Using Simulation Technology to Improve Profitability In the Polymer Industry

Transcription

1 Using Simulation Technology to Improve Profitability In the Polymer Industry David A. Tremblay* Aspen Technology Inc. Ten Canal Park Cambridge MA, USA Key words: Polyester, PET, Poly(ethylene terephthalate), process simulation, optimization Prepared for presentation at the AIChE Annual Meeting, Houston Texas, March 14-19, 1999 Copyright David A. Tremblay, Aspen Technology Incorporated, AIChE shall not be responsible for statements or opinions contained in papers or printed in its publications

2 Using Simulation Technology to Improve Profitability In the Polymer Industry David A. Tremblay* Aspen Technology Inc. Ten Canal Park Cambridge MA, USA Copyright David A. Tremblay, Abstract Process simulation is a valuable tool to increase the profitability of polyester processes by reducing costs, increasing yield, and improving product quality. Although simulation has been heavily used in the chemical process industries for several decades, the polymer manufacturing industry has only begun to take advantage of this technology during the past five to ten years. Recently, the commercial development of polymer process simulation packages, such as Polymers Plus, has made it possible to simulate polymer processes in a simple and straightforward manner. In this discussion, we will examine the technical challenges that must be overcome to develop and validate a polyester process model. Several case studies will be presented. Finally, we will review how a rigorous process model can be leveraged to support additional business needs including operator training and process control. Copyright 1999 Page 1 of 19

3 Process Description Most polyethylene terephthalate (PET) is produced from purified terephthalic acid (TPA) and ethylene glycol (EG). Although many process configurations are found in the polyester industry, they all involve a series of three or more reactors. For demonstration purposes, we have developed a model of a typical five-reactor process, as shown in Figure 1. Solid terephthalic acid is mixed with ethylene glycol in carefully metered amounts. The mole ratio of ethylene glycol to TPA is a critical process variable, so many plants use control schemes to adjust the glycol feed rate to keep the paste density constant (the density is a good indicator of mole ratio). The resulting paste is fed to the first reactor, which is known as a primary esterification reactor or PE. Typically, the PE is operated at a pressure of 1-8 bar and a temperature of C. At lower temperatures the reactor performance is limited by the solubility of TPA in the oligomer. The behavior of the reactor is highly non-ideal because the apparent reactor volume depends on the amount of solid TPA. At higher temperatures the reactor performance is limited by the solid-liquid mass-transfer rate. Under these conditions, the reactor performance depends on the TPA particle size. Oligomer from the primary esterifier is fed to the secondary esterifier (SE). The secondary esterifier is usually run close to atmospheric conditions with temperatures a bit higher than the PE. Frequently, the SE is divided into several chambers to enhance the effectiveness of the reactor. In our model, we assume the SE is divided into three equal-sized chambers. Each chamber is represented as an ideal CSTR reactor. These assumptions are justified by sensitivity studies that indicate that vapor back mixing between the stages has little influence on the model predictions. Primary Esterification Column Secondary Esterification Column Spray Condenser and Vacuum System Steam Solid TPA Steam Steam Makeup Glycol Make-up EG Water Water Catalyst Additives Recycle EG Recycle EG Bypass Recycle EG Crude EG to Recovery Paste Catalyst Additives Paste Tank Primary Esterification Reactor Secondary Esterification Reactor Low Polymerizer Intermediate Polymerizer High Polymerizer Figure 1. Process flow diagram of a typical five-reactor direct esterification PET process, including the reactor train and vapor recovery system. Copyright 1999 Page 2 of 19

4 The vapor from each esterification reactor is rectified in a multi-stage distillation column. In industry, many processes use one column to support both reactors. The columns remove water and other volatile reaction by-products, including acetaldehyde. Excess ethylene glycol is recovered and returned to the paste tank and the esterification reactors. The recycle rate to each esterification reactor can be manipulated to control the local monomer ratio. The third reactor, or low polymerizer, is typically composed of a simple CSTR. The low polymerizer (LP) operates at a medium vacuum pressure ( Torr). This stage strips off most of the excess ethylene glycol and water remaining in the polymer. In most plants, the polymer intrinsic viscosity in the low polymerizer is below 0.2 dl/g, and the LP behaves ideally. At higher viscosity levels, the low polymerizer becomes increasing mass-transfer limited. The final reactors, known as the intermediate polymerizer (IP) and high polymerizer (HP), operate at lower vacuum pressures, often as low as one Torr. Many plants use disk-ring reactors, which contain a number of annular disks attached to a rotating shaft. Polymer flows through holes cut into the disks. As the disks rotate they generate a surface film, which enhances the evaporation rate. Due to the high viscosity of the polymer, the performance of the finishing reactors is limited by the liquid-vapor masstransfer rate. This makes the reactor performance a function of the shaft rotation rate, as well as the temperature, pressure, and throughput. The vapor from the polymerization reactors is recovered using a cascade of spray condensers. The spray condensers recover most of the ethylene glycol generated by the reactions. The ethylene glycol recovered in the spray condensers may be further purified or recycled directly to the paste tank, depending on the product grade. There are several factors that must be considered to simulate the reactors in a melt polyester process. These include non-ideal mixing, mass-transfer limitations, and uncertainty in the true operating volume. Many industrial reactors contain baffles that divide the reactor into two or more mixing zones. These reactors can be represented as a series of CSTRs. Recycle streams can be used to account for back mixing in the liquid and vapor phases. The finishing reactors can be simulated as a series of CSTR reactors, with each space between successive disks represented as one ideal mixing stage [1]. In the model presented here, we simulate the IP and HP as mass-transfer-limited plug-flow reactors. Simulation studies indicate that the dynamic and steady state responses of both models are in good agreement when there are five or more ideal mixing stages. Component Characterization In conventional chemical processes, component characterization is straightforward. The molecular structure of each of the reactants is well defined. In a polymerization process, however, the polymer is composed of a distribution of molecules. The average properties of the distribution change as the reactions proceed. In our model, we characterize the polymer using the segment approach, in which the reactions are written in terms of monomers and polymer repeat units and end groups. Using this approach, we define an end-group and repeat segment associated with each monomer. Additional segments are defined to account for some of the side reactions that occur in this process. Figure 2 summarizes the main components and segments in our model. Copyright 1999 Page 3 of 19

5 Name Description Structure H 2 O Water H 2 O EG Ethylene-glycol HO(CH 2 ) 2 OH TPA Dissolved terephthalic acid O O TPA S Solid terephthalic acid HO C C OH DEG Diethylene-glycol HO(CH 2 ) 2 O(CH 2 ) 2 OH AA Acetaldehyde H(C=O)CH 3 PET Polyethylene terephthalate Structure made up of segments t-eg Ethylene-glycol end segment ~O(CH 2 ) 2 OH b-eg Ethylene-glycol repeat segment ~O(CH 2 ) 2 O~ t-tpa Terephthalic acid end segment O O C C OH b-tpa Terephthalic acid repeat segment O C O C t-deg Diethylene-glycol end segment ~O(CH 2 ) 2 O(CH 2 ) 2 OH b-deg Diethylene-glycol repeat segment ~O(CH 2 ) 2 O(CH 2 ) 2 O~ t-vinyl Oxyvinyl end segment ~OCH=CH 2 Figure 2. Components, including polymer segments, included in the model. Note that the prefixes t and b refer to terminal (end group) and bound (repeat) segments. Segments provide a convenient basis for defining reaction stoichiometry and for calculating end-use properties. The model tracks the mass and mole flow rates of the monomers, water, acetaldehyde, DEG, and each of the segments. The mass flow rate of the polymer component is calculated from the sum of the mass flow rate of the individual segments. The model also tracks the mole flow rate of the polymer (the zeroth moment of the molecular weight distribution). Secondary properties, such as the acid end group content and intrinsic viscosity, are calculated from component flow rates and polymer moments. The physical properties of the polymer, such as density, enthalpy, and heat capacity, are calculated using group contribution techniques based on the segmental composition. The polymer component is assumed to be non-volatile. End-use properties, such as end-group concentrations, intrinsic viscosity, and DEG content, are calculated from the mole flow rates of monomers and polymer segments. The definitions of these properties are documented at the end of this article. Copyright 1999 Page 4 of 19

6 Phase Equilibrium The model considers solid-liquid and liquid-vapor phase equilibrium. For TPA, the solid-liquid equilibrium is calculated from the solubility constant, which was fit against solubility data over a wide range of temperatures: H m S m xtpaγ TPA = ln K s = RT R For convenience the polymer is defined to have a fixed reference mole weight. The mole fractions and molar activity coefficient are calculated on an apparent component basis using this reference mole weight. The concentration of the volatile components at the liquid-vapor interface is calculated using the activity coefficient and vapor pressure of each component: v x γ P y P i i i = The activity coefficients are calculated using the polymer-nrtl equation [2]. Using this equation, the activity coefficients depend on the apparent mole fractions and binary interaction parameters. Since the polymer is the main solvent in the system, the water-polymer and ethylene glycol-polymer interaction parameters control the phase equilibrium in the reactors. The NRTL binary parameters are critical constants in the model because the reaction rates and mass-transfer rates depend on the liquid-phase concentrations. The activity coefficient of water controls the relationship between the predicted acid value and the reactor pressure. When the activity coefficient is high, the predicted acid value is very sensitive to the reactor pressure. When the activity coefficient is low, the predicted acid value is less sensitive to pressure. Thus, the water-polymer interaction parameters can be fit against process data taken over a range of operating pressures. The activity coefficient of ethylene glycol controls the relationship between the intrinsic viscosity and pressure in the finishing reactors. The higher the activity coefficient, the stronger the predicted trend between the intrinsic viscosity and pressure. Thus, the ethylene glycol-polymer interaction parameter can be fit against IV/pressure data. Reaction Kinetics The reaction mechanisms and kinetics of the direct esterification process are examined in many open sources. The rate parameters used in our model are based on our interpretation of experimental work published by Yokoyama [3,4], Otton and Ratton [5,6], and Ravindrananth and Mashelkar [7,8]. The main reactions in the process are shown in Figure 3. In the early stages of the process, esterification reactions (1-4 in the figure) are dominant. These reactions are reversible with equilibrium constants close to unity. Polymerization reactions (5 and 6) involve the nucleophilic attack of the terminal ester group in one chain by the terminal alcohol group of a second chain. These reactions lead to rapid molecular weight growth. The polymerization reactions are also reversible, with equilibrium constant slightly below unity. Rearrangement reactions (7 and 8) involve ester groups inside the chain. These reactions are responsible for randomizing the molecular weight distribution and redistributing segments inside the polymer chains. Since the number of internal ester groups is much higher than the number of terminal ester groups, the molecular weight distribution approaches the most-probable distribution. i Copyright 1999 Page 5 of 19

7 # Reaction Stoichiometry Population Balance 1 EG + TPA t-eg t-tpa + H 2 O M + M P 2 + W 2 EG + t-tpa t-eg b-tpa~ + H 2 O M + P n P n+1 + W 3 ~t-eg + TPA ~b-eg t-tpa + H 2 O P n + M P n+1 + W 4 ~t-eg + t-tpa ~b-eg b-tpa~ + H 2 O P n + P m P n+m + W 5 ~t-eg + t-tpa t-eg ~b-eg t-tpa + EG P n + P 2 P n+1 + M 6 ~t-eg + ~b-tpa t-eg ~b-eg b-tpa~ + EG P n + P m P n+m-1 + M 7 ~t-eg + t-tpa b-eg~ ~b-eg t-tpa + t-eg~ P n + P m P n+1 + P m-1 8 ~t-eg + ~b-tpa b-eg~ ~b-eg b-tpa~ + t-eg~ P n + P m P n+q + P m-q 9 ~b-tpa t-eg + EG ~t-tpa + DEG P n + M P n + M 10 ~b-tpa t-eg + ~t-eg ~t-tpa + t-deg P n + P m P n-1 + P m 11 ~b-tpa t-eg ~t-tpa + AA P n P n-1 + AA 12 ~b-tpa b-eg~ ~t-tpa + ~t-vinyl P n P n-m +P m 13 ~t-eg + ~b-tpa t-vinyl ~b-tpa b-eg + AA P n + P m P n-m-1 + AA Notes: The double-tilde indicates that two segments are attached by a covalent single bond A tilde ~ before or after a segment indicates that one side of the segment is attached to a chain P n indicates a linear polymer chain composed of n segments. M refers to monomers, W refers to water Figure 3. A summary of the reactions included in the model. Analogous reactions involving various combinations of EG, DEG and their respective segments are also included in the model. Using this technique, the smallest polymer chain has a length of two segments (this is equivalent to one PET repeat unit). A number of side reactions are also involved in the process. These include thermal scission and the formation of diethylene glycol and acetaldehyde. All of the side reactions have a strong influence on the quality of the polymer. The DEG content, for example, affects the viscosity, density, and dying characteristics of the polyester. The scission reactions influence the acid content and yellowness of the polymer. Scission and acetaldehyde formation reduce the polymer yield (these reactions lead to the loss of ethylene glycol in the form of acetaldehyde). A good model must consider these side reactions in order to identify economic opportunities related to the improvement of yield and quality. Diethylene glycol segments are formed throughout the process, especially in the esterification reactors. There are substantial debates about the exact mechanism by which the DEG is formed. One proposed mechanism involves a reaction between a molecule of ethylene glycol or an ethylene glycol end group and a cyclic transition state generated by terminal glycol ester groups. Another proposed mechanism Copyright 1999 Page 6 of 19

8 involves a two-step process in which the terminal glycol group in one chain undergoes a scission reaction to form ethylene oxide, which subsequently reacts with monomeric ethylene glycol or with an ethylene glycol end group in a second chain. Both of these mechanisms result in second-order reactions as shown in reactions 9 and 10 in Figure 3. Two types of thermal scission reactions occur. Thermal scission involving the terminal glycol group generates an acid group and ethylene oxide. The ethylene oxide may react with another molecule to form DEG as described above, or it may rearrange to form acetaldehyde (reaction 11). Scission reactions inside the chain generate vinyl end groups and acid end groups (reaction 12). Subsequent polycondensation reactions at the oxyvinyl ester group consume these vinyl groups and generate a vinyl alcohol, which spontaneously rearranges to for acetaldehyde (reaction 13). These reactions destroy alcohol groups and generate acid groups. This has a profound influence on the acid content and molecular weight of the polymer. Since the scission reactions have higher activation energies than the polymerization and esterification reactions, the process is very sensitive to the temperature of the finishing reactors. A number of other reactions are likely to occur, especially at high temperatures and in the presence of trace amounts of oxygen. These reactions lead to the generation of color bodies in the polymer chain. For simplicity, these reactions are not considered in our model. With sufficient data, however, these reactions can be characterized through correlations generated by traditional methods or regressed from the L/a/b color data and operating conditions using a neural network. The esterification and polymerization reactions are acid-catalyzed. Various metal compounds, including diantimony triacetate and germanium oxide, are also used to catalyze the reaction rates. These metal compounds are inhibited by unreacted alcohol groups [9]. In the first few reactors the concentration of acid and alcohol groups is very high, so the acid catalysis mechanism dominates. Metal catalysis dominates in the polymerization reactors. Phosphate compounds are added to the polymer to stabilize the catalysts, reducing the thermal scission rates. Our model accounts for both catalyst inhibition mechanisms. Model Validation Even though the rate constants and other parameters in the model can be determined from literature sources, it is still critical to fine-tune the model against process data. Each plant has its own idiosyncrasies. Heat- and mass-transfer coefficients are equipment-specific. The operating volumes of the reactors are usually poorly characterized. Flow meters may not be calibrated properly. Contaminants in the raw material may influence the side reactions in the process. To account for these factors, the model must be tuned against real process data. Validation is also an important means of reaching organization-wide agreement on the quality and reliability of the model. Testing the model against process data clarifies the strengths and weaknesses of the model. Since simulation models are used to find new operating conditions, there must be convincing proof that the model is representative of the plant. Validation data should be collected over as wide a range of operating conditions as possible. To validate a steady-state model, the data should reflect stable operating conditions. Ideally, the data should be collected over several shifts and averaged. Collecting data in this fashion may allow the model developer to evaluate the stability of the process and to weed out invalid or atypical data. Validating dynamic models is a bit more difficult. Data needs to be collected during process upsets or during start up, shut down, and grade transition operations. In some cases, it is necessary to artificially Copyright 1999 Page 7 of 19

9 disturb the process by making a step change in one or more of the operating conditions. These data make it possible to determine the various time constants in the system. For example, by making a step change in the temperature set point of a reactor, one can determine the thermal inertia of the reactor. Each data set should include all of the operating conditions and feed conditions in the plant. Ideally, the oligomer should be sampled at the outlet of each reactor. Each sample should be analyzed for the end group content, intrinsic viscosity, and DEG content. These data can be used to fine-tune the various reaction rate constants. In developing and validating a model, it is critical to remember what a model really is a simplified representation of the plant. Simulation models are subject to the law of diminishing returns, unnecessary details and complications should be avoided. No model is perfect, and no model can reproduce plant data with perfect fidelity. There are several sources of differences between the model predictions and process data, including analytical error, imperfect calibration of flow meters and liquid levels, deviations from steady state conditions, and simplifying assumptions built into the simulation. Case Study #1: Using the Model to Evaluate the Influence of Feed Mole Ratio The ratio of EG to TPA in the feed is a key process parameter. Optimizing this ratio can result in improved quality and higher production rates for a process. In this example we carried out a sensitivity study to evaluate the influence of the feed mole ratio on the process, holding the reactor operating conditions constant. The results of this study are summarized in Figure 4, below. As shown, there is an optimal mole ratio at which the intrinsic viscosity is a maximum. Although the production rate was held constant in this example, the maximum intrinsic viscosity can be translated into a maximum production rate at constant IV. The optimal mole ratio depends on the operating conditions of the reactors, so there is no universal best mole ratio at which to run a given plant. The optimal mole ratio is influenced by the thermal scission and acetaldehyde formation reactions, which destroy glycol end groups. At very low mole ratios, the final intrinsic viscosity drops of quickly. Under these conditions, all of the polymer end groups are terminated by acid ends, which cannot react with each other. In effect, the polymer becomes capped and the growth stops. At very high glycol/tpa ratios, the polymer has mostly alcohol ends. The alcohol end groups undergo polymerization reactions, so there is substantial growth. This reaction, however, is not favored (the equilibrium constant is less than one). At intermediate mole ratios, the polymer chains grow by esterification and polymerization. The esterification reaction is favored (the equilibrium constant is greater than one), so the reaction is less limited by chemical equilibrium. Even more importantly, the esterification reaction generates water instead of ethylene glycol. Water is far more volatile than glycol, so it is easier to remove from the polymer melt. This also favors the forward reaction. Copyright 1999 Page 8 of 19

10 Intrinsic Viscosity, dl/g Feed Mole Ratio EG/TPA Intrinsic Viscosity Acid Content Figure 4. Product acid content and intrinsic viscosity as a function of the feed mole ratio at constant throughput. All reactor operating conditions are held constant for this study. These results demonstrate that there is an optimal mole ratio for the process. The optimal mole ratio depends on the throughput and operating conditions Acid Content, mmol/kg Case Study #2: Increasing Throughput In the previous study we examined the influence of the feed mole ratio on the product acid content and intrinsic viscosity. The results are intriguing because they show that there is an optimal mole ratio. However, a simple sensitivity study leaves many questions unanswered. For example, what are the best operating conditions for each reactor? What production rate can be obtained if the intrinsic viscosity is held constant? Process optimization studies can answer these questions. In an optimization study, one or more process variables are manipulated to minimize or maximize an objective function while meeting constraints. Manipulated variables may include operating conditions, such as temperatures and pressures, feed flow rates, catalyst and additive levels, and other factors that can be controlled in the process. The upper and lower limit of each variable is specified to ensure the optimization finds a feasible set of operating conditions. Product quality is usually the key constraint. There are tight quality specifications for any given product grade. Typically, these specifications include the DEG content, acid end-group concentration, and intrinsic viscosity. In addition, there may be physical constraints on the equipment, for example, a reactor may be limited by the available duty or hot oil supply. In an optimization study, these constraints are defined as equality or inequality constraints. Equality constraints set the target and tolerance of a given model prediction, for example, IV=0.610± Inequality constraints represent lower or upper limits in the predicted variables. Copyright 1999 Page 9 of 19

11 We must select an objective function to optimize. The objective function can be any continuous numerical quantity, such as the production rate, mole ratio, and so on. The optimization tool can minimize or maximize the objective function. In this example we maximized production rate by manipulating several process variables including the reactor temperatures and pressures, the catalyst and stabilizer levels, and the feed mole ratio. We set constraints on the intrinsic viscosity, the concentration of acid and vinyl end groups, and the DEG content. The simulation results are summarized in Table 1. Variable Type Variable Lower Upper Initial Optimized Bound Bound Value Value Objective Function PET production rate, kg/hr Constraints Intrinsic viscosity, dl/g Acid content, mmol/kg DEG content, weight % Vinyl content, mmol/kg Manipulated Variables TPA feed mass flow, kg/hr Feed mole ratio EG/TPA Sb 2 O 3 concentration, PPM H 3 PO 4 concentration, PPM Fraction of EG recycled to PE Fraction of EG recycled to SE PE temperature, deg C PE pressure, Torr SE temperature, deg C LP temperature, deg C LP pressure, Torr IP temperature, deg C IP pressure, torr HP temperature deg C HP pressure, torr Table 1. Results of a process optimization study for the five-reactor process shown in Figure 1. In most optimization studies a number of variables reach their bounds. In this case, the production rate is limited by the constraints on the acid content and vinyl content. The results of the optimization run are very interesting. The model indicates that it is possible to achieve higher production rates by increasing the polymerization temperatures. Note that the quality of the polymer is not sacrificed. The acid value and vinyl content can be maintained at higher temperatures and throughputs because the reactor residence times are reduced as the throughput increases. The model predicts that the finishing reactors should operate at the lowest possible pressure. This is not surprising because these reactors are mass-transfer limited. By reducing the reactor pressure, we increase the concentration gradient between the bulk liquid phase and the liquid-vapor interface. Lower pressures lead to higher evaporation rates, improving the effectiveness of the reactors. Copyright 1999 Page 10 of 19

12 Predicting the best pressure and temperature of the low polymerizer is difficult. If the pressure is too low or the temperature is too high, too much of the residual ethylene glycol is lost. This reduces the mole ratio, which may shift the process away from the optimal mole ratio. Table 1, above, lists the initial and final values of the objective function, constraints, and manipulated variables. Note that several of the manipulated variables reach their upper and lower bounds. The variables that do not reach the bounds may be at optimal conditions. In some cases, the manipulated variables are limited by the constraints. For example, in this process the temperature of the high polymerizer cannot be higher than C without violating the acid and vinyl end-group constraints. Table 2, below, summarizes the polymer streams at the base case and after optimization. Note that the final acid content is much higher in the optimal case. This accelerates the reaction rates in the polymerization reactors. When the process is operated at such high temperatures, however, more of the ethylene glycol is lost to side reactions, so the feed mole ratio must be higher. Although many product grades have tighter quality constraints on the acid content, high acid content may be desirable when the polymer is used as the feedstock for a solid-state polymerization process. In this example, ethylene glycol is recycled from the distillation column to the primary and secondary esterification reactors. A portion of the ethylene glycol is removed from the secondary esterification stage. The recycle rates to the primary and secondary esterification reactors are included as manipulated variables in this optimization study. This allows the model to find the optimal mole ratio in each esterification stage. Antimony and phosphate levels were also included in this study. As expected, the model drives the catalyst level to the upper bound and the phosphate level to the lower bound. At higher production rates, higher catalyst levels are offset by lower residence times. The optimization study identified thirty five percent additional capacity over the base-case conditions. These results are very high because the base-case conditions reported here reflect industry averages. In most plants, years of fine-tuning the process have led to operation far above the design capacity. Even in very mature plants, however, optimization studies may identify an additional five to ten percent capacity. Process economics are summarized in Table 3. The prices of TPA, ethylene glycol, and PET are based on the commodity market reports for January The utility prices are estimated based on the process heat duties and current energy prices in the United States. We assume that the increase in throughput has no influence on the process labor costs. These figures demonstrate that even with today s narrow margins, increasing the capacity of an existing plant can be very profitable. For this 170 ton per day plant, a five- percent increase in capacity represents over one million US dollars per annum. Copyright 1999 Page 11 of 19

13 Stream Conditions Before Optimization Reactor PE SE LP IP HP Total Flow kg/hr Temperature, deg C Absolute pressure, torr Antimony Oxide, wt PPM Phosphoric Acid, wt PPM Degree of Esterification Acid content, mmol/kg Hydroxyl content, mmol/kg Vinyl content, mmol/kg Saponification, mmol/kg Intrinsic viscosity, dl/g DEG content, weight % Number average DP Number average Mn Stream Conditions After Optimization Reactor PE SE LP IP HP Total Flow kg/hr Temperature, deg C Absolute pressure, torr Antimony Oxide, wt PPM Phosphoric Acid, wt PPM Degree of Esterification Acid content, mmol/kg Hydroxyl content, mmol/kg Vinyl content, mmol/kg Saponification, mmol/kg Intrinsic viscosity, dl/g DEG content, weight % Number average DP Number average Mn Table 2. Stream conditions for the base-case conditions and for conditions optmized to obtain maximum production rates. Copyright 1999 Page 12 of 19

14 Optimized production rate metric ton / hour Original production rate metric ton / hour Additional throughput metric ton / hour x 24 hours / day = metric ton / day x 365 days / year = metric ton / year Selling price of polyester x $ 948 $ / metric ton Additional revenue $ 20,585,775 $ / year TPA feed rate at optimum metric ton / hour Original TPA feed rate metric ton / hour Additional TPA flow rate metric ton/hour x 24 hours / day = metric ton / day x 365 days / year = metric ton / year Price of fiber-grade TPA x $ 507 $ / metric ton Additional TPA costs $ 9,386,039 $ / year EG feed rate at optimum metric ton / hour Original EG feed rate metric ton / hour Additional TPA flow rate metric ton / hour x 24 hours / day = metric ton / day x 365 days / year = metric ton / year Price of fiber-grade EG x $ 310 $ / metric ton Additional EG costs $ 2,821,508 $ / year Utility costs $ 30 $ / metric ton Additional throughput x metric ton / year $ 651,449 $ / year Revenue from additional sales $ 20,585,775 $ / year Additional raw material costs $ (12,207,548) $ / year Additional utility costs $ (651,449) $ / year Net return $ 7,726,779 $ / year Price indices based on January 1999 spot market Table 3. Process economic calculations for the throughput optimization study. The monomer prices reported here are based on the spot-market prices for the second week of January Utility prices are estimated. We assume a constant utility price per mass of polymer, independent of the operating condtions. Case Study #3: Reducing Costs Polyester is projected to be in oversupply until the middle of the next decade. Under these circumstances, cost cutting becomes essential to survival. From a process engineering point of view, the Copyright 1999 Page 13 of 19

15 most promising ways to cut costs in an existing plant are to improve yield, use less raw material, and reduce energy costs. Steady-state process models can address all of these issues. Energy and raw material costs are linked to the feed mole ratio. At lower mole ratios, raw material costs are reduced because less ethylene glycol is consumed. The recycle rate between the esterification reactors and the distillation columns increases with the mole ratio. At lower mole ratios, the reactor duty and column condenser duties are reduced. In this example we applied multivariable optimization to reduce the process costs at constant throughput. Constraints are defined to keep the intrinsic viscosity, end group concentrations, and DEG within quality specifications. The objective of the optimization study was to minimize the ethylene glycol feed rate. In this case, there is much less room for improvement because there is a minimum feasible mole ratio. The model identified conditions to achieve a reduction of two percent in the glycol feed flow rate at constant throughput, which corresponds to a reduction in the feed mole ratio from 1.10 to Further, the model indicates that the major variable influencing the ethylene glycol loss rate is the pressure of the low polymerizer. The optimization results are summarized in Tables 4-6. Variable Type Variable Lower Upper Initial Optimized Bound Bound Value Value Objective Function EG Mass Flow Rate, kg/hr Constraints Intrinsic viscosity, dl/g Acid content, mmol/kg DEG content, weight % Vinyl content, mmol/kg Manipulated Variables Feed mole ratio EG/TPA Fraction of EG recycled to PE Fraction of EG recycled to SE PE temperature, deg C PE pressure, Torr SE temperature, deg C LP temperature, deg C LP pressure, Torr IP temperature, deg C IP pressure, torr HP temperature deg C HP pressure, torr Table 4. Case 3 optimization results. The objective is to reduce costs by reducing the excess mole ratio. Catalyst and additive levels and reactor volumes are held constant. The ethylene glycol reduction would have been higher if the base-case conditions met the DEG content constraint. The optimization study increases the pressure and temperature in the primary esterifier to meet this constraint. Since the DEG content is very sensitive to mole ratio, these variables reach their upper bounds. Copyright 1999 Page 14 of 19

16 The stream conditions are summarized in Table 5. These can be compared to the base case conditions shown above in Table 2. Reactor PE SE LP IP HP Antimony Oxide, wt PPM Phosphoric Acid, wt PPM Degree of Esterification Acid content, mmol/kg Hydroxyl content, mmol/kg Vinyl content, mmol/kg Saponification, mmol/kg Intrinsic viscosity, dl/g DEG content, weight % Number average DP Number average Mn Table 5. Stream summary for case-2. Note that the final DEG content meets the specified constraint, even though the base case conditions did not meet this constraint. The economic benefits of reducing the ethylene glycol feed flow rate are summarized in Table 6. As shown, the benefits are relatively small. This reflects today s low ethylene glycol prices and the fact that the base case condition was close to the minimum mole ratio. In addition to the 41 k$/year savings in raw material, there are secondary benefits including reduced heat duty and cooling duty in the esterification section. The primary esterifier heat duty is decreased by three percent, and the column condenser duty is reduced by nearly ten percent. There are also additional savings in crude glycol recovery costs. Original EG feed rate metric ton / hour Optimized EG feed rate metric ton / hour Reduction in EG flow rate metric ton / hour x 24 hours / day = metric ton / day x 365 days / year = metric ton / year Price of fiber-grade EG x $ 310 $ / metric ton Savings in EG costs $ 40,734 $ / year Table 6. Direct cost savings associated with the reduction in mole ratio at constant throughput. Not shown are secondary savings including decreased heat and cooling duties and a small reduction in the amount of crude EG to be purified. Copyright 1999 Page 15 of 19

17 Other Applications of Simulation Technology Dynamic process models are key tools for improving yield and reducing process variability. Using a dynamic process model, one can compare alternate control schemes to find the fastest and most stable control strategy. A dynamic process model can also be used to evaluate and improve grade transition strategies. A sufficiently detailed dynamic process model can be adapted for use in operator training systems. For models to be applied in these applications, they must be able to run in real time. Further, they must faithfully reproduce the process and control system dynamics. This requires a very detailed and robust model. Ideally, such models should emulate or communicate through the person-machine interface used by the real control system. Rigorous models can support efforts to develop advanced control and on-line optimization systems. Typically, the complexity and computational performance of first-principles rigorous models prevent such models from being used directly in on-line applications. These models can be used, however, to help generate a gain matrix. A gain matrix is a database that represents the response of each process variable with respect to all other process variables. This database is required to train a fast-running linearized or neural-net model that can be implemented in open- or closed-loop control. Conclusions When used properly, process simulation is a powerful tool to improve process profitability. The melt polyester process involves many process variables, and the interactions among these variables are complex. A simulation model captures these interactions and makes them easier to visualize and understand. Process optimization is the most powerful off-line application of these models. By simultaneously adjusting a number of process variables, it is possible to take advantage of tradeoffs between temperature and residence time, temperature and pressure, and mole ratio and other process variables. This allows the model to identify improved operating conditions, even in very mature plants. For a typical polyester process, the economic benefits of applying a model to improve existing process lines may range into millions of dollars per year. Dynamic models can be used on-line or off-line to improve the process stability. This results in higher yields of first quality products, reduced downtime, and shorter grade transitions. These models can be further leveraged for operator training. To effectively apply simulation, the models must be tuned and validated against process data. This is important for two reasons. First, there are a number of parameters, such as heat transfer coefficients and level calibration curves, which are unique to a particular process line. Second, the models must be well proven before they gain the political acceptance required to support major engineering decisions in an operating plant. The models described herein represents the efforts of many of my associates in Aspen Technology as well as the input of a number of engineers and managers in the process industries. Further, the models and data are based on many works published in the scientific literature, especially those listed below. Copyright 1999 Page 16 of 19

18 References [1] Cheong, Seong Ill, and Kyu Yong Choi, Modeling of a Continuous Rotating Disk Polycondensation Reactor in the Synthesis of Thermoplastic Polyesters, J. Applied Polymer Science, Vol. 61, (1996). [2] Chen, Chau-Chyun, A Segment-Based Local Composition Model for the Gibbs Energy of Polymer Solutions, Fluid Phase Equilibria, Vol. 83, (1993). [3] Yokoyama, H, T. Sano, T. Chijiwa, and R. Kajya, A Simulation Method for Ethylene Glycol Terephthalate Polycondensation Process, J. Japan Petroleum Institute, Vol. 21, No. 4, (1978). [4] Yokoyama, H, T. Sano, T. Chijiwa, and R. Kajya, Influence of Catalyst, Stabilizer, and Temperature on the Polymerization of Ethylene Glycol Terephthalate, J. Japan Petroleum Institute, Vol. 21, No. 3, (1978). [5] Otton, Jean and Serge Ratton, Investigation of the Formation of Poly(ethylene Terephthalate) with Model Molecules: Kinetics and Mechanism of the Catalytic Esterification and Alcoholysis Reactions I. Carboxylic Acid Catalysis (Monofunctional Reactants), J. Applied Polymer Science: Part A: Polymer Chemistry, Vol. 26, (1988). [6] Otton, Jean and Serge Ratton, Investigation of the Formation of Poly(ethylene Terephthalate) with Model Molecules: Kinetics and Mechanism of the Catalytic Esterification and Alcoholysis Reactions II. Catalysis by Metallic Derivatives (Monofunctional Reactants), J. Applied Polymer Science: Part A: Polymer Chemistry, Vol. 26, (1988). [7] Ravindrananth, K. and R.A. Mashelkar, Polyethylene Terephthalate I. Chemistry, Thermodynamics, and Transport Properties, Chemical Engineering Science, Vol. 41, No. 9, , (1986). [8] Ravindrananth, K. and R.A. Mashelkar, Polyethylene Terephthalate II. Engineering Analysis, Chemical Engineering Science, Vol. 41, No. 12, , (1986). [9] Hovenkamp, S.G., Kinetic Aspects of Catalyzed Reactions in the Formation of Poly(ethylene Terephthalate), J. of Polymer Science Part A-1, Vol. 9 (1971). Copyright 1999 Page 17 of 19

19 Polymer Property Definitions Acid Content DEG Content Esterification IV Saponification Vinyl Content Equivalent concentration of acid end groups in polymer, mmole acid / kg liquid: 2 ftpa + 2 ftpa( s) + ft TPA 6 10 liquid mass flow rate, kg/hr Equivalent weight percent of DEG in the polymer: ( fdeg + ft DEG + fb DEG ) M DEG 2 10 liquid mass flow rate, kg/hr Degree of esterification (percent conversion of acid end groups): ( 1 acid content / saponification )10 2 Intrinsic Viscosity, dl/g: 1.07x10 4 ( number average molecular weight) Equivalent concentration of ester groups in polymer, mmole ester / kg liquid: 2( ftpa + ftpa( s) + ft TPA + fb TPA ) 6 10 liquid mass flow rate, kg/hr Concentration of oxyvinyl end groups in polymer, mmol / kg: 2 f 6 t vinyl 10 liquid mass flow rate, kg/hr Definition of Symbols K s f γ i M i P P v i R T x i y i H m S m Solubility constant of solid TPA Molar flow rate, kmole/hr Activity coefficient (apparent mole basis) Component index Heat of melting of solid TPA Molecular weight of component i Total pressure Vapor pressure of component i Ideal gas constant Entropy of melting of solid TPA Absolute temperature, deg K Apparent mole fraction of component i in the liquid phase Apparent mole fraction component i in the vapor phase Copyright 1999 Page 18 of 19