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Process modeling for the synthesis of unsaturated polyester.

INTRODUCTION

The American chemist Wallace Carothers has discovered in the late 1920s that reactions between dibasic acids and diols produce molecules with a high molecular weight (1). These molecules contain multiple ester linkage and are therefore named polyester. The polyesterification of dicarboxylic acids with diols is a commonly applied process in the polymer industry. Polyesterification reactions are usually equilibrium controlled), (and continuous removal of water is necessary to obtain high conversions. Thus), (the polyesters are produced in semibatch reactors and usually a distillation column is directly coupled to the reactor vessel in order to avoid excessive loss of the reactants during a batch and separate nearly pure water from the polymer mixture in the reactor to increase conversion.

The kinetics of the polyesterification reaction between dicarboxylic acids and diols was studied for the first time by Flory in 1939 (2). Since then), (a large number of kinetic models have been reported for the polyesterification reaction (2-9). Flory (2) has investigated that the reaction order of self-catalyzed polyesterification changes during the reaction. The reaction follows first order with respect to the acid at the beginning and second order at the end of the reaction. This increase in reaction order is due to the fact that the dielectric constant of the mixture decreases with the conversion), (which in turn affects the equilibrium ionization constant of the acid (3), (4), (Fang et al. (3) developed a rate equation for the polyesterification reaction), (which takes into account these phenomena. However), (this implies an introduction of a large number of adjustable parameters in the rate equation. Beigzadeh et al. (5) has studied the polyesterification of adipic and fumaric acid (FA) with ethylene glycol), (both in the absence and presence of a foreign acid and subsequently attempted to fit the data to a number of models. They conclude that only the model proposed by Chen and Wu (6) gives a satisfactory fit to experimental observations. However), (this model does not include the changing rate order phenomena. The models proposed by Flory (2), (Fang et al. (3), (Tang and Yao (7), (and Lin and Hsieh (8) are found to be incapable of reproducing the experimental data. Paatero et al. (4) and Salmi et al. (9) have proposed simple rate equation for polyesterification reaction), (which could describe the polyesterification over the entire range of conversions. The proposed rate equation by Paatero et al. (4) and Salmi et al. (91 consists of only two adjustable parameters.

The synthesis of polyester is carried out with a combination of different reagents for varying physical and chemical properties (10). One of the reagents in the synthesis of polyester is always unsaturated carboxylic acid (10). The presence of unsaturated carboxylic acids essentially leads to a complex reaction mechanism. The double-bond of the acid undergoes cis-trans (maleate fumarate) isomerization (11), (and the-double bond saturation takes place through the Ordelt reaction (12). The kinetics of the maleate fumarate isomerization with different glycols has been studied and confirmed that the isomerization reaction is acid catalyzed and of second order with respect to the carboxylic acid (11). The kinetics of the electrophilic addition of alcohol to the double bond of the carboxylic acids is studied by Fradet and Marechal (12), (who used unsaturated dicarboxylic acids and propylene glycol as model compounds and showed that the reaction is acid catalyzed and of first order with respect to the carboxylic acid and the alcohol. Although the reactions appearing in this kind of polyesterification are well known), (detailed kinetics studies of the esterification reaction and side reactions of different carboxylic acids and diols mixtures are limited (13). Only Paatero et al. (4) and Salmi et al. (9) have reported a detailed kinetic model for the reactions between maleic anhydride and propy lene glycol. They have used empirical functions to fit distillate composition profiles with experimental data. Fitting is required to correct the liquid phase mass balance. However, the fitted empirical parameters are limited to isothermal and isobaric operating conditions, which is not a case in the industrial application. Hence, although the kinetic model is complete, it cannot describe the complete process due to incapability of predicting vapor phase composition, which is an important factor to describe the combined reactive separation system.

The complete process model for the synthesis of unsaturated polyester process should be composed of (1) a detailed kinetic model consisting of changing order rate equations for polyesterification, isomerization, and double-bond saturation reactions, (2) a thermodynamic model to obtain components compositions at interphase of vapor and liquid, and (3) a mass transfer model to predict mass transfer from liquid-to-vapor phase. To the best of our knowledge, such a complete process model for the nonlinear polyesterification process is not yet addressed in the scientific literature. In earlier work (13), we reported a dynamic model for a batch reactor that includes detailed kinetics describing the change of rate order during the reaction and the ideal behavior thermodynamic model. However, the ideal behavior assumption prohibits a reliable prediction of the vapor-liquid equilibrium, and thus the concentration of components in the vapor and liquid phase. Therefore, in the present work, we have extended the previously developed reaction model with nonideal behavior thermodynamics to improve the description of the vapor-liquid equilibrium. Nonideal behavior of the unsaturated polyester mixture and the effect of an unsaturated polyester mixture on the activity of the components have to our knowledge not been addressed yet in the scientific literature.

The aim of the present work is to develop the process model for the synthesis of unsaturated polyester and to show how the incorporation of vapor-liquid equilibrium data improves the description of polyester kinetics. In addition to that, the vapor phase compositions predicted by ideal behavior thermodynamics and nonideal behavior thermodynamics are compared, and an improvement in the vapor phase composition prediction is noticed. The process model is developed in Aspen Custom Modeler, and the polyesterification of maleic anhydride with propylene glycol is used as model reaction in this study. This model is validated with the experimental data obtained from Salmi et al. (91), Larry et al. (14), and Korbar et al. (15).

Kinetic Modeling

Theory. The synthesis of unsaturated polyester from maleic anhydride and propylene glycol involves four types of reactions. First, the reactants, anhydride (A) and glycol (G) are mixed and heated to temperatures higher than 60-80[degrees]C. A very fast exothermic reaction ([DELTA]H = -40 KJ/mol) occurs and produces an acid end group (COOH) and a alcohol end group (OH) with an ester (E) bridge as shown in Eq. l.

A + G [right arrow] COOH + E + OH (1)

Esterification proceeds by the reaction between acid and alcohol end groups to form new ester bridges (POLY) and water or by reaction of a glycol hydroxyl group with an acid end group to form an ester bridge (POLY) and water as shown in Eq.2.

COOH + OH [left and right arrow] 5 POLY + WATER (2)

Half of the water is consumed in the ring opening reaction as the ring of anhydride opens by reacting with water. The double bond of the acid undergoes cis-trans isomerization (11), and the double-bond saturation takes place through the Ordelt reaction (12). The double bond in maleic acid (MA) is isomerized at the higher reaction temperatures and produces fumaric acid (FA) according to Eq. 3.

Cis(MA) [left and right arrow] Trans(FA) (3)

When the reaction temperature exceeds 180[degrees]C MA effectively relieves the strain by transforming to the more planar trans-fumarate isomer, which reduces the steric congestion (16), (17). The corresponding fumarate polymers are subject to less steric interference as the trans form and are able to assume a planar configuration, displaying reactivity almost 20 times of the maleate reaction products in subsequent copolymerization reaction with styrene (18). The isomerization of maleate esters and oligomers to the corresponding fumarate derivatives during the polyester fication process is of fundamental importance in the development of optimum physical characteristics (10). The fumarate derivative gives stability to the polyester (10). Hence, the byproducts resulting from the side reactions are not regarded as a loss. The double bond in MA is saturated by reaction with glycol and produces saturated acid (SACID) according to Eq. 4.

Dbb(MA) + OH [left and right arrow] SatDbb(SACID) (4)

The saturation of the double bond causes cross-linking in the polymer, and ~10-20% of the double bonds are saturated in the preparation of the polyester (10), (12). This side reaction occurs in the first reaction stage, and the destruction of unsaturation is favored by higher initial temperatures. The thermal polymerization of maleic anhydride double bonds can also occur at elevated temperature, which results in an optimum temperature for polyester production. The optimal temperature of the polyester process to avoid destruction of unsaturation and found optimal temperature is between 210 and 220[degrees]C (10).

Rate Equation. The three types of carboxylic acid (MA, FA, and SACID) functional groups are involved in the esterification reaction. These three carboxylic acid functional groups produce three ester functional groups via an esterification reaction. The isomerized FA and saturated SACID functional groups esterify and produce isomerized polyester ([POLY.sub.2D]) arid saturated polyester ([POLY.sub.s]) functional groups, respectively. Polyester ([POLY.sub.ID]) functional group produces from maleic anhydride, which also isomerizes and saturates to produce isomerized polyester ([POLY.sub.2D]) and saturated polyester ([POLY.sub.s]) functional groups, respectively. The FA and POLY2D functional groups also saturate and produce SACID and [POLY.sub.s] functional groups, respectively. The overall six basic functional groups of the carboxylic acids and esters and hydroxyl group with their abbreviations are depicted in Table 1.
TABLE 1. The functional groups in the polyesterification of
maleic anhydride and 1,2-propylene glycol. Abbreviation

Functional group          Abbreviation             Structure

Propylene glycol (PG)     [R.sup.']OH     [MATHEMATICAL EXPRESSION
end group                                 NOT REPRODUCIBLE IN ASCII]
Maleic acid (MA)          R[COOH.sub.1D]  [MATHEMATICAL EXPRESSION
end group                                 NOT REPRODUCIBLE IN ASCII]
Fumaric acid (FA)         R[COOH.sub.2D]  [MATHEMATICAL EXPRESSION
end group                                 NOT REPRODUCIBLE IN ASCII]
Saturated acid            R[COOH.sub.S]   [MATHEMATICAL EXPRESSION
(SACID) end group                         NOT REPRODUCIBLE IN ASCII]
Maleale polyester         R[COOR.sup.']   [MATHEMATICAL EXPRESSION
([POLY.sub.2D]) monomer   [COOR.sub.1D]   NOT REPRODUCIBLE IN ASCII]
Fumarate polyester        R[COOR.sup.']   [MATHEMATICAL EXPRESSION
([POLY.sub.2D]) monomer   [COOR.sub.2D]   NOT REPRODUCIBLE IN ASCII]
Saturated polyester       R[COOR.sup.']   [MATHEMATICAL EXPRESSION
([POLY.sub.S]) monomer    [COOR.sub.S]    NOT REPRODUCIBLE IN ASCII]
[MATHEMATICAL EXPRESSION  [R.sup.']       [MATHEMATICAL EXPRESSION
NOT REPRODUCIBLE          refer to        NOT REPRODUCIBLE IN ASCII]
IN ASCII]


The three reactions, esterification, isomerization, and saturation, form a network of nine reactions. These reactions and their rate equations are summarized in Table 2. The esterification), (isomerization), (and saturation reactions have been thoroughly discussed by Paatero et al. (4), (Chen et al. (6), (Salmi et al. (9), (Jedlovcnik et al. (19), (Salmi et al. (20), (and Zetterlund et al. (21). In this modeling), (the rate expressions have been adopted from the literature by Paatero et al. (4), (Salmi et al. (9), (and Salmi et al. (21). The variable rate order expression from Salmi et al. (9) has been changed by setting a different definition of the chemical equilibrium concentration and based on that a new rate expression is derived. Salmi et al. (9) has obtained the rate order (n) expression according to Eqs. 5 and 6 from the semiempirical differential equation dn = -[pn.sup.q][dc.sub.RCOOH].
TABLE 2. Reactions and rate equations.

Reactions                        Rate equations

Eslerificalion reactions:
R[COOH.sub.1D] + [R.sup.']OH     [MATHEMATICAL EXPRESSION NOT
[left and right arrow]           REPRODUCIBLE IN ASCII]
R[COOR.sup.'][COOR.sub.1D] +
[H.sub.2]O
R[COOH.sub.2D] + [R.sup.']OH     [MATHEMATICAL EXPRESSION NOT
[left and right arrow]           REPRODUCIBLE IN ASCII]
R[COOR.sup.'][COOR.sub.2D] +
[H.sub.2]O
R[COOH.sub.S] + [R.sup.']OH      [MATHEMATICAL EXPRESSION NOT
[left and right arrow]           REPRODUCIBLE IN ASCII]
R[COOR.sup.'][COOR.sub.S] +
[H.sub.2]O
Isomerization reactions:
R[COOH.sub.1D] [left and right   [MATHEMATICAL EXPRESSION NOT
arrow] R[COOH.sub.2D]            REPRODUCIBLE IN ASCII]
R[COOR.sub.'][COOR.sub.1D]       [MATHEMATICAL EXPRESSION NOT
[left and right arrow]           REPRODUCIBLE IN ASCII]
R[COOR.sub.'][COOR.sub.2D]
Saturation reactions:
R[COOH.sub.1D] + 0.5             [MATHEMATICAL EXPRESSION NOT
[R.sub.']OH [left and right      REPRODUCIBLE IN ASCII]
arrow] R[COOH.sub.S]
R[COOH.sub.2D] + 0.5             '[MATHEMATICAL EXPRESSION NOT
[R.sub.']OH [left and right      REPRODUCIBLE IN ASCII]
arrow] R[COOH.sub.S]
R[COOR.sup.'][COOR.sub.1D] +     [MATHEMATICAL EXPRESSION NOT
0.5 [R.sub.']OH [left and right  REPRODUCIBLE IN ASCII]
arrow]
R[COOR.sup.'][COOR.sub.S]
R[COOR.sup.'][COOR.sub.2D] +     [MATHEMATICAL EXPRESSION NOT
0.5 [R.sub.']OH [left and right  REPRODUCIBLE IN ASCII]
arrow]
R[COOR.sup.'][COOR.sub.S]


n =[[1-(1-[2.sup.1-q])[C.sub.o]-[C.sub.COOH]/ [C.sub.o]-[C.sub.eq]] (5)

where q is an adjustable exponent. This parameter is fitted in the present work for the maleic anhydride and propylene glycol system. In this system, the parameter q value is 7. The value for proportionality factor p is determined by integration of the differential equation using the limits n = 1, [C.sub.COOH] = [C.sub.0] and n = 2, [C.sub.COOH] = [C.sub.eq][C.sub.0] is the initial concentration of maleic anhydride and Ceq is the equilibrium concentration. Salmi et al. (9) has considered the water and glycol vaporization effect to define the equilibrium concentration of carboxylic acid. In this work, the equilibrium concentration of carboxylic acid is defined by Eq. 7, and the water and glycol vaporization effect is incorporated in the dynamic batch reactor model by introducing the polymer nonrandom theory of liquid (NRTL) thermodynamic model. The conversion of carboxylic acid is given by Eq. 8.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

X=[C.sub.0]-[C.sub.COOH]/[C.sub.0]-[C.sub.eq] (8)

The esterification, isomerization, and saturation reactions are acid catalyzed, and the strongest carboxylic acid gives the dominant catalytic effect. The MA is the strongest acid with respect to all acids in the system. Hence, the main contribution to the catalytic effect is from MA. The kinetic model presented in this work accounts for the autocatalytic effect of the strongest carboxylic acid. Because only total carboxylic acid ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]), total isomerization ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]), and total saturation ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) concentrations can be measured experimentally, it is presumed that all esterification rate constants are equal, all isomerization rate constants are equal, and all saturation rate constants are equal. These rate constants are derived from experimental data of Salmi et al. (9) and depicted in Table 3. The standard deviation of the experimental data is reported between 3 and 8% in Salmi et al. (9), In this work, the pre-exponential constant ([k.sub.o]) and the activation energy ([E.sub.a]) for forward and backward reactions are predicted from linear regression of the Arrhenius law ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) and depicted in Table 4.
TABLE 3. Experimental data from Salmi et at. (91)

7([degrees]C)         [k.sub.E]    [k.sub.E]/         [k.sub.1]
               (kg [mol.sup.-1]  [k.sub.E](-)  (kg [mol.sup.-1]
                   [hr.sup.-1])                    [hr.sup.-1])

160                       0.060            25             1.020
180                       0.130            19             3.000
200                       0.372            40             4.680
220                       0.720            36             7.200

7([degrees]C)    [k.sub.l]/         [k.sub.S]     [k.sub.s]/
               [k.sub.l](-)  (kg [mol.sup.-1]  [k'.sub.s](-)
                                 [hr.sup.-1])

160                    12.5             0.032           0.87
180                    9.10             0.046           2.30
200                    45.0             0.090           2.60
220                    12.4             0.150

[k.sub.E] = [k.sub.1] = [k.sub.2] = [k.sub.3], ... [k'.sub.E]
= [k'.sub.1] = [k'.sub.2] = [k'.sub.3], ... [k'.sub.1] =
[k.sub.4] = [k.sub.5], ... [k.sub.s] = [k.sub.6] = [k.sub.7]
= [k.sub.8] = [k.sub.9], ... [k'.sub.s] = [k'.sub.6] =
[k'.sub.7] = [k'.sub.8] = [k'.sub.9]

TABLE 4. Arrhenius parameters for the polyesterification
reaction between maleic anhydride and propylene glycol.

Forward reaction                Backward reaction

               [K.sub.o] (kg           (k'.sub.o] (kg
               [mol.sub.-l]   [E.sub.a]  [mol.sub.-l]  [E.sub.a]
Reacti on      [hr.sub.-1])   (J/mol)    [hr.sub.-1])  (J/mol)

Esterification  72,000,000    75,000        37,200     59,000
Isomerization    7,620,000    56,000        10,680     41,700
Saturation          16,380    47,000        10,560     49,600


Thermodynamic Modeling

Model Selection. The current unsaturated polyester process is operated at low pressure (1 bar), and, at the end of the process, vacuum is applied to completely remove water from the polymer mixture. As the system is operating at 1 bar, the activity coefficient approach is sufficient to predict the vapor-liquid equilibrium. The vapor phase is ideal, and the partial pressure of species i in the vapor phase, [p.sub.i] equals to

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

where xi is the liquid mole fraction of species i, [y.sub.i]([x.sub.i], T) is the activity coefficient of species i as function of liquid composition [x.sub.i], temperature T and [P.sup.sat][P.sub.sat] is the vapor pressure of pure species i.

The selection of the activity coefficient model is crucial to reliably predict the activity coefficients. None of the present models--Van Laar, Wilson), (NRTL), (UNIQUAC), (Flory-Huggins), (and others--are really mathematically correct), (but each may be useful and superior for specific conditions (22), (23). For strongly nonideal systems), (such as those where strong chemical interactions like hydrogen bonding occur), (the difference in the results from each model may be large. For completely miscible systems), (the Wilson equation can give adequate results (24), (25). If the system is highly polar), (NRTL and UNIQUAC models usually generate the best results (26), (27).

As the unsaturated polyester system is highly polar and nonideal), (the only suitable models are the NRTL and UNIQUAC. From these possible models), (the NRTL model is selected), (because the extension of NRTL model--the polymer NRTL model--includes the effect of polymer properties on the activity coefficients of the components. The main difference between the polymer NRTL model and Flory Huggins model is that in the polymer NRTL activity coefficients model), (the binary interaction parameters are independent of the polymer concentration and the polymer molecular weight (25), (26). Furthermore), (in the case of copolymers), (the polymer NRTL binary parameters are independent of the relative compositions of the repeating units of the polymer chain. The polymer NRTL model (25) is summarized in Table 5), (and the binary interaction parameters of this model for the segment segment interactions), (segment solvent interactions), (and for the solvent solvent interactions are used to predict the activity coefficients of the components including the polymer.

Binary Interaction Parameters Estimation Procedure. The unsaturated polyester process is multicomponent reactive system. The vapor-liquid equilibrium data could be determined experimentally for such reactive system by obtaining the measurements at the temperature where the reaction rates are very slow. However), (such measurements may not be representative for the actual conditions of the combined reaction and separation unit and would be of limited use. Measurements could also be made in the absence of the catalyst if the reaction is catalytic driven. Unfortunately), (the reactions involved in this process are autocatalyzed (2). Thus), (it is impossible to avoid reactions to carry out the vapor-liquid equilibrium experiments.

In the absence of the experimental vapor-liquid equilibrium data), (the activity coefficients at infinite dilution are predicted from the group contribution methods of the modified UNIFAC model proposed by Weldich et al. (27). These activity coefficients at the infinite dilution for each binary system are used to calculate the binary interaction parameters for the polymer NRTL model. Because the polyester process is highly polar, the parameter [[alpha].sub.ij] of the polymer NRTL model for the polar system is equal to 0.3 (27). There are 28 binary pairs required to represent the eight component mixture. The activity coefficients at infinite dilution are only known experimentally for a binary system of propylene glycol and water. The activity coefficient of propylene glycol in water at infinite dilution and at 25[degrees]C is reported to be 1 [+ or -] 0.2 (26). The predicted activity coefficient of propylene glycol in water at infinite dilution and at 25[degrees]C is 1.24, which shows good agreement with the experimental data of Sulieman et al. (28). The predicted interaction parameters of the polymer NRTL model are tabulated in Table 6. These interaction parameters are used to describe the vapor-liquid equilibrium of the unsaturated polyester process.
TABLE 6. The polymer NRTL activity coefficients model
interaction parameters. Component i=1  Component j=2
[b.sub.12]=([g.sub.12]-[g.sub.11])/R


Component  Component  [b.sub.12]  [b.sub.12]

i = 1      i = 2          (g12 -      [g21 -
                          g11)/R     g122]/g

PG         WATER         -248.25      790.27
PG         FA             303.67     -229.11
PG         SACID          398.41     -217.16
PG         POLYs          431.80     -221.43
PG         POLYID         540.32     -129.89
PG         POLY2D         201.60       93.53
WATER      FA             761.89     -354.33
WATER      SACID         1421.77     -567.46
WATER      POLYs         2109.51     -509.44
WATER      POLY,D        1374.88     -266.50
WATER      POLY2D        1565.88      272.87
FA         SACID         -597.18      965.66
FA         POLYs        -1113.58     3084.73
FA         POLYID        -631.65     1126.21
FA         POLY2D         520.63     -229.98
SACID      POLYs         -108.42      109.36
SACID      POLYID         -56.25      290.92
SACID      POLY2D         -56.25      290.92
POLYs      POLY,D         581.21     -416.24
POLYs      POLY2D         581.21     -416.24
POLYID     POLY2D         128.83     -114.78
MAD        POLYID        -631.65     1126.21
MAD        POLY2D         520.63     -229.98
MAD        FA             128.83     -114.78
MAD        SACID         -597.18      965.66
PG         MAD            303.67     -229.11
WATER      MAD            761.89     -354.33
MAD        POLYs        -1113.58     3084.73

For all binary pairs [[alpha].sub.ji] = 0.3


[TABLE 5 OMITTED]

Reactor Model

The dynamic model presented here accounts for a reactor separation system, which consist of a reactor, a flash separation unit, and a distillate accumulator as shown in Fig. 1. Focus is on the reactor and the prediction of the polymerization and properties such as acid value, water content, isomerization fraction, saturation fraction, and molecular weight. The distillation column is model as a flash separator (13). The reaction takes place in the liquid phase. The liquid phase mass balance for component i in the reaction vessel can be written according to,

[dc.sub.i]/dt = [r.sub.i] - [v.sub.i]/[M.sub.0] (10)

where c is the concentration of component i, r is the reaction rate, vi is the vapor phase flow rate, and [M.sub.0] is the initial total mass of the reactant. The vapor-liquid interface can be considered as a double film without reaction, where the mass transfer is mainly limited by the highly viscous liquid phase. Thus, the following equation with the overall mass transfer coefficient [K.sub.1]a and the vapor-liquid equilibrium ratio [k .sub.i]can be written as Eq. 11.

[FIGURE 1 OMITTED]

[v.sub.i] = [K.sub.l]a([x.sub.i]-[y.sub.i]/[K.sub.i]) (11)

The vapor phase mass balance according to Eq. 12 includes the mass transfer from liquid phase and the flow out from the vapor phase of the reactor.

d[y.sub.i]/dt = (-[F.sub.out][y.sub.i]+[v.sub.i])/[v.sub.vap] (12)

where [y.sub.i] is the vapor mole fraction, [F.sub.out] is the out flow from vapor phase, and [v.sub.vap] is the vapor hold up in the reactor. The flow out from the vapor phase is separated to an outgoing vapor flow, V and a liquid flow, L from the flash condenser. The liquid flow is collected in the accumulator. The mole fraction of vapor is calculated by an isothermal flash calculation (29) as,

[Z.sub.i][F.sub.out] = L[x.sub.i] + V[y.sub.i] (13)

[y.sub.i] = [K.sub.i][x.sub.i] [K.sub.i] = [y.sub.i][p.sub.i]/P (14)

where [K.sub.[iota]] is the vapor-liquid equilibrium ratio for component [iota], which is a function of temperature, pressure, liquid mole fraction, and vapor mole fraction. In this work, [K.sub.[iota]] is calculated from the activity coefficients predicted by the polymer NRTL model. pi is the vapor pressure of the pure component [iota], and P is the total pressure of the system. The properties of the liquid melt polymerized polyester: the degree of polymerization (DP), the number-average molecular weight (MWN), and weight-average molecular weight (MWW) are calculated as respectively,

DP = 1/(1-X) (15)

MWN = 158/(1-X) (16)

MWW= 158*(1+X)/(1 - X) (17)

where X is the conversion and 158 is the molecular weight of the repeating unit in the polymer chain.

RESULTS AND DISCUSSION

The dynamic model for a batch reactor equipped with a distillation column can be used for the unsaturated polyester production from different reagents. The simulation results presented in this work are for the reaction of maleic anhydride with propylene glycol. To validate the model, the model is simulated with the operating conditions of experiments. The simulation is performed at the temperatures 160, 180, and 200[degrees]C and at atmospheric pressure. The molar ratio of the anhydride and glycol is 1:1:1. The initial amounts of maleic anhydride and propylene glycol are 5.0 and 5.5 mol, respectively. The simulation is carried out in Aspen Custom Modeler. The dynamic model is validated with experimental results for the acid value, isomerization concentration, unsaturation concentration, distilled mass, and glycol content in the distillate with data from Salmi et al. (9). The acid value presented here is in terms of total carboxylic acid concentration (Ccoof.i) in mol/kg as shown in Fig. 2. The profiles of isomerization concentration (C1) and unsaturation concentration (CD) at 180[degrees]C are shown in Fig. 3. From Figs. 2 and 3, it is clear that the model reliably describes these concentration profiles. Because of the autocatalytic effect of acid and high concentration of MA in the liquid phase at the beginning of the reaction, the carboxylic acid reaction rate is very steep at the beginning of the reaction.

The order of the reaction with respect to carboxylic acid at the beginning of the reaction (0% conversion) is 1 and 2 at the end of the reaction (100% conversion), respectively. The polyesterification reaction is an equilibrium reaction, and thus maximum 88-90% conversion can be obtained. The order of reaction at the end of the process is 1.4 at 200[degrees]C, 1.33 at 180[degrees]C, and 1.25 at I60[degrees]C as illustrated in Fig. 4. The order of reaction increases with the temperature because the order of reaction (Eq. 6) is a function of conversion, and the conversion increases with increasing temperature.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

In the dynamic model to represent the vapor-liquid equilibrium, two thermodynamic models are compared. One is the ideal solution thermodynamic model that obeys Raoult's law, and the second is the polymer NRTL nonideal thermodynamic model. The experimental data for the distilled mass and for the propylene glycol fraction in the distillate are obtained from Salmi et al. (9). An accumulation of the distilled mass ([zeta] = [M.sub.D]/ [M.sub.O], where [M.sub.D] is distilled mass and [M.sub.O] is the initial total mass of the reactants) in the accumulator during the synthesis of unsaturated polyester is plotted in Fig. 5. It can be seen that the distilled mass predicted by the polymer NRTL nonideal thermodynamic model is in good agreement with the experimental data while the distilled mass is under predicted in the case of the ideal behavior modeling compared to the experimental results. The reasons are as follows (1) in the ideal behavior modeling, the assumption has been made that only glycol and water are present in the vapor phase, which is not the case for the nonideal polymer mixture. In principle, any component that is volatile can be present in the vapor phase. It is predicted from the polymer NRTL model that not only the glycol and water are present in the vapor phase but also the maleic and FA. Polyester ([POLY.sub.1D] + [POLY.sub.2D] + [POLY.sub.s]) and SACID are not present in the vapor phase. This is due to the nonvolatile nature and high molecular weight of the polyester and the SACID. (2) In the ideal behavior modeling, the activity coefficients for the components are kept constant value of 1 and obey Raoult's law. However, in the nonideal polymer mixture, there is always a positive or negative deviation from Raoult's law, and the activity coefficient differs from the value of 1. The regression coefficient (R2) for the dimensionless distilled mass is 0.980 in the ideal behavior modeling and 0.995 in the nonideal behavior modeling, which confirms the improvement in predictive capabilities of the vapor phase compositions by the polymer NRTL model.

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

The weight fraction of the propylene glycol in the distillate is plotted in Fig. 6. The propylene glycol weight fraction in the distillate is significantly overpredicted using the ideal behavior thermodynamic model compared to the experimental data. The regression coefficient ([R.sub.2]) for the weight fraction of propylene glycol is 0.97 for the nonideal behavior modeling, which confirms that the polymer NRTL model reliably predicted the weight fraction of propylene glycol. Because the effect of the polymer properties such as (i) chain length, (ii) molecular size, and (iii) molecule structure are not accounted on the activity coefficients in the ideal behavior modeling. However, it is accounted with the help of polymer NRTL model in the nonideal behavior modeling.

The isomerization concentration ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) and the saturation concentration ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII])increases at higher temperature as shown in Figs. 7 and 8, respectively. The isomerization concentration increases steeply at the beginning of the reaction and reaches a peak value. Then, the isomerization concentration decreases and at the end of the process isomerization reaction reaches equilibrium. The rate of the isomerization reaction is higher than the rate of the polyesterification reaction at the beginning of the reaction. Therefore, maleate-formed acid and ester effectively relieve the strain by transforming to the more planar trans-fumarate isomer and produces fumarate-formed acid and esters. The maleate formed acid and ester and isomerized formed acid and esters saturate by breaking the double bond with glycol. Thus, the saturation concentration increases throughout the reaction and reaches an equilibrium as shown in Fig. 8. Because of a high temperature adaption at the beginning of the reaction, the double-bond saturation increases steeply. The saturation effect of the double bond of an unsaturated acid can be lowered by setting the process at a low initial temperature.

The concentration of each functional group and the [H.sub.2]O concentration is shown in Fig. 9. The total carboxylic acid concentration, total isomerization concentration, and total saturation concentration are calculated from the functional groups illustrated in Fig. 9. The total concentration of carboxylic acid is a summation of the functional groups [COOH.sub.1D], [COOH.sub.2D], and [COOH.sub.s], the total isomerization concentration is a summation of the functional groups [COOH.sub.2D] and [COOH.sup.'] [COOH.sub.2D], and the total saturation concentration is a summation of the functional groups [COOH.sub.s] and [COOH.sup.'] [COOH.sub.2D]. The maleate to fumarate percentage is calculated from the concentration of these functional groups and found to be 92%, which corresponds to the results reported by Parker et al. (10) and Larry et al. (14). Frandet et al. (12) have reported 15-20% loss of double bond due to the saturation of maleic anhydride with propylene glycol. The model predicts 19% of double bond loss during the synthesis, which shows good agreement with the saturation composition reported by Frandet et al. (12) The product distribution in maleate-formed esters, fumarate-formed ester, and saturated ester of melt polymerized polyester is shown in Fig. 10.

The DP, number-average molecular weight, and weight-average molecular weight derived from conversion and molecular weight of repeating unit are calculated according to Eqs. (15-17), respectively. The DP is between 8 and 10. To validate the number-average molecular weight profile with the industrial data reported in Korbar et al. (15), the model is simulated with the temperature profile shown in Fig. 11. It can be seen from Fig. 11 that the number--average molecular weight throughout the process is in good agreement with the industrial data reported in Korbar et al. (15).

CONCLUSIONS

The aim in this work was to develop a process model for the synthesis of unsaturated polyester. We find that the polymer NRTL model significantly improved the prediction capability of the process model compared to the ideal-behavior modeling. The behavior of the model system, the polyesterification of the unsaturated carboxylic acid and two side reactions, isomerization, and double bond saturation are reliably predicted. We conclude that the process model, which consists of kinetics with changing rate order connected with the polymer NRTL thermodynamic model, give a better representation of the industrial unsaturated polyester process. The validated process model can also be used for the unsaturated polyester synthesis from reagents other than maleic anhydride and propylene glycol with appropriate kinetic and thermodynamic parameters, respectively.

[FIGURE 10 OMITTED]

[FIGURE 11 OMITTED]

ACKNOWLEDGMENTS

This is a Dutch Separation Technology Institute (DSTI) project.
NOMENCLATURE

List of Symbols
a               vapor-liquid mass transfer
                area([m.sup.2])
b               interaction parameter in the polymer NRTL
                model
C               concentration (mol [kg.sup.-1])
[E.sub.a]       activation energy (J [mol.sup.-1])
[F.sub.out]     flow to the distillation column from
                reactor (mol [hr.sup.-1])
G               parameter in the polymer NRTL model
k               rate constant (kg
                [mol.sup.-1][hr.sup.-1])
[k.sub.l]       mass transfer coefficient
                (mol[m.sup.-2][hr.sup.-1])
[k.sub.[iota]]  vapor-liquid equilibrium ratio
L               liquid flow from flash condenser
                (mol[hr.sup.-1])
[M.sub,0]       total mass in reactor (kg)
m               characteristic size of component
n               number of moles of component
p               partial pressure (bar)
P               total pressure (bar)
q               fitting parameter in Eq.5
r               reaction rate (mol [kg.sup.-1][hr.sub.-1])
R               gas constant
T                temperature ([degrees]C)
t                time (hr)
v                vapor flow (mol [hr.sup.-1])
V                vapor flow from the flash condenser(mol[hr.sup.-1]
[[nu].sub.vap]   vapor holdup in the reactor (mol)
X                conversion
a                liquid phase mole fraction
y                vapor phase mole fraction
z                mole fraction in Eq. 13
Greek Letter
[zeta]           dimensionless distilled mass
[alpha]          nonrandomness factor in the polymer NRTL model
[gamma]          I activity coefficient
[PHI]            I volume fraction in the polymer NRTL model
[tau]            parameter in the polymer NRTL model

Subscripts ai id Superscripts
1D               cis formed component
2D               trans formed component
D                double bond
E                esterification
i,j              component indexes
I                isomerization
s                saturated component

Abbreviations
Cis              cis formed component
COOH             acid end group
Dbb              unsaturated double bond in MA
DP               degree of polymerization
E                ester
FA               fumaric acid
MA               MA end group
MAD              maleic anhydride
OH               hydroxyl group
[POLY.sub.1D]    maleate formed polyester
[POLY.sub.2D]    fumarate formed polyester
[POLY.sub.s]     saturated polyester
PG               propylene glycol
MWN              number-average molecular weight
MWW              weight-average molecular weight
R                regression coefficient
SatDbb           saturated double bond in MA
Sat acid         saturated acid
Trans            trans formed component


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M. Shah, E. Zondervan, A.B de Haan

Process Systems Engineering Group, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, 5600 MB, The Netherlands

Correspondence to: M. Shah; e-mail: m.shah@tue.nl DOI 10.1002/pen.22038

Published online in Wiley Online Library (wileyonlinelibrary.com). [c] 2011 Society of Plastics Engineers
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Author:Shah, M.; Zondervan, E.; Haan, A.B De
Publication:Polymer Engineering and Science
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Geographic Code:4EUNE
Date:Dec 1, 2011
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