation of the design of sustainable processes and also the improvement of existing ones as assessments can be performed to determine the influence of green engineering principles for initial implementation stages or varying process configurations.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.6b03260. Experimental reactor setup; reaction stoichiometry and reaction rates for PTS, PTF, and PTFTS polymerization; kinetic model development; acid value determination; Pareto frontiers; segment flow, Mn and DPN profiles for all polyesters; graph of cost and heat duty as a function of Mn; and sensitivity analysis for kinetic parameters (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +52-55-59 504000 ext. 7457. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

5. CONCLUSIONS Kinetic modeling, process simulation, and optimization were successfully implemented in Aspen Plus for the polyesterifications of the biomass-derived monomers 2,5-furandicarboxylic acid, succinic acid, and 1,5-pentanediol. The kinetic parameters were estimated for each polyester system by fitting the experimental batch data to a polyesterification model proposed in the literature and regressing the data using the weighted-sum-of-squares method. The a posteriori optimization ε-constraint method was applied to determine the utopia points and compromise solutions. The optimum process temperatures were found to be in the range of 190−225 °C, whereas the processing temperature for PET was found to be 269 °C. The values of the number-average molecular weight (Mn) and degree of polymerization (DPN) for the polyesters were in the ranges of 4.1−4.7 kDa and 42−45, respectively, with a final production of about 1400 kgpolymer·h−1. The sustainability impact of the processes was addressed by means of sustainability performance indicators, providing information on energy consumption, CO2 equivalents released, and efficiency in terms of the relationship between the mass input and the final product. When compared to the production of PET, the productions of the polyfuranoates and succinates achieved better targets and slightly lower final polymer attributes, with an Mn value of 3.6 kDa and a DPN of 38. Higher-molecular-weight resins yield coatings with higher viscosities and improved dry film and mechanical properties, such as mechanical strength. Regarding thermal properties, the glass transition temperature normally increases with Mn. It is important to observe that the range obtained for our polyesters is within the desired range for application as coil coatings, without resulting in practical problems because of an excessive system viscosity. Our work on the characterization of the properties of these polyesters is currently underway. The present process engineering study of this biomass-derived family of polyfuranoates and polysuccinates, namely, PTS, PTF,

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the EPSRC (Grant EP/K014773/1) for funding support. All authors are grateful to the Centre for Materials Discovery (CMD) and the Microbiorefinery (MBR) for access to the high-throughput synthesis and characterization instrumentation. We also thank Dr. Thomas E. Davies and Dr. Solène Cauët for their valuable support, as well as Eugenio Lomelı ́ Guzmán from Transfer Combustión S. de R. L. de C. V. for useful process engineering discussions M.L.-R. is grateful to Consejo Nacional de Ciencia y Tecnologı ́a (CONACYT) for funding support and to Universidad Iberoamericana for the facilities provided.

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I

ABBREVIATIONS b0 = excess of diol B-i = bound segment species i Cj = concentration of species j DPN = degree of polymerization Ea = activation energy (kJ·mol−1) FDCA = 2,5-furandicarboxylic acid GWP = global warming potential (kg·kg−1) K = equilibrium constant k0 = preexponential factor (kg·mol−1·min−1) k1 = kinetic coefficient of the forward water formation reaction k2 = kinetic coefficient of the forward water formation with the terminal diol k3 = kinetic coefficient of the ester interchange reaction k1,3 ′ = kinetic coefficients of the reverse reactions m = diacid reaction order DOI: 10.1021/acs.iecr.6b03260 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Mn = number-average molecular weight (Da) MI = mass intensity (kg·kg−1) n = diol reaction order PTF = poly(pentylene 2,5-furandicarboxylate) PTFTS = poly(1,5-pentylene 2,5-furandicarboxylate-co-1,5pentylene succinate) PTO = 1,5-pentanediol PTS = poly(pentylene succinate) Q = heat duty (kBTU·h−1) R = universal gas constant (J·mol−1·K−1) RSEI = specific energy intensity (kBTU·kg−1) RME = reaction mass efficiency (kg·kg−1) SA = succinic acid ri = reaction rate t = time (min) T = temperature (°C) T-i = terminal segment species i u = gradient of control variables y = state variables yp = estimated parameters

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